NRx Pharmaceuticals (NRXP) S-1 3 Sep 21 IPO registration Financial data

Document and Entity Information

Document and Entity Information	6 Months Ended
	Jun. 30, 2021
Document and Entity Information
Document Type	S-1
Entity Registrant Name	NRX Pharmaceuticals, Inc.
Entity Central Index Key	0001719406
Entity Filer Category	Non-accelerated Filer
Entity Small Business	true
Entity Emerging Growth Company	true
Entity Ex Transition Period	false
Amendment Flag	false

CONSOLIDATED BALANCE SHEETS

CONSOLIDATED BALANCE SHEETS - USD ($)	Dec. 31, 2020	Dec. 31, 2019
Current assets:
Cash	$ 1,858,513	$ 877,421
Accounts receivable, net of allowances of $257,463	831,390
Prepaid expenses and other current assets	240,352	97,585
Total current assets	2,930,255	975,006
Other assets	10,914	10,930
Total assets	2,941,169	985,936
Current liabilities:
Accounts payable (includes $149,067 and $92,744 due to related parties, respectively)	3,153,310	2,073,402
Accrued settlement expense	39,486,139
Accrued clinical site costs	1,547,432
Accrued and other current liabilities	1,728,483	9,649
Dividends payable	7,589	7,589
Convertible notes payable and accrued interest		130,251
Notes payable and accrued interest	248,861	154,190
Total current liabilities	46,164,225
Notes payable and accrued interest	547,827
Convertible notes payable and accrued interest		3,461,805
Total liabilities	46,712,052
Stockholders' equity (deficit):
Convertible preferred stock
Common stock, $0.001 par value, 20,000,000 and 14,060,001 shares authorized; 11,227,676 and 10,686,191 shares issued and outstanding at December 31, 2020 and 2019, respectively	11,228	10,686
Additional paid-in capital	46,365,863
Accumulated deficit	(90,179,720)	(38,402,816)
Total stockholders' equity (deficit)	(43,770,883)	(4,843,405)
Total liabilities and stockholders' equity (deficit)	2,941,169	985,936
Convertible Series A Preferred Stock [Member]
Stockholders' equity (deficit):
Convertible preferred stock	1,000	1,000
Total stockholders' equity (deficit)	1,000	1,000
Convertible Series B-1 Preferred Stock [Member]
Stockholders' equity (deficit):
Convertible preferred stock	1,050	1,050
Total stockholders' equity (deficit)	1,050	1,050
Convertible Series B-1A Preferred Stock [Member]
Stockholders' equity (deficit):
Convertible preferred stock	317	317
Total stockholders' equity (deficit)	317	317
Convertible Series B-2 Preferred Stock [Member]
Stockholders' equity (deficit):
Convertible preferred stock	4
Total stockholders' equity (deficit)	4
As Previously Reported
Current liabilities:
Total current liabilities	46,171,814
Total liabilities	46,719,641
Stockholders' equity (deficit):
Common stock, $0.001 par value, 20,000,000 and 14,060,001 shares authorized; 11,227,676 and 10,686,191 shares issued and outstanding at December 31, 2020 and 2019, respectively	42,974
Additional paid-in capital	46,387,649
Total stockholders' equity (deficit)	$ (43,778,472)	$ (4,850,950)

CONSOLIDATED BALANCE SHEETS (Pa

CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($)	Dec. 31, 2020	Dec. 31, 2019
Allowance for accounts receivable	$ 257,463
Accounts payable, due to related parties	$ 149,067	$ 92,744
Convertible preferred stock, par value	$ 0.001
Convertible preferred stock, shares authorized	50,000,000
Convertible preferred stock, shares issued	0
Convertible preferred stock, shares outstanding	0
Common stock, par value	$ 0.001	$ 0.001
Common stock, shares authorized	500,000,000	14,060,001
Common stock, shares issued	42,973,462	10,686,191
Common stock, shares outstanding	42,973,462	10,686,191
Convertible Series A Preferred Stock [Member]
Convertible preferred stock, par value	$ 0.001	$ 0.001
Convertible preferred stock, shares authorized	1,000,000	1,000,000
Convertible preferred stock, shares issued	1,000,000	1,000,000
Convertible preferred stock, shares outstanding	1,000,000	1,000,000
Convertible preferred stock, liquidation preference	$ 1,000,000	$ 1,000,000
Convertible Series B-1 Preferred Stock [Member]
Convertible preferred stock, par value	$ 0.001	$ 0.001
Convertible preferred stock, shares authorized	1,050,695	1,050,695
Convertible preferred stock, shares issued	1,050,695	1,050,695
Convertible preferred stock, shares outstanding	1,050,695	1,050,695
Convertible preferred stock, liquidation preference	$ 7,964,268	$ 7,964,268
Convertible Series B-1A Preferred Stock [Member]
Convertible preferred stock, par value	$ 0.001	$ 0.001
Convertible preferred stock, shares authorized	316,848	316,848
Convertible preferred stock, shares issued	316,848	316,848
Convertible preferred stock, shares outstanding	316,848	316,848
Convertible preferred stock, liquidation preference	$ 2,159,608	$ 2,159,608
Convertible Series B-2 Preferred Stock [Member]
Convertible preferred stock, par value	$ 0.001	$ 0.001
Convertible preferred stock, shares authorized	100,000	100,000
Convertible preferred stock, shares issued	4,167	0
Convertible preferred stock, shares outstanding	4,167	0
Convertible preferred stock, liquidation preference	$ 50,004	$ 0
As Previously Reported
Common stock, shares authorized	20,000,000
Common stock, shares issued	11,227,676
Common stock, shares outstanding	11,227,676

CONSOLIDATED STATEMENT OF OPERA

CONSOLIDATED STATEMENT OF OPERATIONS - USD ($)	Mar. 28, 2021	Jun. 30, 2021	Mar. 31, 2021	Jun. 30, 2020	Mar. 31, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Operating expenses:
Research and development		$ 4,659,280		$ 1,390,376		$ 7,567,984	$ 1,994,709	$ 10,625,032	$ 3,495,648
General and administrative		12,457,534		525,736		14,558,936	1,141,390	11,435,658	2,767,590
Settlement expense	$ 21,365,641					21,365,641		39,486,139
Reimbursement of expenses from Relief Therapeutics				(2,020,931)		(771,244)	(2,020,931)	(10,160,421)
Total operating expenses		17,116,814		(104,819)		42,721,317	1,115,168	51,386,408	6,263,238
Loss from operations		(17,116,814)		104,819		(42,721,317)	(1,115,168)	(51,386,408)	(6,263,238)
Other expenses:
Interest expense		5,107		2,532		10,288	38,800	56,695	303,057
Loss on conversion of convertible notes payable							306,641	306,641	0
Change in fair value of embedded put							27,160	27,160	162,866
Total other expenses		1,108,841		(2,532)		1,224,470	(372,601)	(390,496)	(465,923)
Loss before tax		(16,007,973)		102,287		(41,496,847)	(1,487,769)	(51,776,904)	(6,729,161)
Tax expense						0		0	0
Net loss		$ (16,007,973)	$ (25,488,874)	$ 102,287	$ (1,590,056)	$ (41,496,847)	$ (1,487,769)	$ (51,776,904)	$ (6,729,161)
Net loss per share Basic and Diluted								$ (4.77)	$ (0.63)
Weighted average common shares outstanding Basic and Diluted								10,845,240	10,690,209

CONSOLIDATED STATEMENT OF CHANG

CONSOLIDATED STATEMENT OF CHANGES IN STOCKHOLDERS' EQUITY (DEFICIT) - USD ($)	As Previously ReportedCommon Stock	As Previously ReportedAdditional Paid-in-Capital	As Previously ReportedAccumulated Deficit	As Previously Reported	Common Stock	Additional Paid-in-Capital	Accumulated Deficit	Convertible Series A Preferred Stock [Member]	Convertible Series B-1A Preferred Stock [Member]	Convertible Series B-1 Preferred Stock [Member]	Convertible Series B-2 Preferred Stock [Member]	Total
Beginning balance at Dec. 31, 2018	$ 10,450	$ 21,302,460	$ (31,672,972)	$ (10,357,695)				$ 1,000	$ 317	$ 1,050
Beginning balance, shares at Dec. 31, 2018	10,449,837							1,000,000	316,848	1,050,695
Common stock issued	$ 536	5,801,466		5,802,002
Common stock issued, shares	536,354
Settlement consideration paid by shareholders in common stock		5,999,994		5,999,994
Stock-based compensation		433,910		433,910
Change in accounting method upon adopting ASU 2018-07		683	(683)
Retired founder shares	$ (300)	300
Retired founder shares, shares	(300,000)
Net Loss			(6,729,161)	(6,729,161)								$ (6,729,161)
Ending balance at Dec. 31, 2019	$ 10,686	33,538,813	(38,402,816)	(4,850,950)	$ 41,249	$ 33,518,162	$ (38,402,816)	$ 1,000	$ 317	$ 1,050		(4,843,405)
Ending balance, shares at Dec. 31, 2019	10,686,191				41,249,200			1,000,000	316,848	1,050,695
Common stock issued					$ 51	176,974						177,025
Common stock issued, shares					50,844
Stock-based compensation						88,803						88,803
Net Loss							(1,590,056)					(1,590,056)
Ending balance at Mar. 31, 2020					$ 41,313	33,833,939	(39,992,872)					(6,117,620)
Ending balance, shares at Mar. 31, 2020					41,313,212
Beginning balance at Dec. 31, 2019	$ 10,686	33,538,813	(38,402,816)	(4,850,950)	$ 41,249	33,518,162	(38,402,816)	$ 1,000	$ 317	$ 1,050		(4,843,405)
Beginning balance, shares at Dec. 31, 2019	10,686,191				41,249,200			1,000,000	316,848	1,050,695
Net Loss												(1,487,769)
Ending balance at Jun. 30, 2020					$ 41,313	33,927,405	(39,890,585)					(5,921,867)
Ending balance, shares at Jun. 30, 2020					41,313,212
Beginning balance at Dec. 31, 2019	$ 10,686	33,538,813	(38,402,816)	(4,850,950)	$ 41,249	33,518,162	(38,402,816)	$ 1,000	$ 317	$ 1,050		(4,843,405)
Beginning balance, shares at Dec. 31, 2019	10,686,191				41,249,200			1,000,000	316,848	1,050,695
Common stock issued	$ 172	2,578,942		2,579,114
Common stock issued, shares	171,796
Common stock issued to settle note conversion	$ 360	3,961,719		3,962,079
Common stock issued to settle note conversion, shares	360,189
Common stock issued to settle accounts payable	$ 10	144,865		144,875
Common stock issued to settle accounts payable, shares	9,500
Reclassification of settlement liability upon issuance of warrant		5,382,905		5,382,905
Stock-based compensation		730,405		730,405
Net Loss			(51,776,904)	(51,776,904)								(51,776,904)
Ending balance at Dec. 31, 2020	$ 11,228	46,387,649	(90,197,720)	(43,778,472)	$ 42,974	46,365,863	(90,179,720)	$ 1,000	$ 317	$ 1,050	$ 4	(43,770,883)
Ending balance, shares at Dec. 31, 2020	11,227,676				42,973,462			1,000,000	316,848	1,050,695	4,167
Beginning balance at Mar. 31, 2020					$ 41,313	33,833,939	(39,992,872)					(6,117,620)
Beginning balance, shares at Mar. 31, 2020					41,313,212
Stock-based compensation						93,466						93,466
Net Loss							102,287					102,287
Ending balance at Jun. 30, 2020					$ 41,313	33,927,405	(39,890,585)					(5,921,867)
Ending balance, shares at Jun. 30, 2020					41,313,212
Series B-2 convertible preferred stock issued		50,000		50,004							$ 4
Series B-2 convertible preferred stock issued, shares											4,167
Beginning balance at Dec. 31, 2020	$ 11,228	46,387,649	(90,197,720)	(43,778,472)	$ 42,974	46,365,863	(90,179,720)	$ 1,000	$ 317	$ 1,050	$ 4	(43,770,883)
Beginning balance, shares at Dec. 31, 2020	11,227,676				42,973,462			1,000,000	316,848	1,050,695	4,167
Common stock issued					$ 333	6,926,753						6,927,086
Common stock issued, shares					333,121
Issuance of common stock for exercise of warrant					$ 1,496	7,498,522						7,500,018
Issuance of common stock for exercise of warrant, shares					1,496,216
Reclassification of settlement liability upon issuance of warrant						60,851,779						60,851,779
Stock-based compensation						371,698						371,698
Net Loss							(25,488,874)					(25,488,874)
Ending balance at Mar. 31, 2021					$ 44,803	122,014,615	(115,668,594)					6,390,824
Ending balance, shares at Mar. 31, 2021					44,802,799
Beginning balance at Dec. 31, 2020	$ 11,228	$ 46,387,649	$ (90,197,720)	$ (43,778,472)	$ 42,974	46,365,863	(90,179,720)	$ 1,000	$ 317	$ 1,050	$ 4	(43,770,883)
Beginning balance, shares at Dec. 31, 2020	11,227,676				42,973,462			1,000,000	316,848	1,050,695	4,167
Net Loss												(41,496,847)
Ending balance at Jun. 30, 2021					$ 48,604	114,190,620	(131,676,567)					(17,437,343)
Ending balance, shares at Jun. 30, 2021					48,603,585
Beginning balance at Mar. 31, 2021					$ 44,803	122,014,615	(115,668,594)					6,390,824
Beginning balance, shares at Mar. 31, 2021					44,802,799
Common stock issued					$ 71	1,562,201						1,562,272
Common stock issued, shares					71,056
Stock-based compensation						938,118						938,118
Net Loss							(16,007,973)					(16,007,973)
Ending balance at Jun. 30, 2021					$ 48,604	$ 114,190,620	$ (131,676,567)					$ (17,437,343)
Ending balance, shares at Jun. 30, 2021					48,603,585

CONSOLIDATED STATEMENTS OF CASH

CONSOLIDATED STATEMENTS OF CASH FLOWS - USD ($)	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
CASH FLOWS FROM OPERATING ACTIVITIES:
Net Loss	$ (51,776,904)	$ (6,729,161)
Adjustments to reconcile net loss to net cash used in operating activities:
Depreciation expense	1,517	859
Stock-based compensation	730,405	433,910
Warrant expense	5,382,905	0
Change in fair value of embedded put	27,160	162,866
Amortization of debt discount	16,475	130,433
Non-cash interest expense	65,103	167,979
Non-cash consulting expense	0	499,994
Non-cash settlement expense	39,486,139	0
Loss on conversion of convertible notes payable	306,641	0
Loss on common stock issued to settle accounts payable	41,617	0
Changes in operating assets and liabilities:
Accounts receivable	(831,390)	0
Prepaid expenses and other assets	(142,788)	(44,937)
Accounts payable	1,183,143	(52,181)
Accrued expenses and other liabilities	3,243,610	(112,087)
Net cash used in operating activities	(2,266,367)	(5,542,325)
CASH FLOWS FROM INVESTING ACTIVITIES
Purchase of computer equipment	1,501	3,552
Net cash used in investing activities	(1,501)	(3,552)
CASH FLOWS FROM FINANCING ACTIVITIES
Proceeds from notes payable	619,842	0
Proceeds from issuance of series B-2 Preferred stock	50,004	0
Proceeds from issuance of Common stock, net of transaction costs	2,579,114	5,802,002
Net cash provided by financing activities	3,248,960	5,802,002
Net increase in cash	981,092	256,125
Cash at beginning of year	877,421	621,296
Cash at end of year	1,858,513	877,421
Non-cash investing and financing activities
Common stock issued to settle accounts payable	144,875	0
Conversion of notes payable into common stock	3,655,438	0
Issuance of common stock warrants as offering costs	30,536	63,337
Settlement consideration paid by shareholders in common stock	0	5,500,000
Short-term note payable issued to settle accounts payable	$ 0	$ 154,190

Organization

Organization	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Organization.
Organization	1. Organization The Business On May 24, 2021, we consummated the business combination, or the Business Combination, contemplated by the Agreement and Plan of Merger (as amended, the “Merger Agreement”), dated December 13, 2020, by and among our company (formerly known as Big Rock Partners Acquisition Corp. (“BRPA”)), NeuroRx, Inc., a Delaware corporation (“NeuroRx”), Big Rock Merger Corp., and a Delaware corporation and wholly-owned, direct subsidiary of BRPA (“Merger Sub”), pursuant to which Big Rock Merger Corp. was merged with and into NeuroRx, with NeuroRx surviving the merger (“Merger”). As a result of the Merger, and upon consummation of the Merger and other transactions contemplated by the Merger Agreement, NeuroRx became a wholly-owned, direct subsidiary of BRPA. Upon the closing of the Business Combination, we changed our name to NRx Pharmaceuticals, Inc. (“NRx Pharmaceuticals,” “NRXP,” “we,” or the “Company”), with the stockholders of NeuroRx becoming stockholders of NRx Pharmaceuticals. The Company is a clinical-stage small molecule pharmaceutical company which develops novel therapeutics for the treatment of central nervous system disorders and life-threatening pulmonary diseases through its wholly-owned operating subsidiary, NeuroRx. On September 21, 2020, we announced a commercial partnership with Relief Therapeutics Holding AG (“Relief”) for global commercialization of RLF-100 (aviptadil acetate) (now reformulated as ZYESAMI TM TM	NeuroRx, Inc. NOTES TO CONSOLIDATED FINANCIAL STATEMENTS 1. Organization The Business NeuroRx, Inc. (the “Company” or “NeuroRx”) was formed on May 20, 2015 and is incorporated in the State of Delaware. The Company established a wholly owned subsidiary, NeuroRx 2015 LTD (Israel), in December 2015, for the purpose of managing the continued development of a subset of the Company’s technology. The Company is a clinical stage pharmaceutical research and development company primarily engaged in the development of a drug regimen to treat patients with depression and suicidal ideation or behavior.

Liquidity

Liquidity	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Liquidity
Liquidity	2. Liquidity As of June 30, 2021, the Company had $13,386,332 in cash. Since inception the Company has experienced net losses and negative cash flows from operations each fiscal year. The Company has no revenues and expects to continue to incur operating losses for the foreseeable future, and may never become profitable. The Company is dependent on its ability to continue to raise equity and/or debt financing to continue operations, and the attainment of profitable operations. The Company has a collaboration agreement with Relief which provided for funding by Relief of certain research and development expenses related to the U.S. development of ZYESAMI TM TM TM COVID-19 Outbreak On January 30, 2020, the World Health Organization (“WHO”) announced a global health emergency because of a new strain of coronavirus originating in Wuhan, China (the “COVID-19 Outbreak”) and the risks to the international community as the virus spreads globally beyond its point of origin. In March 2020, the WHO classified the COVID-19 Outbreak as a pandemic, based on the rapid increase in exposure globally. The full impact of the COVID-19 Outbreak continues to evolve as of the date of this report. If the COVID-19 Outbreak continues, it may have a material adverse effect on the Company’s financial condition, liquidity, and future results of operations for the year ending December 31, 2021 and beyond. Management is actively monitoring the impact of the global pandemic on its financial condition, liquidity, operations, industry, and workforce. Given the daily evolution of the COVID-19 Outbreak and the global responses to curb its spread, the Company is not able to estimate the effects of the COVID-19 Outbreak on its results of operations, financial condition, or liquidity for the year ending December 31, 2021 and beyond.	2. Liquidity As of December 31, 2020, the Company had $1,858,513 in cash. Since inception the Company has experienced net losses and negative cash flows from operations each fiscal year. The Company has no revenues and expects to continue to incur operating losses for the foreseeable future, and may never become profitable. The Company is dependent on its ability to continue to raise equity and/or debt financing to continue operations, and the attainment of profitable operations. The Company has a collaboration agreement with Relief Therapeutics Holdings (“Relief”), which provided for funding by Relief of certain research and development expenses related to the U.S. development of ZYESAMI and the portion of corporate overhead attributable to that program. The proceeds received amounted to $10,160,421 for the year ended December 31, 2020. Subsequent to December 31, 2020, Relief has not reimbursed the Company for any additional expenses related to the IV clinical trials for the ZYESAMI. The IV clinical trials for the ZYESAMI were completed on February 24, 2021. During the first quarter of 2021, the Company sold 43,018 shares of common stock for gross proceeds of $2,495,058, and 79,400 shares of common stock for gross proceeds of $5,716,800. On March 28, 2021, the Company received $7,500,018 from the exercise of a warrant for the purchase of 473,486 shares. Accordingly, the Company believes that it currently has sufficient funds to support operations through the next twelve months from the date the financial statements are issued. The Company intends to use the proceeds of the merger transaction to fund the ZYESAMI inhaled trial for COVID-19. The Company cannot make any assurances that additional financings will be available to it and, if available, on acceptable terms or at all. This could negatively impact the Company’s business and operations and could also lead to the reduction of the Company’s operations. COVID-19 Outbreak On January 30, 2020, the World Health Organization (“WHO”) announced a global health emergency because of a new strain of coronavirus originating in Wuhan, China (the “COVID-19 Outbreak”) and the risks to the international community as the virus spreads globally beyond its point of origin. In March 2020, the WHO classified the COVID-19 Outbreak as a pandemic, based on the rapid increase in exposure globally. The full impact of the COVID-19 Outbreak continues to evolve as of the date of this report. As such, the Company cannot estimate the full magnitude that the pandemic will have on the Company’s business. If the COVID-19 Outbreak continues, it may have a material adverse effect on the Company’s financial condition, liquidity, and future results of operations for the year ending December 31, 2021 and beyond. Management is actively monitoring the impact of the global pandemic on its financial condition, liquidity, operations, industry, and workforce. Given the daily evolution of the COVID-19 Outbreak and the global responses to curb its spread, the Company is not able to estimate the effects of the COVID-19 Outbreak on its results of operations, financial condition, or liquidity for the year ending December 31, 2021 and beyond.

Summary of Significant Accounti

Summary of Significant Accounting Policies	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Summary of Significant Accounting Policies
Summary of Significant Accounting Policies	3. Summary of Significant Accounting Policies Basis of Presentation The accompanying unaudited interim condensed financial statements have been prepared in accordance with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) for interim financial information. Accordingly, they do not include all of the information and footnotes required by GAAP for complete financial statements. In the opinion of management, the unaudited interim condensed financial statements reflect all adjustments, which include only normal recurring adjustments necessary for the fair statement of the balances and results for the periods presented. The results of operations for any interim periods are not necessarily indicative of the results that may be expected for the entire fiscal year or any other interim period. The merger between Merger Sub and NeuroRx was accounted for as a reverse recapitalization in accordance with U.S. GAAP (the “Reverse Recapitalization”). Under this method of accounting, BRPA was treated as the “acquired” company and NeuroRx is treated as the acquirer for financial reporting purposes. Accordingly, for accounting purposes, the Reverse Recapitalization was treated as the equivalent of NeuroRx issuing stock for the net assets of BRPA, accompanied by a recapitalization. The net assets of BRPA are stated at historical cost, with no goodwill or other intangible assets recorded. NeuroRx was determined to be the accounting acquirer based on the following predominant factors: ● NeuroRx’s shareholders have the largest portion of voting rights in the Company; ● the Board and Management are primarily composed of individuals associated with NeuroRx; and ● NeuroRx was the larger entity based on historical operating activity and NeuroRx had the larger employee base at the time of the Merger. The consolidated assets, liabilities and results of operations prior to the Reverse Recapitalization are those of NeuroRx. The shares and corresponding capital amounts and losses per share, prior to the Merger, have been retroactively restated based on shares reflecting the exchange ratio established in the Merger. Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, contingent consideration and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected. Certain Risks and Uncertainties The Company’s activities are subject to significant risks and uncertainties including the risk of failure to secure additional funding to properly execute the Company’s business plan. The Company is subject to risks that are common to companies in the pharmaceutical industry, including, but not limited to, development by the Company or its competitors of new technological innovations, dependence on key personnel, reliance on third party manufacturers, protection of proprietary technology, and compliance with regulatory requirements. Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. (Refer to Note 12) Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of June 30, 2021, the Company has recorded an allowance for doubtful accounts of $5,470,897 as the Company does not expect to collect on amounts due to the Company owed from Relief. Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss. Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received. Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company. Modification of stock options and warrants A change in any of the terms or conditions of stock options and warrants is accounted for as a modification. Incremental stock-based compensation cost is measured as the excess, if any, of the fair value of the modified option over the fair value of the original option/warrant immediately before its terms are modified, measured based on the fair value of the ordinary shares and other pertinent factors at the modification date. For vested stock options and warrants to board members, we recognize incremental compensation cost in the period the modification occurs. For unvested stock options, we recognize over the remaining requisite service period, the sum of the incremental compensation cost and the remaining unrecognized compensation cost for the original award on the modification date. If the fair value of the modified option is lower than the fair value of the original option immediately before modification, the minimum compensation cost we recognize is the cost of the original award. The accounting for incremental fair value of warrants is based on the specific facts and circumstances related to the modification which may result in a reduction of additional paid-in capital, recognition of costs for services rendered, or recognized as a deemed dividend. Warrants The Company accounts for warrants as either equity-classified or liability-classified instruments based on an assessment of the warrant’s specific terms and applicable authoritative guidance in Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) 480, Distinguishing Liabilities from Equity Derivatives and Hedging For issued or modified warrants that meet all of the criteria for equity classification, the warrants are required to be recorded as a component of additional paid-in capital at the time of issuance. For issued or modified warrants that do not meet all the criteria for equity classification, the warrants are required to be recorded at their initial fair value on the date of issuance, and each balance sheet date thereafter. Changes in the estimated fair value of the warrants are recognized as a non-cash gain or loss on the statements of operations. The fair value of the Placement Warrants was estimated using a Black Scholes valuation approach (see Notes 10 and 12). Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense. Earnings (Loss) Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted earnings per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and other dilutive instruments because their effect would be anti-dilutive in the periods in which we incur a net loss. The following table summarized the basic and diluted earnings per share calculations: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Numerator: ​ ​ ​ ​ ​ ​ ​ ​ Net income (loss) attributable to common stock—basic and diluted $ (16,007,973) $ 102,287 $ (41,496,847) $ (1,487,769) Denominator: ​ ​ ​ ​ ​ ​ ​ ​ Weighted average shares — basic ​ ​ 41,727,480 ​ ​ 33,819,205 ​ ​ 38,709,614 ​ ​ 33,799,503 Effect of other dilutive securities ​ ​ — ​ ​ 2,837,215 ​ ​ — ​ ​ — Weighted average shares — diluted ​ ​ 41,727,480 ​ ​ 36,656,420 ​ ​ 38,709,614 ​ ​ 33,799,503 Basic earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) Diluted earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net earnings (loss) per share attributable to common stock for the periods in which a net loss is presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Stock options 2,919,493 — 2,919,493 1,166,863 Common stock warrants 8,495,316 — 8,495,316 1,670,352 Common stock issuable pursuant to UPOs (Note 10) ​ 600,000 ​ — ​ 600,000 ​ — Common stock warrants pursuant to UPOs (Note 10) ​ 300,000 ​ — ​ 300,000 ​ — Public Rights pursuant to UPOs (Note 10) ​ 60,000 ​ — ​ 60,000 ​ — Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ — ​ Recent Accounting Pronouncements In December 2019, the FASB issued ASU No. 2019-12, Income Taxes: Simplifying the Accounting for Income Taxes In August 2020, the FASB issued ASU 2020-06, Debt — Debt with Conversion and Other Options (Subtopic 470-20) and Derivatives and Hedging — Contracts in Entity’s Own Equity (Subtopic 815-40): Accounting for Convertible Instruments and Contracts in an Entity’s Own Equity In May 2021, the FASB issued ASU 2021-04, Earnings Per Share (Topic 260), Debt — Modifications and Extinguishments (Subtopic 470-50), Compensation — Stock Compensation (Topic 718) and Derivatives and Hedging - Contracts in an Entity's Own Equity (Subtopic 815-40) — Issuer's Accounting for Certain Modifications or Exchange of Freestanding Equity-Classified Written Call Options	3. Summary of Significant Accounting Policies Basis of Presentation The Company’s financial statements have been prepared in conformity with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”). Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, the embedded put feature in convertible notes and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected. Certain Risks and Uncertainties The Company’s activities are subject to significant risks and uncertainties including the risk of failure to secure additional funding to properly execute the Company’s business plan. The Company is subject to risks that are common to companies in the pharmaceutical industry, including, but not limited to, development by the Company or its competitors of new technological innovations, dependence on key personnel, reliance on third party manufacturers, protection of proprietary technology, and compliance with regulatory requirements. Cash and Cash Equivalents The Company considers all highly liquid investments purchased with original maturities of 90 days or less at acquisition to be cash equivalents. As of December 31, 2020 and 2019, the Company does not have any cash equivalents. Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. Fair value measurements discussed herein are based upon certain market assumptions and pertinent information available to management as of and during the years ended December 31, 2020 and 2019. The carrying amount of accounts payable approximated fair value as they are short term in nature. The fair value of warrants issued for services is estimated based on the Black-Scholes model during the years ended December 31, 2020 and 2019. The carrying value of notes payable and convertible notes payable approximated the estimated fair values due to their recent issuances. The estimated fair value of the warrants and embedded put, represent Level 3 measurements. Foreign Currency The Company’s functional currency is the U.S. dollar. The functional currency of our foreign operation is the respective local currency. Assets and liabilities of foreign operation denominated in local currencies are translated at the spot rate in effect at the applicable reporting date. The consolidated statements of operations are translated at the weighted average rate of exchange during the applicable period. The resulting unrealized cumulative translation adjustment is not material to the financial statements. Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of December 31, 2020, the Company has recorded an allowance for doubtful accounts of $257,463. Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss. Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received. Derivative Financial Instruments The Company does not use derivative instruments to hedge exposures to interest rate, market, or foreign currency risks. The Company evaluates all of its financial instruments, to determine if such instruments contain features that qualify as embedded derivatives. Embedded derivatives must be separately measured from the host contract if all the requirements for bifurcation are met. The assessment of the conditions surrounding the bifurcation of embedded derivatives depends on the nature of the host contract. Bifurcated embedded derivatives are recognized at fair value, with changes in fair value recognized in the statement of operations each period. Bifurcated embedded derivatives are classified with the related host contract in the Company’s balance sheet. Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company. Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes (“ASC 740”), which provides for deferred taxes using an asset and liability approach. The Company recognizes deferred tax assets and liabilities for the expected future tax consequences of events that have been included in the financial statements or tax returns. Deferred tax assets and liabilities are determined based on the difference between the financial statement and tax basis of assets and liabilities using enacted tax rates in effect for the year in which the differences are expected to reverse. Valuation allowances are provided, if based upon the weight of available evidence, it is more likely than not that some or all of the deferred tax assets will not be realized. The Company accounts for uncertain tax positions in accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense. Loss Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted loss per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and convertible preferred stock because their effect would be anti-dilutive due to our net loss. Since the Company had a net loss in each of the periods presented, basic and diluted net loss per common share are the same. The calculation of basic and diluted net loss per share attributable to common stock was as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Numerator: ​ ​ ​ ​ ​ ​ Net loss attributable to common stock—basic and diluted ​ $ (51,776,904) ​ $ (6,729,161) ​ ​ ​ ​ ​ ​ ​ Denominator: ​ ​ Weighted average shares—basic and diluted ​ 10,845,240 ​ 10,690,209 ​ ​ ​ ​ ​ ​ ​ Net loss per share attributable to common stock—basic and diluted ​ $ (4.77) ​ $ (0.63) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net loss per share attributable to common stock for the periods presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ Year Ended December 31, ​ 2020 2019 Convertible preferred stock as if converted 2,371,710 2,367,543 Stock options 486,755 333,588 Common stock warrants 620,054 57,473 ​ Recent Accounting Pronouncements In June 2018, the FASB issued ASU 2018-07, which simplifies the accounting for nonemployee share-based payment transactions. The amendments specify that Topic 718 applies to all share-based payment transactions in which a grantor acquires goods or services to be used or consumed in a grantor’s own operations by issuing share-based payment awards. The Company adopted ASU 2018-07 as of January 1, 2019, which resulted in a cumulative effect charge of $683 to accumulated deficit.

Accrued and Other Current Liabi

Accrued and Other Current Liabilities	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Accrued and other current liabilities
Accrued and Other Current Liabilities	6. Accrued and Other Current Liabilities Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Accrued and other current liabilities: ​ ​ ​ ​ ​ ​ Accrued research and development expenses $ 826,442 $ 586,426 Accrued employee expenses ​ ​ 77,196 ​ ​ 530,500 Professional services ​ 185,170 ​ 606,553 Other accrued expenses ​ 417,529 ​ 5,004 Total accrued and other current liabilities ​ $ 1,506,337 ​ $ 1,728,483 ​	4. Accrued and Other Current Liabilities Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Accrued and other current liabilities: ​ ​ Professional services ​ $ 606,553 ​ $ — Accrued research and development expenses ​ 586,426 ​ — Accrued employee expenses ​ 530,500 ​ — Other accrued liabilities ​ 5,004 ​ 9,649 Total accrued and other current liabilities ​ $ 1,728,483 ​ $ 9,649 ​

Convertible Notes Payable

Convertible Notes Payable	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Convertible Notes Payable [Member]
Convertible Notes Payable	7. Convertible Notes Payable On February 12, 2020, a Qualified Financing Event (as defined below) occurred when the Company received cumulative investment proceeds in excess of $10,000,000 from the sale and issuance of common shares. The fair value of the Company’s common shares was $10.63 per share. The 2017 Notes (as defined below) and the 2018 Notes (as defined below) in the aggregate principal amount of $2,800,000 were converted into 1,005,458 common shares (at the discounted price of $2.78 per share), and the related unpaid and accrued interest totaling $369,660 were also converted into 132,739 common shares of the Company (at the discounted price of $2.78 per share). Additionally, the Company recognized a loss on extinguishment for the difference between the carrying value of the convertible notes, unamortized debt discount, and the value of the embedded put option and the fair value of the common shares of $0 and $306,641 during the three months ended and six months ended June 30, 2020, respectively. The Company issued the shares of common stock pursuant to this conversion on September 23, 2020. 2017 Convertible Notes Payable On November 16, 2017 and November 19, 2017, the Company issued convertible notes (“2017 Notes”), as amended for aggregate gross proceeds of $2,500,000. The 2017 Notes accrued interest at a rate of 6% per annum and principal and interest were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. 2018 Convertible Notes Payable On January 5, 2018 and April 25, 2018, the Company issued convertible notes (“2018 Notes”), as amended for aggregate gross proceeds of $300,000. The 2018 Notes accrued interest at a rate of 6% per annum and were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. The January 5, 2018 note for $100,000 was not amended and interest was unpaid, as such, that note and related accrued interest were classified as current liabilities. The April 25, 2018 note for $200,000 was amended similar to the 2017 Notes to accrue interest and to be paid at maturity with the principal. The proceeds received upon issuing the 2017 Notes and 2018 Notes were first allocated to the fair value of the embedded put with the remainder to the debt host instrument. The Company recognized a loss of $0 and $0 during the three months ended June 30, 2021 and 2020, respectively, and $0 and $27,160 during the six months ended June 30, 2021 and 2020, respectively, due to the estimated increase in fair value of the embedded put. The discount is amortized to interest expense over the term of the debt. The Company amortized debt discount of $0 to interest expense during the three months ended June 30, 2021 and 2020, and $0 and $16,454 during the six months ended June 30,2021 and 2020, respectively. The Company paid no interest during the three months ended and six months ended June 30, 2021 and 2020.	5. Convertible Notes Payable ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Convertible Notes: ​ ​ ​ ​ ​ ​ 2017 convertible notes payable due November 2021 ​ $ — ​ $ 2,500,000 2018 convertible note payable due January 2022 ​ — ​ 100,000 2018 convertible notes payable due April 2022 ​ — ​ 200,000 Fair value of embedded put ​ — ​ 738,602 Debt discount ​ — ​ (296,437) Carrying value of convertible notes ​ $ — ​ $ 3,242,165 Accrued interest ​ — ​ 349,891 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056 ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Convertible Notes: ​ ​ Convertible notes payable and accrued interest, current ​ $ — ​ $ 130,251 Convertible notes payable and accrued interest, non-current ​ — ​ 3,461,805 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056 ​ On February 12, 2020, a Qualified Financing Event (as defined below) occurred when the Company received cumulative investment proceeds in excess of $10,000,000 from the sale and issuance of common shares. The fair value of the Company’s common shares were $11.00 per share. The 2017 Notes (as defined below) and the 2018 Notes (as defined below) in the aggregate principal amount of $2,800,000 were converted into 318,183 common shares (at the discounted price of $8.80 per share), and the related unpaid and accrued interest totaling $369,660 were also converted into 42,006 common shares of the Company (at the discounted price of $8.80 per share). Additionally, the Company recognized a loss on extinguishment for the difference between the carrying value of the convertible notes, unamortized debt discount, and the value of the embedded put option and the fair value of the common shares issued of $306,641 during the year ended December 31, 2020. 2017 Convertible Notes Payable On November 16, 2017 and November 19, 2017, the Company issued convertible notes (“2017 Notes”), as amended for aggregate gross proceeds of $2,500,000. The 2017 Notes accrued interest at a rate of 6% per annum and principal and interest were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. 2018 Convertible Notes Payable On January 5, 2018 and April 25, 2018, the Company issued convertible notes (“2018 Notes”), as amended for aggregate gross proceeds of $300,000. The 2018 Notes accrued interest at a rate of 6% per annum and were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. The January 5, 2018 note for $100,000 was not amended and interest was unpaid, as such, that note and related accrued interest were classified as current liabilities. The April 25, 2018 note for $200,000 was amended similar to the 2017 Notes to accrue interest and to be paid at maturity with the principal. Upon closing of a public offering of the Company’s common stock, each of the 2017 Notes and 2018 Notes settle by providing the holder with a variable number of shares sold in the offering with an aggregate fair value determined by reference to the debt principal. In this scenario, the value that the holder receives at settlement does not vary with the value of the Company’s common stock, so the settlement provision was not a typical conversion option. Rather, the share settlement feature was considered a contingent redemption provision (i.e., a contingent embedded put). The Company evaluated the embedded put features in accordance with ASC 815-15-25. The embedded puts are not clearly and closely related to the debt host instrument and therefore have been separately measured at fair value, with subsequent changes in fair value recognized in the Statement of Operations. The proceeds received upon issuing the 2017 Notes and 2018 Notes were first allocated to the fair value of the embedded put with the remainder to the debt host instrument. The Company recorded a $493,982 and $57,204 debt discount upon issuance of the 2017 and 2018 convertible notes, respectively. The Company recognized a loss of $27,160 and $162,866 during the years ended December 31, 2020 and 2019, respectively, due to the estimated increase in fair value of the embedded put. Management used a scenario-based analysis to estimate the fair value of the embedded put features at issuance of the 2017 Notes and 2018 Notes and as of December 31, 2019. The discount is amortized to interest expense over the term of the debt. The Company amortized debt discount of $16,475 and $130,433 to interest expense during the years ended December 31, 2020 and 2019, respectively. The Company paid no interest during the years ended December 31, 2020 and 2019.

Notes Payable

Notes Payable	12 Months Ended
	Dec. 31, 2020
Notes Payable.
Notes Payable	6. Notes Payable ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Note Payable — Related Party ​ $ 154,190 ​ $ 154,190 Relief Therapeutics Loan ​ 500,000 ​ — Paycheck Protection Program Loan ​ 119,842 ​ — Carrying value of notes payable ​ 774,032 ​ 154,190 Accrued interest ​ 22,656 ​ — Total notes payable and accrued interest ​ $ 796,688 ​ $ 154,190 ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Notes payable: ​ ​ Notes payable and accrued interest, current ​ $ 248,861 ​ $ 154,190 Notes payable and accrued interest, non-current ​ 547,827 ​ — Total notes payable and accrued interest ​ $ 796,688 ​ $ 154,190 ​ Note Payable — Related Party On July 1, 2019, the Company converted certain accounts payable into a loan (the “Note Payable — Related Party”) with a related party in the amount of $154,190. The loan, in the form of a promissory note, matures on July 1, 2020. The principal amount of the loan and any accrued but unpaid interest shall be due and payable beginning July 1, 2019. All payments shall be applied first to accrued but unpaid interest, and then to outstanding principal. If not sooner paid, the entire remaining indebtedness (including accrued interest) shall be due and payable on July 1, 2020. The loan bears interest, compounded daily, at 6% annual interest. The loan continues to accrue interest as it was not paid off upon maturity. Relief Therapeutics Loan On April 6, 2020, the Company entered into a loan agreement with Relief Therapeutics (the “Relief Therapeutics Loan”) in the amount of $500,000. The loan matures on April 6, 2022 Paycheck Protection Program Loan On April 28, 2020, the Company received $119,842 in loan funding from the Paycheck Protection Program (the “PPP Loan”), established pursuant to the Coronavirus Aid, Relief, and Economic Security Act (the “CARES Act”) and administered by the U.S. Small Business Administration (“SBA”). The unsecured PPP Loan accrues interest on the outstanding principal at the rate of 1% per annum, and there is a six month deferment period until equal installment payments of $6,744 of principal and interest are due. The term of the PPP Loan is two years. To the extent the loan amount is not forgiven under the PPP, the Company is obligated to make equal monthly payments of principal and interest, beginning seven months from the date of the Note, until the maturity date. The Loan amount may be eligible for forgiveness pursuant to (1) at least 75% of the loan proceeds are used to cover payroll costs and the remainder is used for mortgage interest, rent and utility costs over the eight week period after the loan is made, and (2) the number of employees and compensation levels are generally maintained. Forgiveness of the loan is dependent on the Company having initially qualified for the loan and qualifying for the forgiveness of such loan based on future adherence to the forgiveness criteria. The Company used the entire PPP Loan for qualifying payroll expenses, and filed for loan forgiveness on December 30, 2020, though no assurance is provided that the Company will obtain forgiveness of the PPP Loan in whole or in part.

Commitments and Contingencies

Commitments and Contingencies	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	9. Commitments and Contingencies Operating Lease The Company leases office space on a month-to-month basis. The rent expense for the three months ended June 30, 2021 and 2020 was $48,776 and $9,087, respectively, and for the six months ended June 30, 2021 and 2020 was $55,393 and $17,902, respectively. Sponsored Research Agreement with National Jewish Health On February 8 2021, the Company entered into a Sponsored Research Agreement (“Research Agreement”) with National Jewish Health (“NJ Health”), a Colorado not-for-profit institution. Under the terms of the Research Agreement, NRx Pharmaceuticals agreed to sponsor a research study at NJ Health relating to the impact of NRx Pharmaceuticals' Aviptadil on propagation of SARS-CoV-2 in alveolar type II cells in vitro (the “Study”). In return for performance of the Study under the Research Agreement, NRx Pharmaceuticals has committed to pay NJ Health approximately $360,450. During the three months ended and six months ended June 30, 2021, NRx Pharmaceuticals paid NJ Health $0 and $126,157, respectively, of the total committed amount. Aviptadil Manufacturing, Production, Supply and Distribution Agreements On August 25, 2020, NRx Pharmaceuticals and Nephron Pharmaceuticals Corporation (“Nephron”) signed an agreement for the manufacturing of finished pharmaceutical product of Aviptadil intravenous formulation and the development of an inhaled (nebulizer) formulation of Aviptadil. Nephron will serve as the exclusive and primary supplier of the product for both clinical and commercial purposes, supplying 100% of the Company’s annual requirements. The Company has agreed to purchase products from Nephron for a fixed price. On September 29, 2020, NRx Pharmaceuticals and Cardinal Health signed an exclusive distribution agreement, as well as a 3rd party logistics agreement on October 1, 2020. Cardinal Health will manage warehousing, distribution, invoicing for the potential sale of Aviptadil in the United States and Puerto Rico. On October 9, 2020, NRx Pharmaceuticals signed an agreement with Polypeptide for the supply of GMP grade Active Pharmaceutical Ingredient (API) Aviptadil (VIP). This gives NRx Pharmaceuticals a second source of procuring API. The Company has agreed to purchase a total of $1,010,000 worth of product and services over the contract. On January 4, 2021 NRx Pharmaceuticals and Aerogen Limited (“Aerogen”) signed a supply agreement for the supply of certain products, including the Aerogen Solo Nebulizer System and Aerogen Ultra, solely for the purposes of carrying out clinical trials relating to inhalation delivery of Aviptadil for treatment of pulmonary insufficiency and respiratory distress in COVID-19 patients. Pill Tracker is an agent of NRx Pharmaceuticals per the supply agreement (see Note 14). Relief Therapeutics Collaboration Agreement On September 18, 2020, the Company entered into a collaboration agreement with Relief for the clinical development and if approved the sale of Aviptadil. The collaboration provides for funding by Relief of certain clinical trials. If such candidate is approved by the FDA, the Company shall receive 50% of net product profits from the product sales in the NRx Pharmaceuticals territory, which includes the United States, Canada, and Israel; 15% of net product profits from the product sales in the Relief Therapeutics territory, which includes the European Union, Switzerland, Iceland, Norway, the UK, the Channel Islands, Liechtenstein, Monaco, Andorra, Malta, San Marino, and Vatican City; and 20% of net product profits from the product sales in all other countries. During 2021, the Company invoiced Relief $5,984,679 for reimbursable expenses and received $770,444 in payments from Relief for these reimbursable expenses. The Company recorded an allowance for doubtful accounts of $5,470,897 as of June 30, 2021, due to the fact that the Company does not expect to receive payment for the remaining invoices, thus fully reserving for the accounts receivable balance. As of the date of this filing, Relief has reimbursed NRx Pharmaceuticals $10,904,065 for expenses, but has subsequently declined to pay approximately $6 million in invoiced costs associated with conduct of the IV clinical trial, reformulation, and manufacture of ZYESAMI TM Share Subscription Facility Agreement — GEM NeuroRx previously entered into a share subscription facility agreement (“GEM Agreement”) with GEM Global Yield LLC SCS and GEM Yield Bahamas Limited (collectively, referred to as “GEM”) with a three-year term. Subject to the successful listing of the shares of NeuroRx on an Exchange (any nationally recognized stock exchange or exchange platform in the world on which the Company will list its shares), GEM grants NeuroRx an option to require GEM to subscribe for shares from the Company for up to an aggregate value of approximately $95.6 million. The agreement also included certain provisions which would not meet the U.S. requirements to issue registered shares. If NeuroRx was listed or completes a private transaction which results in a change of control of the Company, NeuroRx would issue GEM a warrant and pay a commitment fee of $1.9 million. Absent a listing of NeuroRx shares or a private transaction with a change of control during the three-year term, NeuroRx would have no obligations under the agreement. The reverse merger contemplated by the Merger Agreement would not have resulted in a listing of NeuroRx shares or a change in control. In November 2020, GEM introduced NeuroRx to BRPA. To resolve uncertainties around the application of the GEM Agreement post-Merger, NeuroRx and GEM agreed in March 2021 to issue a warrant to GEM and for the parties to use their good faith efforts to amend the GEM Agreement to meet U.S. requirements to issue registered shares. The warrant is not conditional upon any further events or completion of the merger. The warrant was issued March 28, 2021, for 3,329,812 shares of NeuroRx common stock at an exercise price of $3.19 per share (the “GEM Warrant”) and the parties agreed that GEM would immediately partially exercise the warrant for the purchase of 1,496,216 shares (“Initial Exercised Shares”) for $7,500,018. The GEM Warrant will be valid for a period of three years from the date NeuroRx’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction of the type contemplated by the Merger Agreement. This contingent liability at December 31, 2020, represented an obligation that resulted in the issuance of certain equity at a discounted per share price. As the amount was deemed probable and estimable at December 31, 2020, NeuroRx recorded a liability of $39,486,139 to reflect the fair value of the GEM Warrant. On March 28, 2021, NeuroRx recorded additional settlement liability of $21,365,641 to reflect the change in the fair value of the Company’s common stock. On March 28, 2021, NeuroRx reclassed the settlement liability to equity upon the issuance of the GEM Warrant. NeuroRx was required to register the Initial Exercised Shares on (a) the same registration statement on Form S-4 (or such other registration statement, if changed) in connection with the Merger, or (b) such other registration statement in connection with any other transaction which results in a public listing of NeuroRx. In addition, no later than 90 days following the consummation of the Big Rock merger, the Company was required to file with the SEC a registration statement to register under the Securities Act the resale by GEM of all shares issuable under the GEM Warrant other than the Initial Exercised Shares, which was filed with the Company's S-1 in July 2021. The GEM Warrant also includes “piggyback” registration rights. Subsequent to June 30, 2021, GEM exercised the remaining GEM Warrant for the purchase of 1,833,596 shares (adjusted for the Merger, discussed in Note 10) for gross proceeds to the Company of $9,186,316 and the GEM Warrant was extinguished.	7. Commitments and Contingencies Operating Lease The Company leases office space on a month-to-month basis. The rent expense for the years ended December 31, 2020 and 2019 was $54,649 and $42,040, respectively. Litigation —  Settlement Liability In September of 2018, Sarah Herzog Memorial Hospital Ezrat Nashim filed suit against NeuroRx, Inc., the founding shareholders alleging a dispute as to the ownership and use of intellectual property related to anti-depressants and anti-psychotics. Prior to service of the lawsuit, in December of 2018 all parties to the referenced action submitted to voluntary non-binding mediation, and reached an agreement in principle to settle the matter. The agreement provided for licensing of certain technology (“Herzog License”), future low single digit royalties upon commercialization, certain milestone payments and the transfer of 500,000 shares of NeuroRx, Inc. common stock to Sarah Herzog Memorial Hospital Ezrat Nashim (250,000 of which were transferred from the Jonathan Javitt Living Trust and 250,000 of which were transferred from Glytech, LLC a company wholly owned by Daniel Javitt). The milestone payments for developmental and commercial milestones each range from $100,000 to $750,000. Annual maintenance fees range up to $150,000. At December 31, 2018, the Company accrued $5,616,732 (representing the fair value of such shares of $5,500,000 and legal costs of $116,732) as settlement liability expense. The final settlement was signed in April 2019, pursuant to which, 500,000 shares were transferred to Herzog with an approximate fair value of $5,500,000. This charge was recorded pursuant to ASC 260, which deems consideration paid by control parties to have been paid by the Company. In connection with this settlement, 300,000 founder shares were returned to the Company and retired in 2019. In October of 2019, the founding shareholders of the Company transferred 45,454 shares of common stock with a fair value of $499,994 to a former adviser to release and discharge the Company from any obligation to the former adviser or transfer any additional securities. This charge was recorded as of September 30, 2019, by the Company as consulting expense even though the consideration was paid from the stock accounts of the founders without dilution to the Company pursuant to ASC 260, which deems consideration paid by control parties to have been paid by the Company. As of December 31, 2020, there was no further litigation against the Company. Milestone Payments Pursuant to the legal settlement, which included the license of intellectual property rights from SHMH, an ongoing royalty of 1% — 2.5% of NRX-101 gross sales shall be due SHMH, together with milestone payments of $250,000, upon completion of phase 3 trials and commercial sale of NRX-101. The milestone payments for developmental and commercial milestones each range from $100,000 to $750,000. Annual maintenance fees range up to $150,000. Aviptadil Manufacturing, Production and Distribution Agreements On August 25, 2020, NeuroRx and Nephron Pharmaceuticals Corporation (“Nephron”) signed an agreement for the manufacturing of finished pharmaceutical product of Aviptadil intravenous formulation and the development of an inhaled (nebulizer) formulation of Aviptadil. Nephron will serve as the exclusive and primary supplier of the product for both clinical and commercial purposes, supplying 100% of the Company’s annual requirements. The Company has agreed to purchase products from Nephron for a fixed price. On September 29, 2020, NeuroRx and Cardinal Health signed an exclusive distribution agreement, as well as a 3rd party logistics agreement on October 1, 2020. Cardinal Health will manage warehousing, distribution, invoicing for the potential sale of Aviptadil in the United States and Puerto Rico. On October 9, 2020, NeuroRx signed an agreement with Polypeptide for the supply of GMP grade Active Pharmaceutical Ingredient (API) Aviptadil (VIP). This gives NeuroRx a second source of procuring API. The Company has agreed to purchase a total of $1,010,000 worth of product and services over the contract. Relief Therapeutics Collaboration Agreement On September 18, 2020, the Company entered into a collaboration agreement with Relief for the clinical development and if approved the sale of Aviptadil. The collaboration provides for funding by Relief of certain clinical trials. If such candidate is approved by the FDA, the Company shall receive 50% of net product profits from the product sales in the NeuroRx territory, which includes the United States, Canada, and Israel; 15% of net product profits from the product sales in the Relief Therapeutics territory, which includes the European Union, Switzerland, Iceland, Norway, the UK, the Channel Islands, Liechtenstein, Monaco, Andorra, Malta, San Marino, and Vatican City; and 20% of net product profits from the product sales in all other countries. During 2020, the Company invoiced Relief $10,160,421 for reimbursable expenses and received $9,329,031 in payments from Relief for these reimbursable expenses. As of December 31, 2020, the Company had an accounts receivable balance due from Relief of $831,390, net of an allowance for doubtful accounts of $257,463. As of May 11, 2021, Relief has reimbursed NeuroRx $10,612,750 for expenses, but has not paid approximately $4,000,000 in invoiced costs associated with conduct of the IV clinical trial, reformulation, and manufacture of ZYESAMI. As of May 11, 2021, Relief has not funded the costs of the inhaled trial. NeuroRx has advised Relief that NeuroRx is funding those costs with other capital. Share Subscription Facility Agreement - GEM The Company previously entered into a share subscription facility agreement (“GEM Agreement”) with GEM Global Yield LLC SCS and GEM Yield Bahamas Limited (collectively, referred to as “GEM”) with a three-year term. Subject to the successful listing of the shares of NeuroRx on an Exchange (any nationally recognized stock exchange or exchange platform in the world on which the Company will list its shares), GEM grants the Company an option to require GEM to subscribe for shares from the Company for up to an aggregate value of approximately $95.6 million. The agreement also included certain provisions which would not meet the U.S. requirements to issue registered shares. If NeuroRx was listed or completes a private transaction which results in a change of control of the Company, the Company would issue GEM a warrant and pay a commitment fee of $1.9 million. Absent a listing of NeuroRx shares or a private transaction with a change of control during the three-year term, the Company would have no obligations under the agreement. A reverse merger would not result in a listing of NeuroRx shares or a change in control. In November 2020, GEM introduced the Company to Big Rock. Although the Company has taken the position that the reverse merger transaction contemplated by the Merger Agreement (as defined below) would not require the issuance of the warrant, to resolve uncertainties around the application of the GEM Agreement, the Company and GEM agreed in March 2021 to issue a warrant to GEM and for the parties to use their good faith efforts to amend the GEM Agreement to meet U.S. requirements to issue registered shares. The warrant is not conditional upon any further events or completion of the merger. The warrant was issued March 28, 2021, for 1,053,738 shares of NeuroRx common stock at an exercise price of $15.84 per share (the “GEM Warrant”) and the parties agreed that GEM would immediately partially exercise the warrant for the purchase of 473,486 shares (“Initial Exercised Shares”) for $7.5 million. The GEM Warrant will be valid for a period of three years from the date the Company’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction. This contingent liability at December 31, 2020, represented an obligation that resulted in the issuance of certain equity at a discounted per share price. As the amount was deemed probable and estimable by the Company at December 31, 2020, the Company recorded a liability of $39,486,139 to reflect the fair value of the GEM Warrant. The Company is required to register the Initial Exercised Shares on (a) the same registration statement on Form S-4 (or such other registration statement, if changed) in connection with the Big Rock merger, or (b) such other registration statement in connection with any other transaction which results in a public listing of the Company. In addition, no later than 90 days following the consummation of the Big Rock merger, the Company is required to file with the SEC a registration statement to register under the Securities Act the resale by GEM of all shares issuable under the GEM Warrant other than the Initial Exercised Shares. The GEM Warrant also includes “piggyback” registration rights. Merger with Big Rock Partners Acquisition Corp. On December 13 2020, the Company entered into an Agreement and Plan of Merger (“Merger Agreement”) with Big Rock. Under the terms of the transaction, Big Rock will issue to NeuroRx’s current equity holders an aggregate of 50 million shares (“Per Share Merger Consideration”) of Big Rock common stock for their interests in NeuroRx. Subject to certain conditions, an aggregate of 25 million additional shares of Big Rock common stock (“Earnout Shares”) will be issued to NeuroRx pre-merger equity holders if, prior to December 31, 2022, (1) the Company’s COVID-19 drug receives emergency use authorization by the FDA and (2) the FDA accepts the Company’s filing of its application to approve the Company’s COVID-19 drug. In addition, subject to certain conditions, $100 million (“Earnout Cash”) may be payable to NeuroRx pre-merger equity holders if, prior to December 31, 2022, either (1) FDA approval of the Company’s COVID-19 Drug is obtained and the Company’s COVID-19 Drug is listed in the FDA’s “Orange Book” and (2) FDA approval of the Company’s Antidepressant Drug Regimen is obtained and the Company’s Antidepressant Drug Regimen is listed in the FDA’s “Orange Book”. The Boards of Directors of both NeuroRx and Big Rock have unanimously approved the proposed transaction. Completion of the transaction is subject to approval by stockholders of NeuroRx and Big Rock and other customary closing conditions.

Equity

Equity	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Equity
Equity	10. Equity Common Stock Upon closing of the Merger, pursuant to the terms of the Second Amended and Restated Certificate of Incorporation, the Company authorized 500,000,000 shares of common stock with a par value $0.001. As discussed in Note 4, we have retroactively adjusted the shares issued and outstanding prior to May 24, 2021 to give effect to the Exchange Ratio established in the Merger Agreement to determine the number of shares of common stock into which they were converted. The Company sold 65,526 and 0 shares of common stock during the three months ended June 30, 2021 and 2020, respectively, and received gross proceeds of $1,436,274 and $0, respectively. The Company sold 398,647 and 50,844 shares of common stock during the six months ended June 30, 2021 and 2020, respectively, and received gross proceeds of $8,363,132 and $176,990, respectively. Pursuant to the Merger Agreement, BRPA and EarlyBirdCapital, Inc., the representative of the underwriters of BRPA’s initial public offering (“EBC”), entered into an amendment (“BCMA Amendment Agreement”) to the Business Combination Marketing Agreement, dated as of November 20, 2017 (“BCMA”), by and between BRPA and EBC. The BCMA Amendment Agreement provided that, in lieu of the cash fee payable to EBC pursuant to the BCMA, BRPA will issue to EBC at the Effective Time an aggregate of 200,000 shares of Common Stock and the BCMA (as amended by the BCMA Amendment Agreement) will terminate immediately following the Effective Time. The Company recognized the fair value of the 200,000 shares of Common Stock issued pursuant to the BCMA of $4,850,000 within general and administrative in the Unaudited Condensed Consolidated Statements of Operations for the three and six months ended June 30, 2021. Preferred Stock Upon closing of the Merger, pursuant to the terms of the Second Amended and Restated Certificate of Incorporation, the Company authorized 50,000,000 shares of preferred stock with a par value $0.001. Series A, B-1, and B-1A Preferred Stock Prior to the Merger, the Company had authorized and issued 1,000,000 shares of Series A convertible preferred stock, 1,050,695 shares of Series B-1 convertible preferred stock, and 316,848 shares of Series B-1A convertible preferred stock, par value of $0.001 per share, which was convertible into one share of common stock for each preferred share (collectively, the “Preferred Stock”) at any time, at the option of the holder. The Preferred Stock were not redeemable and the related stockholders were entitled to a subordinated liquidation preference should NeuroRx liquidate or wind up operations. The preferences also included voting rights on an as-converted basis, ride-along rights, and an anti-dilution provision. The liquidation preference was $1.00 per share for the Series A convertible preferred stock, $7.58 per share for the Series B-1 convertible preferred stock, and $6.82 per share for the Series B-1A convertible preferred stock, plus any declared but unpaid dividends. Upon an initial public offering or merger under certain conditions the Preferred Stock automatically converted into common stock. On May 24, 2021, pursuant to the Merger (as described in Note 4), 2,367,543 outstanding shares of Preferred Stock were automatically converted into 7,480,836 shares of common stock pursuant to the Exchange Ratio. Series B-2 Preferred Stock In 2020, the Company authorized the issuance of 100,000 shares of Series B-2 Convertible Preferred Stock (the “B-2 Preferred Stock”), par value of $0.001 per share, convertible into one share of common stock for each share of B-2 Preferred Stock held. In March 2020, 4,167 shares of B-2 Preferred Stock were issued. The B-2 Preferred stock were not redeemable and the related stockholders were entitled to a subordinated liquidation preference should NeuroRx liquidate or wind up operations. The preferences also included voting rights on an as-converted basis, ride-along rights, and an anti-dilution provision. The liquidation preference was $12.00 per share plus any declared but unpaid dividends. The B-2 Preferred Stock could be converted into one share of common stock (subject to adjustments for stock splits, recapitalization) at any time, at the option of the holder. Upon an initial public offering or merger under certain conditions the B-2 Preferred Stock automatically converted into common stock. On May 24, 2021, pursuant to the Merger (as described in Note 4), 4,167 outstanding shares of B-2 Preferred stock were automatically converted into 13,168 shares of common stock pursuant to the Exchange Ratio. Common Stock Warrants On March 28, 2021, NeuroRx issued 3,329,812 fully vested common stock warrants, exercisable at a per share price of $3.19 until they expire on March 27, 2024 to GEM (See Note 8). The fair value on the date of issuance was $60,851,779. Upon issuance, 1,496,216 warrants were immediately exercised generating gross proceeds of $7,500,018. Subsequent to June 30, 2021, GEM exercised the remaining GEM Warrant for the purchase of 1,833,596 shares for gross proceeds of $9,186,316 and the GEM Warrant was extinguished. The grant date fair value of common stock warrants is determined using the Black Scholes option-pricing model. The Company estimates its expected stock volatility based on historical volatility of publicly traded peer companies. The estimated fair value of common stock is based on sales to third parties. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ 2021 ​ 2020 Strike price ​ $ 24.25 $ 3.19 ​ Volatility rate ​ 80.0 % ​ 80.0 % Risk-free rate ​ 0.03%-0.32 % ​ 0.19%-0.28 % Expected term ​ 0.57-4.42 ​ 3.00-5.00 ​ Dividend yield ​ — ​ — ​ ​ Substitute Warrants In connection with the Merger, each warrant of NeuroRx that was outstanding and unexercised immediately prior to the Effective Time (whether vested or unvested) was assumed by BRPA and converted into the Substitute Warrants, based on the Option Exchange Ratio (of 4.96), and will continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the former warrant. Each Substitute Warrant will be exercisable for a number of whole shares of Common Stock equal to the product of the number of shares of NeuroRx common stock underlying such NeuroRx warrant multiplied by the Option Exchange Ratio, and the per share exercise price of such Substitute Warrant will be equal to the quotient determined by dividing the exercise price per share of NeuroRx common stock by the Option Exchange Ratio. As discussed in Note 4, this ratio incorporates the achievement of the Earnout Shares Milestone and Earnout Cash Milestone. The incremental shares above the Exchange Ratio (of 3.16) upon exercise would be held back pending the outcome of the contingencies and only released if such are achieved. The percentage of total shares of Common Stock subject to each Substitute Warrant that is vested immediately following the Effective Time will equal the percentage of total shares of NeuroRx common stock subject to each NeuroRx warrant that is vested immediately prior to the Effective Time. In the event that either the Earnout Shares Milestone or the Earnout Cash Milestone does not occur prior to December 31, 2022, each Substitute Warrant will be adjusted such that the number of shares of Common Stock subject to each adjusted Substitute Warrant, the exercise price per share of each adjusted Substitute Warrant and the aggregate intrinsic value of each adjusted Substitute Warrant will equal the respective number of shares, exercise price per share and aggregate intrinsic value that would have resulted following the adjustment of the applicable underlying Substitute Warrant had the conversion of NeuroRx warrants into the Substitute Warrants been applied using the Exchange Ratio (3.16:1) as adjusted accordingly to reflect the impact of the respective milestone not being met. If neither the Earnout Shares Milestone nor the Earnout Cash Milestone occurs, each Substitute Warrant will be adjusted based on the Exchange Ratio. If any Substitute Warrants are exercised prior to the earlier of (i) the date that both the Earnout Shares Milestone and Earnout Cash Milestone occur and (ii) December 31, 2022, a sufficient number of shares of Common Stock will be held back pending the applicable adjustment to such Substitute Warrants. Following the determination of that adjustment, NRx Pharmaceuticals will retain any shares forfeited by the warrant holder in connection with the adjustment and return any remaining shares to the warrant holder. Upon the closing of the Merger, the outstanding and unexercised NeuroRx warrants became warrants to purchase an aggregate 4,909,066 shares of the Company’s common stock with an average exercise price of $2.50 per share. The Company accounted for the Substitute Warrants as a modification of the existing warrants. Incremental fair value, measured as the excess, if any, of the fair value of the modified warrants over the fair value of the original warrants immediately before its terms are modified, is measured based on the fair value of the underlying shares and other pertinent factors at the modification date. The fair value of the original NeuroRx warrants and Substitute Warrants was determined using the Black-Scholes option-pricing model with the following assumptions for each: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Original Warrants Substitute Warrants Strike price ​ $ 7.58-$15.84 ​ $ 1.53-$3.19 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.03%-0.32 % 0.03%-0.32 % Expected term ​ 0.57-4.42 ​ 0.57-4.42 ​ Dividend yield ​ — ​ — ​ ​ With respect to warrants held by certain members of our Board of Directors, the Substitute Warrants were determined to be within the scope of ASC 718 and were fully vested at the Effective Date. Further, the Substitute Warrants were determined to contain both service-based and performance-based vesting conditions (i.e., the achievement of the Earnout Cash and/or Earnout Share Milestones). The Company determined it was not probable that the Earnout Cash or Earnout Share Milestone would be met on the Effective Date and at June 30, 2021. Accordingly, the Company will only recognize incremental compensation cost related to the portion of the Substitute Warrants subject to service-based vesting conditions only. The Company will reevaluate the probability of the Earnout Cash and/or Earnout Share Milestones being met and recognize any unamortized incremental compensation cost accordingly in the period during which it becomes probable the milestones will be met. The Company recognized incremental compensation on the modification date totaling $2,330,572 which was recognized in General and administrative in the Unaudited Condensed Consolidated Statements of Operations for the three and six months ended June 30, 2021, respectively. Unamortized compensation costs related to performance-based vesting conditions of the Substitute Warrants as of the modification date was $23,760,993. With respect to the remaining outstanding warrants, the incremental fair value of the Substitute Warrants of $2,691,799 was recognized as a deemed dividend as the Company concluded there is a transfer of value from the common shareholders to the holders of the Substitute Warrants as the change in the number of underlying shares and the decreased exercise price would result in the common shareholders becoming more diluted if and when the Substitute Warrants are converted. As the Company is in an accumulated deficit position as of the modification date, the resulting deemed dividend is recorded as a reduction of additional paid-in capital with a corresponding offset recorded to additional paid-in capital (i.e., net impact to additional paid-in capital of $0). Further, in the event the Earnout Shares Milestone and Earnout Cash Milestones are met, the Company will recognized an additional deemed dividend of $24,379,657 and $3,068,732, respectively, if and when such conditions are met. Assumed Public Warrants Prior to the Merger, the Company had outstanding 3,450,000 Public Warrants. Each Public Warrant entitles the holder to purchase one The Company may redeem the Public Warrants: ● in whole and not in part; ● at a price of $0.01 per warrant; ● at any time during the exercise period; ● upon a minimum of 30 days ’ prior written notice of redemption; ● if, and only if, the last sale price of the Company’s common stock equals or exceeds $21.00 per share for any 20 trading days within a 30 -trading day period ending on the third business day prior to the date on which the Company sends the notice of redemption to the warrant holders; and ● if, and only if, there is a current registration statement in effect with respect to the shares of common stock underlying such warrants. Certain of the above conditions have not been met to redeem the Public Warrants. If the Company calls the Public Warrants for redemption, management will have the option to require all holders that wish to exercise the Public Warrants to do so on a “cashless basis,” as described in the warrant agreement. The exercise price and number of shares of common stock issuable upon exercise of the warrants may be adjusted in certain circumstances including in the event of a stock dividend, or recapitalization, reorganization, merger or consolidation. However, the warrants will not be adjusted for issuance of common stock at a price below its exercise price. Additionally, in no event will the Company be required to net cash settle the warrants. Assumed Placement Warrants Prior to the Merger, the Company had outstanding 136,250 Placement Warrants. The Placement Warrants are identical to the Public Warrants except that the Placement Warrants (i) are not redeemable by the Company and (ii) may be exercised for cash or on a cashless basis, so long as they are held by the initial purchaser or any of its permitted transferees. If the Placement Warrants are held by someone other than the initial purchasers or their permitted transferees, the Placement Warrants will be redeemable by the Company and exercisable by such holders on the same basis as the Public Warrants. The Placement Warrants are not indexed to the Company’s common shares in the manner contemplated by ASC 815-40-15 because the holder of the instrument is not an input into the pricing of a fixed-for-fixed option on equity shares. The Company classifies the Placement Warrants as derivative liabilities in its Unaudited Condensed Consolidated Balance Sheet as of June 30, 2021. The Company measures the fair value of the warrants at the end of each reporting period and recognizes changes in the fair value from the prior period in the Company’s operating results for the current period. The Company recognized a gain on the change in fair value of the Placement Warrants for the three and six months ended June 30, 2021 and 2020 of $1,468,649 and $0, respectively. Refer to Note 13 for discussion of fair value measurement of the warrant liabilities. The following table provides the activity for all warrants for the respective periods. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Aggregate ​ ​ Total Warrants ​ Term ​ Exercise Price ​ Intrinsic Value Outstanding as of December 31, 2020 (as previously reported) 620,055 11.08 ​ $ 14.61 ​ $ 22,127,594 Retroactive application of reverse recapitalization (Note 4) ​ 2,455,415 ​ — ​ ​ (13.53) ​ ​ — Outstanding as of December 31, 2020, effect of Merger (Note 4) ​ 3,075,470 ​ 4.34 ​ ​ 1.09 ​ ​ 150,955,963 Issued 3,329,812 3.00 ​ 3.19 ​ 111,082,528 Exercised (1,496,216) ​ ​ (3.19) ​ (49,913,766) Outstanding as of March 31, 2021 4,909,066 3.74 ​ $ 1.78 ​ $ 244,574,345 Issued 3,586,250 5.00 ​ 11.50 ​ 45,724,688 Outstanding as of June 30, 2021 8,495,316 4.09 ​ $ 24.78 ​ $ 42,385,824 ​ Assumed Unit Purchase Options Prior to the Merger, the Company had outstanding options to purchase up to 600,000 Units exercisable at $10.00 per Unit (or an aggregate exercise price of $6,000,000) commencing on the Effective Time. Each Unit consists of one one one five Conversion of Rights Prior to the Merger, the Company had outstanding 6,900,000 and 272,500 Public Rights and Placement Rights, respectively. At the Effective Time, each holder of a right received one-tenth (1/10) of one share of Common Stock at the Effective Time, even if the holder of such right redeemed all shares held by it in connection with the Merger, resulting in the issuance of 717,250 shares of Common Stock to holders of such rights. No fractional shares were issued upon conversion of the rights. No additional consideration was required to be paid by a holder of rights in order to receive its additional shares at the Effective Time, as the consideration related thereto has been included in the original unit purchase price paid for by investors in the Company's Initial Public Offering. The shares issuable upon conversion of the rights will be freely tradable (except to the extent held by affiliates of the Company).	8. Equity Common Stock On March 1, 2020, the Company’s board of directors authorized an increase to the authorized share capital from 14,060,001 shares of common stock to 20,000,000 shares of common stock with a par value of $0.001 per share. The Company sold 171,796 and 536,354 shares of common stock during the years ended December 31, 2020 and 2019, respectively and received gross proceeds of $2,579,114 and net proceeds of $5,802,002, respectively. The Company issued 9,500 shares of common stock with a fair value of $144,875 in settlement of accounts payable worth $103,258, and recognized a loss of $41,617 for the difference during the year ended December 31, 2020 and did not issue any such shares during the year ended December 31, 2019. Preferred Stock Series A, B-1, and B-1A Preferred Stock The Company has authorized issued B-1A per share convertible into Series B-2 Preferred Stock In 2020, the Company authorized the issuance of 100,000 shares of Series B-2 Convertible Preferred Stock, par value of $0.001 per share, convertible into one share of Common Stock for each share of Series B-2 Convertible Preferred Stock held. In March 2020, 4,167 Series B-2 stock were issued. The Series B-2 Preferred stock are not redeemable and the related stockholders are entitled to a subordinated liquidation preference should the Company liquidate or wind up operations. The preferences also include voting rights on an as-converted basis, ride-along rights, and an anti-dilution provision. The liquidation preference is $12.00 per share plus any declared but unpaid dividends. The B-2 Convertible Preferred shares can be converted into one share of Common Stock (subject to adjustments for stock splits, recapitalization) at any time, at the option of the holder. Upon an initial public offering or merger under certain conditions the Series B-2 Preferred Stock will automatically convert into common stock. Common Stock Warrants On January 31, 2019, the Company issued 8,846 fully vested common stock warrants, exercisable at a per share price of $11.00 until they expire on January 30, 2024, to a vendor for financial advisory services provided in connection with the sale of the Company’s common stock. The fair value on the date of issuance was $7.16 per warrant for a total fair value of $63,337. On July 6, 2020, the Company issued 4,000 fully vested common stock warrants, exercisable at a per share price of $15.25 until they expire on July 5, 2023, to a vendor for financial advisory services provided in connection with the sale of the Company’s common stock. The fair value on the date of issuance was $7.63 per warrant for a total fair value of $30,536. On July 15, 2020, the Company issued 279,291 fully vested common stock warrants, exercisable at a per share price of $15.25 until they expire on July 14, 2025, to a board member. The fair value on the date of issuance was $9.63 per warrant for a total fair value of $2,689,684. On October 23, 2020, the Company issued 139,645 and 139,645 fully vested common stock warrants, exercisable at a per share price of $15.25 until they expire on October 22, 2025, to a board member, respectively. The fair value on the date of issuance was $9.64 per warrant for a total fair value of $2,693,221. The following table provides the activity in warrants for the respective periods. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Average ​ ​ Total Warrants Term Exercise Price Intrinsic Value Outstanding as of December 31, 2018 ​ 48,627 ​ 2.88 ​ $ 7.90 ​ $ — Issued 8,846 5.00 ​ 11.00 ​ — Outstanding as of December 31, 2019 57,473 2.22 ​ $ 8.38 ​ $ — Issued 562,581 4.99 ​ 15.25 ​ 20,112,271 Outstanding as of December 31, 2020 620,054 11.08 ​ $ 14.61 ​ $ 22,127,594 ​ The grant date fair value of common stock warrants is determined using the Black Scholes option-pricing model. The Company is a private company and estimates its expected stock volatility based on historical volatility of publicly traded peer companies. The estimated fair value of the Company’s common stock is based on sales to third parties. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Strike price $ 15.25 ​ $ 11.00 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.19%-0.28 % 2.40 % Expected term ​ 3.00-5.00 ​ 5.00 ​ Dividend yield ​ — ​ — ​ ​

Stock-Based Compensation

Stock-Based Compensation	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Stock-Based Compensation
Stock-Based Compensation	11. Stock-Based Compensation 2016 Omnibus Incentive Plan Prior to the Merger, NeuroRx maintained its 2016 Omnibus Incentive Plan (the “2016 Plan”), under which NeuroRx granted incentive stock options, restricted stock awards, other stock-based awards, or other cash-based awards to employees, directors, and non-employee consultants. The maximum aggregate shares of common stock that was subject to awards and issuable under the 2016 Plan was 3,472,000. In connection with the Merger, each NeuroRx stock option that was outstanding and unexercised immediately prior to the Effective Time (whether vested or unvested) was assumed by BRPA and converted into an option to acquire an adjusted number of shares of Common Stock at an adjusted exercise price per share (the “Substitute Options”), and will continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the former option. In connection with the Merger, each option of NeuroRx that was outstanding and unexercised immediately prior to the Effective Time (whether vested or unvested) was assumed by BRPA and converted into the Substitute Options, based on the Option Exchange Ratio (of 4.96), and will continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the former option. Each Substitute Option will be exercisable for a number of whole shares of Common Stock equal to the product of the number of shares of NeuroRx common stock underlying such NeuroRx option multiplied by the Option Exchange Ratio, and the per share exercise price of such Substitute Option will be equal to the quotient determined by dividing the exercise price per share of NeuroRx common stock by the Option Exchange Ratio. As discussed in Note 4, this ratio incorporates the achievement of the Earnout Shares Milestone and Earnout Cash Milestone. The incremental shares above the Exchange Ratio (of 3.16) upon exercise would be held back pending the outcome of the contingencies and only released if such are achieved. The percentage of total shares of Common Stock subject to each Substitute Option that is vested immediately following the Effective Time will equal the percentage of total shares of NeuroRx common stock subject to each NeuroRx option that is vested immediately prior to the Effective Time. In the event that either the Earnout Shares Milestone or the Earnout Cash Milestone does not occur prior to December 31, 2022, each Substitute Option will be adjusted such that the number of shares of Common Stock subject to each adjusted Substitute Option, the exercise price per share of each adjusted Substitute Option and the aggregate intrinsic value of each adjusted Substitute Option will equal the respective number of shares, exercise price per share and aggregate intrinsic value that would have resulted following the adjustment of the applicable underlying Substitute Option had the conversion of NeuroRx options into the Substitute Options been applied using the Exchange Ratio as adjusted accordingly to reflect the impact of the respective milestone not being met. If neither the Earnout Shares Milestone nor the Earnout Cash Milestone occurs, each Substitute Option will be adjusted based on the Exchange Ratio. As stated in the Merger Agreement, if any Substitute Options are exercised prior to the earlier of (i) the date that both the Earnout Shares Milestone and Earnout Cash Milestone occur and (ii) December 31, 2022, a sufficient number of shares of Common Stock will be held back pending the applicable adjustment to such Substitute Options. Following the determination of that adjustment, NRx Pharmaceuticals will retain any shares forfeited by the option holder in connection with the adjustment and return any remaining shares to the option holder. Upon the closing of the Merger, the outstanding and unexercised NeuroRx stock options became options to purchase an aggregate 2,895,423 shares of the Company’s Common Stock at an average exercise price of $1.50 per share. The Company accounted for the Substitute Options as a modification of the existing options. Incremental compensation costs, measured as the excess, if any, of the fair value of the modified options over the fair value of the original options immediately before its terms are modified, is measured based on the fair value of the underlying shares and other pertinent factors at the modification date. The fair value of the original NeuroRx options and Substitute Options was determined using the Black-Scholes option-pricing model with the following assumptions for each: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Original Options Substitute Options Strike price ​ $ 1.00-$72.30 ​ $ 0.20-$14.58 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.07%-0.79 % 0.07%-0.79 % Expected term ​ 0.18-5.99 ​ 0.18-5.99 ​ Dividend yield ​ — ​ — ​ ​ The Substitute Options contain both service-based and performance-based vesting conditions (i.e., the achievement of the Earnout Cash and/or Earnout Share Milestones). The Company determined it was not probable that the Earnout Cash or Earnout Share Milestone would be met on the Effective Date and at June 30, 2021. Accordingly, the Company will only recognize incremental compensation cost related to the portion of the Substitute Options subject to service-based vesting conditions only. The Company will reevaluate the probability of the Earnout Cash and/or Earnout Share Milestones being met and recognize any unamortized incremental compensation cost accordingly in the period during which it becomes probable the milestones will be met. For vested Substitute Options, the Company recognized incremental compensation on the modification date totaling $1,014,640, of which $993,500 and $21,140 was recognized in General and administrative and Research and development, respectively, in the Unaudited Condensed Consolidated Statements of Operations for the three and six months ended June 30, 2021, respectively. For unvested Substitute Options, the Company will recognize incremental compensation over the remaining requisite service period, the sum of the incremental compensation cost and the remaining unrecognized compensation cost for the original award on the modification date, taking into consideration the probability of the achievement of the Earnout Cash and/or Earnout Share Milestones. Incremental compensation costs related to unvested Substitute Options as of the modification date was $25,877,473. 2021 Omnibus Incentive Plan At the Effective Time, the Company adopted the 2021 Omnibus Incentive Plan (the “2021 Plan”). As of June 30, 2021, 5,373,049 shares of Common Stock are authorized for issuance pursuant to awards under the 2021 Plan, inclusive of any shares of Common Stock subject to stock options, restricted stock awards or other awards that were assumed in the Merger and terminate as a result of being unexercised or are forfeited or repurchased by the Company, with the maximum number of shares to be added to the 2021 Plan equal to 5,373,049 shares of Common Stock. As of June 30, 2021, 2,919,493 shares have been awarded and 2,453,556 shares remain available for issuance under the 2021 Plan. The 2021 Plan permits the granting of incentive stock options, restricted stock awards, other stock-based award or other cash-based awards to employees, directors, and non-employee consultants. Option Awards The fair value of each employee and non-employee stock option grant is estimated on the date of grant using the Black-Scholes option-pricing model. The Company is a public company and lacks company-specific historical and implied volatility information. Therefore, it estimates its expected stock volatility based on the historical volatility of a publicly traded set of peer companies. Due to the lack of historical exercise history, the expected term of the Company’s stock options for employees has been determined utilizing the “simplified” method for awards. The risk-free interest rate is determined by reference to the U.S. Treasury yield curve. Expected dividend yield is zero based on the fact that the Company has never paid cash dividends and does not expect to pay any cash dividends in the foreseeable future. Additionally, certain options granted contain terms that require all unvested options to immediately vest a) upon the approval of a New Drug Application (NDA) by the US Food and Drug Administration for NRX-101, or b) immediately preceding a change in control of the Company, whichever occurs first. The grant date fair value of employee and non-employee stock option awards is determined using the Black Scholes option-pricing model. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 December 31, 2020 Exercise price $ 11.69-$23.41 ​ $ 2.22-$3.07 ​ Risk-free rate of interest ​ 0.79%-1.24 % 0.79%-0.79 % Expected term (years) ​ 5.5-6.5 ​ 4.7-5.9 ​ Expected stock price volatility ​ 80 % 80 % Dividend yield ​ — ​ — ​ ​ The following table summarizes the Company’s employee and non-employee stock option activity under the Plan for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ Weighted ​ average ​ Aggregate ​ ​ Number of ​ average ​ remaining ​ intrinsic ​ shares exercise price term (years) value Outstanding as of December 31, 2020 (as previously reported) 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Retroactive application of reverse recapitalization 1,927,548 ​ (8.62) ​ ​ ​ Outstanding as of December 31, 2020, effect of Merger 2,414,303 ​ $ 2.17 8.2 ​ $ 53,659,966 Options granted 210,800 ​ ​ 11.69 9.8 ​ ​ 3,825,276 Forfeited (198,400) ​ ​ (2.22) — ​ ​ (6,587,328) Outstanding as of March 31, 2021 ​ 2,426,703 ​ $ 14.58 ​ 8.7 ​ $ 30,388,510 Options granted ​ 587,030 ​ ​ 14.94 ​ 9.9 ​ ​ — Forfeited ​ (89,280) ​ ​ (7.86) ​ — ​ ​ (339,082) Exercised ​ (4,960) ​ ​ (3.07) ​ — ​ ​ (42,385) Outstanding as of June 30, 2021 ​ 2,919,493 ​ $ 5.25 ​ 9.0 ​ $ 20,558,299 Options vested and exercisable as of June 30, 2021 ​ 1,095,294 ​ $ 1.50 ​ 6.1 ​ $ 11,106,829 ​ The aggregate intrinsic value in the above table is calculated as the difference between fair value of the Company’s common stock price and the exercise price of the stock options. The weighted average grant date fair value per share for employee stock and non-employee option grants during the three months ended and six months ended June 30, 2021, respectively was $14.31 and $18.37. The weighted average grant date fair value per share for employee stock and non-employee option grants during the three months ended and six months ended June 30, 2020, respectively was $1.25 and $1.25. At June 30, 2021, the total unrecognized compensation related to unvested employee and non-employee stock option awards granted, including unrecognized compensation costs related to Substitute Options of $25,877,473, was $33,610,165, of which the Company expects to recognize $9,117,887 over a weighted-average period of approximately 1.89 years. The following table summarizes the Company’s recognition of stock-based compensation for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three months ended June 30, ​ Six months ended June 30, ​ 2021 2020 2021 2020 Stock-based compensation expense ​ ​ ​ ​ General and administrative ​ $ 4,094,549 ​ $ 50,881 ​ $ 4,438,583 ​ $ 117,469 Regulatory and process development ​ 188,781 ​ 42,585 ​ 216,445 ​ 64,800 Total stock-based compensation expense ​ $ 4,283,330 ​ $ 93,466 ​ $ 4,655,028 ​ $ 182,269 ​	9. Stock-Based Compensation The Company’s 2016 Omnibus Incentive Plan (the “Plan”) permits the granting of incentive stock options, restricted stock awards, other stock-based award or other cash-based awards. The maximum aggregate shares of common stock that may be subject to awards and issued under the Plan is 500,000. In December 2020, the Company’s board of directors authorized an additional 200,000 shares of common stock options to be authorized under the Plan for a total of 700,000 authorized shares. At December 31, 2020, 486,755 shares have been awarded and 213,245 shares remain available for issuance under the Plan. Option Awards The fair value of each employee and non-employee stock option grant is estimated on the date of grant using the Black-Scholes option-pricing model. The Company is a private company and lacks company-specific historical and implied volatility information. Therefore, it estimates its expected stock volatility based on the historical volatility of a publicly traded set of peer companies. Due to the lack of historical exercise history, the expected term of the Company’s stock options for employees has been determined utilizing the “simplified” method for awards. The risk-free interest rate is determined by reference to the U.S. Treasury yield curve. Expected dividend yield is zero based on the fact that the Company has never paid cash dividends and does not expect to pay any cash dividends in the foreseeable future. Additionally, certain options granted contain terms that require all unvested options to immediately vest a) upon the approval of a New Drug Application (NDA) by the US Food and Drug Administration for NRX-101, or b) immediately preceding a change in control of the Company, whichever occurs first. The fair value of the Company’s common stock, which equaled the exercise price of stock options granted during the years ended December 31, 2020 and 2019, respectively, was determined based on sales of the Company’s shares at arm’s length to unrelated third parties. The grant date fair value of employee and non-employee stock option awards is determined using the Black Scholes option-pricing model. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 ​ Exercise price ​ $ 11.00‑$15.25 $ 11.00 ​ Risk-free rate of interest ​ 0.30%‑0.49 % ​ 1.54%‑1.73 % Expected term (years) ​ 5.5 6.5 ​ 6.0 6.5 ​ Expected stock price volatility ​ 80 % ​ 80 % Dividend yield ​ — ​ — ​ ​ The following table summarizes the Company’s employee and non-employee stock option activity under the Plan for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ ​ average ​ ​ ​ ​ ​ ​ ​ Weighted ​ remaining ​ Aggregate ​ ​ Number of ​ average ​ contractual ​ intrinsic ​ ​ shares ​ exercise price ​ life (in years) ​ value Outstanding as of December 31, 2018 355,408 ​ $ 5.74 8.2 ​ $ 1,782,729 Granted 28,180 ​ 11.00 9.6 ​ Forfeited/Cancelled (50,000) ​ — — ​ — Outstanding as of December 31, 2019 333,588 ​ $ 5.74 7.2 ​ $ 1,782,729 Granted 266,500 ​ 14.37 9.7 ​ 9,761,125 Forfeited /Cancelled (113,333) ​ — — ​ — Outstanding as of December 31, 2020 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Options vested and exercisable as of December 31, 2020 329,489 ​ $ 6.31 4.0 ​ $ 14,723,342 ​ The aggregate intrinsic value in the above table is calculated as the difference between fair value of the Company’s common stock price and the exercise price of the stock options. The weighted average grant date fair value per share for employee stock and non-employee option grants during the years ended December 31, 2020 and 2019 was $9.64 and $7.69, respectively. At December 31, 2020, the total unrecognized compensation related to unvested employee and non-employee stock option awards granted was $2,193,874, which the Company expects to recognize over a weighted-average period of approximately 2.09 years. Stock-based compensation expense related to stock options, in aggregate, has been reported in general and administrative expense in the amount of $332,065 and $321,087 and research and development expense in the amount of $398,340 and $112,823 in the Company’s statements of operations for the years ended December 31, 2020 and 2019, respectively.

Income Taxes

Income Taxes	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Income Taxes.
Income Taxes	13. Income Taxes The Company recorded no provision or benefit for income tax expense for the six months ended June 30, 2021. For all periods presented, the pretax losses incurred by the Company received no corresponding tax benefit because the Company concluded that it is more likely than not that the Company will be unable to realize the value of any resulting deferred tax assets. The Company will continue to assess its position in future periods to determine if it is appropriate to reduce a portion of its valuation allowance in the future. On March 27, 2020, Congress enacted the CARES Act to provide certain relief as a result of the COVID-19 pandemic. The CARES Act, among other things, includes provisions relating to net operating loss carryback periods, alternative minimum tax credit refunds, and modification to the net interest deduction limitations. The CARES Act did not have a material impact on the Company’s consolidated financial statements for the six months ended June 30, 2021. The Company continues to monitor any effects on its financial statements that may result from the CARES Act. Upon consummation of the Merger, a change in control was deemed to have occurred and the Company's net operating loss carrybacks could be subject to limitations. The Company has no open tax audits with any taxing authority as of June 30, 2021.	10. Income Taxes A reconciliation of the statutory U.S. federal income tax rate to the Company’s effective tax rate consist of the following: ​ ​ ​ ​ ​ ​ ​ ​ For the Years ​ ​ Ended ​ ​ ​ December 31, ​ ​ ​ 2020 2019 Statutory federal income tax benefit (21.00) % (21.00) % Permanent items (0.04) % 0.01 % Foreign rate differential 0.01 % (0.02) % State taxes, net of federal tax benefit (1.74) % 0.60 % Change in valuation allowance 23.01 % 22.23 % R&D credit (0.24) % (1.90) % Other — % 0.07 % Effective tax rate — % — % ​ The components of income tax provision (benefit) are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ ​ 2020 2019 Federal: ​ ​ Current ​ $ — ​ $ — Deferred ​ (11,015,759) ​ (1,496,712) State and Local: ​ ​ Current ​ — ​ — Deferred ​ (900,789) ​ 39,574 Foreign: ​ ​ Current ​ — ​ — Deferred ​ 2,867 ​ (8,412) Change in valuation allowance ​ 11,913,681 ​ 1,465,550 Total ​ $ — ​ $ — ​ Deferred income taxes reflect the net tax effects of temporary differences between the carrying value of assets and liabilities for financial reporting purposes and amounts used for income tax purposes. The temporary differences that give rise to deferred tax assets and liabilities are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Deferred tax assets (liabilities): ​ ​ ​ ​ ​ ​ Net operating loss carryforwards ​ $ 8,243,959 ​ $ 6,943,988 Convertible notes payable discount and embedded derivative ​ — ​ 101,521 Common stock warrants ​ 1,405,796 ​ 179,271 Israel net operating loss carryforwards ​ 128,469 ​ 131,336 Founder share options ​ 469,062 ​ 472,195 Stock-based compensation ​ 681,446 ​ 497,315 Settlement liability ​ 9,005,860 ​ — Bonus accrual ​ 120,995 ​ — Other ​ 58,721 ​ — R&D credit ​ 375,000 ​ 250,000 ​ ​ 20,489,308 ​ 8,575,626 Valuation allowance ​ (20,489,308) ​ (8,575,626) Deferred tax assets, net of allowance ​ $ — ​ $ — ​ As of December 31, 2020 and 2019, the Company had federal and state net operating loss carryforwards of approximately $37,000,000 and $31,200,000, respectively. As of December 31, 2020 and 2019, the Company had approximately $559,000 and $547,000 of foreign net operating loss carryforwards, respectively. The federal, state and foreign net operating loss carryforwards generated in the tax years from 2015 to 2020 will begin to expire, if not utilized, by 2035. Utilization of the net operating loss carryforwards may be subject to an annual limitation according to Section 382 of the Internal Revenue Code of 1986 as amended, and similar provisions. The Company has determined, based upon available evidence, that it is more likely than not that all of the net deferred tax asset will not be realized and, accordingly, has provided a full valuation allowance against its net deferred tax asset. Management considers the scheduled reversal of deferred tax liabilities, projected future taxable income, net operating loss carryback potential, and tax planning strategies in making these assessments. The Company recorded approximately $1,000,000 as a reduction of the deferred tax asset due to uncertain tax positions that if recognized would reduce Federal and state net operating loss carryforwards and R&D credit carryforwards. In the next twelve months, the Company plans to file amended returns to reduce a portion of its uncertain tax position recorded in the current year. The Company recognizes interest accrued to unrecognized tax benefits and penalties as income tax expense. The Company accrued total penalties and interest of $0 during the years ended December 31, 2020 and 2019 and in total, as of December 31, 2020 and 2019 has recognized penalties and interest of $0. The Company files tax returns as prescribed by the tax laws of the jurisdictions in which they operate. In the normal course of business, the Company is subject to examination by federal and foreign jurisdictions where applicable based on the statute of limitations that apply in each jurisdiction. As of December 31, 2020, open years related to all jurisdictions are 2019, 2018, 2017, 2016 and 2015. The Company has no open tax audits with any taxing authority as of December 31, 2020.

Related Party Transactions

Related Party Transactions	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Related Party Transactions
Related Party Transactions	14. Related Party Transactions The Company licenses patents that are owned by Glytech, LLC, pursuant to a license agreement (the Glytech Agreement). Glytech, LLC is owned by a co-founder and former Director of the Company, and therefore, a related party. The Glytech agreement requires that the Company pay Glytech for ongoing scientific support and also reimburse Glytech for expenses of obtaining and maintaining patents that are licensed to NRx Pharmaceuticals. During the three months ended June 30, 2021 and 2020 the Company paid a co-founder $125,000 and $0, respectively, and during the six months ended June 30, 2021 and 2020, $125,000 and $82,569, respectively, for continuing technology support services and reimbursed expenses. These support services are ongoing. The Fourth Amendment to the Glytech Agreement, effective as of December 31, 2020, includes an equity value-triggered transfer of Excluded Technology from Glytech to NRx Pharmaceuticals. The Excluded Technology is defined in the Glytech Agreement as any technology, and any know-how related thereto, covered in the licensed patents that do not recite either D-cycloserine or lurasidone individually or jointly. This definition would cover pharmaceutical formulations, including some that NRx Pharmaceuticals considers “pipeline” or “future product” opportunities, that contain a combination of pharmaceutical components different from those contained in NRX-100 and NRX-101. The Excluded Technology will transfer to the Company for no additional consideration if the value of NRx Pharmaceuticals equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost. The Company believes the criteria have been met pending the registration of Glytech shares. The CEO of the Company is a major shareholder in the Company. Therefore, his services are deemed to be a related party transaction. He serves the company on a full-time basis and has an employment agreement with the Company and received compensation of $137,500 and $53,125 during the three months ended June 30, 2021 and 2020, respectively, and $286,250 and $121,875 during the six months ended June 30, 2021 and 2020, respectively. The services are ongoing. The CEO’s son provides services related to website, IT, and marketing support under the supervision of the Company’s Chief Commercial Officer, who is responsible for assuring that the services are provided on financial terms that are at market. NRx Pharmaceuticals paid this family member a total of $11,100 and $18,605 during the three months ended June 30, 2021 and 2020, respectively, and $29,740 and $40,770 during the six months ended June 30, 2021 and 2020, respectively. In addition, NRx Pharmaceuticals pays Pill Tracker 2015 Ltd. (“Pill Tracker”) for services relating to the development of the inhaled use form of aviptadil. The CEO’s son and our CEO are the chief executive officer and the board chairman, respectively, of Pill Tracker. NRx Pharmaceuticals paid Pill Tracker $254,936 and $0 during the three months ended June 30, 2021 and 2020, respectively, and $395,757 and $0 during the six months ended June 30, 2021 and 2020, respectively. The CEO’s other son, as a medical doctor, provides research services related to the development of the inhaled use form of aviptadil, under the supervision of the CEO, who is responsible for assuring that the services are provided on financial terms that are at market. NRx Pharmaceuticals paid this family member a total of $4,615 and $4,820 during the three months ended June 30, 2021 and 2020, respectively, and $6,110 and $4,820 during the six months ended June 30, 2021 and 2020, respectively. Included in accounts payable were $44,201 and $149,067 due to the above related parties as of June 30, 2021 and December 31, 2020, respectively.	11. Related Party Transactions The Company licenses patents that are owned by Glytech, LLC, pursuant to a license agreement (the Glytech Agreement). Glytech, LLC is owned by a co-founder and Director of the Company, and therefore, a related party. The Glytech agreement requires that the Company pay Glytech for ongoing scientific support and also reimburse Glytech for expenses of obtaining and maintaining patents that are licensed to NeuroRx. During the years ended December 31, 2020 and 2019, the Company paid a co-founder $272,929 and $464,720, respectively, for continuing technology support services and reimbursed expenses. These support services are ongoing. The Fourth Amendment to the Glytech Agreement, effective as of December 31, 2020, includes an equity value-triggered transfer of Excluded Technology from Glytech to NeuroRx. The Excluded Technology is defined in the Glytech Agreement as any technology, and any know-how related thereto, covered in the licensed patents that do not recite either D-cycloserine or lurasidone individually or jointly. This definition would cover pharmaceutical formulations, including some that NeuroRx considers “pipeline” or “future product” opportunities, that contain a combination of pharmaceutical components different from those contained in NRX-100 and NRX-101. The Excluded Technology will transfer to the Company for no additional consideration if the value of NeuroRx equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost. The CEO of the Company is a major shareholder in the Company. Therefore, his services are deemed to be a related party transaction. He serves the company on a full-time basis and has an employment agreement with the Company and received compensation of $456,459 and $452,400 during the years ended December 31, 2020 and 2019, respectively. The services are ongoing. The CEO’s son provides services related to website, IT, and marketing support under the supervision of the Company’s Chief Commercial Officer, who is responsible for assuring that the services are provided on financial terms that are at market. NeuroRx paid this family member a total of $85,915 and $48,000 during the years ended December 31, 2020 and 2019, respectively. In addition, NeuroRx pays Pill Tracker 2015 Ltd. (“Pill Tracker”) for services relating to the development of the inhaled use form of aviptadil. The CEO’s son and our CEO are the chief executive officer and the board chairman, respectively, of Pill Tracker. NeuroRx paid Pill Tracker $271,082 during the year ended December 31, 2020. NeuroRx made no payments to Pill Tracker in 2019. The CEO’s other son, as a medical doctor, provides research services related to the development of the inhaled use form of aviptadil, under the supervision of the CEO, who is responsible for assuring that the services are provided on financial terms that are at market. NeuroRx paid this family member a total of $11,650 during the year ended December 31, 2020. NeuroRx made no payments to this family member in 2019. Included in accounts payable were $149,067 and $92,744 due to the above related parties as of December 31, 2020 and 2019, respectively.

Subsequent Events

Subsequent Events	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Subsequent Events
Subsequent Events	15. Subsequent Events Warrants Exercised Subsequent to June 30, 2021, the Company received $9,186,316 from the exercise of a warrant for the purchase of 1,833,596 shares. Related Party Transaction Subsequent to June 30, 2021, the Company and Pill TM ​	12. Subsequent Events Issuance of Common Stock Subsequent to December 31, 2020, the Company sold 43,018 shares of common stock for gross proceeds of $2,495,058, and 79,400 shares of common stock for gross proceeds of $5,716,800. Issuance of Stock Option Awards Subsequent to December 31, 2020, the Company granted 42,500 stock option awards. The stock options will vest three years from the date of grant. Aviptadil Supply Agreement On January 4, 2021 NeuroRx and Aerogen Limited (“Aerogen”) signed a supply agreement for the supply of certain products, including the Areogen Solo Nebulizer System and Aerogen Ultra, solely for the purposes of carrying out clinical trials relating to inhalation delivery of RLF-100 (aviptadil) for treatment of pulmonary insufficiency and respiratory distress in COVID-19 patients. Pill Tracker is an agent of NeuroRx per the supply agreement and the first purchase order for products amounted to $54,315.

Summary of Significant Accoun_2

Summary of Significant Accounting Policies (Policies)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Summary of Significant Accounting Policies
Basis of Presentation	Basis of Presentation The accompanying unaudited interim condensed financial statements have been prepared in accordance with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) for interim financial information. Accordingly, they do not include all of the information and footnotes required by GAAP for complete financial statements. In the opinion of management, the unaudited interim condensed financial statements reflect all adjustments, which include only normal recurring adjustments necessary for the fair statement of the balances and results for the periods presented. The results of operations for any interim periods are not necessarily indicative of the results that may be expected for the entire fiscal year or any other interim period. The merger between Merger Sub and NeuroRx was accounted for as a reverse recapitalization in accordance with U.S. GAAP (the “Reverse Recapitalization”). Under this method of accounting, BRPA was treated as the “acquired” company and NeuroRx is treated as the acquirer for financial reporting purposes. Accordingly, for accounting purposes, the Reverse Recapitalization was treated as the equivalent of NeuroRx issuing stock for the net assets of BRPA, accompanied by a recapitalization. The net assets of BRPA are stated at historical cost, with no goodwill or other intangible assets recorded. NeuroRx was determined to be the accounting acquirer based on the following predominant factors: ● NeuroRx’s shareholders have the largest portion of voting rights in the Company; ● the Board and Management are primarily composed of individuals associated with NeuroRx; and ● NeuroRx was the larger entity based on historical operating activity and NeuroRx had the larger employee base at the time of the Merger. The consolidated assets, liabilities and results of operations prior to the Reverse Recapitalization are those of NeuroRx. The shares and corresponding capital amounts and losses per share, prior to the Merger, have been retroactively restated based on shares reflecting the exchange ratio established in the Merger.	Basis of Presentation The Company’s financial statements have been prepared in conformity with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”).
Use of Estimates	Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, contingent consideration and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected.	Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, the embedded put feature in convertible notes and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected.
Certain Risks and Uncertainties		Certain Risks and Uncertainties The Company’s activities are subject to significant risks and uncertainties including the risk of failure to secure additional funding to properly execute the Company’s business plan. The Company is subject to risks that are common to companies in the pharmaceutical industry, including, but not limited to, development by the Company or its competitors of new technological innovations, dependence on key personnel, reliance on third party manufacturers, protection of proprietary technology, and compliance with regulatory requirements.
Cash and Cash Equivalents		Cash and Cash Equivalents The Company considers all highly liquid investments purchased with original maturities of 90 days or less at acquisition to be cash equivalents. As of December 31, 2020 and 2019, the Company does not have any cash equivalents.
Fair Value of Financial Instruments	Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. (Refer to Note 12)	Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. Fair value measurements discussed herein are based upon certain market assumptions and pertinent information available to management as of and during the years ended December 31, 2020 and 2019. The carrying amount of accounts payable approximated fair value as they are short term in nature. The fair value of warrants issued for services is estimated based on the Black-Scholes model during the years ended December 31, 2020 and 2019. The carrying value of notes payable and convertible notes payable approximated the estimated fair values due to their recent issuances. The estimated fair value of the warrants and embedded put, represent Level 3 measurements.
Foreign Currency		Foreign Currency The Company’s functional currency is the U.S. dollar. The functional currency of our foreign operation is the respective local currency. Assets and liabilities of foreign operation denominated in local currencies are translated at the spot rate in effect at the applicable reporting date. The consolidated statements of operations are translated at the weighted average rate of exchange during the applicable period. The resulting unrealized cumulative translation adjustment is not material to the financial statements.
Accounts Receivable	Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of June 30, 2021, the Company has recorded an allowance for doubtful accounts of $5,470,897 as the Company does not expect to collect on amounts due to the Company owed from Relief.	Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of December 31, 2020, the Company has recorded an allowance for doubtful accounts of $257,463.
Concentration of Credit Risk and Off-Balance Sheet Risk	Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss.	Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss.
Research and Development Costs	Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received.	Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received.
Derivative Financial Instruments		Derivative Financial Instruments The Company does not use derivative instruments to hedge exposures to interest rate, market, or foreign currency risks. The Company evaluates all of its financial instruments, to determine if such instruments contain features that qualify as embedded derivatives. Embedded derivatives must be separately measured from the host contract if all the requirements for bifurcation are met. The assessment of the conditions surrounding the bifurcation of embedded derivatives depends on the nature of the host contract. Bifurcated embedded derivatives are recognized at fair value, with changes in fair value recognized in the statement of operations each period. Bifurcated embedded derivatives are classified with the related host contract in the Company’s balance sheet.
Stock-Based Compensation	Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company. Modification of stock options and warrants A change in any of the terms or conditions of stock options and warrants is accounted for as a modification. Incremental stock-based compensation cost is measured as the excess, if any, of the fair value of the modified option over the fair value of the original option/warrant immediately before its terms are modified, measured based on the fair value of the ordinary shares and other pertinent factors at the modification date. For vested stock options and warrants to board members, we recognize incremental compensation cost in the period the modification occurs. For unvested stock options, we recognize over the remaining requisite service period, the sum of the incremental compensation cost and the remaining unrecognized compensation cost for the original award on the modification date. If the fair value of the modified option is lower than the fair value of the original option immediately before modification, the minimum compensation cost we recognize is the cost of the original award. The accounting for incremental fair value of warrants is based on the specific facts and circumstances related to the modification which may result in a reduction of additional paid-in capital, recognition of costs for services rendered, or recognized as a deemed dividend.	Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company.
Income Taxes	Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense.	Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes (“ASC 740”), which provides for deferred taxes using an asset and liability approach. The Company recognizes deferred tax assets and liabilities for the expected future tax consequences of events that have been included in the financial statements or tax returns. Deferred tax assets and liabilities are determined based on the difference between the financial statement and tax basis of assets and liabilities using enacted tax rates in effect for the year in which the differences are expected to reverse. Valuation allowances are provided, if based upon the weight of available evidence, it is more likely than not that some or all of the deferred tax assets will not be realized. The Company accounts for uncertain tax positions in accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense.
Loss Per Share	Earnings (Loss) Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted earnings per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and other dilutive instruments because their effect would be anti-dilutive in the periods in which we incur a net loss. The following table summarized the basic and diluted earnings per share calculations: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Numerator: ​ ​ ​ ​ ​ ​ ​ ​ Net income (loss) attributable to common stock—basic and diluted $ (16,007,973) $ 102,287 $ (41,496,847) $ (1,487,769) Denominator: ​ ​ ​ ​ ​ ​ ​ ​ Weighted average shares — basic ​ ​ 41,727,480 ​ ​ 33,819,205 ​ ​ 38,709,614 ​ ​ 33,799,503 Effect of other dilutive securities ​ ​ — ​ ​ 2,837,215 ​ ​ — ​ ​ — Weighted average shares — diluted ​ ​ 41,727,480 ​ ​ 36,656,420 ​ ​ 38,709,614 ​ ​ 33,799,503 Basic earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) Diluted earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net earnings (loss) per share attributable to common stock for the periods in which a net loss is presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Stock options 2,919,493 — 2,919,493 1,166,863 Common stock warrants 8,495,316 — 8,495,316 1,670,352 Common stock issuable pursuant to UPOs (Note 10) ​ 600,000 ​ — ​ 600,000 ​ — Common stock warrants pursuant to UPOs (Note 10) ​ 300,000 ​ — ​ 300,000 ​ — Public Rights pursuant to UPOs (Note 10) ​ 60,000 ​ — ​ 60,000 ​ — Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ — ​	Loss Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted loss per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and convertible preferred stock because their effect would be anti-dilutive due to our net loss. Since the Company had a net loss in each of the periods presented, basic and diluted net loss per common share are the same. The calculation of basic and diluted net loss per share attributable to common stock was as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Numerator: ​ ​ ​ ​ ​ ​ Net loss attributable to common stock—basic and diluted ​ $ (51,776,904) ​ $ (6,729,161) ​ ​ ​ ​ ​ ​ ​ Denominator: ​ ​ Weighted average shares—basic and diluted ​ 10,845,240 ​ 10,690,209 ​ ​ ​ ​ ​ ​ ​ Net loss per share attributable to common stock—basic and diluted ​ $ (4.77) ​ $ (0.63) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net loss per share attributable to common stock for the periods presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ Year Ended December 31, ​ 2020 2019 Convertible preferred stock as if converted 2,371,710 2,367,543 Stock options 486,755 333,588 Common stock warrants 620,054 57,473
Recent Accounting Pronouncements	Recent Accounting Pronouncements In December 2019, the FASB issued ASU No. 2019-12, Income Taxes: Simplifying the Accounting for Income Taxes In August 2020, the FASB issued ASU 2020-06, Debt — Debt with Conversion and Other Options (Subtopic 470-20) and Derivatives and Hedging — Contracts in Entity’s Own Equity (Subtopic 815-40): Accounting for Convertible Instruments and Contracts in an Entity’s Own Equity In May 2021, the FASB issued ASU 2021-04, Earnings Per Share (Topic 260), Debt — Modifications and Extinguishments (Subtopic 470-50), Compensation — Stock Compensation (Topic 718) and Derivatives and Hedging - Contracts in an Entity's Own Equity (Subtopic 815-40) — Issuer's Accounting for Certain Modifications or Exchange of Freestanding Equity-Classified Written Call Options	Recent Accounting Pronouncements In June 2018, the FASB issued ASU 2018-07, which simplifies the accounting for nonemployee share-based payment transactions. The amendments specify that Topic 718 applies to all share-based payment transactions in which a grantor acquires goods or services to be used or consumed in a grantor’s own operations by issuing share-based payment awards. The Company adopted ASU 2018-07 as of January 1, 2019, which resulted in a cumulative effect charge of $683 to accumulated deficit.

Summary of Significant Accoun_3

Summary of Significant Accounting Policies (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Summary of Significant Accounting Policies
Schedule of Calculation of Basic and Diluted Net Loss Per Share Attributable to Common Stock	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Numerator: ​ ​ ​ ​ ​ ​ ​ ​ Net income (loss) attributable to common stock—basic and diluted $ (16,007,973) $ 102,287 $ (41,496,847) $ (1,487,769) Denominator: ​ ​ ​ ​ ​ ​ ​ ​ Weighted average shares — basic ​ ​ 41,727,480 ​ ​ 33,819,205 ​ ​ 38,709,614 ​ ​ 33,799,503 Effect of other dilutive securities ​ ​ — ​ ​ 2,837,215 ​ ​ — ​ ​ — Weighted average shares — diluted ​ ​ 41,727,480 ​ ​ 36,656,420 ​ ​ 38,709,614 ​ ​ 33,799,503 Basic earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) Diluted earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04)	The calculation of basic and diluted net loss per share attributable to common stock was as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Numerator: ​ ​ ​ ​ ​ ​ Net loss attributable to common stock—basic and diluted ​ $ (51,776,904) ​ $ (6,729,161) ​ ​ ​ ​ ​ ​ ​ Denominator: ​ ​ Weighted average shares—basic and diluted ​ 10,845,240 ​ 10,690,209 ​ ​ ​ ​ ​ ​ ​ Net loss per share attributable to common stock—basic and diluted ​ $ (4.77) ​ $ (0.63)
Schedule of Outstanding Shares of Common Stock Equivalents Excluded From Diluted Net Loss Per Share	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Stock options 2,919,493 — 2,919,493 1,166,863 Common stock warrants 8,495,316 — 8,495,316 1,670,352 Common stock issuable pursuant to UPOs (Note 10) ​ 600,000 ​ — ​ 600,000 ​ — Common stock warrants pursuant to UPOs (Note 10) ​ 300,000 ​ — ​ 300,000 ​ — Public Rights pursuant to UPOs (Note 10) ​ 60,000 ​ — ​ 60,000 ​ — Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ —	The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net loss per share attributable to common stock for the periods presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ Year Ended December 31, ​ 2020 2019 Convertible preferred stock as if converted 2,371,710 2,367,543 Stock options 486,755 333,588 Common stock warrants 620,054 57,473

Accrued and Other Current Lia_2

Accrued and Other Current Liabilities (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Accrued and other current liabilities
Schedule of accrued and other current liabilities	​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Accrued and other current liabilities: ​ ​ ​ ​ ​ ​ Accrued research and development expenses $ 826,442 $ 586,426 Accrued employee expenses ​ ​ 77,196 ​ ​ 530,500 Professional services ​ 185,170 ​ 606,553 Other accrued expenses ​ 417,529 ​ 5,004 Total accrued and other current liabilities ​ $ 1,506,337 ​ $ 1,728,483	Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Accrued and other current liabilities: ​ ​ Professional services ​ $ 606,553 ​ $ — Accrued research and development expenses ​ 586,426 ​ — Accrued employee expenses ​ 530,500 ​ — Other accrued liabilities ​ 5,004 ​ 9,649 Total accrued and other current liabilities ​ $ 1,728,483 ​ $ 9,649

Convertible Notes Payable (Tabl

Convertible Notes Payable (Tables)	12 Months Ended
	Dec. 31, 2020
Convertible Notes Payable.
Schedule of convertible notes payable and accrued interest	​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Convertible Notes: ​ ​ ​ ​ ​ ​ 2017 convertible notes payable due November 2021 ​ $ — ​ $ 2,500,000 2018 convertible note payable due January 2022 ​ — ​ 100,000 2018 convertible notes payable due April 2022 ​ — ​ 200,000 Fair value of embedded put ​ — ​ 738,602 Debt discount ​ — ​ (296,437) Carrying value of convertible notes ​ $ — ​ $ 3,242,165 Accrued interest ​ — ​ 349,891 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056 ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Convertible Notes: ​ ​ Convertible notes payable and accrued interest, current ​ $ — ​ $ 130,251 Convertible notes payable and accrued interest, non-current ​ — ​ 3,461,805 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056

Notes Payable (Tables)

Notes Payable (Tables)	12 Months Ended
	Dec. 31, 2020
Notes Payable.
Notes payable and accrued interest	​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Note Payable — Related Party ​ $ 154,190 ​ $ 154,190 Relief Therapeutics Loan ​ 500,000 ​ — Paycheck Protection Program Loan ​ 119,842 ​ — Carrying value of notes payable ​ 774,032 ​ 154,190 Accrued interest ​ 22,656 ​ — Total notes payable and accrued interest ​ $ 796,688 ​ $ 154,190 ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Notes payable: ​ ​ Notes payable and accrued interest, current ​ $ 248,861 ​ $ 154,190 Notes payable and accrued interest, non-current ​ 547,827 ​ — Total notes payable and accrued interest ​ $ 796,688 ​ $ 154,190

Equity (Tables)

Equity (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Equity
Summary of activity in warrants	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Aggregate ​ ​ Total Warrants ​ Term ​ Exercise Price ​ Intrinsic Value Outstanding as of December 31, 2020 (as previously reported) 620,055 11.08 ​ $ 14.61 ​ $ 22,127,594 Retroactive application of reverse recapitalization (Note 4) ​ 2,455,415 ​ — ​ ​ (13.53) ​ ​ — Outstanding as of December 31, 2020, effect of Merger (Note 4) ​ 3,075,470 ​ 4.34 ​ ​ 1.09 ​ ​ 150,955,963 Issued 3,329,812 3.00 ​ 3.19 ​ 111,082,528 Exercised (1,496,216) ​ ​ (3.19) ​ (49,913,766) Outstanding as of March 31, 2021 4,909,066 3.74 ​ $ 1.78 ​ $ 244,574,345 Issued 3,586,250 5.00 ​ 11.50 ​ 45,724,688 Outstanding as of June 30, 2021 8,495,316 4.09 ​ $ 24.78 ​ $ 42,385,824	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Average ​ ​ Total Warrants Term Exercise Price Intrinsic Value Outstanding as of December 31, 2018 ​ 48,627 ​ 2.88 ​ $ 7.90 ​ $ — Issued 8,846 5.00 ​ 11.00 ​ — Outstanding as of December 31, 2019 57,473 2.22 ​ $ 8.38 ​ $ — Issued 562,581 4.99 ​ 15.25 ​ 20,112,271 Outstanding as of December 31, 2020 620,054 11.08 ​ $ 14.61 ​ $ 22,127,594
Schedule of Assumptions		​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Strike price $ 15.25 ​ $ 11.00 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.19%-0.28 % 2.40 % Expected term ​ 3.00-5.00 ​ 5.00 ​ Dividend yield ​ — ​ — ​

Stock-Based Compensation (Table

Stock-Based Compensation (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Stock-Based Compensation
Schedule of option pricing model	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Original Options Substitute Options Strike price ​ $ 1.00-$72.30 ​ $ 0.20-$14.58 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.07%-0.79 % 0.07%-0.79 % Expected term ​ 0.18-5.99 ​ 0.18-5.99 ​ Dividend yield ​ — ​ — ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 December 31, 2020 Exercise price $ 11.69-$23.41 ​ $ 2.22-$3.07 ​ Risk-free rate of interest ​ 0.79%-1.24 % 0.79%-0.79 % Expected term (years) ​ 5.5-6.5 ​ 4.7-5.9 ​ Expected stock price volatility ​ 80 % 80 % Dividend yield ​ — ​ — ​	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 ​ Exercise price ​ $ 11.00‑$15.25 $ 11.00 ​ Risk-free rate of interest ​ 0.30%‑0.49 % ​ 1.54%‑1.73 % Expected term (years) ​ 5.5 6.5 ​ 6.0 6.5 ​ Expected stock price volatility ​ 80 % ​ 80 % Dividend yield ​ — ​ — ​
Disclosure of share-based compensation arrangements by share-based payment award	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ Weighted ​ average ​ Aggregate ​ ​ Number of ​ average ​ remaining ​ intrinsic ​ shares exercise price term (years) value Outstanding as of December 31, 2020 (as previously reported) 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Retroactive application of reverse recapitalization 1,927,548 ​ (8.62) ​ ​ ​ Outstanding as of December 31, 2020, effect of Merger 2,414,303 ​ $ 2.17 8.2 ​ $ 53,659,966 Options granted 210,800 ​ ​ 11.69 9.8 ​ ​ 3,825,276 Forfeited (198,400) ​ ​ (2.22) — ​ ​ (6,587,328) Outstanding as of March 31, 2021 ​ 2,426,703 ​ $ 14.58 ​ 8.7 ​ $ 30,388,510 Options granted ​ 587,030 ​ ​ 14.94 ​ 9.9 ​ ​ — Forfeited ​ (89,280) ​ ​ (7.86) ​ — ​ ​ (339,082) Exercised ​ (4,960) ​ ​ (3.07) ​ — ​ ​ (42,385) Outstanding as of June 30, 2021 ​ 2,919,493 ​ $ 5.25 ​ 9.0 ​ $ 20,558,299 Options vested and exercisable as of June 30, 2021 ​ 1,095,294 ​ $ 1.50 ​ 6.1 ​ $ 11,106,829 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three months ended June 30, ​ Six months ended June 30, ​ 2021 2020 2021 2020 Stock-based compensation expense ​ ​ ​ ​ General and administrative ​ $ 4,094,549 ​ $ 50,881 ​ $ 4,438,583 ​ $ 117,469 Regulatory and process development ​ 188,781 ​ 42,585 ​ 216,445 ​ 64,800 Total stock-based compensation expense ​ $ 4,283,330 ​ $ 93,466 ​ $ 4,655,028 ​ $ 182,269	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ ​ average ​ ​ ​ ​ ​ ​ ​ Weighted ​ remaining ​ Aggregate ​ ​ Number of ​ average ​ contractual ​ intrinsic ​ ​ shares ​ exercise price ​ life (in years) ​ value Outstanding as of December 31, 2018 355,408 ​ $ 5.74 8.2 ​ $ 1,782,729 Granted 28,180 ​ 11.00 9.6 ​ Forfeited/Cancelled (50,000) ​ — — ​ — Outstanding as of December 31, 2019 333,588 ​ $ 5.74 7.2 ​ $ 1,782,729 Granted 266,500 ​ 14.37 9.7 ​ 9,761,125 Forfeited /Cancelled (113,333) ​ — — ​ — Outstanding as of December 31, 2020 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Options vested and exercisable as of December 31, 2020 329,489 ​ $ 6.31 4.0 ​ $ 14,723,342

Income Taxes (Tables)

Income Taxes (Tables)	12 Months Ended
	Dec. 31, 2020
Income Taxes.
Schedule of Reconciliation of Effective Tax Rate to Statutory Federal Rate	A reconciliation of the statutory U.S. federal income tax rate to the Company’s effective tax rate consist of the following: ​ ​ ​ ​ ​ ​ ​ ​ For the Years ​ ​ Ended ​ ​ ​ December 31, ​ ​ ​ 2020 2019 Statutory federal income tax benefit (21.00) % (21.00) % Permanent items (0.04) % 0.01 % Foreign rate differential 0.01 % (0.02) % State taxes, net of federal tax benefit (1.74) % 0.60 % Change in valuation allowance 23.01 % 22.23 % R&D credit (0.24) % (1.90) % Other — % 0.07 % Effective tax rate — % — %
Schedule of Components of Income Tax Provision (Benefit)	The components of income tax provision (benefit) are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ ​ 2020 2019 Federal: ​ ​ Current ​ $ — ​ $ — Deferred ​ (11,015,759) ​ (1,496,712) State and Local: ​ ​ Current ​ — ​ — Deferred ​ (900,789) ​ 39,574 Foreign: ​ ​ Current ​ — ​ — Deferred ​ 2,867 ​ (8,412) Change in valuation allowance ​ 11,913,681 ​ 1,465,550 Total ​ $ — ​ $ —
Schedule of Deferred Tax Assets and Liabilities	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Deferred tax assets (liabilities): ​ ​ ​ ​ ​ ​ Net operating loss carryforwards ​ $ 8,243,959 ​ $ 6,943,988 Convertible notes payable discount and embedded derivative ​ — ​ 101,521 Common stock warrants ​ 1,405,796 ​ 179,271 Israel net operating loss carryforwards ​ 128,469 ​ 131,336 Founder share options ​ 469,062 ​ 472,195 Stock-based compensation ​ 681,446 ​ 497,315 Settlement liability ​ 9,005,860 ​ — Bonus accrual ​ 120,995 ​ — Other ​ 58,721 ​ — R&D credit ​ 375,000 ​ 250,000 ​ ​ 20,489,308 ​ 8,575,626 Valuation allowance ​ (20,489,308) ​ (8,575,626) Deferred tax assets, net of allowance ​ $ — ​ $ —

Liquidity (Details)

Liquidity (Details) - USD ($)	Mar. 28, 2021	Mar. 31, 2021	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Schedule Of Liquidity
Cash			$ 13,386,332	$ 995,985	$ 1,858,513	$ 877,421	$ 621,296
Proceeds from collaboration agreement			771,244		10,160,421
Net proceeds from issuance of common stock			$ 8,489,082	$ 176,990	$ 2,579,114	$ 5,802,002
Proceeds from exercise of warrants	$ 7,500,018
Warrants and rights outstanding	473,486	4,909,066	8,495,316		3,075,470
Subsequent Event | Transaction One
Schedule Of Liquidity
Net proceeds from issuance of common stock		$ 2,495,058
Common stock issued, shares		43,018
Subsequent Event | Transaction Two
Schedule Of Liquidity
Net proceeds from issuance of common stock		$ 5,716,800
Common stock issued, shares		79,400

Summary of Significant Accoun_4

Summary of Significant Accounting Policies - Schedule of Calculation of Basic and Diluted Net Loss Per Share Attributable to Common Stock (Details) - USD ($)	3 Months Ended		6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Numerator:
Net loss attributable to common stock-basic and diluted					$ (51,776,904)	$ (6,729,161)
Denominator:
Weighted average shares-basic and diluted					10,845,240	10,690,209
Net loss per share attributable to common stock-basic and diluted					$ (4.77)	$ (0.63)
Adjusted net income (loss)	$ (271,830,043)	$ 102,287	$ (297,318,917)	$ (1,487,769)

Summary of Significant Accoun_5

Summary of Significant Accounting Policies - Schedule of Outstanding Shares of Common Stock Equivalents Excluded From Diluted Net Loss Per Share (Details) - shares	3 Months Ended	6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Convertible Preferred Stock [Member]
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share				2,371,710	2,367,543
Stock Options [Member]
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	2,919,493	2,919,493	1,166,863	486,755	333,588
Common stock warrant [Member]
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	8,495,316	8,495,316	1,670,352	620,054	57,473

Summary of Significant Accoun_6

Summary of Significant Accounting Policies - Additional Information (Details) - USD ($)	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019	Jan. 01, 2019
Summary of Significant Accounting Policies
Allowance for doubtful accounts	$ 5,470,897	$ 257,463
Accumulated deficit	$ (131,676,567)	$ (90,179,720)	$ (38,402,816)	$ 683

Accrued and Other Current Lia_3

Accrued and Other Current Liabilities (Details) - USD ($)	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Accrued and other current liabilities
Professional services	$ 185,170	$ 606,553
Accrued research and development expenses	826,442	586,426
Accrued employee expenses	77,196	530,500
Other accrued liabilities		5,004	$ 9,649
Total accrued and other current liabilities	$ 1,506,337	$ 1,728,483	$ 9,649

Convertible Notes Payable - Tot

Convertible Notes Payable - Total convertible notes payable and accrued interest (Details) - USD ($)	Dec. 31, 2020	Dec. 31, 2019
Note payable	$ 796,688	$ 154,190
Fair value of embedded put		738,602
Debt discount		(296,437)
Carrying value of convertible notes		3,242,165
Accrued interest		349,891
Convertible notes payable and accrued interest, current		130,251
Convertible notes payable and accrued interest, non-current		3,461,805
Total convertible notes payable and accrued interest		3,592,056
2017 Convertible Notes Payable Due November 2021 [Member]
Note payable		2,500,000
2018 Convertible Notes Payable Due January 2022 [Member]
Note payable		100,000
2018 Convertible Notes Payable Due April 2022 [Member]
Note payable		$ 200,000

Convertible Notes Payable - Add

Convertible Notes Payable - Additional Information (Details) - USD ($)	Feb. 12, 2020	Apr. 25, 2018	Nov. 19, 2017	Nov. 16, 2017	Apr. 25, 2018	Dec. 31, 2020	Dec. 31, 2019	Jun. 30, 2021	Apr. 06, 2020	Jan. 05, 2018
Schedule of Convertible Notes [Line Items]
Sale and issuance of common shares	$ 10,000,000
Fair value per share	$ 11
Accrued interest converted into common stock	132,739
Discounted price per share	$ 8.80
Accrued interest	$ 369,660
Fair value of the common shares issued						$ 306,641
Interest rate						6.00%		6.00%	2.00%
Accrued interest							$ 349,891
Debt discount							296,437
Amortization debt discount						$ 16,475	130,433
Convertible Debt [Member]
Schedule of Convertible Notes [Line Items]
Aggregate principal amount of convertible notes	$ 2,800,000
Accrued interest converted into common stock	1,005,458
Discounted price per share	$ 8.80
Two Thousand And Seventeen Convertible Notes [Member]
Schedule of Convertible Notes [Line Items]
Convertible notes gross proceeds			$ 2,500,000	$ 2,500,000
Interest rate			6.00%
Principal and interest maturity date			4 years
Sale of stock			$ 10,000,000
Conversion price description			outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price
Accrued interest		$ 200,000			$ 200,000
Two Thousand And Eighteen Note [Member]
Schedule of Convertible Notes [Line Items]
Convertible notes gross proceeds		$ 300,000
Interest rate		6.00%			6.00%
Principal and interest maturity date		4 years
Sale of stock		$ 10,000,000
Conversion price description		outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price.
Accrued interest										$ 100,000
Two Thousand Seventeen And Eighteen Convertible Notes Payable[Member]
Schedule of Convertible Notes [Line Items]
Debt discount						493,982	57,204
Recognized loss						$ 27,160	$ 162,866
Two Thousand Eighteen Convertible Notes Payable [Member]
Schedule of Convertible Notes [Line Items]
Convertible notes gross proceeds					$ 300,000
As Previously Reported
Schedule of Convertible Notes [Line Items]
Accrued interest converted into common stock	42,006
As Previously Reported | Convertible Debt [Member]
Schedule of Convertible Notes [Line Items]
Accrued interest converted into common stock	318,183

Notes Payable - Notes payable a

Notes Payable - Notes payable and Accrued Interest (Details) - USD ($)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019	Feb. 12, 2020
Note Payable - Related Party	$ 154,190	$ 154,190	$ 154,190
Carrying value of notes payable	654,190	774,032	154,190
Accrued interest	31,976	22,656		$ 369,660
Note payable	686,166	796,688	154,190
Notes payable and accrued interest, current	173,694	248,861	154,190
Notes payable and accrued interest, non-current	512,472	547,827
Total notes payable and accrued interest		796,688	$ 154,190
Relief Therapeutics Loan [Member]
Note Payable - Related Party	$ 500,000	500,000
Paycheck Protection Program Loans [Member]
Note Payable - Related Party		$ 119,842

Notes Payable - Additional Info

Notes Payable - Additional Information (Details) - USD ($)	Apr. 28, 2020	Apr. 06, 2020	Jul. 01, 2019	Jun. 30, 2021	Dec. 31, 2020
Related party loan			$ 154,190
Interest rate		2.00%		6.00%	6.00%
Related party loan		$ 500,000
Debt Instrument, Maturity Date		Apr. 6, 2022
Loan term	2 years
Loan forgiveness, description	The Loan amount may be eligible for forgiveness pursuant to (1) at least 75% of the loan proceeds are used to cover payroll costs and the remainder is used for mortgage interest, rent and utility costs over the eight week period after the loan is made, and (2) the number of employees and compensation levels are generally maintained.
Pay Check Protection Program [Member]
Loan funding	$ 119,842
Principal and interest due	$6,744
Outstanding principal rate	1.00%

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($)

May 14, 2021

May 11, 2021

Mar. 28, 2021

Dec. 13, 2020

Aug. 25, 2020

Oct. 31, 2019

Apr. 30, 2019

Dec. 31, 2018

Jun. 30, 2021

Jun. 30, 2020

Jun. 30, 2021

Jun. 30, 2020

Dec. 31, 2020

Dec. 31, 2019

Oct. 09, 2020

Commitments And Contingencies Line Items

Rent expense

$ 48,776

$ 9,087

$ 55,393

$ 17,902

$ 54,649

$ 42,040

Settlement liability expense

$ 5,616,732

Transfer of shares, value

5,500,000

Legal costs

116,732

Founder returned shares

300,000

Percentage of company's annual requirements

100.00%

Account receivable, net

831,390

Allowance for doubtful accounts

5,470,897

5,470,897

257,463

Accrued Settlement Expense

39,486,139

Settlement Expense

$ 21,365,641

21,365,641

39,486,139

G E M Warrant [Member]

Commitments And Contingencies Line Items

Warrant issued

3,329,812

Warrants to purchase shares

1,496,216

Warrants to purchase shares, amount

$ 7,500,018

Warrants expire period

The GEM Warrant will be valid for a period of three years from the date NeuroRx’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction of the type contemplated by the Merger Agreement.

Accrued Settlement Expense

39,486,139

G E M Warrant [Member] | Subsequent Event

Commitments And Contingencies Line Items

Warrant issued

1,053,738

Exercise price of warrant

$ 15.84

Warrants to purchase shares

473,486

Warrants to purchase shares, amount

$ 7,500,000

Warrants expire period

The GEM Warrant will be valid for a period of three years from the date the Company’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction.

Former Adviser [Member]

Commitments And Contingencies Line Items

Transfer of shares

45,454

Transfer of shares, value

$ 499,994

Maximum [Member]

Commitments And Contingencies Line Items

Annual maintenance fees

$ 150,000

Jonathan Javitt Living Trust [Member]

Commitments And Contingencies Line Items

Transfer of shares

250,000

Glytech LLC [Member]

Commitments And Contingencies Line Items

Transfer of shares

250,000

Sarah Herzog Memorial Hospital Ezrat Nashim [Member]

Commitments And Contingencies Line Items

Transfer of shares

500,000

500,000

Milestone payments

$ 250,000

Transfer of shares, value

$ 5,500,000

Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Minimum [Member]

Commitments And Contingencies Line Items

Royalty percentage

1.00%

Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Maximum [Member]

Commitments And Contingencies Line Items

Annual maintenance fees

$ 150,000

Royalty percentage

2.50%

Development Milestone [Member] | Minimum [Member]

Commitments And Contingencies Line Items

Milestone payments

$ 100,000

Development Milestone [Member] | Maximum [Member]

Commitments And Contingencies Line Items

Milestone payments

$ 750,000

Development Milestone [Member] | Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Minimum [Member]

Commitments And Contingencies Line Items

Milestone payments

$ 100,000

Development Milestone [Member] | Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Maximum [Member]

Commitments And Contingencies Line Items

Milestone payments

750,000

Relief Therapeutics Collaboration Agreement [Member]

Commitments And Contingencies Line Items

Reimbursable expenses

$ 10,904,065

$ 10,612,750

5,984,679

10,160,421

Account receivable, net

831,390

Reimbursable expenses received

770,444

9,329,031

Allowance for doubtful accounts

$ 5,470,897

$ 5,470,897

257,463

Invoiced costs

$ 6,000,000

$ 4,000,000

Big Rock Partners Acquisition Corp [Member] | Merger Agreement [Member]

Commitments And Contingencies Line Items

Closing Consideration shares

50,000,000

Earnout Shares Milestone

25,000,000

Earnout Cash Milestone

$ 100,000,000

Earnout Shares Milestone Description

an aggregate of 25 million additional shares of Big Rock common stock (“Earnout Shares”) will be issued to NeuroRx pre-merger equity holders if, prior to December 31, 2022, (1) the Company’s COVID-19 drug receives emergency use authorization by the FDA and (2) the FDA accepts the Company’s filing of its application to approve the Company’s COVID-19 drug

Earnout Cash Milestone Description

In addition, subject to certain conditions, $100 million (“Earnout Cash”) may be payable to NeuroRx pre-merger equity holders if, prior to December 31, 2022, either (1) FDA approval of the Company’s COVID-19 Drug is obtained and the Company’s COVID-19 Drug is listed in the FDA’s “Orange Book” and (2) FDA approval of the Company’s Antidepressant Drug Regimen is obtained and the Company’s Antidepressant Drug Regimen is listed in the FDA’s “Orange Book”.

GEM Share Subcription Facility Agreement [Member]

Commitments And Contingencies Line Items

Share subscription value

95,600,000

Commitment fee

$ 1,900,000

Share subscription agreement term

3 years

Polypeptide [Member]

Commitments And Contingencies Line Items

Purchase commitments

$ 1,010,000

Equity - Schedule of Warrants (

Equity - Schedule of Warrants (Detail) - USD ($)	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018	Jun. 30, 2021	Mar. 31, 2021
Class of Warrant or Right [Line Items]
Ending Balance	3,075,470
Outstanding, weighted average exercise price	$ 1.09			$ 24.78	$ 1.78
As Previously Reported
Class of Warrant or Right [Line Items]
Beginning Balance	57,473	48,627
Issued	562,581	8,846
Ending Balance	620,055	57,473	48,627
Weighted average remaining term, issued	4 years 11 months 26 days	5 years
Outstanding, weighted average remaining term	11 years 29 days	2 years 2 months 19 days	2 years 10 months 17 days
Weighted average exercise price,issued	$ 15.25	$ 11
Outstanding, weighted average exercise price	$ 14.61	$ 8.38	$ 7.90
Outstanding, average intrinsic value	$ 22,127,594
Average intrinsic value,issued	$ 20,112,271

Equity - Schedule of Assumption

Equity - Schedule of Assumptions (Detail) - $ / shares	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Class of Warrant or Right [Line Items]
Strike price			$ 11
Dividend yield	0.00%	0.00%
Minimum [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 11.69	$ 2.22
Expected term	5 years 6 months	4 years 8 months 12 days	6 years
Maximum [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 23.41	$ 3.07
Expected term	6 years 6 months	5 years 10 months 24 days	6 years 6 months
Common stock warrant [Member]
Class of Warrant or Right [Line Items]
Strike price		$ 15.25	$ 11
Volatility rate		80.00%	80.00%
Risk-free rate			2.40%
Expected term			5 years
Dividend yield		0.00%	0.00%
Common stock warrant [Member] | Minimum [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 7.58
Risk-free rate		0.19%
Expected term	6 months 25 days	3 years
Common stock warrant [Member] | Maximum [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 15.84
Risk-free rate		0.28%
Expected term	4 years 5 months 1 day	5 years
As Previously Reported | Minimum [Member]
Class of Warrant or Right [Line Items]
Strike price		$ 11
Expected term		5 years 6 months
As Previously Reported | Maximum [Member]
Class of Warrant or Right [Line Items]
Strike price		$ 15.25
Expected term		6 years 6 months

Equity - Additional Information

Equity - Additional Information (Detail) - USD ($)	Oct. 23, 2020	Jul. 15, 2020	Jul. 06, 2020	Jan. 31, 2019	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019	Mar. 31, 2021	Mar. 01, 2020
StockholdersEquityLineItems
Common stock, shares authorized					500,000,000		500,000,000		500,000,000	14,060,001		14,060,001
Common stock, par value					$ 0.001		$ 0.001		$ 0.001	$ 0.001		$ 0.001
Proceeds from issuance of Common stock, net of transaction costs							$ 8,489,082	$ 176,990	$ 2,579,114	$ 5,802,002
Debt conversion, converted instrument, amount									$ 3,655,438	$ 0
Loss on settlement of accounts payable							$ 120,810
Convertible preferred stock, shares authorized					50,000,000		50,000,000		50,000,000
Convertible preferred stock, shares issued					0		0		0
Convertible preferred stock, par value					$ 0.001		$ 0.001		$ 0.001
Warrant, exercise price per share					$ 24.78		$ 24.78		$ 1.09		$ 1.78
Common Stock
StockholdersEquityLineItems
Common stock, shares authorized												20,000,000
Common stock issued, shares					65,526	0	398,647	50,844	171,796	536,354
Proceeds from issuance of Common stock, net of transaction costs					$ 1,436,274	$ 0	$ 8,363,132	$ 176,990	$ 2,579,114	$ 5,802,002
Common shares issued									9,500
Debt conversion, original debt, amount									$ 144,875
Loss on settlement of accounts payable									41,617
Common Stock | Accounts Payable [Member]
StockholdersEquityLineItems
Debt conversion, original debt, amount									$ 103,258
Convertible Series A Preferred Stock [Member]
StockholdersEquityLineItems
Convertible preferred stock, shares authorized									1,000,000	1,000,000
Convertible preferred stock, shares issued									1,000,000	1,000,000
Convertible preferred stock, par value									$ 0.001	$ 0.001
Preferred stock, conversion basis									one share of Common Stock for each preferred share
Convertible preferred stock,liquidation preference per share									$ 1
Convertible Series B-1 Preferred Stock [Member]
StockholdersEquityLineItems
Convertible preferred stock, shares authorized									1,050,695	1,050,695
Convertible preferred stock, shares issued									1,050,695	1,050,695
Convertible preferred stock, par value									$ 0.001	$ 0.001
Preferred stock, conversion basis									one share of Common Stock for each preferred share
Convertible preferred stock,liquidation preference per share									$ 7.58
Convertible Series B-1A Preferred Stock [Member]
StockholdersEquityLineItems
Convertible preferred stock, shares authorized									316,848	316,848
Convertible preferred stock, shares issued									316,848	316,848
Convertible preferred stock, par value									$ 0.001	$ 0.001
Preferred stock, conversion basis									one share of Common Stock for each preferred share
Convertible preferred stock,liquidation preference per share									$ 6.82
Convertible Series B-2 Preferred Stock [Member]
StockholdersEquityLineItems
Convertible preferred stock, shares authorized									100,000	100,000
Convertible preferred stock, shares issued									4,167	0
Convertible preferred stock, par value									$ 0.001	$ 0.001
Preferred stock, conversion basis									one share of Common Stock for each share of Series B-2 Convertible Preferred Stock
Convertible preferred stock,liquidation preference per share									$ 12
Common stock warrants [Member]
StockholdersEquityLineItems
Warrant issued	139,645	279,291	4,000	8,846
Warrant, exercise price per share	$ 15.25	$ 15.25	$ 15.25	$ 11
Warrant expiry date	Oct. 22, 2025	Jul. 14, 2025	Jul. 5, 2023	Jan. 30, 2024
Fair value on the date of issuance	$ 2,693,221	$ 2,689,684	$ 30,536	$ 63,337
Warrant, fair valued price per share	$ 9.64	$ 9.63	$ 7.63	$ 7.16

Stock Based Compensation - Addi

Stock Based Compensation - Additional Information (Details) - USD ($)	3 Months Ended		6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2016
Equity Incentive Plan [Line Items]
Weighted average grant date fair value	$ 14.31	$ 1.25	$ 18.37	$ 1.25	$ 9.64	$ 7.69
Unrecognized compensation	$ 33,610,165		$ 33,610,165		$ 2,193,874
Weighted average period			1 year 10 months 20 days		2 years 1 month 2 days
Stock-based compensation expense allocated	4,283,330	$ 93,466	$ 4,655,028	$ 182,269
General and Administrative Expense [Member]
Equity Incentive Plan [Line Items]
Stock-based compensation expense allocated	4,094,549	50,881	4,438,583	117,469	$ 332,065	$ 321,087
Research and Development Expense [Member]
Equity Incentive Plan [Line Items]
Stock-based compensation expense allocated	$ 188,781	$ 42,585	$ 216,445	$ 64,800	$ 398,340	$ 112,823
2016 Omnibus Inventive Plan [Member]
Equity Incentive Plan [Line Items]
Share-based compensation arrangement by share-based payment award, number of shares authorized	3,472,000		3,472,000		700,000		500,000
Share-based compensation arrangement by share-based payment award, number of additional shares authorized					200,000
Share-based compensation arrangement by share-based payment award, shares granted					486,755
Share-based compensation arrangement by share-based payment award, number of shares available for grant					213,245

Stock Based Compensation - Summ

Stock Based Compensation - Summary of grant date of stock option award (Details) - $ / shares	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price			$ 11
Risk-free rate of interest	0.79%	0.79%
Expected stock price volatility	80.00%	80.00%	80.00%
Dividend yield	0.00%	0.00%
Minimum [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price	$ 11.69	$ 2.22
Risk-free rate of interest		0.30%	1.54%
Expected term (years)	5 years 6 months	4 years 8 months 12 days	6 years
Maximum [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price	$ 23.41	$ 3.07
Risk-free rate of interest		0.49%	1.73%
Expected term (years)	6 years 6 months	5 years 10 months 24 days	6 years 6 months

Share based compensation - Summ

Share based compensation - Summary of stock option activity (Details) - USD ($)	3 Months Ended		12 Months Ended
	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Outstanding, Number of shares		2,414,303
Granted		210,800
Forfeited /Cancelled		(198,400)
Outstanding, Number of shares	2,919,493		2,414,303
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Outstanding, Weighted average exercise price		$ 2.17
Granted		11.69
Forfeited		$ 2.22
Outstanding, Weighted average exercise price	$ 5.25		$ 2.17
Outstanding, intrinsic value
Outstanding, intrinsic value		$ 53,659,966
Granted		3,825,276
Forfeited		$ (6,587,328)
Outstanding, intrinsic value	$ 20,558,299		$ 53,659,966
Outstanding, weighted remaining contractual life (in years)
Granted		9 years 9 months 18 days
Outstanding, weighted remaining contractual life (in years)	9 years		8 years 2 months 12 days
As Previously Reported
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Outstanding, Number of shares		486,755	333,588	355,408
Granted			266,500	28,180
Forfeited /Cancelled			(113,333)	(50,000)
Outstanding, Number of shares			486,755	333,588	355,408
Options vested and exercisable			329,489
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Outstanding, Weighted average exercise price		$ 10.79	$ 5.74	$ 5.74
Granted			14.37	11
Outstanding, Weighted average exercise price			10.79	$ 5.74	$ 5.74
Options vested and exercisable			$ 6.31
Outstanding, intrinsic value
Outstanding, intrinsic value		$ 19,571,655	$ 1,782,729	$ 1,782,729
Granted			9,761,125
Outstanding, intrinsic value			19,571,655	$ 1,782,729	$ 1,782,729
Options vested and exercisable			$ 14,723,342
Outstanding, weighted remaining contractual life (in years)
Granted			9 years 8 months 12 days	9 years 7 months 6 days
Outstanding, weighted remaining contractual life (in years)			8 years 9 months 18 days	7 years 2 months 12 days	8 years 2 months 12 days
Options vested and exercisable, Weighted remaining contractual life (in years)			4 years

Income Taxes - Schedule of Reco

Income Taxes - Schedule of Reconciliation of Effective Tax rate (Details)	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Income Taxes.
Statutory federal income tax benefit	(21.00%)	(21.00%)
Permanent items	(0.04%)	0.01%
Foreign rate differential	0.01%	(0.02%)
State taxes, net of federal tax benefit	(1.74%)	0.60%
Change in valuation allowance	23.01%	22.23%
R&D credit	(0.24%)	(1.90%)
Other		0.07%
Effective tax rate	0.00%	0.00%

Income Taxes - Schedule of Comp

Income Taxes - Schedule of Components of Income Tax Provision (Benefit) (Details) - USD ($)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Federal
Current		$ 0	$ 0
Deferred		(11,015,759)	(1,496,712)
State and Local
Current		0	0
Deferred		(900,789)	39,574
Foreign
Current		0	0
Deferred		2,867	(8,412)
Change in valuation allowance		11,913,681	1,465,550
Total	$ 0	$ 0	$ 0

Income Taxes - Schedule of Defe

Income Taxes - Schedule of Deferred Tax Assets and Liabilities (Details) - USD ($)	Dec. 31, 2020	Dec. 31, 2019
Income Taxes.
Net operating loss carryforwards	$ 8,243,959	$ 6,943,988
Convertible notes payable discount and embedded derivative		101,521
Common stock warrants	1,405,796	179,271
Israel net operating loss carryforwards	128,469	131,336
Founder share options	469,062	472,195
Stock-based compensation	681,446	497,315
Settlement liability	9,005,860
Bonus accrual	120,995
Other	58,721
R&D credit	375,000	250,000
Total deferred tax assets before valuation allowance	20,489,308	8,575,626
Valuation allowance	(20,489,308)	(8,575,626)
Deferred tax assets, net of allowance	$ 0	$ 0

Income Taxes - Additional Infor

Income Taxes - Additional Information (Details) - USD ($)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Deferred tax asset due to uncertain tax posistionsDeferred tax asset due to uncertain tax posistions		$ 1,000,000
Accrued penalties and interest,total		0	$ 0
Recognized penalties and interest		0	0
Provision or benefit for income tax expense	$ 0	0	0
Federal and State
Net operating loss carryovers		37,000,000	31,200,000
Foreign Tax Authority
Net operating loss carryovers		$ 559,000	$ 547,000

Related Party Transactions (Det

Related Party Transactions (Details) - USD ($)	3 Months Ended		6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Related Party Transaction [Line Items]
Accounts payable due to related parties	$ 44,201		$ 44,201		$ 149,067	$ 92,744
CEO
Related Party Transaction [Line Items]
Compensation amount received related to related party transaction	137,500	$ 53,125	286,250	$ 121,875	456,459	452,400
Neuro Rx | Glytech Agreement
Related Party Transaction [Line Items]
Continuing technology support services and reimbursed expenses	125,000	0	$ 125,000	82,569	$ 272,929	464,720
Related party transaction description			The Excluded Technology will transfer to the Company for no additional consideration if the value of NRx Pharmaceuticals equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost.		The Excluded Technology will transfer to the Company for no additional consideration if the value of NeuroRx equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost.
Neuro Rx | CEO
Related Party Transaction [Line Items]
Payment to related party					$ 11,650
Neuro Rx | Chief Commercial Officer
Related Party Transaction [Line Items]
Payment to related party	11,100	18,605	$ 29,740	40,770	85,915	$ 48,000
Neuro Rx | Chief Executive Officer and Chairman of Board
Related Party Transaction [Line Items]
Payment to related party	$ 254,936	$ 0	$ 395,757	$ 0	$ 271,082

Subsequent Events (Details)

Subsequent Events (Details) - USD ($)	Jan. 04, 2021	Jan. 31, 2021	Mar. 31, 2021	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Subsequent Event [Line Items]
Net proceeds from issuance of common stock				$ 8,489,082	$ 176,990	$ 2,579,114	$ 5,802,002
Stock option awards granted			210,800
Subsequent Event
Subsequent Event [Line Items]
Stock option awards granted		42,500
Stock options, vesting period		3 years
Subsequent Event | Aerogen Limited
Subsequent Event [Line Items]
Purchase order for products amounted	$ 54,315
Transaction One | Subsequent Event
Subsequent Event [Line Items]
Issuance of common stock shares		43,018
Net proceeds from issuance of common stock		$ 2,495,058
Transaction Two | Subsequent Event
Subsequent Event [Line Items]
Issuance of common stock shares		79,400
Net proceeds from issuance of common stock		$ 5,716,800

CONDENSED CONSOLIDATED BALANCE

CONDENSED CONSOLIDATED BALANCE SHEETS	Jun. 30, 2021USD ($)
Current assets:
Cash	$ 13,386,332
Prepaid expenses and other current assets	5,147,650
Total current assets	18,533,982
Other assets	12,730
Total assets	18,546,712
Current liabilities:
Accounts payable (includes $44,201 and $149,067 due to related parties)	6,268,319
Accrued and other current liabilities	1,506,337
Accrued clinical site costs	1,133,312
Earnout Cash liability	25,874,896
Warrant liabilities	515,025
Notes payable and accrued interest	173,694
Total current liabilities	35,471,583
Notes payable and accrued interest	512,472
Total liabilities	35,984,055
Stockholders' equity (deficit):
Preferred stock, $0.001 par value, 50,000,000 shares authorized; 0 shares issued and outstanding at September 30, 2021 and December 31, 2020, respectively
Additional paid-in capital	114,190,620
Accumulated deficit	(131,676,567)
Total stockholders' equity (deficit)	(17,437,343)
Total liabilities and stockholders' equity (deficit)	$ 18,546,712

CONDENSED CONSOLIDATED BALANC_2

CONDENSED CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($)	Jun. 30, 2021	Dec. 31, 2020	Mar. 01, 2020	Dec. 31, 2019
Statement of Financial Position [Abstract]
Allowance for accounts receivable	$ 5,470,897	$ 257,463
Accounts payable, due to related parties	$ 44,201	$ 149,067		$ 92,744
Preferred stock, par value	$ 0.001	$ 0.001
Preferred stock, shares authorized	50,000,000	50,000,000
Preferred stock, shares issued	0	0
Preferred stock, shares outstanding	0	0
Common stock, par value	$ 0.001	$ 0.001	$ 0.001	$ 0.001
Common stock, shares authorized	500,000,000	500,000,000	14,060,001	14,060,001
Common stock, shares issued	48,603,585	42,973,462		10,686,191
Common stock, shares outstanding	48,603,585	42,973,462		10,686,191

CONDENSED CONSOLIDATED STATEMEN

CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS - USD ($)	3 Months Ended	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2021	Jun. 30, 2020
Operating expenses:
Research and development	$ 4,659,280	$ 7,567,984	$ 1,994,709
General and administrative	12,457,534	14,558,936	1,141,390
Settlement expense		21,365,641
Reimbursement of expenses from Relief Therapeutics		(771,244)	(2,020,931)
Total operating expenses	17,116,814	42,721,317	1,115,168
Income (loss) from operations	(17,116,814)	(42,721,317)	(1,115,168)
Other (income) expenses:
Gain on extinguishment of debt		(120,810)
Interest expense	5,107	10,288	38,800
Change in fair value of warrant liability	(1,468,649)	(1,468,649)
Change in fair value of Earnout Cash liability	354,701	354,701
Change in fair value of embedded put			27,160
Loss on conversion of convertible notes payable			306,641
Total other (income) expenses	(1,108,841)	(1,224,470)	372,601
Loss before tax	(16,007,973)	(41,496,847)	(1,487,769)
Provision for income taxes		0
Net loss	(16,007,973)	(41,496,847)	(1,487,769)
Deemed dividend - warrants	(2,691,799)	(2,691,799)
Deemed dividend - Earnout Shares	253,130,272	253,130,272
Net income (loss) attributable to common stockholders	$ (271,830,043)	$ (297,318,917)	$ (1,487,769)
Net earnings (loss) per share:
Basic	$ (0.38)	$ (1.07)	$ (0.04)
Diluted	(0.38)	(1.07)	(0.04)
Net earnings (loss) per share attributable to common stockholders:
Basic	(6.51)	(7.68)	(0.04)
Diluted	$ (6.51)	$ (7.68)	$ (0.04)
Weighted average common shares outstanding:
Basic	41,727,480	38,709,614	33,799,503
Diluted	41,727,480	38,709,614	33,799,503

CONDENSED CONSOLIDATED STATEM_2

CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY (DEFICIT) - USD ($)	Convertible Series A Preferred Stock [Member]	Convertible Series B-1A Preferred Stock [Member]	Convertible Series B-1 Preferred Stock [Member]	Convertible Series B-2 Preferred Stock [Member]	Common Stock	Additional Paid-in-Capital	Accumulated Deficit	Total
Beginning balance at Dec. 31, 2018			$ 1,050
Beginning balance, shares at Dec. 31, 2018			1,050,695
Net (loss) income								$ (6,729,161)
Ending balance at Dec. 31, 2019			$ 1,050		$ 41,249	$ 33,518,162	$ (38,402,816)	(4,843,405)
Ending balance, shares at Dec. 31, 2019			1,050,695		41,249,200
Retroactive application of reverse recapitalization	$ (1,000)	$ (317)	$ (1,050)		$ 30,563	(20,651)		7,545
Retroactive application of reverse recapitalization (in shares)	(1,000,000)	(316,848)	(1,050,695)		30,563,009
Balance (as previously reported) at Dec. 31, 2019	$ 1,000	$ 317	$ 1,050	$ 0	$ 10,686	33,538,813	(38,402,816)	(4,850,950)
Balance (as previously reported) (in shares) at Dec. 31, 2019	1,000,000	316,848	1,050,695	0	10,686,191
Common stock issued					$ 51	176,974		177,025
Common stock issued, shares					50,844
Series B-2 convertible preferred stock issued					$ 13	50,000		50,013
Series B-2 convertible preferred stock issued (in shares)					13,168
Stock-based compensation						88,803		88,803
Net (loss) income							(1,590,056)	(1,590,056)
Ending balance at Mar. 31, 2020					$ 41,313	33,833,939	(39,992,872)	(6,117,620)
Ending balance, shares at Mar. 31, 2020					41,313,212
Beginning balance at Dec. 31, 2019			$ 1,050		$ 41,249	33,518,162	(38,402,816)	(4,843,405)
Beginning balance, shares at Dec. 31, 2019			1,050,695		41,249,200
Balance (as previously reported) at Dec. 31, 2019	$ 1,000	$ 317	$ 1,050	$ 0	$ 10,686	33,538,813	(38,402,816)	(4,850,950)
Balance (as previously reported) (in shares) at Dec. 31, 2019	1,000,000	316,848	1,050,695	0	10,686,191
Net (loss) income								(1,487,769)
Ending balance at Jun. 30, 2020					$ 41,313	33,927,405	(39,890,585)	(5,921,867)
Ending balance, shares at Jun. 30, 2020					41,313,212
Beginning balance at Dec. 31, 2019			$ 1,050		$ 41,249	33,518,162	(38,402,816)	(4,843,405)
Beginning balance, shares at Dec. 31, 2019			1,050,695		41,249,200
Balance (as previously reported) at Dec. 31, 2019	$ 1,000	$ 317	$ 1,050	$ 0	$ 10,686	33,538,813	(38,402,816)	(4,850,950)
Balance (as previously reported) (in shares) at Dec. 31, 2019	1,000,000	316,848	1,050,695	0	10,686,191
Net (loss) income								(51,776,904)
Ending balance at Dec. 31, 2020			$ 1,050	$ 4	$ 42,974	46,365,863	(90,179,720)	(43,770,883)
Ending balance, shares at Dec. 31, 2020			1,050,695	4,167	42,973,462
Beginning balance at Mar. 31, 2020					$ 41,313	33,833,939	(39,992,872)	(6,117,620)
Beginning balance, shares at Mar. 31, 2020					41,313,212
Stock-based compensation						93,466		93,466
Net (loss) income							102,287	102,287
Ending balance at Jun. 30, 2020					$ 41,313	33,927,405	(39,890,585)	(5,921,867)
Ending balance, shares at Jun. 30, 2020					41,313,212
Retroactive application of reverse recapitalization	$ (1,000)	$ (317)	$ (1,050)	$ (4)	$ 31,746	(21,786)		7,589
Retroactive application of reverse recapitalization (in shares)	(1,000,000)	(316,848)	(1,050,695)	(4,167)	31,745,786
Beginning balance at Dec. 31, 2020			$ 1,050	$ 4	$ 42,974	46,365,863	(90,179,720)	(43,770,883)
Beginning balance, shares at Dec. 31, 2020			1,050,695	4,167	42,973,462
Balance (as previously reported) at Dec. 31, 2020	$ 1,000	$ 317	$ 1,050	$ 4	$ 11,228	46,387,649	(90,179,720)	(43,778,472)
Balance (as previously reported) (in shares) at Dec. 31, 2020	1,000,000	316,848	1,050,695	4,167	11,227,676
Common stock issued					$ 333	6,926,753		6,927,086
Common stock issued, shares					333,121
Proceeds from issuance of common stock for exercise of warrant					$ 1,496	7,498,522		7,500,018
Proceeds from issuance of common stock for exercise of warrant (in shares)					1,496,216
Reclassification of settlement liability upon issuance of warrant						60,851,779		60,851,779
Stock-based compensation						371,698		371,698
Net (loss) income							(25,488,874)	(25,488,874)
Ending balance at Mar. 31, 2021					$ 44,803	122,014,615	(115,668,594)	6,390,824
Ending balance, shares at Mar. 31, 2021					44,802,799
Beginning balance at Dec. 31, 2020			$ 1,050	$ 4	$ 42,974	46,365,863	(90,179,720)	(43,770,883)
Beginning balance, shares at Dec. 31, 2020			1,050,695	4,167	42,973,462
Balance (as previously reported) at Dec. 31, 2020	$ 1,000	$ 317	$ 1,050	$ 4	$ 11,228	46,387,649	(90,179,720)	(43,778,472)
Balance (as previously reported) (in shares) at Dec. 31, 2020	1,000,000	316,848	1,050,695	4,167	11,227,676
Net (loss) income								(41,496,847)
Ending balance at Jun. 30, 2021					$ 48,604	114,190,620	(131,676,567)	(17,437,343)
Ending balance, shares at Jun. 30, 2021					48,603,585
Beginning balance at Mar. 31, 2021					$ 44,803	122,014,615	(115,668,594)	6,390,824
Beginning balance, shares at Mar. 31, 2021					44,802,799
Common stock issued					$ 71	1,562,201		1,562,272
Common stock issued, shares					71,056
Effect of Merger and recapitalization, net of redemptions and issuance costs of $1,412,846					$ 2,530	(26,618,326)		(26,615,796)
Effect of Merger and recapitalization, net of redemptions and issuance costs of $1,412,846 (in shares)					2,529,730
Common stock issued pursuant to PIPE financing, net of issuance costs of $1,900,000					$ 1,000	8,099,000		8,100,000
Common stock issued pursuant to PIPE financing, net of issuance costs of $14,232 (in shares)					1,000,000
Common stock issued for advisor services					$ 200	4,849,800		4,850,000
Common stock issued for advisor services (in shares)					200,000
Modification of option awards pursuant to Merger						1,014,640		1,014,640
Modification of warrants pursuant to Merger						2,330,572		2,330,572
Stock-based compensation						938,118		938,118
Net (loss) income							(16,007,973)	(16,007,973)
Ending balance at Jun. 30, 2021					$ 48,604	$ 114,190,620	$ (131,676,567)	$ (17,437,343)
Ending balance, shares at Jun. 30, 2021					48,603,585

CONDENSED CONSOLIDATED STATEM_3

CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY (DEFICIT) (Parenthetical)	3 Months Ended
	Jun. 30, 2021USD ($)
CONSOLIDATED STATEMENT OF CHANGES IN STOCKHOLDERS' EQUITY (DEFICIT)
Net of redemptions and issuance costs	$ 1,412,846
PIPE financing, net of issuance costs	$ 1,900,000

CONDENSED CONSOLIDATED STATEM_4

CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS	6 Months Ended
	Jun. 30, 2021USD ($)
CASH FLOWS FROM OPERATING ACTIVITIES:
Net Loss	$ (41,496,847)
Adjustments to reconcile net loss to net cash used in operating activities:
Depreciation expense	967
Stock-based compensation	4,655,028
Gain on extinguishment of debt	(120,810)
Change in fair value of warrant liability	(1,468,649)
Change in fair value of cash earnout liability	354,701
Non-cash interest expense	10,288
Non-cash settlement expense	21,365,641
Non-cash consulting expense	4,850,000
Changes in operating assets and liabilities:
Accounts receivable	831,390
Prepaid expenses and other assets	(4,847,806)
Accounts payable	2,562,762
Accrued expenses and other liabilities	(1,104,791)
Net cash used in operating activities	(14,408,126)
CASH FLOWS FROM INVESTING ACTIVITIES
Purchase of computer equipment	(2,783)
Net cash used in investing activities	(2,783)
CASH FLOWS FROM FINANCING ACTIVITIES
Net proceeds from issuance of common stock	8,489,082
Proceeds from exercise of warrant	7,500,018
Effect of Merger, net of transaction costs	11,049,628
Repayment of notes payable assumed in Merger	(1,100,000)
Net cash provided by financing activities	25,938,728
Net increase in cash	11,527,819
Cash at beginning of year	1,858,513
Cash at end of year	13,386,332
Non-cash investing and financing activities
Reclassification of settlement liability upon issuance of warrant	60,851,779
Extinguishment of Paycheck Protection Program Loan	$ 120,810

Organization_2

Organization	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Organization.
Organization	1. Organization The Business On May 24, 2021, we consummated the business combination, or the Business Combination, contemplated by the Agreement and Plan of Merger (as amended, the “Merger Agreement”), dated December 13, 2020, by and among our company (formerly known as Big Rock Partners Acquisition Corp. (“BRPA”)), NeuroRx, Inc., a Delaware corporation (“NeuroRx”), Big Rock Merger Corp., and a Delaware corporation and wholly-owned, direct subsidiary of BRPA (“Merger Sub”), pursuant to which Big Rock Merger Corp. was merged with and into NeuroRx, with NeuroRx surviving the merger (“Merger”). As a result of the Merger, and upon consummation of the Merger and other transactions contemplated by the Merger Agreement, NeuroRx became a wholly-owned, direct subsidiary of BRPA. Upon the closing of the Business Combination, we changed our name to NRx Pharmaceuticals, Inc. (“NRx Pharmaceuticals,” “NRXP,” “we,” or the “Company”), with the stockholders of NeuroRx becoming stockholders of NRx Pharmaceuticals. The Company is a clinical-stage small molecule pharmaceutical company which develops novel therapeutics for the treatment of central nervous system disorders and life-threatening pulmonary diseases through its wholly-owned operating subsidiary, NeuroRx. On September 21, 2020, we announced a commercial partnership with Relief Therapeutics Holding AG (“Relief”) for global commercialization of RLF-100 (aviptadil acetate) (now reformulated as ZYESAMI TM TM	NeuroRx, Inc. NOTES TO CONSOLIDATED FINANCIAL STATEMENTS 1. Organization The Business NeuroRx, Inc. (the “Company” or “NeuroRx”) was formed on May 20, 2015 and is incorporated in the State of Delaware. The Company established a wholly owned subsidiary, NeuroRx 2015 LTD (Israel), in December 2015, for the purpose of managing the continued development of a subset of the Company’s technology. The Company is a clinical stage pharmaceutical research and development company primarily engaged in the development of a drug regimen to treat patients with depression and suicidal ideation or behavior.

Liquidity_2

Liquidity	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Liquidity
Liquidity	2. Liquidity As of June 30, 2021, the Company had $13,386,332 in cash. Since inception the Company has experienced net losses and negative cash flows from operations each fiscal year. The Company has no revenues and expects to continue to incur operating losses for the foreseeable future, and may never become profitable. The Company is dependent on its ability to continue to raise equity and/or debt financing to continue operations, and the attainment of profitable operations. The Company has a collaboration agreement with Relief which provided for funding by Relief of certain research and development expenses related to the U.S. development of ZYESAMI TM TM TM COVID-19 Outbreak On January 30, 2020, the World Health Organization (“WHO”) announced a global health emergency because of a new strain of coronavirus originating in Wuhan, China (the “COVID-19 Outbreak”) and the risks to the international community as the virus spreads globally beyond its point of origin. In March 2020, the WHO classified the COVID-19 Outbreak as a pandemic, based on the rapid increase in exposure globally. The full impact of the COVID-19 Outbreak continues to evolve as of the date of this report. If the COVID-19 Outbreak continues, it may have a material adverse effect on the Company’s financial condition, liquidity, and future results of operations for the year ending December 31, 2021 and beyond. Management is actively monitoring the impact of the global pandemic on its financial condition, liquidity, operations, industry, and workforce. Given the daily evolution of the COVID-19 Outbreak and the global responses to curb its spread, the Company is not able to estimate the effects of the COVID-19 Outbreak on its results of operations, financial condition, or liquidity for the year ending December 31, 2021 and beyond.	2. Liquidity As of December 31, 2020, the Company had $1,858,513 in cash. Since inception the Company has experienced net losses and negative cash flows from operations each fiscal year. The Company has no revenues and expects to continue to incur operating losses for the foreseeable future, and may never become profitable. The Company is dependent on its ability to continue to raise equity and/or debt financing to continue operations, and the attainment of profitable operations. The Company has a collaboration agreement with Relief Therapeutics Holdings (“Relief”), which provided for funding by Relief of certain research and development expenses related to the U.S. development of ZYESAMI and the portion of corporate overhead attributable to that program. The proceeds received amounted to $10,160,421 for the year ended December 31, 2020. Subsequent to December 31, 2020, Relief has not reimbursed the Company for any additional expenses related to the IV clinical trials for the ZYESAMI. The IV clinical trials for the ZYESAMI were completed on February 24, 2021. During the first quarter of 2021, the Company sold 43,018 shares of common stock for gross proceeds of $2,495,058, and 79,400 shares of common stock for gross proceeds of $5,716,800. On March 28, 2021, the Company received $7,500,018 from the exercise of a warrant for the purchase of 473,486 shares. Accordingly, the Company believes that it currently has sufficient funds to support operations through the next twelve months from the date the financial statements are issued. The Company intends to use the proceeds of the merger transaction to fund the ZYESAMI inhaled trial for COVID-19. The Company cannot make any assurances that additional financings will be available to it and, if available, on acceptable terms or at all. This could negatively impact the Company’s business and operations and could also lead to the reduction of the Company’s operations. COVID-19 Outbreak On January 30, 2020, the World Health Organization (“WHO”) announced a global health emergency because of a new strain of coronavirus originating in Wuhan, China (the “COVID-19 Outbreak”) and the risks to the international community as the virus spreads globally beyond its point of origin. In March 2020, the WHO classified the COVID-19 Outbreak as a pandemic, based on the rapid increase in exposure globally. The full impact of the COVID-19 Outbreak continues to evolve as of the date of this report. As such, the Company cannot estimate the full magnitude that the pandemic will have on the Company’s business. If the COVID-19 Outbreak continues, it may have a material adverse effect on the Company’s financial condition, liquidity, and future results of operations for the year ending December 31, 2021 and beyond. Management is actively monitoring the impact of the global pandemic on its financial condition, liquidity, operations, industry, and workforce. Given the daily evolution of the COVID-19 Outbreak and the global responses to curb its spread, the Company is not able to estimate the effects of the COVID-19 Outbreak on its results of operations, financial condition, or liquidity for the year ending December 31, 2021 and beyond.

Summary of Significant Accoun_7

Summary of Significant Accounting Policies	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Summary of Significant Accounting Policies
Summary of Significant Accounting Policies	3. Summary of Significant Accounting Policies Basis of Presentation The accompanying unaudited interim condensed financial statements have been prepared in accordance with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) for interim financial information. Accordingly, they do not include all of the information and footnotes required by GAAP for complete financial statements. In the opinion of management, the unaudited interim condensed financial statements reflect all adjustments, which include only normal recurring adjustments necessary for the fair statement of the balances and results for the periods presented. The results of operations for any interim periods are not necessarily indicative of the results that may be expected for the entire fiscal year or any other interim period. The merger between Merger Sub and NeuroRx was accounted for as a reverse recapitalization in accordance with U.S. GAAP (the “Reverse Recapitalization”). Under this method of accounting, BRPA was treated as the “acquired” company and NeuroRx is treated as the acquirer for financial reporting purposes. Accordingly, for accounting purposes, the Reverse Recapitalization was treated as the equivalent of NeuroRx issuing stock for the net assets of BRPA, accompanied by a recapitalization. The net assets of BRPA are stated at historical cost, with no goodwill or other intangible assets recorded. NeuroRx was determined to be the accounting acquirer based on the following predominant factors: ● NeuroRx’s shareholders have the largest portion of voting rights in the Company; ● the Board and Management are primarily composed of individuals associated with NeuroRx; and ● NeuroRx was the larger entity based on historical operating activity and NeuroRx had the larger employee base at the time of the Merger. The consolidated assets, liabilities and results of operations prior to the Reverse Recapitalization are those of NeuroRx. The shares and corresponding capital amounts and losses per share, prior to the Merger, have been retroactively restated based on shares reflecting the exchange ratio established in the Merger. Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, contingent consideration and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected. Certain Risks and Uncertainties The Company’s activities are subject to significant risks and uncertainties including the risk of failure to secure additional funding to properly execute the Company’s business plan. The Company is subject to risks that are common to companies in the pharmaceutical industry, including, but not limited to, development by the Company or its competitors of new technological innovations, dependence on key personnel, reliance on third party manufacturers, protection of proprietary technology, and compliance with regulatory requirements. Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. (Refer to Note 12) Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of June 30, 2021, the Company has recorded an allowance for doubtful accounts of $5,470,897 as the Company does not expect to collect on amounts due to the Company owed from Relief. Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss. Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received. Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company. Modification of stock options and warrants A change in any of the terms or conditions of stock options and warrants is accounted for as a modification. Incremental stock-based compensation cost is measured as the excess, if any, of the fair value of the modified option over the fair value of the original option/warrant immediately before its terms are modified, measured based on the fair value of the ordinary shares and other pertinent factors at the modification date. For vested stock options and warrants to board members, we recognize incremental compensation cost in the period the modification occurs. For unvested stock options, we recognize over the remaining requisite service period, the sum of the incremental compensation cost and the remaining unrecognized compensation cost for the original award on the modification date. If the fair value of the modified option is lower than the fair value of the original option immediately before modification, the minimum compensation cost we recognize is the cost of the original award. The accounting for incremental fair value of warrants is based on the specific facts and circumstances related to the modification which may result in a reduction of additional paid-in capital, recognition of costs for services rendered, or recognized as a deemed dividend. Warrants The Company accounts for warrants as either equity-classified or liability-classified instruments based on an assessment of the warrant’s specific terms and applicable authoritative guidance in Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) 480, Distinguishing Liabilities from Equity Derivatives and Hedging For issued or modified warrants that meet all of the criteria for equity classification, the warrants are required to be recorded as a component of additional paid-in capital at the time of issuance. For issued or modified warrants that do not meet all the criteria for equity classification, the warrants are required to be recorded at their initial fair value on the date of issuance, and each balance sheet date thereafter. Changes in the estimated fair value of the warrants are recognized as a non-cash gain or loss on the statements of operations. The fair value of the Placement Warrants was estimated using a Black Scholes valuation approach (see Notes 10 and 12). Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense. Earnings (Loss) Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted earnings per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and other dilutive instruments because their effect would be anti-dilutive in the periods in which we incur a net loss. The following table summarized the basic and diluted earnings per share calculations: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Numerator: ​ ​ ​ ​ ​ ​ ​ ​ Net income (loss) attributable to common stock—basic and diluted $ (16,007,973) $ 102,287 $ (41,496,847) $ (1,487,769) Denominator: ​ ​ ​ ​ ​ ​ ​ ​ Weighted average shares — basic ​ ​ 41,727,480 ​ ​ 33,819,205 ​ ​ 38,709,614 ​ ​ 33,799,503 Effect of other dilutive securities ​ ​ — ​ ​ 2,837,215 ​ ​ — ​ ​ — Weighted average shares — diluted ​ ​ 41,727,480 ​ ​ 36,656,420 ​ ​ 38,709,614 ​ ​ 33,799,503 Basic earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) Diluted earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net earnings (loss) per share attributable to common stock for the periods in which a net loss is presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Stock options 2,919,493 — 2,919,493 1,166,863 Common stock warrants 8,495,316 — 8,495,316 1,670,352 Common stock issuable pursuant to UPOs (Note 10) ​ 600,000 ​ — ​ 600,000 ​ — Common stock warrants pursuant to UPOs (Note 10) ​ 300,000 ​ — ​ 300,000 ​ — Public Rights pursuant to UPOs (Note 10) ​ 60,000 ​ — ​ 60,000 ​ — Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ — ​ Recent Accounting Pronouncements In December 2019, the FASB issued ASU No. 2019-12, Income Taxes: Simplifying the Accounting for Income Taxes In August 2020, the FASB issued ASU 2020-06, Debt — Debt with Conversion and Other Options (Subtopic 470-20) and Derivatives and Hedging — Contracts in Entity’s Own Equity (Subtopic 815-40): Accounting for Convertible Instruments and Contracts in an Entity’s Own Equity In May 2021, the FASB issued ASU 2021-04, Earnings Per Share (Topic 260), Debt — Modifications and Extinguishments (Subtopic 470-50), Compensation — Stock Compensation (Topic 718) and Derivatives and Hedging - Contracts in an Entity's Own Equity (Subtopic 815-40) — Issuer's Accounting for Certain Modifications or Exchange of Freestanding Equity-Classified Written Call Options	3. Summary of Significant Accounting Policies Basis of Presentation The Company’s financial statements have been prepared in conformity with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”). Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, the embedded put feature in convertible notes and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected. Certain Risks and Uncertainties The Company’s activities are subject to significant risks and uncertainties including the risk of failure to secure additional funding to properly execute the Company’s business plan. The Company is subject to risks that are common to companies in the pharmaceutical industry, including, but not limited to, development by the Company or its competitors of new technological innovations, dependence on key personnel, reliance on third party manufacturers, protection of proprietary technology, and compliance with regulatory requirements. Cash and Cash Equivalents The Company considers all highly liquid investments purchased with original maturities of 90 days or less at acquisition to be cash equivalents. As of December 31, 2020 and 2019, the Company does not have any cash equivalents. Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. Fair value measurements discussed herein are based upon certain market assumptions and pertinent information available to management as of and during the years ended December 31, 2020 and 2019. The carrying amount of accounts payable approximated fair value as they are short term in nature. The fair value of warrants issued for services is estimated based on the Black-Scholes model during the years ended December 31, 2020 and 2019. The carrying value of notes payable and convertible notes payable approximated the estimated fair values due to their recent issuances. The estimated fair value of the warrants and embedded put, represent Level 3 measurements. Foreign Currency The Company’s functional currency is the U.S. dollar. The functional currency of our foreign operation is the respective local currency. Assets and liabilities of foreign operation denominated in local currencies are translated at the spot rate in effect at the applicable reporting date. The consolidated statements of operations are translated at the weighted average rate of exchange during the applicable period. The resulting unrealized cumulative translation adjustment is not material to the financial statements. Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of December 31, 2020, the Company has recorded an allowance for doubtful accounts of $257,463. Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss. Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received. Derivative Financial Instruments The Company does not use derivative instruments to hedge exposures to interest rate, market, or foreign currency risks. The Company evaluates all of its financial instruments, to determine if such instruments contain features that qualify as embedded derivatives. Embedded derivatives must be separately measured from the host contract if all the requirements for bifurcation are met. The assessment of the conditions surrounding the bifurcation of embedded derivatives depends on the nature of the host contract. Bifurcated embedded derivatives are recognized at fair value, with changes in fair value recognized in the statement of operations each period. Bifurcated embedded derivatives are classified with the related host contract in the Company’s balance sheet. Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company. Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes (“ASC 740”), which provides for deferred taxes using an asset and liability approach. The Company recognizes deferred tax assets and liabilities for the expected future tax consequences of events that have been included in the financial statements or tax returns. Deferred tax assets and liabilities are determined based on the difference between the financial statement and tax basis of assets and liabilities using enacted tax rates in effect for the year in which the differences are expected to reverse. Valuation allowances are provided, if based upon the weight of available evidence, it is more likely than not that some or all of the deferred tax assets will not be realized. The Company accounts for uncertain tax positions in accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense. Loss Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted loss per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and convertible preferred stock because their effect would be anti-dilutive due to our net loss. Since the Company had a net loss in each of the periods presented, basic and diluted net loss per common share are the same. The calculation of basic and diluted net loss per share attributable to common stock was as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Numerator: ​ ​ ​ ​ ​ ​ Net loss attributable to common stock—basic and diluted ​ $ (51,776,904) ​ $ (6,729,161) ​ ​ ​ ​ ​ ​ ​ Denominator: ​ ​ Weighted average shares—basic and diluted ​ 10,845,240 ​ 10,690,209 ​ ​ ​ ​ ​ ​ ​ Net loss per share attributable to common stock—basic and diluted ​ $ (4.77) ​ $ (0.63) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net loss per share attributable to common stock for the periods presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ Year Ended December 31, ​ 2020 2019 Convertible preferred stock as if converted 2,371,710 2,367,543 Stock options 486,755 333,588 Common stock warrants 620,054 57,473 ​ Recent Accounting Pronouncements In June 2018, the FASB issued ASU 2018-07, which simplifies the accounting for nonemployee share-based payment transactions. The amendments specify that Topic 718 applies to all share-based payment transactions in which a grantor acquires goods or services to be used or consumed in a grantor’s own operations by issuing share-based payment awards. The Company adopted ASU 2018-07 as of January 1, 2019, which resulted in a cumulative effect charge of $683 to accumulated deficit.

Reverse Recapitalization

Reverse Recapitalization	6 Months Ended
	Jun. 30, 2021
Reverse Recapitalization
Reverse Recapitalization	4. Reverse Recapitalization As discussed in Note 1, on May 24, 2021 (the “Closing Date”), BRPA closed the Business Combination with NeuroRx, as a result of which NeuroRx became a wholly-owned subsidiary of BRPA. While BRPA was the legal acquirer of NeuroRx in the business combination, for accounting purposes, the Merger is treated as a Reverse Recapitalization, whereby NeuroRx is deemed to be the accounting acquirer, and the historical financial statements of NeuroRx became the historical financial statements of BRPA (renamed NRx Pharmaceuticals, Inc.) upon the closing of the Merger. Under this method of accounting, BRPA was treated as the “acquired” company and NeuroRx is treated as the acquirer for financial reporting purposes. Accordingly, for accounting purposes, the Merger was treated as the equivalent of NeuroRx issuing stock for the net assets of BRPA, accompanied by a recapitalization. The net assets of BRPA were stated at historical cost, with no goodwill or other intangible assets recorded. Pursuant to the Merger Agreement, the aggregate consideration payable to stockholders of NeuroRx at the Closing Date consists of 50,000,000 shares (“Closing Consideration”) of BRPA common stock, par value $0.001 per share (“Common Stock”). At the effective time of the Merger (the “Effective Time”), and subject to the terms and conditions of the Merger Agreement, each share of NeuroRx common stock, par value $0.001 per share, and each share of the NeuroRx convertible preferred stock that was convertible into a share of NeuroRx common stock at a one-to-one ratio pursuant to the NeuroRx certificate of incorporation, was converted into Common Stock equal to 3.16 (the “Exchange Ratio”). Each option and warrant of NeuroRx that was outstanding and unexercised immediately prior to the Effective Time (whether vested or unvested) was assumed by BRPA and converted into an option or warrant to acquire an adjusted number of shares of Common Stock at an adjusted exercise price per share, in each case, pursuant to the terms of the Merger Agreement (the “Substitute Options” and the “Substitute Warrants,” respectively), based on an exchange ratio of 4.96:1 (the “Option Exchange Ratio”), and will continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the original instrument. In addition, the securityholders of NeuroRx (including option holders and warrant holders) who own NeuroRx securities immediately prior to the Effective Time received the contingent right to receive the Earnout Shares and Earnout Cash (each as defined below). At the Effective Time, each outstanding share of NeuroRx common stock, including shares of NeuroRx common stock resulting from the conversion of outstanding shares of NeuroRx preferred stock (as calculated pursuant to the NeuroRx certificate of incorporation), immediately prior to the Effective Time, was converted into the right to receive a pro rata portion of the Closing Consideration and the contingent right to receive a pro rata portion of the Earnout Shares and Earnout Cash. Pursuant to the terms of the Merger Agreement, NeuroRx’s securityholders (including option holders and warrant holders) who own NeuroRx securities immediately prior to the Effective Time will have the contingent right to receive their pro rata portion of (i) an aggregate of 25,000,000 shares of Common Stock (“Earnout Shares”), of which 935,608 and 1,920,492 are subject to the terms and conditions of the Substitute Options and Substitute Warrants, if, prior to December 31, 2022, the NeuroRx COVID-19 Drug (i.e., ZYESAMI TM TM TM In the event that either the Earnout Shares Milestone or the Earnout Cash Milestone does not occur prior to December 31, 2022, each Substitute Option and Substitute Warrant will be adjusted such that the number of shares of Common Stock subject to each adjusted Substitute Option or Substitute Warrant, the exercise price per share of each adjusted Substitute Option or Substitute Warrant and the aggregate intrinsic value of each adjusted Substitute Option or Substitute Warrant will equal the respective number of shares, exercise price per share and aggregate intrinsic value that would have resulted following the adjustment of the applicable underlying such option or warrant had the conversion of the legacy NeuroRx option and warrants into the Substitute Options or Substitute Warrants been applied using the Exchange Ratio (3.16:1). If neither the Earnout Shares Milestone nor the Earnout Cash Milestone occurs, each Substitute Option and Warrant will be adjusted based on the Exchange Ratio. If any Substitute Options or Substitute Warrants are exercised prior to the earlier of (i) the date that both the Earnout Shares Milestone and Earnout Cash Milestone occur and (ii) December 31, 2022, a sufficient number of shares of Common Stock will be held in escrow pending the applicable adjustment to such Substitute Options or Substitute Warrants. Following the determination of that adjustment, NRx Pharmaceuticals will retain any shares forfeited by the option or warrant holder in connection with the adjustment and return any remaining shares to the option or warrant holder. In connection with the Merger, a number of subscribers (each, a “Subscriber”) purchased from the Company an aggregate of 1,000,000 shares of Common Stock (the “PIPE”), for a purchase price of $10.00 per share and an aggregate purchase price of $10,000,000 (the “PIPE Shares”), pursuant to separate subscription agreements (each, a “Subscription Agreement”) entered into prior to the Closing Date. The following table reconciles the elements of the Merger to the Unaudited Condensed Consolidated Statement of Cash Flows for the six months ended June 30, 2021: ​ ​ ​ ​ ​ Recapitalization Cash - BRPA trust and cash, net of redemptions ​ $ 4,362,474 Cash - PIPE financing, net of transaction costs ​ 8,100,000 Less: transaction costs and advisory fees allocated to NRXP equity ​ (1,412,846) Effect of Merger, net of redemptions and transaction costs ​ $ 11,049,628 ​ The following table reconciles the elements of the Merger to the Unaudited Condensed Consolidated Statements of Changes in Stockholders' Equity (Deficit) for the six months ended June 30, 2021: ​ ​ ​ ​ ​ Recapitalization Cash - BRPA trust and cash, net of redemptions ​ $ 4,362,474 Non-cash net working capital assumed from BRPA ​ (961,555) Less: notes payable assumed from BRPA ​ (1,100,000) Less: fair value of assumed Placement Warrants ​ (1,983,674) Less: fair value of Earnout Cash ​ (25,520,195) Less: transaction costs and advisory fees allocated to NRXP equity ​ (1,412,846) Effect of Merger, net of redemptions and transaction costs ​ $ (26,615,796) ​ The following table details the number of shares of common stock issued immediately following the consummation of the Merger: ​ ​ ​ ​ Number of Shares Common stock, outstanding prior to Merger 552,412 Less: redemption of BRPA shares (216) Common stock of BRPA 552,196 BRPA Founder and private shares, net of forfeited shares of 875,216 1,260,284 Shares issued in PIPE Financing 1,000,000 Shares issued for services 200,000 Shares issued pursuant to conversion of Public and Private Rights 717,250 Merger and PIPE financing shares - common stock 3,729,730 NeuroRx shares - common stock (1) 44,873,855 Total shares of common stock immediately after Merger 48,603,585 ​ (1) The number of NeuroRx common stock was determined from the 14,200,586 shares of NeuroRx common stock outstanding immediately prior to the closing of the Merger converted at the Exchange Ratio. All fractional shares were rounded down.

Prepaid Expenses and Other Curr

Prepaid Expenses and Other Current Assets	6 Months Ended
	Jun. 30, 2021
Prepaid Expenses and Other Current Assets
Prepaid Expenses and Other Current Assets	5. Prepaid Expenses and Other Current Assets Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 December 31, 2020 Prepaid expenses and other current assets: ​ (Unaudited) ​ Prepaid insurance ​ $ 3,347,172 ​ $ 49,029 Prepaid manufacturing expenses ​ 1,407,500 ​ — Other prepaid expenses ​ 341,336 ​ 164,772 Prepaid income taxes ​ 51,642 ​ — Other current assets ​ — ​ $ 26,551 Total accrued and other current liabilities ​ $ 5,147,650 ​ $ 240,352 ​

Accrued and Other Current Lia_4

Accrued and Other Current Liabilities	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Accrued and other current liabilities
Accrued and Other Current Liabilities	6. Accrued and Other Current Liabilities Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Accrued and other current liabilities: ​ ​ ​ ​ ​ ​ Accrued research and development expenses $ 826,442 $ 586,426 Accrued employee expenses ​ ​ 77,196 ​ ​ 530,500 Professional services ​ 185,170 ​ 606,553 Other accrued expenses ​ 417,529 ​ 5,004 Total accrued and other current liabilities ​ $ 1,506,337 ​ $ 1,728,483 ​	4. Accrued and Other Current Liabilities Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Accrued and other current liabilities: ​ ​ Professional services ​ $ 606,553 ​ $ — Accrued research and development expenses ​ 586,426 ​ — Accrued employee expenses ​ 530,500 ​ — Other accrued liabilities ​ 5,004 ​ 9,649 Total accrued and other current liabilities ​ $ 1,728,483 ​ $ 9,649 ​

Convertible Notes Payable_2

Convertible Notes Payable	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Convertible Notes Payable [Member]
Convertible Notes Payable	7. Convertible Notes Payable On February 12, 2020, a Qualified Financing Event (as defined below) occurred when the Company received cumulative investment proceeds in excess of $10,000,000 from the sale and issuance of common shares. The fair value of the Company’s common shares was $10.63 per share. The 2017 Notes (as defined below) and the 2018 Notes (as defined below) in the aggregate principal amount of $2,800,000 were converted into 1,005,458 common shares (at the discounted price of $2.78 per share), and the related unpaid and accrued interest totaling $369,660 were also converted into 132,739 common shares of the Company (at the discounted price of $2.78 per share). Additionally, the Company recognized a loss on extinguishment for the difference between the carrying value of the convertible notes, unamortized debt discount, and the value of the embedded put option and the fair value of the common shares of $0 and $306,641 during the three months ended and six months ended June 30, 2020, respectively. The Company issued the shares of common stock pursuant to this conversion on September 23, 2020. 2017 Convertible Notes Payable On November 16, 2017 and November 19, 2017, the Company issued convertible notes (“2017 Notes”), as amended for aggregate gross proceeds of $2,500,000. The 2017 Notes accrued interest at a rate of 6% per annum and principal and interest were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. 2018 Convertible Notes Payable On January 5, 2018 and April 25, 2018, the Company issued convertible notes (“2018 Notes”), as amended for aggregate gross proceeds of $300,000. The 2018 Notes accrued interest at a rate of 6% per annum and were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. The January 5, 2018 note for $100,000 was not amended and interest was unpaid, as such, that note and related accrued interest were classified as current liabilities. The April 25, 2018 note for $200,000 was amended similar to the 2017 Notes to accrue interest and to be paid at maturity with the principal. The proceeds received upon issuing the 2017 Notes and 2018 Notes were first allocated to the fair value of the embedded put with the remainder to the debt host instrument. The Company recognized a loss of $0 and $0 during the three months ended June 30, 2021 and 2020, respectively, and $0 and $27,160 during the six months ended June 30, 2021 and 2020, respectively, due to the estimated increase in fair value of the embedded put. The discount is amortized to interest expense over the term of the debt. The Company amortized debt discount of $0 to interest expense during the three months ended June 30, 2021 and 2020, and $0 and $16,454 during the six months ended June 30,2021 and 2020, respectively. The Company paid no interest during the three months ended and six months ended June 30, 2021 and 2020.	5. Convertible Notes Payable ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Convertible Notes: ​ ​ ​ ​ ​ ​ 2017 convertible notes payable due November 2021 ​ $ — ​ $ 2,500,000 2018 convertible note payable due January 2022 ​ — ​ 100,000 2018 convertible notes payable due April 2022 ​ — ​ 200,000 Fair value of embedded put ​ — ​ 738,602 Debt discount ​ — ​ (296,437) Carrying value of convertible notes ​ $ — ​ $ 3,242,165 Accrued interest ​ — ​ 349,891 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056 ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Convertible Notes: ​ ​ Convertible notes payable and accrued interest, current ​ $ — ​ $ 130,251 Convertible notes payable and accrued interest, non-current ​ — ​ 3,461,805 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056 ​ On February 12, 2020, a Qualified Financing Event (as defined below) occurred when the Company received cumulative investment proceeds in excess of $10,000,000 from the sale and issuance of common shares. The fair value of the Company’s common shares were $11.00 per share. The 2017 Notes (as defined below) and the 2018 Notes (as defined below) in the aggregate principal amount of $2,800,000 were converted into 318,183 common shares (at the discounted price of $8.80 per share), and the related unpaid and accrued interest totaling $369,660 were also converted into 42,006 common shares of the Company (at the discounted price of $8.80 per share). Additionally, the Company recognized a loss on extinguishment for the difference between the carrying value of the convertible notes, unamortized debt discount, and the value of the embedded put option and the fair value of the common shares issued of $306,641 during the year ended December 31, 2020. 2017 Convertible Notes Payable On November 16, 2017 and November 19, 2017, the Company issued convertible notes (“2017 Notes”), as amended for aggregate gross proceeds of $2,500,000. The 2017 Notes accrued interest at a rate of 6% per annum and principal and interest were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. 2018 Convertible Notes Payable On January 5, 2018 and April 25, 2018, the Company issued convertible notes (“2018 Notes”), as amended for aggregate gross proceeds of $300,000. The 2018 Notes accrued interest at a rate of 6% per annum and were due and payable four years from the date of issuance. Upon either a sale of the Company’s assets or all of its capital stock, or a change of control, the principal balance would double and be repaid. Upon closing of either a sale of the Company’s shares for at least $10,000,000 or a public offering of the Company’s securities (“Qualified Financing Event”), the outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price. The January 5, 2018 note for $100,000 was not amended and interest was unpaid, as such, that note and related accrued interest were classified as current liabilities. The April 25, 2018 note for $200,000 was amended similar to the 2017 Notes to accrue interest and to be paid at maturity with the principal. Upon closing of a public offering of the Company’s common stock, each of the 2017 Notes and 2018 Notes settle by providing the holder with a variable number of shares sold in the offering with an aggregate fair value determined by reference to the debt principal. In this scenario, the value that the holder receives at settlement does not vary with the value of the Company’s common stock, so the settlement provision was not a typical conversion option. Rather, the share settlement feature was considered a contingent redemption provision (i.e., a contingent embedded put). The Company evaluated the embedded put features in accordance with ASC 815-15-25. The embedded puts are not clearly and closely related to the debt host instrument and therefore have been separately measured at fair value, with subsequent changes in fair value recognized in the Statement of Operations. The proceeds received upon issuing the 2017 Notes and 2018 Notes were first allocated to the fair value of the embedded put with the remainder to the debt host instrument. The Company recorded a $493,982 and $57,204 debt discount upon issuance of the 2017 and 2018 convertible notes, respectively. The Company recognized a loss of $27,160 and $162,866 during the years ended December 31, 2020 and 2019, respectively, due to the estimated increase in fair value of the embedded put. Management used a scenario-based analysis to estimate the fair value of the embedded put features at issuance of the 2017 Notes and 2018 Notes and as of December 31, 2019. The discount is amortized to interest expense over the term of the debt. The Company amortized debt discount of $16,475 and $130,433 to interest expense during the years ended December 31, 2020 and 2019, respectively. The Company paid no interest during the years ended December 31, 2020 and 2019.

Notes Payable_2

Notes Payable	6 Months Ended
	Jun. 30, 2021
Notes Payable.
Notes Payable	8. Notes Payable Note Payable — Related Party On July 1, 2019, the Company converted certain accounts payable into a loan (the “Note Payable — Related Party”) with a related party in the amount of $154,190. The loan, in the form of a promissory note, matures on July 1, 2020. The principal amount of the loan and any accrued but unpaid interest shall be due and payable beginning July 1, 2019. All payments shall be applied first to accrued but unpaid interest, and then to outstanding principal. If not sooner paid, the entire remaining indebtedness (including accrued interest) shall be due and payable on July 1, 2020. The loan bears interest, compounded daily, at 6% annual interest. The loan continues to accrue interest as it was not paid off upon maturity. Relief Therapeutics Loan On April 6, 2020, the Company entered into a loan agreement with Relief Therapeutics (the “Relief Therapeutics Loan”) in the amount of $500,000. The loan matures on April 6, 2022 and bears interest at 2% per annum payable in arrears. Paycheck Protection Program Loan On April 28, 2020, the Company received $119,842 in loan funding from the Paycheck Protection Program (the “PPP Loan”), established pursuant to the Coronavirus Aid, Relief, and Economic Security Act (the “CARES Act”) and administered by the U.S. Small Business Administration (“SBA”). The unsecured PPP Loan accrues interest on the outstanding principal at the rate of 1% per annum, and there is a six month deferment period until equal installment payments of $6,744 of principal and interest are due. The term of the PPP Loan is two years. To the extent the loan amount is not forgiven under the PPP, the Company is obligated to make equal monthly payments of principal and interest, beginning seven months from the date of the Note, until the maturity date. The Loan amount may be eligible for forgiveness pursuant to (1) at least 75% of the loan proceeds are used to cover payroll costs and the remainder is used for mortgage interest, rent and utility costs over the eight week period after the loan is made, and (2) the number of employees and compensation levels are generally maintained. Forgiveness of the loan is dependent on the Company having initially qualified for the loan and qualifying for the forgiveness of such loan based on future adherence to the forgiveness criteria. The Company used the entire PPP Loan for qualifying payroll expenses, and filed for loan forgiveness on December 30, 2020. The Company received full forgiveness of all outstanding principal and accrued and unpaid interest on the PPP Loan as of February 11, 2021. The forgiveness of the PPP Loan qualified for debt extinguishment in accordance with ASC 470-50, Debt Modifications and Extinguishments The following table summarizes the Company's outstanding notes payable as of the respective periods. ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Note Payable — Related Party ​ $ 154,190 ​ $ 154,190 Relief Therapeutics Loan ​ 500,000 ​ 500,000 Paycheck Protection Program Loan ​ — ​ 119,842 Carrying value of notes payable ​ 654,190 ​ 774,032 Accrued interest ​ ​ 31,976 ​ ​ 22,656 Note payable ​ ​ 686,166 ​ ​ 796,688 Notes payable and accrued interest, current ​ $ 173,694 ​ $ 248,861 Notes payable and accrued interest, non-current ​ $ 512,472 ​ $ 547,827 ​

Commitments and Contingencies_2

Commitments and Contingencies	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	9. Commitments and Contingencies Operating Lease The Company leases office space on a month-to-month basis. The rent expense for the three months ended June 30, 2021 and 2020 was $48,776 and $9,087, respectively, and for the six months ended June 30, 2021 and 2020 was $55,393 and $17,902, respectively. Sponsored Research Agreement with National Jewish Health On February 8 2021, the Company entered into a Sponsored Research Agreement (“Research Agreement”) with National Jewish Health (“NJ Health”), a Colorado not-for-profit institution. Under the terms of the Research Agreement, NRx Pharmaceuticals agreed to sponsor a research study at NJ Health relating to the impact of NRx Pharmaceuticals' Aviptadil on propagation of SARS-CoV-2 in alveolar type II cells in vitro (the “Study”). In return for performance of the Study under the Research Agreement, NRx Pharmaceuticals has committed to pay NJ Health approximately $360,450. During the three months ended and six months ended June 30, 2021, NRx Pharmaceuticals paid NJ Health $0 and $126,157, respectively, of the total committed amount. Aviptadil Manufacturing, Production, Supply and Distribution Agreements On August 25, 2020, NRx Pharmaceuticals and Nephron Pharmaceuticals Corporation (“Nephron”) signed an agreement for the manufacturing of finished pharmaceutical product of Aviptadil intravenous formulation and the development of an inhaled (nebulizer) formulation of Aviptadil. Nephron will serve as the exclusive and primary supplier of the product for both clinical and commercial purposes, supplying 100% of the Company’s annual requirements. The Company has agreed to purchase products from Nephron for a fixed price. On September 29, 2020, NRx Pharmaceuticals and Cardinal Health signed an exclusive distribution agreement, as well as a 3rd party logistics agreement on October 1, 2020. Cardinal Health will manage warehousing, distribution, invoicing for the potential sale of Aviptadil in the United States and Puerto Rico. On October 9, 2020, NRx Pharmaceuticals signed an agreement with Polypeptide for the supply of GMP grade Active Pharmaceutical Ingredient (API) Aviptadil (VIP). This gives NRx Pharmaceuticals a second source of procuring API. The Company has agreed to purchase a total of $1,010,000 worth of product and services over the contract. On January 4, 2021 NRx Pharmaceuticals and Aerogen Limited (“Aerogen”) signed a supply agreement for the supply of certain products, including the Aerogen Solo Nebulizer System and Aerogen Ultra, solely for the purposes of carrying out clinical trials relating to inhalation delivery of Aviptadil for treatment of pulmonary insufficiency and respiratory distress in COVID-19 patients. Pill Tracker is an agent of NRx Pharmaceuticals per the supply agreement (see Note 14). Relief Therapeutics Collaboration Agreement On September 18, 2020, the Company entered into a collaboration agreement with Relief for the clinical development and if approved the sale of Aviptadil. The collaboration provides for funding by Relief of certain clinical trials. If such candidate is approved by the FDA, the Company shall receive 50% of net product profits from the product sales in the NRx Pharmaceuticals territory, which includes the United States, Canada, and Israel; 15% of net product profits from the product sales in the Relief Therapeutics territory, which includes the European Union, Switzerland, Iceland, Norway, the UK, the Channel Islands, Liechtenstein, Monaco, Andorra, Malta, San Marino, and Vatican City; and 20% of net product profits from the product sales in all other countries. During 2021, the Company invoiced Relief $5,984,679 for reimbursable expenses and received $770,444 in payments from Relief for these reimbursable expenses. The Company recorded an allowance for doubtful accounts of $5,470,897 as of June 30, 2021, due to the fact that the Company does not expect to receive payment for the remaining invoices, thus fully reserving for the accounts receivable balance. As of the date of this filing, Relief has reimbursed NRx Pharmaceuticals $10,904,065 for expenses, but has subsequently declined to pay approximately $6 million in invoiced costs associated with conduct of the IV clinical trial, reformulation, and manufacture of ZYESAMI TM Share Subscription Facility Agreement — GEM NeuroRx previously entered into a share subscription facility agreement (“GEM Agreement”) with GEM Global Yield LLC SCS and GEM Yield Bahamas Limited (collectively, referred to as “GEM”) with a three-year term. Subject to the successful listing of the shares of NeuroRx on an Exchange (any nationally recognized stock exchange or exchange platform in the world on which the Company will list its shares), GEM grants NeuroRx an option to require GEM to subscribe for shares from the Company for up to an aggregate value of approximately $95.6 million. The agreement also included certain provisions which would not meet the U.S. requirements to issue registered shares. If NeuroRx was listed or completes a private transaction which results in a change of control of the Company, NeuroRx would issue GEM a warrant and pay a commitment fee of $1.9 million. Absent a listing of NeuroRx shares or a private transaction with a change of control during the three-year term, NeuroRx would have no obligations under the agreement. The reverse merger contemplated by the Merger Agreement would not have resulted in a listing of NeuroRx shares or a change in control. In November 2020, GEM introduced NeuroRx to BRPA. To resolve uncertainties around the application of the GEM Agreement post-Merger, NeuroRx and GEM agreed in March 2021 to issue a warrant to GEM and for the parties to use their good faith efforts to amend the GEM Agreement to meet U.S. requirements to issue registered shares. The warrant is not conditional upon any further events or completion of the merger. The warrant was issued March 28, 2021, for 3,329,812 shares of NeuroRx common stock at an exercise price of $3.19 per share (the “GEM Warrant”) and the parties agreed that GEM would immediately partially exercise the warrant for the purchase of 1,496,216 shares (“Initial Exercised Shares”) for $7,500,018. The GEM Warrant will be valid for a period of three years from the date NeuroRx’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction of the type contemplated by the Merger Agreement. This contingent liability at December 31, 2020, represented an obligation that resulted in the issuance of certain equity at a discounted per share price. As the amount was deemed probable and estimable at December 31, 2020, NeuroRx recorded a liability of $39,486,139 to reflect the fair value of the GEM Warrant. On March 28, 2021, NeuroRx recorded additional settlement liability of $21,365,641 to reflect the change in the fair value of the Company’s common stock. On March 28, 2021, NeuroRx reclassed the settlement liability to equity upon the issuance of the GEM Warrant. NeuroRx was required to register the Initial Exercised Shares on (a) the same registration statement on Form S-4 (or such other registration statement, if changed) in connection with the Merger, or (b) such other registration statement in connection with any other transaction which results in a public listing of NeuroRx. In addition, no later than 90 days following the consummation of the Big Rock merger, the Company was required to file with the SEC a registration statement to register under the Securities Act the resale by GEM of all shares issuable under the GEM Warrant other than the Initial Exercised Shares, which was filed with the Company's S-1 in July 2021. The GEM Warrant also includes “piggyback” registration rights. Subsequent to June 30, 2021, GEM exercised the remaining GEM Warrant for the purchase of 1,833,596 shares (adjusted for the Merger, discussed in Note 10) for gross proceeds to the Company of $9,186,316 and the GEM Warrant was extinguished.	7. Commitments and Contingencies Operating Lease The Company leases office space on a month-to-month basis. The rent expense for the years ended December 31, 2020 and 2019 was $54,649 and $42,040, respectively. Litigation —  Settlement Liability In September of 2018, Sarah Herzog Memorial Hospital Ezrat Nashim filed suit against NeuroRx, Inc., the founding shareholders alleging a dispute as to the ownership and use of intellectual property related to anti-depressants and anti-psychotics. Prior to service of the lawsuit, in December of 2018 all parties to the referenced action submitted to voluntary non-binding mediation, and reached an agreement in principle to settle the matter. The agreement provided for licensing of certain technology (“Herzog License”), future low single digit royalties upon commercialization, certain milestone payments and the transfer of 500,000 shares of NeuroRx, Inc. common stock to Sarah Herzog Memorial Hospital Ezrat Nashim (250,000 of which were transferred from the Jonathan Javitt Living Trust and 250,000 of which were transferred from Glytech, LLC a company wholly owned by Daniel Javitt). The milestone payments for developmental and commercial milestones each range from $100,000 to $750,000. Annual maintenance fees range up to $150,000. At December 31, 2018, the Company accrued $5,616,732 (representing the fair value of such shares of $5,500,000 and legal costs of $116,732) as settlement liability expense. The final settlement was signed in April 2019, pursuant to which, 500,000 shares were transferred to Herzog with an approximate fair value of $5,500,000. This charge was recorded pursuant to ASC 260, which deems consideration paid by control parties to have been paid by the Company. In connection with this settlement, 300,000 founder shares were returned to the Company and retired in 2019. In October of 2019, the founding shareholders of the Company transferred 45,454 shares of common stock with a fair value of $499,994 to a former adviser to release and discharge the Company from any obligation to the former adviser or transfer any additional securities. This charge was recorded as of September 30, 2019, by the Company as consulting expense even though the consideration was paid from the stock accounts of the founders without dilution to the Company pursuant to ASC 260, which deems consideration paid by control parties to have been paid by the Company. As of December 31, 2020, there was no further litigation against the Company. Milestone Payments Pursuant to the legal settlement, which included the license of intellectual property rights from SHMH, an ongoing royalty of 1% — 2.5% of NRX-101 gross sales shall be due SHMH, together with milestone payments of $250,000, upon completion of phase 3 trials and commercial sale of NRX-101. The milestone payments for developmental and commercial milestones each range from $100,000 to $750,000. Annual maintenance fees range up to $150,000. Aviptadil Manufacturing, Production and Distribution Agreements On August 25, 2020, NeuroRx and Nephron Pharmaceuticals Corporation (“Nephron”) signed an agreement for the manufacturing of finished pharmaceutical product of Aviptadil intravenous formulation and the development of an inhaled (nebulizer) formulation of Aviptadil. Nephron will serve as the exclusive and primary supplier of the product for both clinical and commercial purposes, supplying 100% of the Company’s annual requirements. The Company has agreed to purchase products from Nephron for a fixed price. On September 29, 2020, NeuroRx and Cardinal Health signed an exclusive distribution agreement, as well as a 3rd party logistics agreement on October 1, 2020. Cardinal Health will manage warehousing, distribution, invoicing for the potential sale of Aviptadil in the United States and Puerto Rico. On October 9, 2020, NeuroRx signed an agreement with Polypeptide for the supply of GMP grade Active Pharmaceutical Ingredient (API) Aviptadil (VIP). This gives NeuroRx a second source of procuring API. The Company has agreed to purchase a total of $1,010,000 worth of product and services over the contract. Relief Therapeutics Collaboration Agreement On September 18, 2020, the Company entered into a collaboration agreement with Relief for the clinical development and if approved the sale of Aviptadil. The collaboration provides for funding by Relief of certain clinical trials. If such candidate is approved by the FDA, the Company shall receive 50% of net product profits from the product sales in the NeuroRx territory, which includes the United States, Canada, and Israel; 15% of net product profits from the product sales in the Relief Therapeutics territory, which includes the European Union, Switzerland, Iceland, Norway, the UK, the Channel Islands, Liechtenstein, Monaco, Andorra, Malta, San Marino, and Vatican City; and 20% of net product profits from the product sales in all other countries. During 2020, the Company invoiced Relief $10,160,421 for reimbursable expenses and received $9,329,031 in payments from Relief for these reimbursable expenses. As of December 31, 2020, the Company had an accounts receivable balance due from Relief of $831,390, net of an allowance for doubtful accounts of $257,463. As of May 11, 2021, Relief has reimbursed NeuroRx $10,612,750 for expenses, but has not paid approximately $4,000,000 in invoiced costs associated with conduct of the IV clinical trial, reformulation, and manufacture of ZYESAMI. As of May 11, 2021, Relief has not funded the costs of the inhaled trial. NeuroRx has advised Relief that NeuroRx is funding those costs with other capital. Share Subscription Facility Agreement - GEM The Company previously entered into a share subscription facility agreement (“GEM Agreement”) with GEM Global Yield LLC SCS and GEM Yield Bahamas Limited (collectively, referred to as “GEM”) with a three-year term. Subject to the successful listing of the shares of NeuroRx on an Exchange (any nationally recognized stock exchange or exchange platform in the world on which the Company will list its shares), GEM grants the Company an option to require GEM to subscribe for shares from the Company for up to an aggregate value of approximately $95.6 million. The agreement also included certain provisions which would not meet the U.S. requirements to issue registered shares. If NeuroRx was listed or completes a private transaction which results in a change of control of the Company, the Company would issue GEM a warrant and pay a commitment fee of $1.9 million. Absent a listing of NeuroRx shares or a private transaction with a change of control during the three-year term, the Company would have no obligations under the agreement. A reverse merger would not result in a listing of NeuroRx shares or a change in control. In November 2020, GEM introduced the Company to Big Rock. Although the Company has taken the position that the reverse merger transaction contemplated by the Merger Agreement (as defined below) would not require the issuance of the warrant, to resolve uncertainties around the application of the GEM Agreement, the Company and GEM agreed in March 2021 to issue a warrant to GEM and for the parties to use their good faith efforts to amend the GEM Agreement to meet U.S. requirements to issue registered shares. The warrant is not conditional upon any further events or completion of the merger. The warrant was issued March 28, 2021, for 1,053,738 shares of NeuroRx common stock at an exercise price of $15.84 per share (the “GEM Warrant”) and the parties agreed that GEM would immediately partially exercise the warrant for the purchase of 473,486 shares (“Initial Exercised Shares”) for $7.5 million. The GEM Warrant will be valid for a period of three years from the date the Company’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction. This contingent liability at December 31, 2020, represented an obligation that resulted in the issuance of certain equity at a discounted per share price. As the amount was deemed probable and estimable by the Company at December 31, 2020, the Company recorded a liability of $39,486,139 to reflect the fair value of the GEM Warrant. The Company is required to register the Initial Exercised Shares on (a) the same registration statement on Form S-4 (or such other registration statement, if changed) in connection with the Big Rock merger, or (b) such other registration statement in connection with any other transaction which results in a public listing of the Company. In addition, no later than 90 days following the consummation of the Big Rock merger, the Company is required to file with the SEC a registration statement to register under the Securities Act the resale by GEM of all shares issuable under the GEM Warrant other than the Initial Exercised Shares. The GEM Warrant also includes “piggyback” registration rights. Merger with Big Rock Partners Acquisition Corp. On December 13 2020, the Company entered into an Agreement and Plan of Merger (“Merger Agreement”) with Big Rock. Under the terms of the transaction, Big Rock will issue to NeuroRx’s current equity holders an aggregate of 50 million shares (“Per Share Merger Consideration”) of Big Rock common stock for their interests in NeuroRx. Subject to certain conditions, an aggregate of 25 million additional shares of Big Rock common stock (“Earnout Shares”) will be issued to NeuroRx pre-merger equity holders if, prior to December 31, 2022, (1) the Company’s COVID-19 drug receives emergency use authorization by the FDA and (2) the FDA accepts the Company’s filing of its application to approve the Company’s COVID-19 drug. In addition, subject to certain conditions, $100 million (“Earnout Cash”) may be payable to NeuroRx pre-merger equity holders if, prior to December 31, 2022, either (1) FDA approval of the Company’s COVID-19 Drug is obtained and the Company’s COVID-19 Drug is listed in the FDA’s “Orange Book” and (2) FDA approval of the Company’s Antidepressant Drug Regimen is obtained and the Company’s Antidepressant Drug Regimen is listed in the FDA’s “Orange Book”. The Boards of Directors of both NeuroRx and Big Rock have unanimously approved the proposed transaction. Completion of the transaction is subject to approval by stockholders of NeuroRx and Big Rock and other customary closing conditions.

Equity_2

Equity	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Equity
Equity	10. Equity Common Stock Upon closing of the Merger, pursuant to the terms of the Second Amended and Restated Certificate of Incorporation, the Company authorized 500,000,000 shares of common stock with a par value $0.001. As discussed in Note 4, we have retroactively adjusted the shares issued and outstanding prior to May 24, 2021 to give effect to the Exchange Ratio established in the Merger Agreement to determine the number of shares of common stock into which they were converted. The Company sold 65,526 and 0 shares of common stock during the three months ended June 30, 2021 and 2020, respectively, and received gross proceeds of $1,436,274 and $0, respectively. The Company sold 398,647 and 50,844 shares of common stock during the six months ended June 30, 2021 and 2020, respectively, and received gross proceeds of $8,363,132 and $176,990, respectively. Pursuant to the Merger Agreement, BRPA and EarlyBirdCapital, Inc., the representative of the underwriters of BRPA’s initial public offering (“EBC”), entered into an amendment (“BCMA Amendment Agreement”) to the Business Combination Marketing Agreement, dated as of November 20, 2017 (“BCMA”), by and between BRPA and EBC. The BCMA Amendment Agreement provided that, in lieu of the cash fee payable to EBC pursuant to the BCMA, BRPA will issue to EBC at the Effective Time an aggregate of 200,000 shares of Common Stock and the BCMA (as amended by the BCMA Amendment Agreement) will terminate immediately following the Effective Time. The Company recognized the fair value of the 200,000 shares of Common Stock issued pursuant to the BCMA of $4,850,000 within general and administrative in the Unaudited Condensed Consolidated Statements of Operations for the three and six months ended June 30, 2021. Preferred Stock Upon closing of the Merger, pursuant to the terms of the Second Amended and Restated Certificate of Incorporation, the Company authorized 50,000,000 shares of preferred stock with a par value $0.001. Series A, B-1, and B-1A Preferred Stock Prior to the Merger, the Company had authorized and issued 1,000,000 shares of Series A convertible preferred stock, 1,050,695 shares of Series B-1 convertible preferred stock, and 316,848 shares of Series B-1A convertible preferred stock, par value of $0.001 per share, which was convertible into one share of common stock for each preferred share (collectively, the “Preferred Stock”) at any time, at the option of the holder. The Preferred Stock were not redeemable and the related stockholders were entitled to a subordinated liquidation preference should NeuroRx liquidate or wind up operations. The preferences also included voting rights on an as-converted basis, ride-along rights, and an anti-dilution provision. The liquidation preference was $1.00 per share for the Series A convertible preferred stock, $7.58 per share for the Series B-1 convertible preferred stock, and $6.82 per share for the Series B-1A convertible preferred stock, plus any declared but unpaid dividends. Upon an initial public offering or merger under certain conditions the Preferred Stock automatically converted into common stock. On May 24, 2021, pursuant to the Merger (as described in Note 4), 2,367,543 outstanding shares of Preferred Stock were automatically converted into 7,480,836 shares of common stock pursuant to the Exchange Ratio. Series B-2 Preferred Stock In 2020, the Company authorized the issuance of 100,000 shares of Series B-2 Convertible Preferred Stock (the “B-2 Preferred Stock”), par value of $0.001 per share, convertible into one share of common stock for each share of B-2 Preferred Stock held. In March 2020, 4,167 shares of B-2 Preferred Stock were issued. The B-2 Preferred stock were not redeemable and the related stockholders were entitled to a subordinated liquidation preference should NeuroRx liquidate or wind up operations. The preferences also included voting rights on an as-converted basis, ride-along rights, and an anti-dilution provision. The liquidation preference was $12.00 per share plus any declared but unpaid dividends. The B-2 Preferred Stock could be converted into one share of common stock (subject to adjustments for stock splits, recapitalization) at any time, at the option of the holder. Upon an initial public offering or merger under certain conditions the B-2 Preferred Stock automatically converted into common stock. On May 24, 2021, pursuant to the Merger (as described in Note 4), 4,167 outstanding shares of B-2 Preferred stock were automatically converted into 13,168 shares of common stock pursuant to the Exchange Ratio. Common Stock Warrants On March 28, 2021, NeuroRx issued 3,329,812 fully vested common stock warrants, exercisable at a per share price of $3.19 until they expire on March 27, 2024 to GEM (See Note 8). The fair value on the date of issuance was $60,851,779. Upon issuance, 1,496,216 warrants were immediately exercised generating gross proceeds of $7,500,018. Subsequent to June 30, 2021, GEM exercised the remaining GEM Warrant for the purchase of 1,833,596 shares for gross proceeds of $9,186,316 and the GEM Warrant was extinguished. The grant date fair value of common stock warrants is determined using the Black Scholes option-pricing model. The Company estimates its expected stock volatility based on historical volatility of publicly traded peer companies. The estimated fair value of common stock is based on sales to third parties. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ 2021 ​ 2020 Strike price ​ $ 24.25 $ 3.19 ​ Volatility rate ​ 80.0 % ​ 80.0 % Risk-free rate ​ 0.03%-0.32 % ​ 0.19%-0.28 % Expected term ​ 0.57-4.42 ​ 3.00-5.00 ​ Dividend yield ​ — ​ — ​ ​ Substitute Warrants In connection with the Merger, each warrant of NeuroRx that was outstanding and unexercised immediately prior to the Effective Time (whether vested or unvested) was assumed by BRPA and converted into the Substitute Warrants, based on the Option Exchange Ratio (of 4.96), and will continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the former warrant. Each Substitute Warrant will be exercisable for a number of whole shares of Common Stock equal to the product of the number of shares of NeuroRx common stock underlying such NeuroRx warrant multiplied by the Option Exchange Ratio, and the per share exercise price of such Substitute Warrant will be equal to the quotient determined by dividing the exercise price per share of NeuroRx common stock by the Option Exchange Ratio. As discussed in Note 4, this ratio incorporates the achievement of the Earnout Shares Milestone and Earnout Cash Milestone. The incremental shares above the Exchange Ratio (of 3.16) upon exercise would be held back pending the outcome of the contingencies and only released if such are achieved. The percentage of total shares of Common Stock subject to each Substitute Warrant that is vested immediately following the Effective Time will equal the percentage of total shares of NeuroRx common stock subject to each NeuroRx warrant that is vested immediately prior to the Effective Time. In the event that either the Earnout Shares Milestone or the Earnout Cash Milestone does not occur prior to December 31, 2022, each Substitute Warrant will be adjusted such that the number of shares of Common Stock subject to each adjusted Substitute Warrant, the exercise price per share of each adjusted Substitute Warrant and the aggregate intrinsic value of each adjusted Substitute Warrant will equal the respective number of shares, exercise price per share and aggregate intrinsic value that would have resulted following the adjustment of the applicable underlying Substitute Warrant had the conversion of NeuroRx warrants into the Substitute Warrants been applied using the Exchange Ratio (3.16:1) as adjusted accordingly to reflect the impact of the respective milestone not being met. If neither the Earnout Shares Milestone nor the Earnout Cash Milestone occurs, each Substitute Warrant will be adjusted based on the Exchange Ratio. If any Substitute Warrants are exercised prior to the earlier of (i) the date that both the Earnout Shares Milestone and Earnout Cash Milestone occur and (ii) December 31, 2022, a sufficient number of shares of Common Stock will be held back pending the applicable adjustment to such Substitute Warrants. Following the determination of that adjustment, NRx Pharmaceuticals will retain any shares forfeited by the warrant holder in connection with the adjustment and return any remaining shares to the warrant holder. Upon the closing of the Merger, the outstanding and unexercised NeuroRx warrants became warrants to purchase an aggregate 4,909,066 shares of the Company’s common stock with an average exercise price of $2.50 per share. The Company accounted for the Substitute Warrants as a modification of the existing warrants. Incremental fair value, measured as the excess, if any, of the fair value of the modified warrants over the fair value of the original warrants immediately before its terms are modified, is measured based on the fair value of the underlying shares and other pertinent factors at the modification date. The fair value of the original NeuroRx warrants and Substitute Warrants was determined using the Black-Scholes option-pricing model with the following assumptions for each: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Original Warrants Substitute Warrants Strike price ​ $ 7.58-$15.84 ​ $ 1.53-$3.19 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.03%-0.32 % 0.03%-0.32 % Expected term ​ 0.57-4.42 ​ 0.57-4.42 ​ Dividend yield ​ — ​ — ​ ​ With respect to warrants held by certain members of our Board of Directors, the Substitute Warrants were determined to be within the scope of ASC 718 and were fully vested at the Effective Date. Further, the Substitute Warrants were determined to contain both service-based and performance-based vesting conditions (i.e., the achievement of the Earnout Cash and/or Earnout Share Milestones). The Company determined it was not probable that the Earnout Cash or Earnout Share Milestone would be met on the Effective Date and at June 30, 2021. Accordingly, the Company will only recognize incremental compensation cost related to the portion of the Substitute Warrants subject to service-based vesting conditions only. The Company will reevaluate the probability of the Earnout Cash and/or Earnout Share Milestones being met and recognize any unamortized incremental compensation cost accordingly in the period during which it becomes probable the milestones will be met. The Company recognized incremental compensation on the modification date totaling $2,330,572 which was recognized in General and administrative in the Unaudited Condensed Consolidated Statements of Operations for the three and six months ended June 30, 2021, respectively. Unamortized compensation costs related to performance-based vesting conditions of the Substitute Warrants as of the modification date was $23,760,993. With respect to the remaining outstanding warrants, the incremental fair value of the Substitute Warrants of $2,691,799 was recognized as a deemed dividend as the Company concluded there is a transfer of value from the common shareholders to the holders of the Substitute Warrants as the change in the number of underlying shares and the decreased exercise price would result in the common shareholders becoming more diluted if and when the Substitute Warrants are converted. As the Company is in an accumulated deficit position as of the modification date, the resulting deemed dividend is recorded as a reduction of additional paid-in capital with a corresponding offset recorded to additional paid-in capital (i.e., net impact to additional paid-in capital of $0). Further, in the event the Earnout Shares Milestone and Earnout Cash Milestones are met, the Company will recognized an additional deemed dividend of $24,379,657 and $3,068,732, respectively, if and when such conditions are met. Assumed Public Warrants Prior to the Merger, the Company had outstanding 3,450,000 Public Warrants. Each Public Warrant entitles the holder to purchase one The Company may redeem the Public Warrants: ● in whole and not in part; ● at a price of $0.01 per warrant; ● at any time during the exercise period; ● upon a minimum of 30 days ’ prior written notice of redemption; ● if, and only if, the last sale price of the Company’s common stock equals or exceeds $21.00 per share for any 20 trading days within a 30 -trading day period ending on the third business day prior to the date on which the Company sends the notice of redemption to the warrant holders; and ● if, and only if, there is a current registration statement in effect with respect to the shares of common stock underlying such warrants. Certain of the above conditions have not been met to redeem the Public Warrants. If the Company calls the Public Warrants for redemption, management will have the option to require all holders that wish to exercise the Public Warrants to do so on a “cashless basis,” as described in the warrant agreement. The exercise price and number of shares of common stock issuable upon exercise of the warrants may be adjusted in certain circumstances including in the event of a stock dividend, or recapitalization, reorganization, merger or consolidation. However, the warrants will not be adjusted for issuance of common stock at a price below its exercise price. Additionally, in no event will the Company be required to net cash settle the warrants. Assumed Placement Warrants Prior to the Merger, the Company had outstanding 136,250 Placement Warrants. The Placement Warrants are identical to the Public Warrants except that the Placement Warrants (i) are not redeemable by the Company and (ii) may be exercised for cash or on a cashless basis, so long as they are held by the initial purchaser or any of its permitted transferees. If the Placement Warrants are held by someone other than the initial purchasers or their permitted transferees, the Placement Warrants will be redeemable by the Company and exercisable by such holders on the same basis as the Public Warrants. The Placement Warrants are not indexed to the Company’s common shares in the manner contemplated by ASC 815-40-15 because the holder of the instrument is not an input into the pricing of a fixed-for-fixed option on equity shares. The Company classifies the Placement Warrants as derivative liabilities in its Unaudited Condensed Consolidated Balance Sheet as of June 30, 2021. The Company measures the fair value of the warrants at the end of each reporting period and recognizes changes in the fair value from the prior period in the Company’s operating results for the current period. The Company recognized a gain on the change in fair value of the Placement Warrants for the three and six months ended June 30, 2021 and 2020 of $1,468,649 and $0, respectively. Refer to Note 13 for discussion of fair value measurement of the warrant liabilities. The following table provides the activity for all warrants for the respective periods. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Aggregate ​ ​ Total Warrants ​ Term ​ Exercise Price ​ Intrinsic Value Outstanding as of December 31, 2020 (as previously reported) 620,055 11.08 ​ $ 14.61 ​ $ 22,127,594 Retroactive application of reverse recapitalization (Note 4) ​ 2,455,415 ​ — ​ ​ (13.53) ​ ​ — Outstanding as of December 31, 2020, effect of Merger (Note 4) ​ 3,075,470 ​ 4.34 ​ ​ 1.09 ​ ​ 150,955,963 Issued 3,329,812 3.00 ​ 3.19 ​ 111,082,528 Exercised (1,496,216) ​ ​ (3.19) ​ (49,913,766) Outstanding as of March 31, 2021 4,909,066 3.74 ​ $ 1.78 ​ $ 244,574,345 Issued 3,586,250 5.00 ​ 11.50 ​ 45,724,688 Outstanding as of June 30, 2021 8,495,316 4.09 ​ $ 24.78 ​ $ 42,385,824 ​ Assumed Unit Purchase Options Prior to the Merger, the Company had outstanding options to purchase up to 600,000 Units exercisable at $10.00 per Unit (or an aggregate exercise price of $6,000,000) commencing on the Effective Time. Each Unit consists of one one one five Conversion of Rights Prior to the Merger, the Company had outstanding 6,900,000 and 272,500 Public Rights and Placement Rights, respectively. At the Effective Time, each holder of a right received one-tenth (1/10) of one share of Common Stock at the Effective Time, even if the holder of such right redeemed all shares held by it in connection with the Merger, resulting in the issuance of 717,250 shares of Common Stock to holders of such rights. No fractional shares were issued upon conversion of the rights. No additional consideration was required to be paid by a holder of rights in order to receive its additional shares at the Effective Time, as the consideration related thereto has been included in the original unit purchase price paid for by investors in the Company's Initial Public Offering. The shares issuable upon conversion of the rights will be freely tradable (except to the extent held by affiliates of the Company).	8. Equity Common Stock On March 1, 2020, the Company’s board of directors authorized an increase to the authorized share capital from 14,060,001 shares of common stock to 20,000,000 shares of common stock with a par value of $0.001 per share. The Company sold 171,796 and 536,354 shares of common stock during the years ended December 31, 2020 and 2019, respectively and received gross proceeds of $2,579,114 and net proceeds of $5,802,002, respectively. The Company issued 9,500 shares of common stock with a fair value of $144,875 in settlement of accounts payable worth $103,258, and recognized a loss of $41,617 for the difference during the year ended December 31, 2020 and did not issue any such shares during the year ended December 31, 2019. Preferred Stock Series A, B-1, and B-1A Preferred Stock The Company has authorized issued B-1A per share convertible into Series B-2 Preferred Stock In 2020, the Company authorized the issuance of 100,000 shares of Series B-2 Convertible Preferred Stock, par value of $0.001 per share, convertible into one share of Common Stock for each share of Series B-2 Convertible Preferred Stock held. In March 2020, 4,167 Series B-2 stock were issued. The Series B-2 Preferred stock are not redeemable and the related stockholders are entitled to a subordinated liquidation preference should the Company liquidate or wind up operations. The preferences also include voting rights on an as-converted basis, ride-along rights, and an anti-dilution provision. The liquidation preference is $12.00 per share plus any declared but unpaid dividends. The B-2 Convertible Preferred shares can be converted into one share of Common Stock (subject to adjustments for stock splits, recapitalization) at any time, at the option of the holder. Upon an initial public offering or merger under certain conditions the Series B-2 Preferred Stock will automatically convert into common stock. Common Stock Warrants On January 31, 2019, the Company issued 8,846 fully vested common stock warrants, exercisable at a per share price of $11.00 until they expire on January 30, 2024, to a vendor for financial advisory services provided in connection with the sale of the Company’s common stock. The fair value on the date of issuance was $7.16 per warrant for a total fair value of $63,337. On July 6, 2020, the Company issued 4,000 fully vested common stock warrants, exercisable at a per share price of $15.25 until they expire on July 5, 2023, to a vendor for financial advisory services provided in connection with the sale of the Company’s common stock. The fair value on the date of issuance was $7.63 per warrant for a total fair value of $30,536. On July 15, 2020, the Company issued 279,291 fully vested common stock warrants, exercisable at a per share price of $15.25 until they expire on July 14, 2025, to a board member. The fair value on the date of issuance was $9.63 per warrant for a total fair value of $2,689,684. On October 23, 2020, the Company issued 139,645 and 139,645 fully vested common stock warrants, exercisable at a per share price of $15.25 until they expire on October 22, 2025, to a board member, respectively. The fair value on the date of issuance was $9.64 per warrant for a total fair value of $2,693,221. The following table provides the activity in warrants for the respective periods. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Average ​ ​ Total Warrants Term Exercise Price Intrinsic Value Outstanding as of December 31, 2018 ​ 48,627 ​ 2.88 ​ $ 7.90 ​ $ — Issued 8,846 5.00 ​ 11.00 ​ — Outstanding as of December 31, 2019 57,473 2.22 ​ $ 8.38 ​ $ — Issued 562,581 4.99 ​ 15.25 ​ 20,112,271 Outstanding as of December 31, 2020 620,054 11.08 ​ $ 14.61 ​ $ 22,127,594 ​ The grant date fair value of common stock warrants is determined using the Black Scholes option-pricing model. The Company is a private company and estimates its expected stock volatility based on historical volatility of publicly traded peer companies. The estimated fair value of the Company’s common stock is based on sales to third parties. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Strike price $ 15.25 ​ $ 11.00 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.19%-0.28 % 2.40 % Expected term ​ 3.00-5.00 ​ 5.00 ​ Dividend yield ​ — ​ — ​ ​

Stock-Based Compensation_2

Stock-Based Compensation	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Stock-Based Compensation
Stock-Based Compensation	11. Stock-Based Compensation 2016 Omnibus Incentive Plan Prior to the Merger, NeuroRx maintained its 2016 Omnibus Incentive Plan (the “2016 Plan”), under which NeuroRx granted incentive stock options, restricted stock awards, other stock-based awards, or other cash-based awards to employees, directors, and non-employee consultants. The maximum aggregate shares of common stock that was subject to awards and issuable under the 2016 Plan was 3,472,000. In connection with the Merger, each NeuroRx stock option that was outstanding and unexercised immediately prior to the Effective Time (whether vested or unvested) was assumed by BRPA and converted into an option to acquire an adjusted number of shares of Common Stock at an adjusted exercise price per share (the “Substitute Options”), and will continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the former option. In connection with the Merger, each option of NeuroRx that was outstanding and unexercised immediately prior to the Effective Time (whether vested or unvested) was assumed by BRPA and converted into the Substitute Options, based on the Option Exchange Ratio (of 4.96), and will continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the former option. Each Substitute Option will be exercisable for a number of whole shares of Common Stock equal to the product of the number of shares of NeuroRx common stock underlying such NeuroRx option multiplied by the Option Exchange Ratio, and the per share exercise price of such Substitute Option will be equal to the quotient determined by dividing the exercise price per share of NeuroRx common stock by the Option Exchange Ratio. As discussed in Note 4, this ratio incorporates the achievement of the Earnout Shares Milestone and Earnout Cash Milestone. The incremental shares above the Exchange Ratio (of 3.16) upon exercise would be held back pending the outcome of the contingencies and only released if such are achieved. The percentage of total shares of Common Stock subject to each Substitute Option that is vested immediately following the Effective Time will equal the percentage of total shares of NeuroRx common stock subject to each NeuroRx option that is vested immediately prior to the Effective Time. In the event that either the Earnout Shares Milestone or the Earnout Cash Milestone does not occur prior to December 31, 2022, each Substitute Option will be adjusted such that the number of shares of Common Stock subject to each adjusted Substitute Option, the exercise price per share of each adjusted Substitute Option and the aggregate intrinsic value of each adjusted Substitute Option will equal the respective number of shares, exercise price per share and aggregate intrinsic value that would have resulted following the adjustment of the applicable underlying Substitute Option had the conversion of NeuroRx options into the Substitute Options been applied using the Exchange Ratio as adjusted accordingly to reflect the impact of the respective milestone not being met. If neither the Earnout Shares Milestone nor the Earnout Cash Milestone occurs, each Substitute Option will be adjusted based on the Exchange Ratio. As stated in the Merger Agreement, if any Substitute Options are exercised prior to the earlier of (i) the date that both the Earnout Shares Milestone and Earnout Cash Milestone occur and (ii) December 31, 2022, a sufficient number of shares of Common Stock will be held back pending the applicable adjustment to such Substitute Options. Following the determination of that adjustment, NRx Pharmaceuticals will retain any shares forfeited by the option holder in connection with the adjustment and return any remaining shares to the option holder. Upon the closing of the Merger, the outstanding and unexercised NeuroRx stock options became options to purchase an aggregate 2,895,423 shares of the Company’s Common Stock at an average exercise price of $1.50 per share. The Company accounted for the Substitute Options as a modification of the existing options. Incremental compensation costs, measured as the excess, if any, of the fair value of the modified options over the fair value of the original options immediately before its terms are modified, is measured based on the fair value of the underlying shares and other pertinent factors at the modification date. The fair value of the original NeuroRx options and Substitute Options was determined using the Black-Scholes option-pricing model with the following assumptions for each: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Original Options Substitute Options Strike price ​ $ 1.00-$72.30 ​ $ 0.20-$14.58 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.07%-0.79 % 0.07%-0.79 % Expected term ​ 0.18-5.99 ​ 0.18-5.99 ​ Dividend yield ​ — ​ — ​ ​ The Substitute Options contain both service-based and performance-based vesting conditions (i.e., the achievement of the Earnout Cash and/or Earnout Share Milestones). The Company determined it was not probable that the Earnout Cash or Earnout Share Milestone would be met on the Effective Date and at June 30, 2021. Accordingly, the Company will only recognize incremental compensation cost related to the portion of the Substitute Options subject to service-based vesting conditions only. The Company will reevaluate the probability of the Earnout Cash and/or Earnout Share Milestones being met and recognize any unamortized incremental compensation cost accordingly in the period during which it becomes probable the milestones will be met. For vested Substitute Options, the Company recognized incremental compensation on the modification date totaling $1,014,640, of which $993,500 and $21,140 was recognized in General and administrative and Research and development, respectively, in the Unaudited Condensed Consolidated Statements of Operations for the three and six months ended June 30, 2021, respectively. For unvested Substitute Options, the Company will recognize incremental compensation over the remaining requisite service period, the sum of the incremental compensation cost and the remaining unrecognized compensation cost for the original award on the modification date, taking into consideration the probability of the achievement of the Earnout Cash and/or Earnout Share Milestones. Incremental compensation costs related to unvested Substitute Options as of the modification date was $25,877,473. 2021 Omnibus Incentive Plan At the Effective Time, the Company adopted the 2021 Omnibus Incentive Plan (the “2021 Plan”). As of June 30, 2021, 5,373,049 shares of Common Stock are authorized for issuance pursuant to awards under the 2021 Plan, inclusive of any shares of Common Stock subject to stock options, restricted stock awards or other awards that were assumed in the Merger and terminate as a result of being unexercised or are forfeited or repurchased by the Company, with the maximum number of shares to be added to the 2021 Plan equal to 5,373,049 shares of Common Stock. As of June 30, 2021, 2,919,493 shares have been awarded and 2,453,556 shares remain available for issuance under the 2021 Plan. The 2021 Plan permits the granting of incentive stock options, restricted stock awards, other stock-based award or other cash-based awards to employees, directors, and non-employee consultants. Option Awards The fair value of each employee and non-employee stock option grant is estimated on the date of grant using the Black-Scholes option-pricing model. The Company is a public company and lacks company-specific historical and implied volatility information. Therefore, it estimates its expected stock volatility based on the historical volatility of a publicly traded set of peer companies. Due to the lack of historical exercise history, the expected term of the Company’s stock options for employees has been determined utilizing the “simplified” method for awards. The risk-free interest rate is determined by reference to the U.S. Treasury yield curve. Expected dividend yield is zero based on the fact that the Company has never paid cash dividends and does not expect to pay any cash dividends in the foreseeable future. Additionally, certain options granted contain terms that require all unvested options to immediately vest a) upon the approval of a New Drug Application (NDA) by the US Food and Drug Administration for NRX-101, or b) immediately preceding a change in control of the Company, whichever occurs first. The grant date fair value of employee and non-employee stock option awards is determined using the Black Scholes option-pricing model. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 December 31, 2020 Exercise price $ 11.69-$23.41 ​ $ 2.22-$3.07 ​ Risk-free rate of interest ​ 0.79%-1.24 % 0.79%-0.79 % Expected term (years) ​ 5.5-6.5 ​ 4.7-5.9 ​ Expected stock price volatility ​ 80 % 80 % Dividend yield ​ — ​ — ​ ​ The following table summarizes the Company’s employee and non-employee stock option activity under the Plan for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ Weighted ​ average ​ Aggregate ​ ​ Number of ​ average ​ remaining ​ intrinsic ​ shares exercise price term (years) value Outstanding as of December 31, 2020 (as previously reported) 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Retroactive application of reverse recapitalization 1,927,548 ​ (8.62) ​ ​ ​ Outstanding as of December 31, 2020, effect of Merger 2,414,303 ​ $ 2.17 8.2 ​ $ 53,659,966 Options granted 210,800 ​ ​ 11.69 9.8 ​ ​ 3,825,276 Forfeited (198,400) ​ ​ (2.22) — ​ ​ (6,587,328) Outstanding as of March 31, 2021 ​ 2,426,703 ​ $ 14.58 ​ 8.7 ​ $ 30,388,510 Options granted ​ 587,030 ​ ​ 14.94 ​ 9.9 ​ ​ — Forfeited ​ (89,280) ​ ​ (7.86) ​ — ​ ​ (339,082) Exercised ​ (4,960) ​ ​ (3.07) ​ — ​ ​ (42,385) Outstanding as of June 30, 2021 ​ 2,919,493 ​ $ 5.25 ​ 9.0 ​ $ 20,558,299 Options vested and exercisable as of June 30, 2021 ​ 1,095,294 ​ $ 1.50 ​ 6.1 ​ $ 11,106,829 ​ The aggregate intrinsic value in the above table is calculated as the difference between fair value of the Company’s common stock price and the exercise price of the stock options. The weighted average grant date fair value per share for employee stock and non-employee option grants during the three months ended and six months ended June 30, 2021, respectively was $14.31 and $18.37. The weighted average grant date fair value per share for employee stock and non-employee option grants during the three months ended and six months ended June 30, 2020, respectively was $1.25 and $1.25. At June 30, 2021, the total unrecognized compensation related to unvested employee and non-employee stock option awards granted, including unrecognized compensation costs related to Substitute Options of $25,877,473, was $33,610,165, of which the Company expects to recognize $9,117,887 over a weighted-average period of approximately 1.89 years. The following table summarizes the Company’s recognition of stock-based compensation for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three months ended June 30, ​ Six months ended June 30, ​ 2021 2020 2021 2020 Stock-based compensation expense ​ ​ ​ ​ General and administrative ​ $ 4,094,549 ​ $ 50,881 ​ $ 4,438,583 ​ $ 117,469 Regulatory and process development ​ 188,781 ​ 42,585 ​ 216,445 ​ 64,800 Total stock-based compensation expense ​ $ 4,283,330 ​ $ 93,466 ​ $ 4,655,028 ​ $ 182,269 ​	9. Stock-Based Compensation The Company’s 2016 Omnibus Incentive Plan (the “Plan”) permits the granting of incentive stock options, restricted stock awards, other stock-based award or other cash-based awards. The maximum aggregate shares of common stock that may be subject to awards and issued under the Plan is 500,000. In December 2020, the Company’s board of directors authorized an additional 200,000 shares of common stock options to be authorized under the Plan for a total of 700,000 authorized shares. At December 31, 2020, 486,755 shares have been awarded and 213,245 shares remain available for issuance under the Plan. Option Awards The fair value of each employee and non-employee stock option grant is estimated on the date of grant using the Black-Scholes option-pricing model. The Company is a private company and lacks company-specific historical and implied volatility information. Therefore, it estimates its expected stock volatility based on the historical volatility of a publicly traded set of peer companies. Due to the lack of historical exercise history, the expected term of the Company’s stock options for employees has been determined utilizing the “simplified” method for awards. The risk-free interest rate is determined by reference to the U.S. Treasury yield curve. Expected dividend yield is zero based on the fact that the Company has never paid cash dividends and does not expect to pay any cash dividends in the foreseeable future. Additionally, certain options granted contain terms that require all unvested options to immediately vest a) upon the approval of a New Drug Application (NDA) by the US Food and Drug Administration for NRX-101, or b) immediately preceding a change in control of the Company, whichever occurs first. The fair value of the Company’s common stock, which equaled the exercise price of stock options granted during the years ended December 31, 2020 and 2019, respectively, was determined based on sales of the Company’s shares at arm’s length to unrelated third parties. The grant date fair value of employee and non-employee stock option awards is determined using the Black Scholes option-pricing model. The following assumptions were used during the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 ​ Exercise price ​ $ 11.00‑$15.25 $ 11.00 ​ Risk-free rate of interest ​ 0.30%‑0.49 % ​ 1.54%‑1.73 % Expected term (years) ​ 5.5 6.5 ​ 6.0 6.5 ​ Expected stock price volatility ​ 80 % ​ 80 % Dividend yield ​ — ​ — ​ ​ The following table summarizes the Company’s employee and non-employee stock option activity under the Plan for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ ​ average ​ ​ ​ ​ ​ ​ ​ Weighted ​ remaining ​ Aggregate ​ ​ Number of ​ average ​ contractual ​ intrinsic ​ ​ shares ​ exercise price ​ life (in years) ​ value Outstanding as of December 31, 2018 355,408 ​ $ 5.74 8.2 ​ $ 1,782,729 Granted 28,180 ​ 11.00 9.6 ​ Forfeited/Cancelled (50,000) ​ — — ​ — Outstanding as of December 31, 2019 333,588 ​ $ 5.74 7.2 ​ $ 1,782,729 Granted 266,500 ​ 14.37 9.7 ​ 9,761,125 Forfeited /Cancelled (113,333) ​ — — ​ — Outstanding as of December 31, 2020 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Options vested and exercisable as of December 31, 2020 329,489 ​ $ 6.31 4.0 ​ $ 14,723,342 ​ The aggregate intrinsic value in the above table is calculated as the difference between fair value of the Company’s common stock price and the exercise price of the stock options. The weighted average grant date fair value per share for employee stock and non-employee option grants during the years ended December 31, 2020 and 2019 was $9.64 and $7.69, respectively. At December 31, 2020, the total unrecognized compensation related to unvested employee and non-employee stock option awards granted was $2,193,874, which the Company expects to recognize over a weighted-average period of approximately 2.09 years. Stock-based compensation expense related to stock options, in aggregate, has been reported in general and administrative expense in the amount of $332,065 and $321,087 and research and development expense in the amount of $398,340 and $112,823 in the Company’s statements of operations for the years ended December 31, 2020 and 2019, respectively.

Fair Value Measurements

Fair Value Measurements	6 Months Ended
	Jun. 30, 2021
Fair Value Disclosures [Abstract]
Fair Value Measurements	12. Fair Value Measurements Fair value measurements discussed herein are based upon certain market assumptions and pertinent information available to management as of and during the six months ended June 30, 2021 and the year ended December 31, 2020. The carrying amount of accounts payable approximated fair value as they are short term in nature. The fair value of warrants issued for settlement and services are estimated based on the Black-Scholes model during the six months ended June 30, 2021 and the year ended December 31, 2020. The carrying value of notes payable approximated the estimated fair values due to their recent issuances. Fair Value on a Recurring Basis The Company follows the guidance in ASC 820 for its financial assets and liabilities that are re-measured and reported at fair value at each reporting period, and non-financial assets and liabilities that are re-measured and reported at fair value at least annually. The estimated fair value of the warrant liabilities and Earnout Cash contingent consideration represent Level 3 measurements. The following table presents information about the Company’s liabilities that are measured at fair value on a recurring basis at June 30, 2021 and December 31, 2020, and indicates the fair value hierarchy of the valuation inputs the Company utilized to determine such fair value: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Description Level June 30, 2021 December 31, 2020 Liabilities: ​ ​ ​ ​ ​ ​ ​ ​ Warrant liabilities (Note 10) ​ 3 ​ $ 515,025 ​ $ — Earnout Cash liability (Note 4) 3 ​ $ 25,874,896 ​ $ — ​ Warrant liabilities The Company utilizes a Black-Scholes model approach to value the Placement Warrants at each reporting period, with changes in fair value recognized in the statement of operations. The estimated fair value of the warrant liabilities is determined using Level 3 inputs. Inherent in a binomial options pricing model are assumptions related to expected share-price volatility, expected life, risk-free interest rate and dividend yield. The Company estimates the volatility of its common stock based on historical volatility that matches the expected remaining life of the warrants. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield curve on the grant date for a maturity similar to the expected remaining life of the warrants. The expected life of the warrants is assumed to be equivalent to their remaining contractual term. The dividend rate is based on the historical rate, which the Company anticipates to remain at zero. The significant unobservable inputs used in the Black-Scholes model to measure the warrant liability that are categorized within Level 3 of the fair value hierarchy are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 At Effective Time Stock price on valuation date ​ $ 11.62 ​ $ 24.25 ​ Exercise price per share ​ $ 11.50 ​ $ 11.50 ​ Expected life ​ 4.90 ​ 5.0 ​ Volatility ​ 35.7 % 39.0 % Risk-free rate ​ 0.9 % 0.8 % Dividend yield ​ — % — % Fair value of warrants ​ $ 3.78 ​ $ 14.56 ​ ​ A reconciliation of warrant liabilities is included below: ​ ​ ​ ​ ​ Fair Value Balance as of December 31, 2020 ​ $ — Additions pursuant to Merger ​ 1,983,674 Gain upon re-measurement ​ (1,468,649) Balance as of June 30, 2021 ​ $ 515,025 ​ Earnout Cash liability The fair value of the Earnout Cash liability has been estimated using probability-weighted discounted cash flow models (DCFs) with significant inputs that are not observable in the market and thus represents a Level 3 fair value measurement as defined in ASC 820. The DCFs incorporate Level 3 inputs including estimated discount rates that we believe market participants would consider relevant in pricing and the projected timing and amount of cash flows, which are estimated and developed, considering the uncertainties associated with the obligations. A reconciliation of the Earnout Cash liability is included below: ​ ​ ​ ​ ​ Fair Value Balance as of December 31, 2020 ​ $ — Additions pursuant to Merger ​ 25,520,195 Loss upon re-measurement ​ 354,701 Balance as of June 30, 2021 ​ $ 25,874,896 ​ Fair Value on a Non-Recurring Basis The fair value of the contingent Earnout Shares has been estimated using the trading price of our Common Stock at the Effective Time ($24.25), discounted based on the probability of the Earnout Shares Milestone being met as determined at the Effective Time, and thus represents a Level 2 fair value measurement as defined in ASC 820. The contingent Earnout Shares, if achieved, would be issued to legacy NeuroRx shareholders. The Earnout Shares are a fixed number of shares to be issued to such shareholders on a pro rata basis. The fair value of the contingent Earnout Shares were recognized as a deemed dividend. Upon closing of the Merger, the estimated fair value of the contingent Earnout Shares was $253,130,272 with such amount recognized as a deemed dividend. As the Company is in an accumulated deficit position as of the measurement date, the resulting deemed dividend is recorded as a reduction of additional paid-in capital with a corresponding offset recorded to additional paid-in capital (i.e., net impact to additional paid-in capital of $0).

Income Taxes_2

Income Taxes	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Income Taxes.
Income Taxes	13. Income Taxes The Company recorded no provision or benefit for income tax expense for the six months ended June 30, 2021. For all periods presented, the pretax losses incurred by the Company received no corresponding tax benefit because the Company concluded that it is more likely than not that the Company will be unable to realize the value of any resulting deferred tax assets. The Company will continue to assess its position in future periods to determine if it is appropriate to reduce a portion of its valuation allowance in the future. On March 27, 2020, Congress enacted the CARES Act to provide certain relief as a result of the COVID-19 pandemic. The CARES Act, among other things, includes provisions relating to net operating loss carryback periods, alternative minimum tax credit refunds, and modification to the net interest deduction limitations. The CARES Act did not have a material impact on the Company’s consolidated financial statements for the six months ended June 30, 2021. The Company continues to monitor any effects on its financial statements that may result from the CARES Act. Upon consummation of the Merger, a change in control was deemed to have occurred and the Company's net operating loss carrybacks could be subject to limitations. The Company has no open tax audits with any taxing authority as of June 30, 2021.	10. Income Taxes A reconciliation of the statutory U.S. federal income tax rate to the Company’s effective tax rate consist of the following: ​ ​ ​ ​ ​ ​ ​ ​ For the Years ​ ​ Ended ​ ​ ​ December 31, ​ ​ ​ 2020 2019 Statutory federal income tax benefit (21.00) % (21.00) % Permanent items (0.04) % 0.01 % Foreign rate differential 0.01 % (0.02) % State taxes, net of federal tax benefit (1.74) % 0.60 % Change in valuation allowance 23.01 % 22.23 % R&D credit (0.24) % (1.90) % Other — % 0.07 % Effective tax rate — % — % ​ The components of income tax provision (benefit) are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ ​ 2020 2019 Federal: ​ ​ Current ​ $ — ​ $ — Deferred ​ (11,015,759) ​ (1,496,712) State and Local: ​ ​ Current ​ — ​ — Deferred ​ (900,789) ​ 39,574 Foreign: ​ ​ Current ​ — ​ — Deferred ​ 2,867 ​ (8,412) Change in valuation allowance ​ 11,913,681 ​ 1,465,550 Total ​ $ — ​ $ — ​ Deferred income taxes reflect the net tax effects of temporary differences between the carrying value of assets and liabilities for financial reporting purposes and amounts used for income tax purposes. The temporary differences that give rise to deferred tax assets and liabilities are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Deferred tax assets (liabilities): ​ ​ ​ ​ ​ ​ Net operating loss carryforwards ​ $ 8,243,959 ​ $ 6,943,988 Convertible notes payable discount and embedded derivative ​ — ​ 101,521 Common stock warrants ​ 1,405,796 ​ 179,271 Israel net operating loss carryforwards ​ 128,469 ​ 131,336 Founder share options ​ 469,062 ​ 472,195 Stock-based compensation ​ 681,446 ​ 497,315 Settlement liability ​ 9,005,860 ​ — Bonus accrual ​ 120,995 ​ — Other ​ 58,721 ​ — R&D credit ​ 375,000 ​ 250,000 ​ ​ 20,489,308 ​ 8,575,626 Valuation allowance ​ (20,489,308) ​ (8,575,626) Deferred tax assets, net of allowance ​ $ — ​ $ — ​ As of December 31, 2020 and 2019, the Company had federal and state net operating loss carryforwards of approximately $37,000,000 and $31,200,000, respectively. As of December 31, 2020 and 2019, the Company had approximately $559,000 and $547,000 of foreign net operating loss carryforwards, respectively. The federal, state and foreign net operating loss carryforwards generated in the tax years from 2015 to 2020 will begin to expire, if not utilized, by 2035. Utilization of the net operating loss carryforwards may be subject to an annual limitation according to Section 382 of the Internal Revenue Code of 1986 as amended, and similar provisions. The Company has determined, based upon available evidence, that it is more likely than not that all of the net deferred tax asset will not be realized and, accordingly, has provided a full valuation allowance against its net deferred tax asset. Management considers the scheduled reversal of deferred tax liabilities, projected future taxable income, net operating loss carryback potential, and tax planning strategies in making these assessments. The Company recorded approximately $1,000,000 as a reduction of the deferred tax asset due to uncertain tax positions that if recognized would reduce Federal and state net operating loss carryforwards and R&D credit carryforwards. In the next twelve months, the Company plans to file amended returns to reduce a portion of its uncertain tax position recorded in the current year. The Company recognizes interest accrued to unrecognized tax benefits and penalties as income tax expense. The Company accrued total penalties and interest of $0 during the years ended December 31, 2020 and 2019 and in total, as of December 31, 2020 and 2019 has recognized penalties and interest of $0. The Company files tax returns as prescribed by the tax laws of the jurisdictions in which they operate. In the normal course of business, the Company is subject to examination by federal and foreign jurisdictions where applicable based on the statute of limitations that apply in each jurisdiction. As of December 31, 2020, open years related to all jurisdictions are 2019, 2018, 2017, 2016 and 2015. The Company has no open tax audits with any taxing authority as of December 31, 2020.

Related Party Transactions_2

Related Party Transactions	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Related Party Transactions
Related Party Transactions	14. Related Party Transactions The Company licenses patents that are owned by Glytech, LLC, pursuant to a license agreement (the Glytech Agreement). Glytech, LLC is owned by a co-founder and former Director of the Company, and therefore, a related party. The Glytech agreement requires that the Company pay Glytech for ongoing scientific support and also reimburse Glytech for expenses of obtaining and maintaining patents that are licensed to NRx Pharmaceuticals. During the three months ended June 30, 2021 and 2020 the Company paid a co-founder $125,000 and $0, respectively, and during the six months ended June 30, 2021 and 2020, $125,000 and $82,569, respectively, for continuing technology support services and reimbursed expenses. These support services are ongoing. The Fourth Amendment to the Glytech Agreement, effective as of December 31, 2020, includes an equity value-triggered transfer of Excluded Technology from Glytech to NRx Pharmaceuticals. The Excluded Technology is defined in the Glytech Agreement as any technology, and any know-how related thereto, covered in the licensed patents that do not recite either D-cycloserine or lurasidone individually or jointly. This definition would cover pharmaceutical formulations, including some that NRx Pharmaceuticals considers “pipeline” or “future product” opportunities, that contain a combination of pharmaceutical components different from those contained in NRX-100 and NRX-101. The Excluded Technology will transfer to the Company for no additional consideration if the value of NRx Pharmaceuticals equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost. The Company believes the criteria have been met pending the registration of Glytech shares. The CEO of the Company is a major shareholder in the Company. Therefore, his services are deemed to be a related party transaction. He serves the company on a full-time basis and has an employment agreement with the Company and received compensation of $137,500 and $53,125 during the three months ended June 30, 2021 and 2020, respectively, and $286,250 and $121,875 during the six months ended June 30, 2021 and 2020, respectively. The services are ongoing. The CEO’s son provides services related to website, IT, and marketing support under the supervision of the Company’s Chief Commercial Officer, who is responsible for assuring that the services are provided on financial terms that are at market. NRx Pharmaceuticals paid this family member a total of $11,100 and $18,605 during the three months ended June 30, 2021 and 2020, respectively, and $29,740 and $40,770 during the six months ended June 30, 2021 and 2020, respectively. In addition, NRx Pharmaceuticals pays Pill Tracker 2015 Ltd. (“Pill Tracker”) for services relating to the development of the inhaled use form of aviptadil. The CEO’s son and our CEO are the chief executive officer and the board chairman, respectively, of Pill Tracker. NRx Pharmaceuticals paid Pill Tracker $254,936 and $0 during the three months ended June 30, 2021 and 2020, respectively, and $395,757 and $0 during the six months ended June 30, 2021 and 2020, respectively. The CEO’s other son, as a medical doctor, provides research services related to the development of the inhaled use form of aviptadil, under the supervision of the CEO, who is responsible for assuring that the services are provided on financial terms that are at market. NRx Pharmaceuticals paid this family member a total of $4,615 and $4,820 during the three months ended June 30, 2021 and 2020, respectively, and $6,110 and $4,820 during the six months ended June 30, 2021 and 2020, respectively. Included in accounts payable were $44,201 and $149,067 due to the above related parties as of June 30, 2021 and December 31, 2020, respectively.	11. Related Party Transactions The Company licenses patents that are owned by Glytech, LLC, pursuant to a license agreement (the Glytech Agreement). Glytech, LLC is owned by a co-founder and Director of the Company, and therefore, a related party. The Glytech agreement requires that the Company pay Glytech for ongoing scientific support and also reimburse Glytech for expenses of obtaining and maintaining patents that are licensed to NeuroRx. During the years ended December 31, 2020 and 2019, the Company paid a co-founder $272,929 and $464,720, respectively, for continuing technology support services and reimbursed expenses. These support services are ongoing. The Fourth Amendment to the Glytech Agreement, effective as of December 31, 2020, includes an equity value-triggered transfer of Excluded Technology from Glytech to NeuroRx. The Excluded Technology is defined in the Glytech Agreement as any technology, and any know-how related thereto, covered in the licensed patents that do not recite either D-cycloserine or lurasidone individually or jointly. This definition would cover pharmaceutical formulations, including some that NeuroRx considers “pipeline” or “future product” opportunities, that contain a combination of pharmaceutical components different from those contained in NRX-100 and NRX-101. The Excluded Technology will transfer to the Company for no additional consideration if the value of NeuroRx equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost. The CEO of the Company is a major shareholder in the Company. Therefore, his services are deemed to be a related party transaction. He serves the company on a full-time basis and has an employment agreement with the Company and received compensation of $456,459 and $452,400 during the years ended December 31, 2020 and 2019, respectively. The services are ongoing. The CEO’s son provides services related to website, IT, and marketing support under the supervision of the Company’s Chief Commercial Officer, who is responsible for assuring that the services are provided on financial terms that are at market. NeuroRx paid this family member a total of $85,915 and $48,000 during the years ended December 31, 2020 and 2019, respectively. In addition, NeuroRx pays Pill Tracker 2015 Ltd. (“Pill Tracker”) for services relating to the development of the inhaled use form of aviptadil. The CEO’s son and our CEO are the chief executive officer and the board chairman, respectively, of Pill Tracker. NeuroRx paid Pill Tracker $271,082 during the year ended December 31, 2020. NeuroRx made no payments to Pill Tracker in 2019. The CEO’s other son, as a medical doctor, provides research services related to the development of the inhaled use form of aviptadil, under the supervision of the CEO, who is responsible for assuring that the services are provided on financial terms that are at market. NeuroRx paid this family member a total of $11,650 during the year ended December 31, 2020. NeuroRx made no payments to this family member in 2019. Included in accounts payable were $149,067 and $92,744 due to the above related parties as of December 31, 2020 and 2019, respectively.

Subsequent Events_2

Subsequent Events	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Subsequent Events
Subsequent Events	15. Subsequent Events Warrants Exercised Subsequent to June 30, 2021, the Company received $9,186,316 from the exercise of a warrant for the purchase of 1,833,596 shares. Related Party Transaction Subsequent to June 30, 2021, the Company and Pill TM ​	12. Subsequent Events Issuance of Common Stock Subsequent to December 31, 2020, the Company sold 43,018 shares of common stock for gross proceeds of $2,495,058, and 79,400 shares of common stock for gross proceeds of $5,716,800. Issuance of Stock Option Awards Subsequent to December 31, 2020, the Company granted 42,500 stock option awards. The stock options will vest three years from the date of grant. Aviptadil Supply Agreement On January 4, 2021 NeuroRx and Aerogen Limited (“Aerogen”) signed a supply agreement for the supply of certain products, including the Areogen Solo Nebulizer System and Aerogen Ultra, solely for the purposes of carrying out clinical trials relating to inhalation delivery of RLF-100 (aviptadil) for treatment of pulmonary insufficiency and respiratory distress in COVID-19 patients. Pill Tracker is an agent of NeuroRx per the supply agreement and the first purchase order for products amounted to $54,315.

Summary of Significant Accoun_8

Summary of Significant Accounting Policies (Policies)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Summary of Significant Accounting Policies
Basis of Presentation	Basis of Presentation The accompanying unaudited interim condensed financial statements have been prepared in accordance with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) for interim financial information. Accordingly, they do not include all of the information and footnotes required by GAAP for complete financial statements. In the opinion of management, the unaudited interim condensed financial statements reflect all adjustments, which include only normal recurring adjustments necessary for the fair statement of the balances and results for the periods presented. The results of operations for any interim periods are not necessarily indicative of the results that may be expected for the entire fiscal year or any other interim period. The merger between Merger Sub and NeuroRx was accounted for as a reverse recapitalization in accordance with U.S. GAAP (the “Reverse Recapitalization”). Under this method of accounting, BRPA was treated as the “acquired” company and NeuroRx is treated as the acquirer for financial reporting purposes. Accordingly, for accounting purposes, the Reverse Recapitalization was treated as the equivalent of NeuroRx issuing stock for the net assets of BRPA, accompanied by a recapitalization. The net assets of BRPA are stated at historical cost, with no goodwill or other intangible assets recorded. NeuroRx was determined to be the accounting acquirer based on the following predominant factors: ● NeuroRx’s shareholders have the largest portion of voting rights in the Company; ● the Board and Management are primarily composed of individuals associated with NeuroRx; and ● NeuroRx was the larger entity based on historical operating activity and NeuroRx had the larger employee base at the time of the Merger. The consolidated assets, liabilities and results of operations prior to the Reverse Recapitalization are those of NeuroRx. The shares and corresponding capital amounts and losses per share, prior to the Merger, have been retroactively restated based on shares reflecting the exchange ratio established in the Merger.	Basis of Presentation The Company’s financial statements have been prepared in conformity with generally accepted accounting principles in the United States of America (“GAAP”) as determined by Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”).
Use of Estimates	Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, contingent consideration and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected.	Use of Estimates The preparation of financial statements requires management to make estimates and assumptions that affect the reported amounts of assets, liabilities and expenses and the disclosure of contingent assets and liabilities in its financial statements and the reported amounts of expenses during the reporting period. The most significant estimates in the Company’s financial statements relate to the valuation of common and preferred stock, stock options, warrants, the embedded put feature in convertible notes and the valuation allowance of deferred tax assets resulting from net operating losses. These estimates and assumptions are based on current facts, historical experience and various other factors believed to be reasonable under the circumstances, the results of which form the basis for making judgments about the carrying values of assets and liabilities and the recording of expenses that are not readily apparent from other sources. Actual results may differ materially and adversely from these estimates. To the extent there are material differences between the estimates and actual results, the Company’s future results of operations will be affected.
Certain Risks and Uncertainties	Certain Risks and Uncertainties The Company’s activities are subject to significant risks and uncertainties including the risk of failure to secure additional funding to properly execute the Company’s business plan. The Company is subject to risks that are common to companies in the pharmaceutical industry, including, but not limited to, development by the Company or its competitors of new technological innovations, dependence on key personnel, reliance on third party manufacturers, protection of proprietary technology, and compliance with regulatory requirements.
Fair Value of Financial Instruments	Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. (Refer to Note 12)	Fair Value of Financial Instruments ASC 820, Fair Value Measurements The accounting guidance classifies fair value measurements in one of the following three categories for disclosure purposes: Level 1: Quoted prices in active markets for identical assets or liabilities. Level 2: Inputs other than Level 1 prices for similar assets or liabilities that are directly or indirectly observable in the marketplace. Level 3: Unobservable inputs which are supported by little or no market activity and values determined using pricing models, discounted cash flow methodologies, or similar techniques, as well as instruments for which the determination of fair value requires significant judgment or estimation. Fair value measurements discussed herein are based upon certain market assumptions and pertinent information available to management as of and during the years ended December 31, 2020 and 2019. The carrying amount of accounts payable approximated fair value as they are short term in nature. The fair value of warrants issued for services is estimated based on the Black-Scholes model during the years ended December 31, 2020 and 2019. The carrying value of notes payable and convertible notes payable approximated the estimated fair values due to their recent issuances. The estimated fair value of the warrants and embedded put, represent Level 3 measurements.
Accounts Receivable	Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of June 30, 2021, the Company has recorded an allowance for doubtful accounts of $5,470,897 as the Company does not expect to collect on amounts due to the Company owed from Relief.	Accounts Receivable Accounts receivable consist of balances due from collaborative partners. In determining collectability, historical trends are evaluated, and specific partner issues are reviewed on a periodic basis to arrive at appropriate allowances. As of December 31, 2020, the Company has recorded an allowance for doubtful accounts of $257,463.
Concentration of Credit Risk and Off-Balance Sheet Risk	Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss.	Concentration of Credit Risk and Off-Balance Sheet Risk Cash is the only financial instrument that is potentially subject to concentrations of credit risk. The Company’s cash is deposited in accounts at large financial institutions, and amounts may exceed federally insured limits. The Company believes it is not exposed to significant credit risk due to the financial strength of the depository institutions in which the cash is held. The Company has no financial instruments with off-balance sheet risk of loss.
Research and Development Costs	Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received.	Research and Development Costs The Company’s research and development expenses consist primarily of costs associated with the Company’s clinical trials, salaries, payroll taxes, employee benefits, and stock-based compensation charges for those individuals involved in ongoing research and development efforts. Research and development costs are expensed as incurred. Advance payments for goods and services that will be used in future research and development activities are expensed when the activity has been performed or when the goods have been received.
Stock-Based Compensation	Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company. Modification of stock options and warrants A change in any of the terms or conditions of stock options and warrants is accounted for as a modification. Incremental stock-based compensation cost is measured as the excess, if any, of the fair value of the modified option over the fair value of the original option/warrant immediately before its terms are modified, measured based on the fair value of the ordinary shares and other pertinent factors at the modification date. For vested stock options and warrants to board members, we recognize incremental compensation cost in the period the modification occurs. For unvested stock options, we recognize over the remaining requisite service period, the sum of the incremental compensation cost and the remaining unrecognized compensation cost for the original award on the modification date. If the fair value of the modified option is lower than the fair value of the original option immediately before modification, the minimum compensation cost we recognize is the cost of the original award. The accounting for incremental fair value of warrants is based on the specific facts and circumstances related to the modification which may result in a reduction of additional paid-in capital, recognition of costs for services rendered, or recognized as a deemed dividend.	Stock-Based Compensation The Company expenses stock-based compensation to employees and non-employees over the requisite service period based on the estimated grant-date fair value of the awards. The Company accounts for forfeitures as they occur. Stock-based awards with graded-vesting schedules are recognized on a straight-line basis over the requisite service period for each separately vesting portion of the award. The Company estimates the fair value of stock option grants using the Black-Scholes option pricing model, and the assumptions used in calculating the fair value of stock-based awards represent management’s best estimates and involve inherent uncertainties and the application of management’s judgment. All stock-based compensation costs are recorded in general and administrative or research and development costs in the consolidated statements of operations based upon the underlying individual’s role at the Company.
Warrants	Warrants The Company accounts for warrants as either equity-classified or liability-classified instruments based on an assessment of the warrant’s specific terms and applicable authoritative guidance in Financial Accounting Standards Board (“FASB”) Accounting Standards Codification (“ASC”) 480, Distinguishing Liabilities from Equity Derivatives and Hedging For issued or modified warrants that meet all of the criteria for equity classification, the warrants are required to be recorded as a component of additional paid-in capital at the time of issuance. For issued or modified warrants that do not meet all the criteria for equity classification, the warrants are required to be recorded at their initial fair value on the date of issuance, and each balance sheet date thereafter. Changes in the estimated fair value of the warrants are recognized as a non-cash gain or loss on the statements of operations. The fair value of the Placement Warrants was estimated using a Black Scholes valuation approach (see Notes 10 and 12).
Income Taxes	Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense.	Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes (“ASC 740”), which provides for deferred taxes using an asset and liability approach. The Company recognizes deferred tax assets and liabilities for the expected future tax consequences of events that have been included in the financial statements or tax returns. Deferred tax assets and liabilities are determined based on the difference between the financial statement and tax basis of assets and liabilities using enacted tax rates in effect for the year in which the differences are expected to reverse. Valuation allowances are provided, if based upon the weight of available evidence, it is more likely than not that some or all of the deferred tax assets will not be realized. The Company accounts for uncertain tax positions in accordance with the provisions of ASC 740. When uncertain tax positions exist, the Company recognizes the tax benefit of tax positions to the extent that the benefit would more likely than not be realized assuming examination by the taxing authority. The determination as to whether the tax benefit will more likely than not be realized is based upon the technical merits of the tax position as well as consideration of the available facts and circumstances. The Company recognizes any interest and penalties accrued related to unrecognized tax benefits as income tax expense.
Earnings (Loss) Per Share	Earnings (Loss) Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted earnings per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and other dilutive instruments because their effect would be anti-dilutive in the periods in which we incur a net loss. The following table summarized the basic and diluted earnings per share calculations: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Numerator: ​ ​ ​ ​ ​ ​ ​ ​ Net income (loss) attributable to common stock—basic and diluted $ (16,007,973) $ 102,287 $ (41,496,847) $ (1,487,769) Denominator: ​ ​ ​ ​ ​ ​ ​ ​ Weighted average shares — basic ​ ​ 41,727,480 ​ ​ 33,819,205 ​ ​ 38,709,614 ​ ​ 33,799,503 Effect of other dilutive securities ​ ​ — ​ ​ 2,837,215 ​ ​ — ​ ​ — Weighted average shares — diluted ​ ​ 41,727,480 ​ ​ 36,656,420 ​ ​ 38,709,614 ​ ​ 33,799,503 Basic earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) Diluted earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net earnings (loss) per share attributable to common stock for the periods in which a net loss is presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Stock options 2,919,493 — 2,919,493 1,166,863 Common stock warrants 8,495,316 — 8,495,316 1,670,352 Common stock issuable pursuant to UPOs (Note 10) ​ 600,000 ​ — ​ 600,000 ​ — Common stock warrants pursuant to UPOs (Note 10) ​ 300,000 ​ — ​ 300,000 ​ — Public Rights pursuant to UPOs (Note 10) ​ 60,000 ​ — ​ 60,000 ​ — Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ — ​	Loss Per Share Basic loss per share of common stock is computed by dividing net loss attributable to common stockholders by the weighted average number of shares of common stock outstanding for the period. Diluted loss per share excludes, when applicable, the potential impact of stock options, common stock warrant shares, and convertible preferred stock because their effect would be anti-dilutive due to our net loss. Since the Company had a net loss in each of the periods presented, basic and diluted net loss per common share are the same. The calculation of basic and diluted net loss per share attributable to common stock was as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Numerator: ​ ​ ​ ​ ​ ​ Net loss attributable to common stock—basic and diluted ​ $ (51,776,904) ​ $ (6,729,161) ​ ​ ​ ​ ​ ​ ​ Denominator: ​ ​ Weighted average shares—basic and diluted ​ 10,845,240 ​ 10,690,209 ​ ​ ​ ​ ​ ​ ​ Net loss per share attributable to common stock—basic and diluted ​ $ (4.77) ​ $ (0.63) ​ The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net loss per share attributable to common stock for the periods presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ Year Ended December 31, ​ 2020 2019 Convertible preferred stock as if converted 2,371,710 2,367,543 Stock options 486,755 333,588 Common stock warrants 620,054 57,473
Recent Accounting Pronouncements	Recent Accounting Pronouncements In December 2019, the FASB issued ASU No. 2019-12, Income Taxes: Simplifying the Accounting for Income Taxes In August 2020, the FASB issued ASU 2020-06, Debt — Debt with Conversion and Other Options (Subtopic 470-20) and Derivatives and Hedging — Contracts in Entity’s Own Equity (Subtopic 815-40): Accounting for Convertible Instruments and Contracts in an Entity’s Own Equity In May 2021, the FASB issued ASU 2021-04, Earnings Per Share (Topic 260), Debt — Modifications and Extinguishments (Subtopic 470-50), Compensation — Stock Compensation (Topic 718) and Derivatives and Hedging - Contracts in an Entity's Own Equity (Subtopic 815-40) — Issuer's Accounting for Certain Modifications or Exchange of Freestanding Equity-Classified Written Call Options	Recent Accounting Pronouncements In June 2018, the FASB issued ASU 2018-07, which simplifies the accounting for nonemployee share-based payment transactions. The amendments specify that Topic 718 applies to all share-based payment transactions in which a grantor acquires goods or services to be used or consumed in a grantor’s own operations by issuing share-based payment awards. The Company adopted ASU 2018-07 as of January 1, 2019, which resulted in a cumulative effect charge of $683 to accumulated deficit.
Foreign Currency		Foreign Currency The Company’s functional currency is the U.S. dollar. The functional currency of our foreign operation is the respective local currency. Assets and liabilities of foreign operation denominated in local currencies are translated at the spot rate in effect at the applicable reporting date. The consolidated statements of operations are translated at the weighted average rate of exchange during the applicable period. The resulting unrealized cumulative translation adjustment is not material to the financial statements.
Cash and Cash Equivalents		Cash and Cash Equivalents The Company considers all highly liquid investments purchased with original maturities of 90 days or less at acquisition to be cash equivalents. As of December 31, 2020 and 2019, the Company does not have any cash equivalents.

Summary of Significant Accoun_9

Summary of Significant Accounting Policies (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Summary of Significant Accounting Policies
Summary of basic and diluted earnings per share calculations	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Numerator: ​ ​ ​ ​ ​ ​ ​ ​ Net income (loss) attributable to common stock—basic and diluted $ (16,007,973) $ 102,287 $ (41,496,847) $ (1,487,769) Denominator: ​ ​ ​ ​ ​ ​ ​ ​ Weighted average shares — basic ​ ​ 41,727,480 ​ ​ 33,819,205 ​ ​ 38,709,614 ​ ​ 33,799,503 Effect of other dilutive securities ​ ​ — ​ ​ 2,837,215 ​ ​ — ​ ​ — Weighted average shares — diluted ​ ​ 41,727,480 ​ ​ 36,656,420 ​ ​ 38,709,614 ​ ​ 33,799,503 Basic earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04) Diluted earnings (loss) per share ​ $ (0.38) ​ $ — ​ $ (1.07) ​ $ (0.04)	The calculation of basic and diluted net loss per share attributable to common stock was as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ As of December 31, ​ 2020 2019 Numerator: ​ ​ ​ ​ ​ ​ Net loss attributable to common stock—basic and diluted ​ $ (51,776,904) ​ $ (6,729,161) ​ ​ ​ ​ ​ ​ ​ Denominator: ​ ​ Weighted average shares—basic and diluted ​ 10,845,240 ​ 10,690,209 ​ ​ ​ ​ ​ ​ ​ Net loss per share attributable to common stock—basic and diluted ​ $ (4.77) ​ $ (0.63)
Schedule of Outstanding Shares of Common Stock Equivalents Excluded From Diluted Net Loss Per Share	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended June 30, ​ Six Months Ended June 30, ​ 2021 2020 2021 2020 Stock options 2,919,493 — 2,919,493 1,166,863 Common stock warrants 8,495,316 — 8,495,316 1,670,352 Common stock issuable pursuant to UPOs (Note 10) ​ 600,000 ​ — ​ 600,000 ​ — Common stock warrants pursuant to UPOs (Note 10) ​ 300,000 ​ — ​ 300,000 ​ — Public Rights pursuant to UPOs (Note 10) ​ 60,000 ​ — ​ 60,000 ​ — Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ —	The following outstanding shares of common stock equivalents were excluded from the computation of the diluted net loss per share attributable to common stock for the periods presented because their effect would have been anti-dilutive. ​ ​ ​ ​ ​ ​ ​ ​ Year Ended December 31, ​ 2020 2019 Convertible preferred stock as if converted 2,371,710 2,367,543 Stock options 486,755 333,588 Common stock warrants 620,054 57,473

Reverse Recapitalization (Table

Reverse Recapitalization (Tables)	6 Months Ended
	Jun. 30, 2021
Reverse Recapitalization
Schedule of Reconciliation of Merger, Reverse Recapitalization	The following table reconciles the elements of the Merger to the Unaudited Condensed Consolidated Statement of Cash Flows for the six months ended June 30, 2021: ​ ​ ​ ​ ​ Recapitalization Cash - BRPA trust and cash, net of redemptions ​ $ 4,362,474 Cash - PIPE financing, net of transaction costs ​ 8,100,000 Less: transaction costs and advisory fees allocated to NRXP equity ​ (1,412,846) Effect of Merger, net of redemptions and transaction costs ​ $ 11,049,628 ​ The following table reconciles the elements of the Merger to the Unaudited Condensed Consolidated Statements of Changes in Stockholders' Equity (Deficit) for the six months ended June 30, 2021: ​ ​ ​ ​ ​ Recapitalization Cash - BRPA trust and cash, net of redemptions ​ $ 4,362,474 Non-cash net working capital assumed from BRPA ​ (961,555) Less: notes payable assumed from BRPA ​ (1,100,000) Less: fair value of assumed Placement Warrants ​ (1,983,674) Less: fair value of Earnout Cash ​ (25,520,195) Less: transaction costs and advisory fees allocated to NRXP equity ​ (1,412,846) Effect of Merger, net of redemptions and transaction costs ​ $ (26,615,796) ​ The following table details the number of shares of common stock issued immediately following the consummation of the Merger: ​ ​ ​ ​ Number of Shares Common stock, outstanding prior to Merger 552,412 Less: redemption of BRPA shares (216) Common stock of BRPA 552,196 BRPA Founder and private shares, net of forfeited shares of 875,216 1,260,284 Shares issued in PIPE Financing 1,000,000 Shares issued for services 200,000 Shares issued pursuant to conversion of Public and Private Rights 717,250 Merger and PIPE financing shares - common stock 3,729,730 NeuroRx shares - common stock (1) 44,873,855 Total shares of common stock immediately after Merger 48,603,585 ​ (1) The number of NeuroRx common stock was determined from the 14,200,586 shares of NeuroRx common stock outstanding immediately prior to the closing of the Merger converted at the Exchange Ratio. All fractional shares were rounded down.

Prepaid Expenses and Other Cu_2

Prepaid Expenses and Other Current Assets (Tables)	6 Months Ended
	Jun. 30, 2021
Prepaid Expenses and Other Current Assets
Schedule of prepaid expenses and other current assets	​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 December 31, 2020 Prepaid expenses and other current assets: ​ (Unaudited) ​ Prepaid insurance ​ $ 3,347,172 ​ $ 49,029 Prepaid manufacturing expenses ​ 1,407,500 ​ — Other prepaid expenses ​ 341,336 ​ 164,772 Prepaid income taxes ​ 51,642 ​ — Other current assets ​ — ​ $ 26,551 Total accrued and other current liabilities ​ $ 5,147,650 ​ $ 240,352

Accrued and Other Current Lia_5

Accrued and Other Current Liabilities (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Accrued and other current liabilities
Schedule of accrued and other current liabilities	​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Accrued and other current liabilities: ​ ​ ​ ​ ​ ​ Accrued research and development expenses $ 826,442 $ 586,426 Accrued employee expenses ​ ​ 77,196 ​ ​ 530,500 Professional services ​ 185,170 ​ 606,553 Other accrued expenses ​ 417,529 ​ 5,004 Total accrued and other current liabilities ​ $ 1,506,337 ​ $ 1,728,483	Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Accrued and other current liabilities: ​ ​ Professional services ​ $ 606,553 ​ $ — Accrued research and development expenses ​ 586,426 ​ — Accrued employee expenses ​ 530,500 ​ — Other accrued liabilities ​ 5,004 ​ 9,649 Total accrued and other current liabilities ​ $ 1,728,483 ​ $ 9,649

Notes Payable (Tables)_2

Notes Payable (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Notes Payable.
Schedule of Notes Payable and Accrued Interest	​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Note Payable — Related Party ​ $ 154,190 ​ $ 154,190 Relief Therapeutics Loan ​ 500,000 ​ 500,000 Paycheck Protection Program Loan ​ — ​ 119,842 Carrying value of notes payable ​ 654,190 ​ 774,032 Accrued interest ​ ​ 31,976 ​ ​ 22,656 Note payable ​ ​ 686,166 ​ ​ 796,688 Notes payable and accrued interest, current ​ $ 173,694 ​ $ 248,861 Notes payable and accrued interest, non-current ​ $ 512,472 ​ $ 547,827
Schedule of convertible notes payable and accrued interest		​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Convertible Notes: ​ ​ ​ ​ ​ ​ 2017 convertible notes payable due November 2021 ​ $ — ​ $ 2,500,000 2018 convertible note payable due January 2022 ​ — ​ 100,000 2018 convertible notes payable due April 2022 ​ — ​ 200,000 Fair value of embedded put ​ — ​ 738,602 Debt discount ​ — ​ (296,437) Carrying value of convertible notes ​ $ — ​ $ 3,242,165 Accrued interest ​ — ​ 349,891 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056 ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Convertible Notes: ​ ​ Convertible notes payable and accrued interest, current ​ $ — ​ $ 130,251 Convertible notes payable and accrued interest, non-current ​ — ​ 3,461,805 Total convertible notes payable and accrued interest ​ $ — ​ $ 3,592,056
Notes payable and accrued interest		​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Note Payable — Related Party ​ $ 154,190 ​ $ 154,190 Relief Therapeutics Loan ​ 500,000 ​ — Paycheck Protection Program Loan ​ 119,842 ​ — Carrying value of notes payable ​ 774,032 ​ 154,190 Accrued interest ​ 22,656 ​ — Total notes payable and accrued interest ​ $ 796,688 ​ $ 154,190 ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 Notes payable: ​ ​ Notes payable and accrued interest, current ​ $ 248,861 ​ $ 154,190 Notes payable and accrued interest, non-current ​ 547,827 ​ — Total notes payable and accrued interest ​ $ 796,688 ​ $ 154,190

Equity (Tables)_2

Equity (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Class of Stock [Line Items]
Schedule of Assumptions		​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ ​ 2020 2019 Strike price $ 15.25 ​ $ 11.00 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.19%-0.28 % 2.40 % Expected term ​ 3.00-5.00 ​ 5.00 ​ Dividend yield ​ — ​ — ​
Summary of activity in warrants	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Aggregate ​ ​ Total Warrants ​ Term ​ Exercise Price ​ Intrinsic Value Outstanding as of December 31, 2020 (as previously reported) 620,055 11.08 ​ $ 14.61 ​ $ 22,127,594 Retroactive application of reverse recapitalization (Note 4) ​ 2,455,415 ​ — ​ ​ (13.53) ​ ​ — Outstanding as of December 31, 2020, effect of Merger (Note 4) ​ 3,075,470 ​ 4.34 ​ ​ 1.09 ​ ​ 150,955,963 Issued 3,329,812 3.00 ​ 3.19 ​ 111,082,528 Exercised (1,496,216) ​ ​ (3.19) ​ (49,913,766) Outstanding as of March 31, 2021 4,909,066 3.74 ​ $ 1.78 ​ $ 244,574,345 Issued 3,586,250 5.00 ​ 11.50 ​ 45,724,688 Outstanding as of June 30, 2021 8,495,316 4.09 ​ $ 24.78 ​ $ 42,385,824	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ Average ​ Weighted ​ ​ ​ ​ ​ ​ ​ Remaining ​ Average ​ Average ​ ​ Total Warrants Term Exercise Price Intrinsic Value Outstanding as of December 31, 2018 ​ 48,627 ​ 2.88 ​ $ 7.90 ​ $ — Issued 8,846 5.00 ​ 11.00 ​ — Outstanding as of December 31, 2019 57,473 2.22 ​ $ 8.38 ​ $ — Issued 562,581 4.99 ​ 15.25 ​ 20,112,271 Outstanding as of December 31, 2020 620,054 11.08 ​ $ 14.61 ​ $ 22,127,594
Legacy NeuroRx Warrants
Class of Stock [Line Items]
Schedule of Assumptions	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, December 31, ​ 2021 ​ 2020 Strike price ​ $ 24.25 $ 3.19 ​ Volatility rate ​ 80.0 % ​ 80.0 % Risk-free rate ​ 0.03%-0.32 % ​ 0.19%-0.28 % Expected term ​ 0.57-4.42 ​ 3.00-5.00 ​ Dividend yield ​ — ​ — ​
Substitute Warrants
Class of Stock [Line Items]
Schedule of Assumptions	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Original Warrants Substitute Warrants Strike price ​ $ 7.58-$15.84 ​ $ 1.53-$3.19 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.03%-0.32 % 0.03%-0.32 % Expected term ​ 0.57-4.42 ​ 0.57-4.42 ​ Dividend yield ​ — ​ — ​

Stock-Based Compensation (Tab_2

Stock-Based Compensation (Tables)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Stock-Based Compensation
Summary of fair value of the original NeuroRx options and Substitute Options determined using the Black-Scholes option-pricing model	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Original Options Substitute Options Strike price ​ $ 1.00-$72.30 ​ $ 0.20-$14.58 ​ Volatility rate ​ 80.0 % 80.0 % Risk-free rate ​ 0.07%-0.79 % 0.07%-0.79 % Expected term ​ 0.18-5.99 ​ 0.18-5.99 ​ Dividend yield ​ — ​ — ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 December 31, 2020 Exercise price $ 11.69-$23.41 ​ $ 2.22-$3.07 ​ Risk-free rate of interest ​ 0.79%-1.24 % 0.79%-0.79 % Expected term (years) ​ 5.5-6.5 ​ 4.7-5.9 ​ Expected stock price volatility ​ 80 % 80 % Dividend yield ​ — ​ — ​	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ December 31, ​ 2020 2019 ​ Exercise price ​ $ 11.00‑$15.25 $ 11.00 ​ Risk-free rate of interest ​ 0.30%‑0.49 % ​ 1.54%‑1.73 % Expected term (years) ​ 5.5 6.5 ​ 6.0 6.5 ​ Expected stock price volatility ​ 80 % ​ 80 % Dividend yield ​ — ​ — ​
Schedule of share-based compensation arrangements by share-based payment award	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ Weighted ​ average ​ Aggregate ​ ​ Number of ​ average ​ remaining ​ intrinsic ​ shares exercise price term (years) value Outstanding as of December 31, 2020 (as previously reported) 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Retroactive application of reverse recapitalization 1,927,548 ​ (8.62) ​ ​ ​ Outstanding as of December 31, 2020, effect of Merger 2,414,303 ​ $ 2.17 8.2 ​ $ 53,659,966 Options granted 210,800 ​ ​ 11.69 9.8 ​ ​ 3,825,276 Forfeited (198,400) ​ ​ (2.22) — ​ ​ (6,587,328) Outstanding as of March 31, 2021 ​ 2,426,703 ​ $ 14.58 ​ 8.7 ​ $ 30,388,510 Options granted ​ 587,030 ​ ​ 14.94 ​ 9.9 ​ ​ — Forfeited ​ (89,280) ​ ​ (7.86) ​ — ​ ​ (339,082) Exercised ​ (4,960) ​ ​ (3.07) ​ — ​ ​ (42,385) Outstanding as of June 30, 2021 ​ 2,919,493 ​ $ 5.25 ​ 9.0 ​ $ 20,558,299 Options vested and exercisable as of June 30, 2021 ​ 1,095,294 ​ $ 1.50 ​ 6.1 ​ $ 11,106,829 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three months ended June 30, ​ Six months ended June 30, ​ 2021 2020 2021 2020 Stock-based compensation expense ​ ​ ​ ​ General and administrative ​ $ 4,094,549 ​ $ 50,881 ​ $ 4,438,583 ​ $ 117,469 Regulatory and process development ​ 188,781 ​ 42,585 ​ 216,445 ​ 64,800 Total stock-based compensation expense ​ $ 4,283,330 ​ $ 93,466 ​ $ 4,655,028 ​ $ 182,269	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Weighted ​ ​ ​ ​ ​ ​ ​ ​ ​ average ​ ​ ​ ​ ​ ​ ​ Weighted ​ remaining ​ Aggregate ​ ​ Number of ​ average ​ contractual ​ intrinsic ​ ​ shares ​ exercise price ​ life (in years) ​ value Outstanding as of December 31, 2018 355,408 ​ $ 5.74 8.2 ​ $ 1,782,729 Granted 28,180 ​ 11.00 9.6 ​ Forfeited/Cancelled (50,000) ​ — — ​ — Outstanding as of December 31, 2019 333,588 ​ $ 5.74 7.2 ​ $ 1,782,729 Granted 266,500 ​ 14.37 9.7 ​ 9,761,125 Forfeited /Cancelled (113,333) ​ — — ​ — Outstanding as of December 31, 2020 486,755 ​ $ 10.79 8.8 ​ $ 19,571,655 Options vested and exercisable as of December 31, 2020 329,489 ​ $ 6.31 4.0 ​ $ 14,723,342

Fair Value Measurements (Tables

Fair Value Measurements (Tables)	6 Months Ended
	Jun. 30, 2021
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Summary of fair value hierarchy	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Description Level June 30, 2021 December 31, 2020 Liabilities: ​ ​ ​ ​ ​ ​ ​ ​ Warrant liabilities (Note 10) ​ 3 ​ $ 515,025 ​ $ — Earnout Cash liability (Note 4) 3 ​ $ 25,874,896 ​ $ —
Schedule of significant unobservable inputs	The significant unobservable inputs used in the Black-Scholes model to measure the warrant liability that are categorized within Level 3 of the fair value hierarchy are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ June 30, 2021 At Effective Time Stock price on valuation date ​ $ 11.62 ​ $ 24.25 ​ Exercise price per share ​ $ 11.50 ​ $ 11.50 ​ Expected life ​ 4.90 ​ 5.0 ​ Volatility ​ 35.7 % 39.0 % Risk-free rate ​ 0.9 % 0.8 % Dividend yield ​ — % — % Fair value of warrants ​ $ 3.78 ​ $ 14.56 ​
Common stock warrant [Member]
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Schedule of reconciliation of liabilities	A reconciliation of warrant liabilities is included below: ​ ​ ​ ​ ​ Fair Value Balance as of December 31, 2020 ​ $ — Additions pursuant to Merger ​ 1,983,674 Gain upon re-measurement ​ (1,468,649) Balance as of June 30, 2021 ​ $ 515,025 ​
Earnout Cash liability
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Schedule of reconciliation of liabilities	A reconciliation of the Earnout Cash liability is included below: ​ ​ ​ ​ ​ Fair Value Balance as of December 31, 2020 ​ $ — Additions pursuant to Merger ​ 25,520,195 Loss upon re-measurement ​ 354,701 Balance as of June 30, 2021 ​ $ 25,874,896

Liquidity - Additional Informat

Liquidity - Additional Information (Details) - USD ($)	Mar. 28, 2021	Jul. 31, 2021	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Schedule of Liquidity [Line Items]
Cash			$ 13,386,332	$ 995,985	$ 1,858,513	$ 877,421	$ 621,296
Proceeds from collaboration agreement			771,244		10,160,421
Proceeds from issuance of common stock			$ 8,489,082	$ 176,990	$ 2,579,114	$ 5,802,002
Proceeds from issuance of common stock for exercise of warrant	$ 7,500,018
Subsequent Event | Common stock warrant [Member]
Schedule of Liquidity [Line Items]
Common stock issued, shares		1,833,596
Proceeds from issuance of common stock for exercise of warrant		$ 9,186,316

Summary of Significant Accou_10

Summary of Significant Accounting Policies - Additional Information (Details) - USD ($)	Jun. 30, 2021	Dec. 31, 2020
Summary Of Significant Accounting Policies [Abstract]
Allowance for doubtful accounts	$ 5,470,897	$ 257,463

Summary of Significant Accou_11

Summary of Significant Accounting Policies - Schedule of Outstanding Shares of Common Stock Equivalents Excluded From Diluted Net Loss Per Share (Details) - shares	3 Months Ended	6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Convertible Preferred Stock [Member]
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share				2,371,710	2,367,543
Stock Options [Member]
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	2,919,493	2,919,493	1,166,863	486,755	333,588
Common stock warrant [Member]
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	8,495,316	8,495,316	1,670,352	620,054	57,473
Common stock issuable pursuant to UPOs
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	600,000	600,000
Common stock warrants pursuant to UPOs
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	300,000	300,000
Public Rights pursuant to UPOs
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	60,000	60,000
Earnout Shares
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	22,209,280	22,209,280

Summary of Significant Accou_12

Summary of Significant Accounting Policies - basic and diluted earnings per share calculations (Details) - USD ($)	3 Months Ended		6 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Numerator:
Net income (loss) attributable to common stock-basic and diluted	$ (16,007,973)	$ 102,287	$ (41,496,847)	$ (1,487,769)
Denominator:
Weighted average shares - basic	41,727,480	33,819,205	38,709,614	33,799,503
Effect of other dilutive securities		2,837,215
Weighted average shares - diluted	41,727,480	36,656,420	38,709,614	33,799,503
Basic earnings (loss) per share	$ (0.38)		$ (1.07)	$ (0.04)
Diluted earnings (loss) per share	$ (0.38)		$ (1.07)	$ (0.04)

Reverse Recapitalization (Detai

Reverse Recapitalization (Details)	May 24, 2021$ / sharesshares	May 23, 2021	Jun. 30, 2021USD ($)$ / sharesshares	Mar. 31, 2021USD ($)	Mar. 31, 2020USD ($)	Jun. 30, 2021USD ($)$ / sharesshares
Business Acquisition [Line Items]
Deemed dividend - Earnout Shares | $			$ 253,130,272			$ 253,130,272
Earnout shares for common stockholders						22,209,280
Earnout cash for common stockholders | $						$ 88,837,121
Common stock issued | $			$ 1,562,272	$ 6,927,086	$ 177,025
Substitute Warrants
Business Acquisition [Line Items]
Contingent Consideration (in shares)			1,920,492			1,920,492
Substitute Options
Business Acquisition [Line Items]
Contingent Consideration (in shares)			935,608			935,608
Merger agreement
Business Acquisition [Line Items]
Contingent Consideration (in shares)			25,000,000			25,000,000
Contingent Consideration | $			$ 100,000,000			$ 100,000,000
Number of business days for issue of Earnout shares						5 days
Stock Issued During Period, Shares, New Issues						3,729,730
Merger agreement | Subscription agreements
Business Acquisition [Line Items]
Issue price (in dollars per share) | $ / shares			$ 10			$ 10
Stock Issued During Period, Shares, New Issues						1,000,000
Common stock issued | $						$ 10,000,000
Merger agreement | Stockholders of NeuroRx
Business Acquisition [Line Items]
Closing Consideration shares	50,000,000
Issue price (in dollars per share) | $ / shares	$ 0.001
Exchange Ratio	3.16	4.96

Reverse Recapitalization - Equi

Reverse Recapitalization - Equity (Details) - Merger agreement	6 Months Ended
	Jun. 30, 2021USD ($)
Business Acquisition [Line Items]
Cash - BRPA trust and cash, net of redemptions	$ 4,362,474
Cash - PIPE financing, net of transaction costs	8,100,000
Non-cash net working capital assumed from BRPA	(961,555)
Less: notes payable assumed from BRPA	(1,100,000)
Less: fair value of assumed Placement Warrants	(1,983,674)
Less: fair value of Earnout Cash	(25,520,195)
Less: transaction costs and advisory fees allocated to NRXP equity	(1,412,846)
Effect of Merger, net of redemptions and transaction costs	(26,615,796)
Effect of Merger, net of redemptions and transaction costs	$ 11,049,628

Reverse Recapitalization - Cons

Reverse Recapitalization - Consummation of the merger (Details) - shares	May 24, 2021	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Business Acquisition [Line Items]
Total shares of common stock immediately after Merger		48,603,585	42,973,462	10,686,191
Merger agreement
Business Acquisition [Line Items]
Common stock, outstanding prior to Merger		552,412
Less: redemption of BRPA shares		(216)
Common stock of BRPA		552,196
Shares issued in PIPE Financing		1,000,000
Shares issued for services		200,000
Shares issued pursuant to conversion of Public and Private Rights		717,250
Issuance of common stock shares		3,729,730
Total shares of common stock immediately after Merger		48,603,585
Merger agreement | Stockholders of NeuroRx
Business Acquisition [Line Items]
BRPA Founder and private shares, net of forfeited shares of 875,216	50,000,000
NeuroRx shares - common stock (1)		44,873,855
Common stock outstanding upon conversion prior to Merger		14,200,586
Merger agreement | BRPA Founder and private shares
Business Acquisition [Line Items]
BRPA Founder and private shares, net of forfeited shares of 875,216		1,260,284
Number of shares forfeited		875,216

Prepaid Expenses and Other Cu_3

Prepaid Expenses and Other Current Assets (Details) - USD ($)	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Prepaid Expenses and Other Current Assets
Prepaid insurance	$ 3,347,172	$ 49,029
Prepaid manufacturing expenses	1,407,500
Other prepaid expenses	341,336	164,772
Prepaid income taxes	51,642
Other current assets		26,551
Total accrued and other current liabilities	$ 5,147,650	$ 240,352	$ 97,585

Accrued and Other Current Lia_6

Accrued and Other Current Liabilities - Summary of accrued and other current liabilities (Details) - USD ($)	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Accrued and other current liabilities:
Accrued research and development expenses	$ 826,442	$ 586,426
Accrued employee expenses	77,196	530,500
Professional services	185,170	606,553
Other accrued expenses	417,529	5,004
Total accrued and other current liabilities	$ 1,506,337	$ 1,728,483	$ 9,649

Convertible Notes Payable - A_2

Convertible Notes Payable - Additional Information (Details) - USD ($)	Feb. 12, 2020	Apr. 25, 2018	Nov. 19, 2017	Nov. 16, 2017	Jun. 30, 2021	Jun. 30, 2020	Apr. 25, 2018	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019	Apr. 06, 2020	Jan. 05, 2018
Schedule of Convertible Notes [Line Items]
Sale and issuance of common shares	$ 10,000,000
Fair value per share	$ 10.63
Accrued interest converted into common stock	132,739
Discounted price per share	$ 2.78
Accrued interest	$ 369,660				$ 31,976			$ 31,976		$ 22,656
Common stock fair value						$ 0			$ 306,641
Interest rate					6.00%			6.00%		6.00%		2.00%
Accrued interest											$ 349,891
Interest paid					$ 0	0
Debt discount											296,437
Fair value of the common shares issued										$ 306,641
Convertible Debt [Member]
Schedule of Convertible Notes [Line Items]
Aggregate principal amount of convertible notes	$ 2,800,000
Accrued interest converted into common stock	1,005,458
Discounted price per share	$ 2.78
Two Thousand And Seventeen Convertible Notes [Member]
Schedule of Convertible Notes [Line Items]
Convertible notes gross proceeds			$ 2,500,000	$ 2,500,000
Interest rate			6.00%
Principal and interest maturity date			4 years
Sale of stock			$ 10,000,000
Conversion price description			outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price
Accrued interest		$ 200,000					$ 200,000
Two Thousand And Eighteen Note [Member]
Schedule of Convertible Notes [Line Items]
Convertible notes gross proceeds		$ 300,000
Interest rate		6.00%					6.00%
Principal and interest maturity date		4 years
Sale of stock		$ 10,000,000
Conversion price description		outstanding principal balance will be converted into the number of such securities sold at a conversion price equal to 80% of the securities negotiated share price.
Accrued interest													$ 100,000
Two Thousand Seventeen And Eighteen Convertible Notes Payable[Member]
Schedule of Convertible Notes [Line Items]
Recognized gain (loss)at fair value								$ 0	27,160
Amortization debt discount					0	0		0	0
Interest paid								$ 0	$ 16,454
Two Thousand Seventeen And Eighteen Convertible Notes Payable[Member]
Schedule of Convertible Notes [Line Items]
Recognized gain (loss)at fair value					$ 0	$ 0
Debt discount										493,982	57,204
Recognized loss										$ 27,160	$ 162,866
Two Thousand Eighteen Convertible Notes Payable [Member]
Schedule of Convertible Notes [Line Items]
Convertible notes gross proceeds							$ 300,000

Notes Payable - Notes payable_2

Notes Payable - Notes payable and Accrued Interest (Details) - USD ($)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019	Feb. 12, 2020
Note Payable - Related Party	$ 154,190	$ 154,190	$ 154,190
Carrying value of notes payable	(654,190)	(774,032)	(154,190)
Accrued interest	31,976	22,656		$ 369,660
Note payable	686,166	796,688	154,190
Notes payable and accrued interest, current	173,694	248,861	$ 154,190
Notes payable and accrued interest, non-current	512,472	547,827
Relief Therapeutics Loan [Member]
Note Payable - Related Party	$ 500,000	500,000
Paycheck Protection Program Loans [Member]
Note Payable - Related Party		$ 119,842

Notes Payable - Additional In_2

Notes Payable - Additional Information (Details) - USD ($)	Apr. 28, 2020	Apr. 06, 2020	Jul. 01, 2019	Jun. 30, 2021	Dec. 31, 2020
Related party loan			$ 154,190
Interest rate		2.00%		6.00%	6.00%
Related party loan		$ 500,000
Debt Instrument, Maturity Date		Apr. 6, 2022
Loan term	2 years
Loan forgiveness, description	The Loan amount may be eligible for forgiveness pursuant to (1) at least 75% of the loan proceeds are used to cover payroll costs and the remainder is used for mortgage interest, rent and utility costs over the eight week period after the loan is made, and (2) the number of employees and compensation levels are generally maintained.
Outstanding principal written off				$ 119,842
Outstanding accrued and unpaid interest written off				968
Gain on extinguishment of debt				120,810
Relief Therapeutics Loan [Member]
Interest rate		2.00%
Related party loan		$ 500,000
Debt Instrument, Maturity Date		Apr. 6, 2022
Pay Check Protection Program [Member]
Loan funding	$ 119,842
Outstanding principal rate	1.00%
Principal and interest due	$6,744
Gain on extinguishment of debt				$ 120,810

Commitments and Contingencies -

Commitments and Contingencies - Additional Information (Details) - USD ($)

May 14, 2021

May 11, 2021

Mar. 28, 2021

Jan. 04, 2021

Dec. 13, 2020

Aug. 25, 2020

Oct. 31, 2019

Apr. 30, 2019

Dec. 31, 2018

Jul. 31, 2021

Jun. 30, 2021

Jun. 30, 2020

Jun. 30, 2021

Jun. 30, 2020

Dec. 31, 2020

Dec. 31, 2019

Oct. 09, 2020

Commitments and Contingencies [Line Items]

Rent expense

$ 48,776

$ 9,087

$ 55,393

$ 17,902

$ 54,649

$ 42,040

Percentage of company's annual requirements

100.00%

Allowance for doubtful accounts

5,470,897

5,470,897

257,463

Accrued settlement expense

39,486,139

Settlement expense

$ 21,365,641

21,365,641

39,486,139

Proceeds from exercise of warrant

7,500,018

Legal costs

$ 116,732

Founder returned shares

300,000

Settlement liability expense

5,616,732

Transfer of shares, value

5,500,000

G E M Warrant [Member]

Commitments and Contingencies [Line Items]

Warrant issued

3,329,812

Exercise price of warrant

$ 3.19

Warrants to purchase shares

1,496,216

Warrants to purchase shares, amount

$ 7,500,018

Warrants expire period

The GEM Warrant will be valid for a period of three years from the date NeuroRx’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction of the type contemplated by the Merger Agreement.

Accrued settlement expense

39,486,139

Subsequent Event

Commitments and Contingencies [Line Items]

Issuance of common stock for exercise of warrant, shares

1,833,596

Proceeds from exercise of warrant

$ 9,186,316

Subsequent Event | G E M Warrant [Member]

Commitments and Contingencies [Line Items]

Warrant issued

1,053,738

Warrants to purchase shares

473,486

Warrants to purchase shares, amount

$ 7,500,000

Warrants expire period

The GEM Warrant will be valid for a period of three years from the date the Company’s stock is listed for trading on a national securities exchange or consummation of a reverse merger transaction.

Former Adviser [Member]

Commitments and Contingencies [Line Items]

Transfer of shares, value

$ 499,994

Transfer of shares

45,454

Maximum [Member]

Commitments and Contingencies [Line Items]

Annual maintenance fees

$ 150,000

Jonathan Javitt Living Trust [Member]

Commitments and Contingencies [Line Items]

Transfer of shares

250,000

Sarah Herzog Memorial Hospital Ezrat Nashim [Member]

Commitments and Contingencies [Line Items]

Transfer of shares, value

$ 5,500,000

Milestone payments

$ 250,000

Transfer of shares

500,000

500,000

Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Minimum [Member]

Commitments and Contingencies [Line Items]

Royalty percentage

1.00%

Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Maximum [Member]

Commitments and Contingencies [Line Items]

Royalty percentage

2.50%

Annual maintenance fees

$ 150,000

Development Milestone [Member] | Minimum [Member]

Commitments and Contingencies [Line Items]

Milestone payments

$ 100,000

Development Milestone [Member] | Maximum [Member]

Commitments and Contingencies [Line Items]

Milestone payments

$ 750,000

Development Milestone [Member] | Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Minimum [Member]

Commitments and Contingencies [Line Items]

Milestone payments

100,000

Development Milestone [Member] | Sarah Herzog Memorial Hospital Ezrat Nashim [Member] | Maximum [Member]

Commitments and Contingencies [Line Items]

Milestone payments

750,000

Relief Therapeutics Collaboration Agreement [Member]

Commitments and Contingencies [Line Items]

Reimbursable expenses

$ 10,904,065

$ 10,612,750

5,984,679

10,160,421

Reimbursable expenses received

770,444

9,329,031

Allowance for doubtful accounts

5,470,897

$ 5,470,897

$ 257,463

Invoiced costs

$ 6,000,000

$ 4,000,000

Big Rock Partners Acquisition Corp [Member] | Merger Agreement [Member]

Commitments and Contingencies [Line Items]

Earnout Shares Milestone

25,000,000

Earnout Cash Milestone

$ 100,000,000

Earnout Shares Milestone Description

an aggregate of 25 million additional shares of Big Rock common stock (“Earnout Shares”) will be issued to NeuroRx pre-merger equity holders if, prior to December 31, 2022, (1) the Company’s COVID-19 drug receives emergency use authorization by the FDA and (2) the FDA accepts the Company’s filing of its application to approve the Company’s COVID-19 drug

Earnout Cash Milestone Description

In addition, subject to certain conditions, $100 million (“Earnout Cash”) may be payable to NeuroRx pre-merger equity holders if, prior to December 31, 2022, either (1) FDA approval of the Company’s COVID-19 Drug is obtained and the Company’s COVID-19 Drug is listed in the FDA’s “Orange Book” and (2) FDA approval of the Company’s Antidepressant Drug Regimen is obtained and the Company’s Antidepressant Drug Regimen is listed in the FDA’s “Orange Book”.

GEM Share Subscription Facility Agreement

Commitments and Contingencies [Line Items]

Share subscription agreement term

3 years

Share subscription value

95,600,000

$ 95,600,000

Commitment fee

1,900,000

Polypeptide [Member]

Commitments and Contingencies [Line Items]

Purchase commitments

$ 1,010,000

Aerogen Limited | Subsequent Event

Commitments and Contingencies [Line Items]

Purchase order of products

$ 54,315

Sponsored Research Agreement [Member]

Commitments and Contingencies [Line Items]

Research commitments

360,450

Research commitments paid

$ 0

$ 126,157

Equity - Additional Informati_2

Equity - Additional Information (Details)	Mar. 28, 2021USD ($)$ / sharesshares	Jul. 31, 2021USD ($)	Jan. 31, 2021shares	Jun. 30, 2021USD ($)$ / sharesshares	Mar. 31, 2021USD ($)$ / sharesshares	Jun. 30, 2020USD ($)shares	Mar. 31, 2020USD ($)$ / sharesshares	Jun. 30, 2021USD ($)D$ / sharesshares	Jun. 30, 2020USD ($)shares	Dec. 31, 2020USD ($)$ / sharesshares	Dec. 31, 2019USD ($)$ / sharesshares	May 24, 2021shares	Oct. 23, 2020USD ($)$ / shares	Jul. 15, 2020USD ($)$ / shares	Jul. 06, 2020USD ($)$ / shares	Mar. 01, 2020$ / sharesshares	Jan. 31, 2019USD ($)$ / shares
Stockholders Equity [Line Items]
Common stock, shares authorized				500,000,000				500,000,000		500,000,000	14,060,001					14,060,001
Common stock, par value | $ / shares				$ 0.001				$ 0.001		$ 0.001	$ 0.001					$ 0.001
Common stock issued | $				$ 1,562,272	$ 6,927,086		$ 177,025
Proceeds from issuance of common stock | $								$ 8,489,082	$ 176,990	$ 2,579,114	$ 5,802,002
Stock option awards granted					210,800
Compensation expenses | $				$ 4,283,330		$ 93,466		4,655,028	182,269
Conversion of notes payable into common stock | $										$ 3,655,438	0
Loss on settlement of accounts payable | $								$ (120,810)
Preferred stock, shares authorized				50,000,000				50,000,000		50,000,000
Preferred stock, shares issued				0				0		0
Preferred stock, par value | $ / shares				$ 0.001				$ 0.001		$ 0.001
Preferred stock, shares outstanding				0				0		0
Warrant issued					3,329,812
Outstanding, weighted average exercise price | $ / shares				$ 24.78	$ 1.78			$ 24.78		$ 1.09
Proceeds from exercise of warrant | $								$ 7,500,018
Issuance of common stock for exercise of warrant | $					$ 7,500,018
Reclassification of settlement liability upon issuance of warrant | $					$ 60,851,779
Warrants and rights outstanding	473,486			8,495,316	4,909,066			8,495,316		3,075,470
Warrant expense | $								$ (1,468,649)		$ 5,382,905	$ 0
Number of units outstanding				600,000				600,000
Price per unit | $ / shares				$ 10				$ 10
Aggregate exercise price | $				$ 6,000,000				$ 6,000,000
Number of shares per unit								1
Number of shares per right								1
Unit expiration term								5 years
Demand right term								5 years
Piggy back right term								7 years
Fractional shares issued upon conversion of rights								0
Unamortized compensation costs | $				$ 33,610,165				$ 33,610,165		$ 2,193,874
Subsequent Event
Stockholders Equity [Line Items]
Stock option awards granted			42,500
Proceeds from exercise of warrant | $		$ 9,186,316
Issuance of common stock for exercise of warrant | $		1,833,596
Legacy NeuroRx Warrants
Stockholders Equity [Line Items]
Warrant issued				3,586,250
Substitute Warrants
Stockholders Equity [Line Items]
Outstanding, weighted average exercise price | $ / shares				$ 2.50				$ 2.50
Warrants exercised				4,909,066				4,909,066
Deemed dividend - Earnout Shares | $								$ 2,691,799
Reclassification of settlement liability upon issuance of warrant | $								0
Incremental compensation on modification | $				$ 2,330,572				2,330,572
Unamortized compensation costs | $				$ 23,760,993				23,760,993
Additional deemed dividend recognized in the event of earnout shares milestone | $								24,379,657
Additional deemed dividend recognized in the event of earnout cash milestone | $								$ 3,068,732
Public Warrants
Stockholders Equity [Line Items]
Outstanding, weighted average exercise price | $ / shares				$ 11.50				$ 11.50
Warrants and rights outstanding				3,450,000				3,450,000
Number of shares per warrant				1				1
Warrants expiration term				5 years				5 years
Redemption price per warrant (in dollars per share) | $ / shares								$ 0.01
Minimum threshold written notice period for redemption of warrants								30 days
Stock price trigger for redemption of warrants (in dollars per share) | $ / shares								$ 21
Threshold trading days for redemption of warrants | D								20
Redemption period | D								30
Number of warrants per unit								1
Placement Warrants
Stockholders Equity [Line Items]
Warrants and rights outstanding				136,250				136,250
Warrant expense | $				$ 1,468,649		0		$ 1,468,649	0
Public Right
Stockholders Equity [Line Items]
Warrants and rights outstanding				6,900,000				6,900,000
Number of shares per unit								1
Number of shares per right								1
Placement Rights
Stockholders Equity [Line Items]
Warrants and rights outstanding				272,500				272,500
Convertible Series B-1 Preferred Stock [Member]
Stockholders Equity [Line Items]
Preferred stock, shares authorized										1,050,695	1,050,695
Preferred stock, shares issued										1,050,695	1,050,695
Preferred stock, par value | $ / shares										$ 0.001	$ 0.001
Preferred stock, conversion basis										one share of Common Stock for each preferred share
Convertible preferred stock, liquidation preference per share | $ / shares										$ 7.58
Preferred stock, shares outstanding										1,050,695	1,050,695
Convertible Series B-2 Preferred Stock [Member]
Stockholders Equity [Line Items]
Preferred stock, shares authorized										100,000	100,000
Preferred stock, shares issued										4,167	0
Preferred stock, par value | $ / shares										$ 0.001	$ 0.001
Preferred stock, conversion basis										one share of Common Stock for each share of Series B-2 Convertible Preferred Stock
Convertible preferred stock, liquidation preference per share | $ / shares										$ 12
Preferred stock, shares outstanding										4,167	0
Common stock warrants [Member]
Stockholders Equity [Line Items]
Outstanding, weighted average exercise price | $ / shares													$ 15.25	$ 15.25	$ 15.25		$ 11
Warrant expiry date													Oct. 22, 2025	Jul. 14, 2025	Jul. 5, 2023		Jan. 30, 2024
Fair value on the date of issuance | $													$ 2,693,221	$ 2,689,684	$ 30,536		$ 63,337
Warrant, fair valued price per share | $ / shares													$ 9.64	$ 9.63	$ 7.63		$ 7.16
Common stock warrants [Member] | Legacy NeuroRx Warrants
Stockholders Equity [Line Items]
Warrant issued	3,329,812
Outstanding, weighted average exercise price | $ / shares	$ 3.19
Warrant expiry date	Mar. 27, 2024
Fair value on the date of issuance | $	$ 60,851,779
Warrants exercised	1,496,216
Gross proceeds from exercise of warrants | $	$ 7,500,018
Common stock warrants [Member] | Legacy NeuroRx Warrants | Subsequent Event
Stockholders Equity [Line Items]
Proceeds from exercise of warrant | $		1,833,596
Issuance of common stock for exercise of warrant | $		$ 9,186,316
General and Administrative Expense [Member]
Stockholders Equity [Line Items]
Compensation expenses | $				$ 4,094,549		$ 50,881		$ 4,438,583	$ 117,469	$ 332,065	$ 321,087
Common Stock
Stockholders Equity [Line Items]
Common stock, shares authorized																20,000,000
Issuance of common stock shares				65,526		0		398,647	50,844	171,796	536,354
Proceeds from issuance of common stock | $				$ 1,436,274		$ 0		$ 8,363,132	$ 176,990	$ 2,579,114	$ 5,802,002
Stock option awards granted				200,000
Common shares issued										9,500
Debt conversion, original debt, amount | $										$ 144,875
Loss on settlement of accounts payable | $										(41,617)
Common Stock | Accounts Payable [Member]
Stockholders Equity [Line Items]
Debt conversion, original debt, amount | $										$ 103,258
Common Stock | General and Administrative Expense [Member]
Stockholders Equity [Line Items]
Compensation expenses | $				$ 4,850,000				$ 4,850,000
Legacy NeuroRx Preferred Stock | Convertible Series A Preferred Stock [Member]
Stockholders Equity [Line Items]
Preferred stock, shares authorized				1,000,000				1,000,000		1,000,000
Preferred stock, shares issued				1,000,000				1,000,000		1,000,000
Preferred stock, par value | $ / shares				$ 0.001				$ 0.001		$ 0.001
Preferred stock, conversion basis								one share of common stock for each preferred share
Convertible preferred stock, liquidation preference per share | $ / shares				$ 1				$ 1		$ 1
Preferred stock, shares outstanding												2,367,543
Shares issued upon conversion												7,480,836
Legacy NeuroRx Preferred Stock | Convertible Series B-1 Preferred Stock [Member]
Stockholders Equity [Line Items]
Preferred stock, shares authorized				1,050,695				1,050,695		1,050,695
Preferred stock, shares issued				1,050,695				1,050,695		1,050,695
Convertible preferred stock, liquidation preference per share | $ / shares				$ 7.58				$ 7.58		$ 7.58
Legacy NeuroRx Preferred Stock | Convertible Series B-1A Preferred Stock [Member]
Stockholders Equity [Line Items]
Preferred stock, shares authorized				316,848				316,848		316,848
Preferred stock, shares issued				316,848				316,848		316,848
Convertible preferred stock, liquidation preference per share | $ / shares				$ 6.82				$ 6.82		$ 6.82
Legacy NeuroRx Preferred Stock | Convertible Series B-2 Preferred Stock [Member]
Stockholders Equity [Line Items]
Preferred stock, shares authorized										100,000
Preferred stock, shares issued							4,167
Preferred stock, par value | $ / shares										$ 0.001
Preferred stock, conversion basis										one share of common stock for each share of B-2 Preferred Stock
Convertible preferred stock, liquidation preference per share | $ / shares							$ 12			$ 12
Preferred stock, shares outstanding												4,167
Shares issued upon conversion												13,168

Equity - Schedule of Assumpti_2

Equity - Schedule of Assumptions (Details) - $ / shares	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Class of Warrant or Right [Line Items]
Strike price			$ 11
Volatility rate	80.00%	80.00%	80.00%
Risk-free rate of interest, minimum	0.79%	0.79%
Risk-free rate, maximum	1.24%	0.79%
Dividend yield	0.00%	0.00%
Legacy NeuroRx Warrants
Class of Warrant or Right [Line Items]
Strike price	$ 24.25	$ 3.19
Volatility rate	80.00%	80.00%
Risk-free rate of interest, minimum	0.03%	0.19%
Risk-free rate, maximum	0.32%	0.28%
Dividend yield	0.00%	0.00%
Substitute Warrants
Class of Warrant or Right [Line Items]
Volatility rate	80.00%
Risk-free rate of interest, minimum	0.03%
Risk-free rate, maximum	0.32%
Common stock warrant [Member]
Class of Warrant or Right [Line Items]
Strike price		$ 15.25	$ 11
Volatility rate	80.00%
Risk-free rate			2.40%
Risk-free rate of interest, minimum	0.03%
Risk-free rate, maximum	0.32%
Expected term (years)			5 years
Dividend yield		0.00%	0.00%
Minimum [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 11.69	$ 2.22
Risk-free rate of interest, minimum		0.30%	1.54%
Expected term (years)	5 years 6 months	4 years 8 months 12 days	6 years
Minimum [Member] | Legacy NeuroRx Warrants
Class of Warrant or Right [Line Items]
Expected term (years)	6 months 25 days	3 years
Minimum [Member] | Substitute Warrants
Class of Warrant or Right [Line Items]
Strike price	$ 1.53
Expected term (years)	6 months 25 days
Minimum [Member] | Common stock warrant [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 7.58
Risk-free rate		0.19%
Expected term (years)	6 months 25 days	3 years
Maximum [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 23.41	$ 3.07
Risk-free rate of interest, minimum		0.49%	1.73%
Expected term (years)	6 years 6 months	5 years 10 months 24 days	6 years 6 months
Maximum [Member] | Legacy NeuroRx Warrants
Class of Warrant or Right [Line Items]
Expected term (years)	4 years 5 months 1 day	5 years
Maximum [Member] | Substitute Warrants
Class of Warrant or Right [Line Items]
Strike price	$ 3.19
Expected term (years)	4 years 5 months 1 day
Maximum [Member] | Common stock warrant [Member]
Class of Warrant or Right [Line Items]
Strike price	$ 15.84
Risk-free rate		0.28%
Expected term (years)	4 years 5 months 1 day	5 years

Equity - Schedule of Warrants_2

Equity - Schedule of Warrants (Details) - USD ($)	Mar. 28, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020
Total Warrants
Beginning Balance		4,909,066	3,075,470
Issued			3,329,812
Exercised			(1,496,216)
Ending Balance	473,486	8,495,316	4,909,066	3,075,470
Weighted Average Remaining Term
Outstanding at the beginning (in years)		4 years 1 month 2 days	3 years 8 months 26 days	4 years 4 months 2 days
Issued (in years)			3 years
Weighted Average Exercise Price
Outstanding at the beginning (in dollars per share)		$ 1.78	$ 1.09
Issued (in dollars per share)			3.19
Exercised (in dollars per share)			(3.19)
Outstanding at the end (in dollars per share)		$ 24.78	$ 1.78	$ 1.09
Aggregate Intrinsic Value
Outstanding at the beginning (in dollars)		$ 244,574,345	$ 150,955,963
Issued (in dollars)			111,082,528
Exercised (in dollars)			(49,913,766)
Outstanding at the end (in dollars)		$ 42,385,824	$ 244,574,345	$ 150,955,963
Legacy NeuroRx Warrants
Total Warrants
Issued		3,586,250
Weighted Average Remaining Term
Issued (in years)		5 years
Weighted Average Exercise Price
Issued (in dollars per share)		$ 11.50
Aggregate Intrinsic Value
Issued (in dollars)		$ 45,724,688
Substitute Warrants
Weighted Average Exercise Price
Outstanding at the end (in dollars per share)		$ 2.50
Public Warrants
Total Warrants
Ending Balance		3,450,000
Weighted Average Exercise Price
Outstanding at the end (in dollars per share)		$ 11.50
Placement Warrants
Total Warrants
Ending Balance		136,250
As Previously Reported
Total Warrants
Beginning Balance			620,055	57,473
Ending Balance				620,055
Weighted Average Remaining Term
Outstanding at the beginning (in years)				11 years 29 days
Weighted Average Exercise Price
Outstanding at the beginning (in dollars per share)			$ 14.61	$ 8.38
Outstanding at the end (in dollars per share)				$ 14.61
Aggregate Intrinsic Value
Outstanding at the beginning (in dollars)			$ 22,127,594
Outstanding at the end (in dollars)				$ 22,127,594
Adjustment
Total Warrants
Beginning Balance			2,455,415
Ending Balance				2,455,415
Weighted Average Exercise Price
Outstanding at the beginning (in dollars per share)			$ (13.53)
Outstanding at the end (in dollars per share)				$ (13.53)

Equity - Assumed Unit Purchase

Equity - Assumed Unit Purchase Options (Details)	6 Months Ended
	Jun. 30, 2021USD ($)$ / sharesshares
Class of Warrant or Right [Line Items]
Number of units outstanding	600,000
Price per unit | $ / shares	$ 10
Aggregate exercise price | $	$ 6,000,000
Number of shares per unit	1
Number of shares per right	1
Unit expiration term	5 years
Demand right term	5 years
Piggy back right term	7 years
Public Right
Class of Warrant or Right [Line Items]
Number of shares per unit	1
Number of shares per right	1
Public Warrants
Class of Warrant or Right [Line Items]
Number of warrants per unit	1

Equity - Conversion of Rights (

Equity - Conversion of Rights (Details) - shares	6 Months Ended
	Jun. 30, 2021	Mar. 31, 2021	Mar. 28, 2021	Dec. 31, 2020
Class of Warrant or Right [Line Items]
Number of outstanding right	8,495,316	4,909,066	473,486	3,075,470
Number of shares per right	1
Fractional shares issued upon conversion of rights	0
Public Right
Class of Warrant or Right [Line Items]
Number of outstanding right	6,900,000
Number of shares per right	1
Public Warrants
Class of Warrant or Right [Line Items]
Number of outstanding right	3,450,000
Placement Rights
Class of Warrant or Right [Line Items]
Number of outstanding right	272,500
Merger agreement
Class of Warrant or Right [Line Items]
Issuance of Common Stock to holders of rights	717,250

Stock Based Compensation - Ad_2

Stock Based Compensation - Additional Information (Details) - USD ($)	3 Months Ended		6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019	Mar. 31, 2021	Dec. 31, 2016
Equity Incentive Plan [Line Items]
Options to purchase shares of common Stock	2,919,493		2,919,493		2,414,303
Exercise price	$ 5.25		$ 5.25		$ 2.17
Expected dividend yield			0.00%
Weighted average grant date fair value	$ 14.31	$ 1.25	$ 18.37	$ 1.25	$ 9.64	$ 7.69
Unrecognized compensation	$ 33,610,165		$ 33,610,165		$ 2,193,874
Weighted-average period			1 year 10 months 20 days		2 years 1 month 2 days
Stock-based compensation expense allocated	4,283,330	$ 93,466	$ 4,655,028	$ 182,269
Substitute Options
Equity Incentive Plan [Line Items]
Share-based Payment Arrangement, Plan Modification, Incremental Cost			25,877,473
General and Administrative Expense [Member]
Equity Incentive Plan [Line Items]
Stock-based compensation expense allocated	4,094,549	50,881	4,438,583	117,469	$ 332,065	$ 321,087
Research and Development Expense [Member]
Equity Incentive Plan [Line Items]
Stock-based compensation expense allocated	$ 188,781	$ 42,585	$ 216,445	$ 64,800	$ 398,340	$ 112,823
2016 Omnibus Inventive Plan [Member]
Equity Incentive Plan [Line Items]
Share-based compensation arrangement by share-based payment award, number of shares authorized	3,472,000		3,472,000		700,000			500,000
Options to purchase shares of common Stock	2,895,423		2,895,423				2,426,703
Exercise price	$ 1.50		$ 1.50				$ 14.58
Share-based compensation arrangement by share-based payment award, number of additional shares authorized					200,000

Stock Based Compensation - Lega

Stock Based Compensation - Legacy NeuroRx 2016 Omnibus Incentive Plan - Stock option (Details) - $ / shares	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price			$ 11
Volatility rate	80.00%	80.00%	80.00%
Risk-free rate of interest, minimum	0.79%	0.79%
Risk-free rate, maximum	1.24%	0.79%
Dividend yield	0.00%	0.00%
2016 Omnibus Inventive Plan [Member] | Original Options [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Volatility rate	80.00%
Risk-free rate of interest, minimum	0.07%
Risk-free rate, maximum	0.79%
2016 Omnibus Inventive Plan [Member] | Substitute Options
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Volatility rate	80.00%
Risk-free rate of interest, minimum	0.07%
Minimum [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 11.69	$ 2.22
Risk-free rate of interest, minimum		0.30%	1.54%
Expected term (years)	5 years 6 months	4 years 8 months 12 days	6 years
Minimum [Member] | 2016 Omnibus Inventive Plan [Member] | Original Options [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 1
Expected term (years)	2 months 4 days
Minimum [Member] | 2016 Omnibus Inventive Plan [Member] | Substitute Options
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 0.20
Expected term (years)	2 months 4 days
Maximum [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 23.41	$ 3.07
Risk-free rate of interest, minimum		0.49%	1.73%
Expected term (years)	6 years 6 months	5 years 10 months 24 days	6 years 6 months
Maximum [Member] | 2016 Omnibus Inventive Plan [Member] | Original Options [Member]
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 72.30
Expected term (years)	5 years 11 months 26 days
Maximum [Member] | 2016 Omnibus Inventive Plan [Member] | Substitute Options
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 14.58
Risk-free rate, maximum	0.79%
Expected term (years)	5 years 11 months 26 days

Stock Based Compensation - Le_2

Stock Based Compensation - Legacy NeuroRx 2016 Omnibus Incentive Plan (Details)	6 Months Ended
	Jun. 30, 2021USD ($)
Vested substitute options
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Share-based Payment Arrangement, Plan Modification, Incremental Cost	$ 1,014,640
Vested substitute options | General and Administrative Expense [Member]
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Share-based Payment Arrangement, Plan Modification, Incremental Cost	993,500
Vested substitute options | Research and Development Expense [Member]
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Share-based Payment Arrangement, Plan Modification, Incremental Cost	21,140
Unvested substitute options
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Share-based Payment Arrangement, Plan Modification, Incremental Cost	$ 25,877,473

Stock Based Compensation - 2021

Stock Based Compensation - 2021 Omnibus Incentive Plan (Details) - 2021 Omnibus Incentive Plan	6 Months Ended
	Jun. 30, 2021shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized for issuance	5,373,049
Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Net of Forfeitures	2,919,493
Number of shares remain available for issuance	2,453,556

Stock Based Compensation - Su_2

Stock Based Compensation - Summary of grant date of stock option award (Details) - $ / shares	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price			$ 11
Risk-free rate of interest, minimum	0.79%	0.79%
Risk-free rate of interest, maximum	1.24%	0.79%
Expected stock price volatility	80.00%	80.00%	80.00%
Dividend yield	0.00%	0.00%
Minimum [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price	$ 11.69	$ 2.22
Risk-free rate of interest, minimum		0.30%	1.54%
Expected term	5 years 6 months	4 years 8 months 12 days	6 years
Maximum [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price	$ 23.41	$ 3.07
Risk-free rate of interest, minimum		0.49%	1.73%
Expected term	6 years 6 months	5 years 10 months 24 days	6 years 6 months

Share based compensation - Su_2

Share based compensation - Summary of stock option activity (Details) - USD ($)	3 Months Ended		12 Months Ended
	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Number of shares
Outstanding, Number of shares		2,414,303
Granted		210,800
Forfeited		(198,400)
Outstanding, Number of shares	2,919,493		2,414,303
Weighted average exercise price
Outstanding, Weighted average exercise price		$ 2.17
Granted (in dollars per share)		11.69
Forfeited (in dollars per share)		$ (2.22)
Outstanding, Weighted average exercise price	$ 5.25		$ 2.17
Weighted average remaining contractual life (in years)
Outstanding at the beginning (in years)	9 years		8 years 2 months 12 days
Granted (in years)		9 years 9 months 18 days
Aggregate intrinsic value
Outstanding, intrinsic value		$ 53,659,966
Granted (in dollars)		3,825,276
Forfeited (in dollars)		$ (6,587,328)
Outstanding, intrinsic value	$ 20,558,299		$ 53,659,966
2016 Omnibus Inventive Plan [Member]
Number of shares
Outstanding, Number of shares	2,426,703
Granted	587,030
Exercised	(4,960)
Forfeited	(89,280)
Outstanding, Number of shares	2,895,423	2,426,703
Weighted average exercise price
Outstanding, Weighted average exercise price	$ 14.58
Granted (in dollars per share)	14.94
Exercised (in dollars per share)	(3.07)
Forfeited (in dollars per share)	(7.86)
Outstanding, Weighted average exercise price	$ 1.50	$ 14.58
Weighted average remaining contractual life (in years)
Outstanding at the beginning (in years)		8 years 8 months 12 days
Granted (in years)	9 years 10 months 24 days
Aggregate intrinsic value
Outstanding, intrinsic value	$ 30,388,510
Exercised (in dollars)	(42,385)
Forfeited (in dollars)	$ (339,082)
Outstanding, intrinsic value		$ 30,388,510
2021 Omnibus Incentive Plan
Number of shares
Options vested and exercisable	1,095,294
Weighted average exercise price
Options cancelled (in dollars per share)	$ 1.50
Weighted average remaining contractual life (in years)
Options vested and exercisable	6 years 1 month 6 days
Aggregate intrinsic value
Options vested and exercisable	$ 11,106,829
As Previously Reported
Number of shares
Outstanding at the beginning (as previously reported)			486,755
Outstanding, Number of shares		486,755	333,588	355,408
Granted			266,500	28,180
Forfeited			(113,333)	(50,000)
Outstanding, Number of shares			486,755	333,588	355,408
Options vested and exercisable			329,489
Weighted average exercise price
Outstanding at the beginning (as previously reported)			$ 10.79
Outstanding, Weighted average exercise price		$ 10.79	5.74	$ 5.74
Granted (in dollars per share)			14.37	11
Outstanding, Weighted average exercise price			10.79	$ 5.74	$ 5.74
Options vested and exercisable			$ 6.31
Weighted average remaining contractual life (in years)
Outstanding at the beginning (as previously reported) (in years)			8 years 9 months 18 days
Outstanding at the beginning (in years)			8 years 9 months 18 days	7 years 2 months 12 days	8 years 2 months 12 days
Granted (in years)			9 years 8 months 12 days	9 years 7 months 6 days
Options vested and exercisable			4 years
Aggregate intrinsic value
Outstanding at the beginning (as previously reported) (in dollars)			$ 19,571,655
Outstanding, intrinsic value		$ 19,571,655	1,782,729	$ 1,782,729
Granted (in dollars)			9,761,125
Outstanding, intrinsic value			19,571,655	$ 1,782,729	$ 1,782,729
Options vested and exercisable			$ 14,723,342
Adjustment
Number of shares
Retroactive application of reverse recapitalization			1,927,548
Weighted average exercise price
Retroactive application of reverse recapitalization			$ (8.62)

Share based compensation - Reco

Share based compensation - Recognition of stock-based compensation (Details) - USD ($)	3 Months Ended		6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation expense allocated	$ 4,283,330	$ 93,466	$ 4,655,028	$ 182,269
Unrecognized compensation costs expected to be recognized	9,117,887		9,117,887
General and Administrative Expense [Member]
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation expense allocated	4,094,549	50,881	4,438,583	117,469	$ 332,065	$ 321,087
Research and Development Expense [Member]
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation expense allocated	$ 188,781	$ 42,585	$ 216,445	$ 64,800	$ 398,340	$ 112,823

Fair Value Measurements (Detail

Fair Value Measurements (Details) - Level 3 - USD ($)	Jun. 30, 2021	Dec. 31, 2020
Liabilities:
Warrant liabilities (Note 10)	$ 515,025	$ 0
Earnout Cash liability (Note 4)	$ 25,874,896	$ 0

Fair Value Measurements - Signi

Fair Value Measurements - Significant unobservable inputs (Details) - $ / shares	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020
Fair Value Disclosures [Abstract]
Stock price on valuation date	$ 11.62	$ 24.25
Exercise price per share	$ 11.50	$ 11.50
Expected life	4 years 10 months 24 days	5 years
Volatility	35.70%	39.00%
Risk-free rate	0.90%	0.80%
Fair value of warrants	$ 3.78	$ 14.56

Fair Value Measurements - Recon

Fair Value Measurements - Reconciliation of warrant liabilities (Details)	6 Months Ended
	Jun. 30, 2021USD ($)
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Additions pursuant to Merger	$ 25,520,195
Gain upon re-measurement	354,701
Balance at the ending balance	25,874,896
Common stock warrant [Member]
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Additions pursuant to Merger	1,983,674
Gain upon re-measurement	(1,468,649)
Balance at the ending balance	$ 515,025

Fair Value Measurements - Rec_2

Fair Value Measurements - Reconciliation of Earnout Cash liability (Details)	6 Months Ended
	Jun. 30, 2021USD ($)
Fair Value Disclosures [Abstract]
Additions pursuant to Merger	$ 25,520,195
Loss upon re-measurement	354,701
Balance at the ending balance	$ 25,874,896

Fair Value Measurements - Fair

Fair Value Measurements - Fair value on a Recurring Basis (Details) - USD ($)	3 Months Ended	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2021
Fair Value Disclosures [Abstract]
Trading price		$ 24.25
Deemed dividend - Earnout Shares	$ 253,130,272	$ 253,130,272
Net impact to additional paid-in capital		$ 0

Income Taxes (Details)

Income Taxes (Details) - USD ($)	6 Months Ended	12 Months Ended
	Jun. 30, 2021	Dec. 31, 2020	Dec. 31, 2019
Deferred tax asset due to uncertain tax positions		$ 1,000,000
Accrued penalties and interest,total		0	$ 0
Recognized penalties and interest		0	0
Tax expense	$ 0	0	0
Federal and State
Net operating losses carryforwards		37,000,000	31,200,000
Foreign Tax Authority
Net operating losses carryforwards		$ 559,000	$ 547,000

Related Party Transactions (D_2

Related Party Transactions (Details) - USD ($)	3 Months Ended		6 Months Ended		12 Months Ended
	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Related Party Transaction [Line Items]
Accounts payable due to related parties	$ 44,201		$ 44,201		$ 149,067	$ 92,744
CEO
Related Party Transaction [Line Items]
Compensation amount received related to related party transaction	137,500	$ 53,125	286,250	$ 121,875	456,459	452,400
Neuro Rx | Chief Executive Officer Son [Member]
Related Party Transaction [Line Items]
Payment to related party	4,615	4,820	6,110	4,820
Neuro Rx | Chief Executive Officer and Chairman of Board
Related Party Transaction [Line Items]
Payment to related party	254,936	0	395,757	0	271,082
Neuro Rx | Chief Commercial Officer
Related Party Transaction [Line Items]
Payment to related party	11,100	18,605	29,740	40,770	85,915	48,000
Neuro Rx | CEO
Related Party Transaction [Line Items]
Payment to related party					11,650
Neuro Rx | Glytech Agreement
Related Party Transaction [Line Items]
Continuing technology support services and reimbursed expenses	$ 125,000	$ 0	$ 125,000	$ 82,569	$ 272,929	$ 464,720
Related party transaction description			The Excluded Technology will transfer to the Company for no additional consideration if the value of NRx Pharmaceuticals equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost.		The Excluded Technology will transfer to the Company for no additional consideration if the value of NeuroRx equity held by Glytech exceeds $50,000,000 at any time prior to August 6, 2022. After August 6, 2022, the additional IP will transfer to the Company at no cost.

Subsequent Events (Details)_2

Subsequent Events (Details) - USD ($)	1 Months Ended		3 Months Ended	6 Months Ended
	Jul. 31, 2021	Jan. 31, 2021	Mar. 31, 2021	Jun. 30, 2021
Subsequent Event [Line Items]
Proceeds from exercise of warrant				$ 7,500,018
Issuance of common stock for exercise of warrant			$ 7,500,018
Subsequent Event
Subsequent Event [Line Items]
Proceeds from exercise of warrant	$ 9,186,316
Issuance of common stock for exercise of warrant	1,833,596
Stock options, vesting period		3 years
Subsequent Event | Provision of additional support of inhaled ZYESAMITM in phase 2/3 clinical trials
Subsequent Event [Line Items]
Related party costs	$ 157,110