NRx Pharmaceuticals (NRXP) 10-Q/A 12 Aug 22 2021 Q3 Quarterly report (amended) Financial data

Cover

Cover - shares	9 Months Ended
	Sep. 30, 2021	Nov. 12, 2021
Document Type	10-Q/A
Amendment Flag	true
Amendment Description	NRX Pharmaceuticals, Inc. (the “Company,” “we,” “us” or “our”) is filing this Amendment No. 1 to its Quarterly Report on Form 10-Q for the quarterly period ended September 30, 2021 (this “Quarterly Report”) to amend and restate certain items in its Quarterly Report on Form 10-Q for the quarterly period ended September 30, 2021 originally filed with the Securities and Exchange Commission (the “SEC”) on November 15, 2021 (the “Original Quarterly Report”). The Original Quarterly Report should no longer be relied upon due to insufficient review procedures related to complex warrant transactions.
Document Period End Date	Sep. 30, 2021
Document Fiscal Year Focus	2021
Document Fiscal Period Focus	Q3
Current Fiscal Year End Date	--12-31
Entity Registrant Name	NRX Pharmaceuticals, Inc.
Entity Central Index Key	0001719406
Entity File Number	001-39412
Entity Tax Identification Number	82-2844431
Entity Filer Category	Non-accelerated Filer
Entity Small Business	true
Entity Emerging Growth Company	true
Entity Ex Transition Period	true
Entity Shell Company	false
Document Quarterly Report	true
Document Transition Report	false
Entity Interactive Data Current	Yes
Entity Current Reporting Status	No
Entity Incorporation, State or Country Code	DE
Entity Address, State or Province	DE
Entity Address, Address Line One	1201 Orange Street
Entity Address, Address Line Two	Suite 600
Entity Address, City or Town	Wilmington
Entity Address, Postal Zip Code	19801
City Area Code	484
Local Phone Number	254-6134
Entity Common Stock, Shares Outstanding		58,810,338
Common Stock
Title of 12(b) Security	Common Stock, par value $0.001 per share
Trading Symbol	NRXP
Security Exchange Name	NASDAQ
Common stock warrants
Title of 12(b) Security	Warrants to purchase one share of Common Stock
Trading Symbol	NRXPW
Security Exchange Name	NASDAQ

CONDENSED CONSOLIDATED BALANCE

CONDENSED CONSOLIDATED BALANCE SHEETS - USD ($)	Sep. 30, 2021	Dec. 31, 2020
Current assets:
Cash	$ 38,883,569	$ 1,858,513
Account receivable, net of allowance of $257,463 as of December 31, 2020		831,390
Prepaid expenses and other current assets	6,350,889	240,352
Total current assets	45,234,458	2,930,255
Other assets	15,921	10,914
Total assets	45,250,379	2,941,169
Current liabilities:
Accounts payable (includes $0 and $149,067 due to related parties)	5,559,412	3,153,310
Accrued and other current liabilities	1,995,961	1,728,483
Accrued clinical site costs	1,154,042	1,547,432
Earnout Cash liability	26,283,238
Warrant liabilities	1,261,550
Notes payable and accrued interest	515,059	248,861
Accrued settlement expense		39,486,139
Total current liabilities	36,769,262	46,164,225
Notes payable and accrued interest		547,827
Total liabilities	36,769,262	46,712,052
Stockholders' equity (deficit):
Preferred stock
Common stock, $0.001 par value, 500,000,000 shares authorized; 0 and 42,973,462 shares issued and outstanding at September 30, 2021 and December 31, 2020, respectively	54,810	42,974
Additional paid-in capital	161,261,845	46,365,863
Accumulated deficit	(152,835,538)	(90,179,720)
Total stockholders' equity (deficit)	8,481,117	(43,770,883)
Total liabilities and stockholders' equity	$ 45,250,379	$ 2,941,169

CONDENSED CONSOLIDATED BALANC_2

CONDENSED CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($)	Sep. 30, 2021	Dec. 31, 2020
Allowance for accounts receivable		$ 257,463
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
Common stock, shares authorized	500,000,000	500,000,000
Common stock, shares issued	54,810,338	42,973,462
Common stock, shares outstanding	0	42,973,462

CONDENSED CONSOLIDATED STATEMEN

CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS (Unaudited) - USD ($)	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Operating expenses:
Research and development	$ 6,275,911	$ 4,331,709	$ 13,843,895	$ 6,326,416
General and administrative	13,823,240	3,753,704	28,382,177	4,895,092
Settlement expense			21,365,641
Reimbursement of expenses from Relief Therapeutics		(2,936,214)	(771,244)	(4,957,145)
Total operating expenses	20,099,151	5,149,199	62,820,469	6,264,363
Income (loss) from operations	(20,099,151)	(5,149,199)	(62,820,469)	(6,264,363)
Other (income) expenses:
Gain on extinguishment of debt			(120,810)
Interest expense	5,368	12,513	15,656	51,317
Change in fair value of warrant liabilities	16,536,470		(822,539)
Change in fair value of Earnout Cash liability	408,342		763,043
Change in fair value of embedded put				27,160
Loss on conversion of convertible notes payable				306,641
Total other (income) expenses	16,950,180	12,513	(164,650)	385,118
Loss before tax	(37,049,331)	(5,161,712)	(62,655,819)	(6,649,481)
Provision for income taxes			0
Net loss	(37,049,331)	(5,161,712)	(62,655,819)	(6,649,481)
Deemed dividend - Earnout Shares			(255,822,071)
Net loss attributable to common stockholders	$ (37,049,331)	$ (5,161,712)	$ (318,477,890)	$ (6,649,481)
Net loss per share:
Basic	$ (0.72)	$ (0.15)	$ (1.45)	$ (0.20)
Diluted	(0.72)	(0.15)	(1.45)	(0.20)
Net loss per share attributable to common stockholders:
Basic	(0.72)	(0.15)	(7.36)	(0.20)
Diluted	$ (0.72)	$ (0.15)	$ (7.36)	$ (0.20)
Weighted average common shares outstanding:
Basic	51,739,452	34,139,672	43,290,675	33,799,503
Diluted	51,739,452	34,139,672	43,290,675	33,799,503

CONDENSED CONSOLIDATED STATEM_2

CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY (DEFICIT) (Unaudited) - USD ($)	Convertible Series A Preferred Stock Preferred Stock	Convertible Series B-1A Preferred Stock Preferred Stock	Convertible Series B-1 Preferred Stock Preferred Stock	Convertible Series B-2 Preferred Stock Preferred Stock	Preferred Stock	Common Stock	Additional Paid-in Capital	Accumulated Deficit	Total
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
Beginning balance at Dec. 31, 2019						$ 41,249	33,518,162	(38,402,816)	(4,843,405)
Beginning balance (in shares) at Dec. 31, 2019						41,249,200
Common stock issued						$ 51	176,974		177,025
Common stock issued (in 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 income (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 (in shares) at Mar. 31, 2020						41,313,212
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
Beginning balance at Dec. 31, 2019						$ 41,249	33,518,162	(38,402,816)	$ (4,843,405)
Beginning balance (in shares) at Dec. 31, 2019						41,249,200
Common stock issued to settle note conversion (in shares)									1,138,199
Net income (loss)									$ (6,649,481)
Ending balance at Sep. 30, 2020						$ 42,744	42,180,599	(45,052,297)	(2,828,954)
Ending balance (in shares) at Sep. 30, 2020						42,743,945
Beginning balance at Mar. 31, 2020						$ 41,313	33,833,939	(39,992,872)	(6,117,620)
Beginning balance (in shares) at Mar. 31, 2020						41,313,212
Stock-based compensation							93,466		93,466
Net income (loss)								102,287	102,287
Ending balance at Jun. 30, 2020						$ 41,313	33,927,405	(39,890,585)	(5,921,867)
Ending balance (in shares) at Jun. 30, 2020						41,313,212
Common stock issued						$ 293	1,411,774		1,412,067
Common stock issued (in shares)						292,534
Common stock issued to settle note conversion						$ 1,138	3,960,988		3,962,126
Common stock issued to settle note conversion (in shares)						1,138,199
Warrants issued as compensation for services							2,689,684		2,689,684
Stock-based compensation							190,749		190,749
Net income (loss)								(5,161,712)	(5,161,712)
Ending balance at Sep. 30, 2020						$ 42,744	42,180,599	(45,052,297)	(2,828,954)
Ending balance (in shares) at Sep. 30, 2020						42,743,945
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
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
Beginning balance at Dec. 31, 2020						$ 42,974	46,365,863	(90,179,720)	(43,770,883)
Beginning balance (in shares) at Dec. 31, 2020						42,973,462
Common stock issued						$ 333	6,926,753		6,927,086
Common stock issued (in 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 income (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 (in shares) at Mar. 31, 2021						44,802,799
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
Beginning balance at Dec. 31, 2020						$ 42,974	46,365,863	(90,179,720)	(43,770,883)
Beginning balance (in shares) at Dec. 31, 2020						42,973,462
Effect of Merger and recapitalization, net of redemptions and issuance costs									(64,836,244)
Issuance of common stock for exercise of warrants and Unit Purchase Options									$ 47,319,504
Common stock issued for consulting services (in shares)									834,045
Net income (loss)									$ (62,655,819)
Ending balance at Sep. 30, 2021						$ 54,810	161,261,845	(152,835,538)	8,481,117
Ending balance (in shares) at Sep. 30, 2021						54,810,338
Beginning balance at Mar. 31, 2021						$ 44,803	122,014,615	(115,668,594)	6,390,824
Beginning balance (in shares) at Mar. 31, 2021						44,802,799
Common stock issued						$ 71	1,562,201		1,562,272
Common stock issued (in shares)						71,056
Effect of Merger and recapitalization, net of redemptions and issuance costs						$ 2,530	(64,838,774)		(64,836,244)
Effect of Merger and recapitalization, net of redemptions and issuance costs (in shares)						2,529,730
Common stock issued pursuant to PIPE financing, net of issuance costs						$ 1,000	8,099,000		8,100,000
Common stock issued pursuant to PIPE financing, net of issuance costs (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 income (loss)								(117,613)	(117,613)
Ending balance at Jun. 30, 2021						$ 48,604	75,970,172	(115,786,207)	(39,767,431)
Ending balance (in shares) at Jun. 30, 2021						48,603,585
Common stock issued						$ 511	1,134,305		$ 1,134,816
Common stock issued (in shares)						511,065			511,065
Common stock and warrants issued in private placement, net of issuance costs						$ (2,727)	(27,355,496)		$ (27,358,223)
Common stock and warrants issued in private placement, net of issuance costs (in shares)						2,727,273
Issuance of common stock for exercise of warrants and Unit Purchase Options						$ 2,334	47,317,170		47,319,504
Issuance of common stock for exercise of warrants and Unit Purchase Options (in shares)						2,334,370
Common stock issued for consulting services						$ 634	7,924,877		$ 7,925,511
Common stock issued for consulting services (in shares)						634,045			634,045
Stock-based compensation							1,559,825		$ 1,559,825
Net income (loss)								(37,049,331)	(37,049,331)
Ending balance at Sep. 30, 2021						$ 54,810	$ 161,261,845	$ (152,835,538)	$ 8,481,117
Ending balance (in shares) at Sep. 30, 2021						54,810,338

CONDENSED CONSOLIDATED STATEM_3

CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY (DEFICIT) (Unaudited) (Parenthetical) - USD ($)	3 Months Ended
	Sep. 30, 2021	Jun. 30, 2021
CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY (DEFICIT) (Unaudited)
Merger and recapitalization, redemptions and issuance costs		$ 1,412,846
PIPE financing, issuance costs		$ 1,900,000
Common stock and warrants issued in private placement, issuance costs	$ 3,668,737

CONDENSED CONSOLIDATED STATEM_4

CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($)	9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020
CASH FLOWS FROM OPERATING ACTIVITIES:
Net Loss	$ (62,655,819)	$ (6,649,481)
Adjustments to reconcile net loss to net cash used in operating activities:
Depreciation expense	1,605	1,110
Stock-based compensation	6,214,853	373,018
Warrant expense		2,689,684
Gain on extinguishment of debt	(120,810)
Change in fair value of warrant liabilities	(822,539)
Change in fair value of Earnout Cash liability	763,043
Change in fair value of embedded put		27,160
Amortization of debt discount		16,475
Non-cash interest expense	15,655	35,198
Non-cash settlement expense	21,365,641
Non-cash consulting expense	12,775,511
Loss on conversion of notes payable		306,641
Changes in operating assets and liabilities:
Accounts receivable	831,390	(1,254,090)
Prepaid expenses and other assets	(6,051,045)	(460,586)
Accounts payable	1,853,855	1,330,175
Accrued expenses and other liabilities	(594,437)	1,726,402
Net cash used in operating activities	(26,423,097)	(1,858,294)
CASH FLOWS FROM INVESTING ACTIVITIES
Purchase of computer equipment	(6,612)
Net cash used in investing activities	(6,612)
CASH FLOWS FROM FINANCING ACTIVITIES
Proceeds from notes payable		629,523
Proceeds from issuance of series B-2 Preferred stock		50,004
Proceeds from issuance of common stock, net of transaction costs	9,623,899	1,589,103
Proceeds from issuance of common stock for exercise of warrant	16,699,489
Proceeds from issuance of common stock and warrants issued in private placement, net of issuance costs	27,358,223
Effect of Merger, net of transaction costs	11,049,628
Repayment of notes payable assumed in Merger	(1,100,000)
Repayment of notes payable - related party	(176,474)
Net cash provided by financing activities	63,454,765	2,268,630
Net increase in cash	37,025,056	410,336
Cash at beginning of period	1,858,513	877,421
Cash at end of period	38,883,569	1,287,757
Non-cash investing and financing activities
Reclassification of settlement liability upon issuance of warrant	60,851,779
Reclassification of legacy NeuroRx warrants to warrant liability	38,220,448
Reclassification of warrant liability upon exercise of warrant	38,120,032
Extinguishment of Paycheck Protection Program Loan	120,810
Issuance of common stock warrants as offering costs	$ 1,026,957	30,536
Conversion of notes payable into common stock		$ 3,655,461

Organization

Organization	9 Months Ended
	Sep. 30, 2021
Organization
Organization	1. Organization The Business On May 24, 2021 (“Effective Time”), we consummated the business combination (“Merger”) 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., a Delaware corporation and wholly-owned, direct subsidiary of BRPA (“Merger Sub”), pursuant to which Merger Sub was merged with and into NeuroRx, with NeuroRx surviving the 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 Merger, we changed our name to NRX Pharmaceuticals, Inc., with the stockholders of NeuroRx becoming stockholders of NRX Pharmaceuticals. Unless the context suggests otherwise, references to “NRx Pharmaceuticals,” “NeuroRx”, “NRXP,” “we,” or the “Company” refer to NRX Pharmaceuticals, Inc. and, where appropriate, its subsidiaries. The Company is a clinical-stage pharmaceutical company that develops novel therapeutics for the treatment of central nervous system disorders and both the treatment and prevention of life-threatening pulmonary diseases through its wholly-owned operating subsidiary, NeuroRx. The Company's foundation product, NRX-101 (d-Cyloserine/Lurasidone), for the treatment of suicidal bipolar depression, has been awarded Fast Track designation, Breakthrough Therapy designation, a Special Protocol Agreement, and a Biomarker Letter of Support by the US Food and Drug Administration (FDA). NRX-101 is covered by multiple US and foreign patents, including a recently-issued Composition of Matter patent (U.S. Patent No. 10,583,138) that was transferred to NRx by Glytech, Inc. On September 18, 2020, the Company entered into a collaboration agreement with Relief Therapeutics Holding AG (“Relief”) for the clinical development and, if approved, the sale of Aviptadil. The collaboration agreement provides for funding by Relief of certain clinical trials, formulation and manufacturing of Aviptadil as well as establishing specified sales territories for each party and share of the profits in those territori but has subsequently declined to reimburse the Company for additional costs of the IV clinical trial, formulation and manufacture of Aviptadil (reformulated as ZYESAMI®). Relief has additionally declined to fund the costs of the inhaled ZYESAMI clinical trial. The Company advised Relief that the Company is funding those costs with other capital. See Note 10 “Commitments and Contingencies” for additional Information regarding the Company and Relief ​ ​

Liquidity

Liquidity	9 Months Ended
	Sep. 30, 2021
Liquidity
Liquidity	2. Liquidity As of September 30, 2021, the Company had $38,883,569 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. On August 23, 2021, the Company completed a private placement (the “Private Placement”) and issued 2,727,273 shares of common stock for a purchase price of $11.00 per share and Preferred Investment Options (the “Preferred Investment Options”, and, collectively with the shares of common stock issued under the Private Placement, the “Securities”) to purchase up to an aggregate of 2,727,273 shares of common stock for a purchase price of $12.00. The aggregate gross proceeds to the Company from the Private Placement were approximately $30,000,000, before deducting placement agent fees and other offering expenses. Accordingly, the Company believes that it currently has sufficient funds and, if necessary, the ability to reduce expenditures, to support operations through the next twelve months from the date the condensed consolidated financial statements are issued. 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. Aside from our COVID-19 related trials, as a result of the COVID-19 Outbreak, most of our other trials have been halted. Except as otherwise discussed in the preceding sentence and otherwise in this Quarterly Report on Form 10-Q, there have been no material changes or impact of COVID-19 on our business. However, the full impact of the COVID-19 Outbreak continues to evolve as of the date hereof. 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. Management is actively monitoring the impact of the global pandemic on its financial condition, liquidity, operations, industry, and workforce.

Summary of Significant Accounti

Summary of Significant Accounting Policies	9 Months Ended
	Sep. 30, 2021
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 the 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 presentation of the balance sheet, statements of operations and cash flows for the interim 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 was accounted for as a reverse recapitalization in accordance with GAAP (the “Reverse Recapitalization”). Under this method of accounting, BRPA is 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 13) 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. 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. For a Type 1 (probable-to-probable) modification, incremental stock-based compensation cost is measured as the excess, if any, of the fair value of the modified option/warrant over the fair value of the original option/warrant immediately before its terms are modified, measured based on the fair value of the 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 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 liability classified and recorded at their initial fair value on the date of issuance and remeasured at fair value 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 and the fair value of the Substitute Warrants was estimated using a modified Black Scholes valuation approach which applies a probability factor based on the probabilities of achieving the Earnout Cash Milestone and/or Earnout Shares Milestone at each reporting period (see Notes 11 and 13). Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes 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 when the effect would be anti-dilutive in the periods. 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 September 30, ​ Nine Months Ended September 30, ​ 2021 2020 2021 2020 Stock options 2,388,811 — 2,388,811 1,754,623 Common stock warrants 9,305,790 — 9,305,790 1,690,192 Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ — Earnout Shares from exercised Substitute Options and Substitute Warrants ​ 1,229,925 ​ — ​ 1,229,925 ​ — ​ 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 separation models required under current GAAP. The ASU removes certain settlement conditions that are required for equity contracts to qualify for the derivative scope exception and it also simplifies the diluted earnings per share calculation in certain areas. The ASU is effective for fiscal years beginning after December 15, 2023, including interim periods within those fiscal years. Early adoption is permitted, but no earlier than fiscal years beginning after December 15, 2020 and adoption must be as of the beginning of the Company’s annual fiscal year. We adopted ASU 2020-06 on January 1, 2021, with no material impact on our financial statements. 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

Restatement of Previously Issue

Restatement of Previously Issued Financial Statements	9 Months Ended
	Sep. 30, 2021
Restatement of Previously Issued Financial Statements
Restatement of Previously Issued Financial Statements	4. Restatement of Previously Issued Financial Statements The Company has restated its condensed consolidated balance sheet as of September 30, 2021, and its condensed consolidated statements of operations, stockholders’ equity (deficit) for the three- and nine-month periods ended September 30, 2021, and condensed consolidated statement of cash flows for the nine month period ended September 30, 2021, along with certain related notes to such restated condensed consolidated financial statements. The errors that caused the Company to conclude that its financial statements should be restated are the result of a misapplication of the guidance on accounting for certain Substitute Warrants, which was identified in connection with the preparation of our condensed consolidated financial statements as of and for the quarter ended June 30, 2022. Based on ASC 815-40, Contracts in Entity’s Own Equity The Company determined that the condensed consolidated financial statements should be restated to reflect the modification of the Substitute Warrants as a liability, with subsequent changes in their estimated fair value recorded as non-cash income or expense in the statements of operations for all periods since modification on May 24, 2021. In addition to the restatement of the condensed consolidated financial statements, the Company has also restated the following notes for the three- and nine-month period ended September 30, 2021, to reflect the error corrections noted above. • Note 3 – Summary of Significant Accounting Policies • Note 5 - Reverse Recapitalization • Note 10 - Commitment and Contingencies • Note 11 - Equity • Note 13 – Fair Value Measurements The following table represents the estimated fair value of the Company’s Substitute Warrants liabilities recorded on our condensed consolidated balance sheet along with changes in fair value which are recorded as other income and expense on our condensed consolidated statement of operations. The Company’s prior and updated accounting for the Substitute Warrants do not have any effect on the Company’s previously reported or future cash flows or cash. The tables summarize the effect of the restatement on each financial statement line item as of the dates, and for the period, indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Balance Sheet as of September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Warrant liabilities $ 775,263 $ 486,287 $ 1,261,550 Total current liabilities ​ ​ 36,282,975 ​ ​ 486,287 ​ ​ 36,769,262 Total liabilities ​ ​ 36,282,975 ​ ​ 486,287 ​ ​ 36,769,262 Additional paid-in capital ​ ​ 161,362,260 ​ ​ (100,415) ​ ​ 161,261,845 Accumulated deficit ​ ​ (152,449,666) ​ ​ (385,872) ​ ​ (152,835,538) Total stockholders' equity (deficit) ​ ​ 8,967,404 ​ ​ (486,287) ​ ​ 8,481,117 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Operations for the three months ended September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Change in fair value of warrant liabilities $ 260,238 $ 16,276,232 $ 16,536,470 Total other (income) expenses ​ ​ 673,948 ​ ​ 16,276,232 ​ ​ 16,950,180 Loss before tax ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) Net loss ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) Net loss attributable to common stockholders ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) Net loss per share, basic and diluted ​ $ (0.40) ​ ​ (0.32) ​ ​ (0.72) Net loss per share attributable to common stockholders, basic and diluted ​ $ (0.40) ​ ​ (0.32) ​ ​ (0.72) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Operations for the nine months ended September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Change in fair value of warrant liabilities $ (1,208,412) $ 385,873 $ (822,539) Total other (income) expenses ​ ​ (550,523) ​ ​ 385,873 ​ ​ (164,650) Loss before tax ​ ​ (62,269,946) ​ ​ (385,873) ​ ​ (62,655,819) Net loss ​ ​ (62,269,946) ​ ​ (385,873) ​ ​ (62,655,819) Net loss attributable to common stockholders ​ ​ (318,092,017) ​ ​ (385,873) ​ ​ (318,477,890) Net loss per share, basic and diluted ​ $ (1.44) ​ ​ (0.01) ​ ​ (1.45) Net loss per share attributable to common stockholders, basic and diluted ​ $ (7.35) ​ ​ (0.01) ​ ​ (7.36) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Stockholders' Equity (Deficit) for the nine months ended September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Effect of Merger and recapitalization, net of redemptions and issuance costs of $1,412,846 $ (26,615,796) $ (38,220,448) $ (64,836,244) Issuance of common stock for exercise of warrants and Unit Purchase Options ​ ​ 9,199,471 ​ ​ 38,120,033 ​ ​ 47,319,504 Net loss for the three months ended September 30, 2021 ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Cash Flows for the nine months ended September 30, 2021 (unaudited) As Reported Adjustment As Restated CASH FLOWS FROM OPERATING ACTIVITIES: ​ ​ ​ ​ ​ ​ ​ ​ Net Loss ​ $ (62,269,946) ​ $ (385,873) ​ $ (62,655,819) Adjustments to reconcile net loss to net cash and used in operating activities: ​ ​ ​ ​ ​ ​ ​ ​ ​ Change in fair value of warrant liabilities ​ ​ (1,208,412) ​ ​ 385,873 ​ ​ (822,539) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Supplemental disclosure of cash flow information: ​ ​ ​ ​ ​ ​ ​ ​ ​ Non-cash investing and financing activities ​ ​ ​ ​ ​ ​ ​ ​ ​ Reclassification of legacy NeuroRx warrants to warrant liabilities ​ ​ - ​ ​ 38,220,448 ​ ​ 38,220,448 Reclassification of warrant liability upon exercise of warrant ​ ​ - ​ ​ 38,120,032 ​ ​ 38,120,032 ​

Reverse Recapitalization

Reverse Recapitalization	9 Months Ended
	Sep. 30, 2021
Reverse Recapitalization
Reverse Recapitalization	5. Reverse Recapitalization As discussed in Note 1, on May 24, 2021 (the “Closing Date”), BRPA closed the Merger 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 Merger, 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 is 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 consisted 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 shares (the “Exchange Ratio”). In addition, the stockholders of NeuroRx who owned 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 was converted into the right to receive a pro rata portion of the the contingent right to receive a pro rata portion of the Earnout Shares and Earnout Cash (after consideration of the Substitute Options and Substitute Warrants (as further discussed below). Pursuant to the terms of the Merger Agreement, NeuroRx’s stockholders who owned NeuroRx securities immediately prior to the Effective Time would have the contingent right to receive their pro rata portion of (i) an aggregate of up to 25,000,000 shares of Common Stock (“Earnout Shares”), less 935,608 and 1,920,492, respectively, which are subject to the terms and conditions of the Substitute Options and Substitute Warrants (each as defined below), if, prior to December 31, 2022, the NeuroRx COVID-19 Drug (i.e., ZYESAMI TM TM TM of the NeuroRx Antidepressant Drug Regimen (i.e., NRX-100/101) and the listing of the NeuroRx Antidepressant Drug Regimen (i.e., NRX-100/101) in the FDA’s “Orange Book,” in each case prior to December 31, 2022 (the occurrence of either of clauses (x) or (y), the “Earnout Cash Milestone”). If the Earnout Shares Milestone is achieved, the Earnout Shares will be issued within five (5) Business Days after the occurrence of the Earnout Shares Milestone. If the Earnout Cash Milestone is achieved, the Merger Agreement does not require the Earnout Cash to be delivered to NeuroRx securityholders within any specified period of time, and the board of directors of NRx Pharmaceuticals will use its good faith judgment to determine the date to pay the Earnout Cash. The Earnout Cash Milestone was recognized as a deemed dividend at the Closing Date and a contingent liability measured at its estimated fair value at the Closing Date and will be remeasured at fair value each period end thereafter until earned or December 31, 2022 (see Note 13). The Earnout Shares Milestone was recognized as a deemed dividend at the Closing date and was classified within equity (see Note 13). The benefit of the contingent right to receive Earnout Cash and Earnout Shares for option and warrant holders occurs through the Option Exchange Ratio (as defined below) and therefore the amount of Earnout Shares and Earnout Cash for common stockholders is approximately $88,837,121 and 22,209,280 shares, respectively. 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 would continue to be governed by substantially the same terms and conditions, including vesting, as were applicable to the original instruments. 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 automatically adjusted based on the Merger Agreement 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 nine months ended September 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 nine months ended September 30, 2021: ​ ​ ​ ​ ​ Recapitalization (As restated) 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 legacy NeuroRx Warrants ​ ​ (38,220,448) 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 ​ $ (64,836,244) ​ 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	9 Months Ended
	Sep. 30, 2021
Prepaid Expenses and Other Current Assets
Prepaid Expenses and Other Current Assets	6. Prepaid Expenses and Other Current Assets Prepaid expenses and other current assets consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, 2021 December 31, 2020 ​ ​ ​ (Unaudited) ​ ​ ​ Prepaid expenses and other current assets: ​ ​ ​ Prepaid insurance ​ $ 3,767,488 ​ $ 49,029 Prepaid manufacturing expenses ​ 1,407,500 ​ — Prepaid clinical development expenses ​ ​ 720,686 ​ ​ — Other prepaid expenses ​ 455,215 ​ 164,772 Other current assets ​ — ​ $ 26,551 Total prepaid expenses and other current assets ​ $ 6,350,889 ​ $ 240,352 ​

Accrued and Other Current Liabi

Accrued and Other Current Liabilities	9 Months Ended
	Sep. 30, 2021
Accrued and Other Current Liabilities
Accrued and Other Current Liabilities	7. Accrued and Other Current Liabilities Accrued and other current liabilities consisted of the following at the dates indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Accrued and other current liabilities: ​ ​ ​ ​ ​ ​ Accrued research and development expenses $ 625,139 $ 586,426 Accrued employee expenses ​ ​ — ​ ​ 530,500 Professional services ​ 685,802 ​ 606,553 Accrued insurance expenses ​ ​ 651,835 ​ ​ — Other accrued expenses ​ 33,185 ​ 5,004 Total accrued and other current liabilities ​ $ 1,995,961 ​ $ 1,728,483 ​

Convertible Notes Payable

Convertible Notes Payable	9 Months Ended
	Sep. 30, 2021
Convertible Notes Payable
Convertible Notes Payable	8. 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 nine months ended September 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 a 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 proceeds received upon issuing the 2017 Notes and the 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 September 30, 2021 and 2020, respectively, and $0 and $27,160 during the nine months ended September 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 September 30, 2021 and 2020, and $0 and $16,475 during the nine months ended September 30, 2021 and 2020, respectively. The Company paid no interest during the three months ended and nine months ended September 30, 2021 and 2020.

Notes Payable

Notes Payable	9 Months Ended
	Sep. 30, 2021
Notes Payable.
Notes Payable	9. Notes Payable Relief Therapeutics Loan On April 6, 2020, the Company entered into a loan agreement with Relief (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 Loan, the Company is obligated to make equal monthly payments of principal and interest, beginning seven months from the date of the PPP Loan note, until the maturity date. The PPP Loan amount may be eligible for forgiveness in the event that (1) at least 75% of the PPP 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 PPP Loan is made, and (2) the number of employees and compensation levels are generally maintained. Forgiveness of the PPP Loan is dependent on the Company having initially qualified for the PPP Loan and qualifying for the forgiveness of such PPP 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 Note Payable -- Vendor On July 1, 2019, the Company converted certain accounts payable into a loan (the “Note Payable — Vendor”) with a vendor in the amount of $154,190. The loan matured on July 1, 2020. The loan bears interest, compounded daily, at 6% annual interest. As of September 30, 2021, the note payable was paid in full. The following table summarizes the Company's outstanding notes payable as of the respective periods. ​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Relief Therapeutics loan ​ $ 500,000 ​ $ 500,000 Paycheck Protection Program loan ​ — ​ 119,842 Note payable — vendor ​ ​ — ​ ​ 154,190 Carrying value of notes payable ​ 500,000 ​ 774,032 Accrued interest ​ ​ 15,059 ​ ​ 22,656 Note payable ​ ​ 515,059 ​ ​ 796,688 Notes payable and accrued interest, current ​ $ 515,059 ​ $ 248,861 Notes payable and accrued interest, non-current ​ $ — ​ $ 547,827 ​

Commitments and Contingencies

Commitments and Contingencies	9 Months Ended
	Sep. 30, 2021
Commitments and Contingencies
Commitments and Contingencies	10. Commitments and Contingencies Operating Lease The Company leases office space on a month-to-month basis. The rent expense for the three months ended September 30, 2021 and 2020 was $9,162 and $14,174, respectively, and for the nine months ended September 30, 2021 and 2020 was $64,555 and $32,076, 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 $399,320. During the three months ended and nine months ended September 30, 2021, NRx Pharmaceuticals paid NJ Health $90,112 and $216,269, respectively, of the total committed amount. Aviptadil Manufacturing, Production, Supply and Distribution Agreements On August 25, 2020, the Company 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, the Company 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, the Company signed an agreement with PolyPeptide Group, North America for the supply of Good Manufacturing Practice (GMP) grade Active Pharmaceutical Ingredient (API) Aviptadil (VIP). This gives NRx Pharmaceuticals a significant reduction in the cost of procuring API. The Company has agreed to purchase a total of $5,255,000 worth of product and services, of which $1,407,500 has been paid for and recorded as a prepaid asset on the Company’s balance sheet as of September 30, 2021. On January 4, 2021, the Company 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 Ltd. (PillTracker) is an agent of the Company per the supply agreement (see Note 15) and is managing the supply agreement at the Company’s request. On July 1, 2021, NRx Pharmaceuticals and BriLife LLC signed an agreement for a Phase II Inhaled clinical trial of Aviptadil in the nation of Georgia with a total cost of approximately $7,400,000. The contract is cancelable with 60 days’ notice. The Phase II Inhaled clinical trial of Aviptadil in the nation of Georgia has not begun and the Company may decide not to proceed with this trial. 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 agreement provides for funding by Relief of certain clinical trials, formulation and manufacturing of Aviptadil, as well as establishing specified sales territories for each party and share of the profits in those territories for “Product” as defined in the collaboration agreement. Relief has reimbursed the Company $10.9 million for expenses related to COVID-19 but has subsequently declined to reimburse the Company for additional costs of Research and Development, including the IV clinical trial, the inhaled use trial, formulation and manufacture of ZYESAMI (Aviptadil), statistical analysis, and regulatory filings. The financial statements reflect $13.8 million in unreimbursed Research and Development costs in the nine months ended September 30, 2021, prior to the allocation of corporate overhead. Additional unreimbursed costs were reported for the year ended December 31, 2020. The Company advised Relief that the Company is funding those costs with other capital. On October 6, 2021, Relief filed a lawsuit against the Company and its CEO claiming that the Company failed to honor its obligations under the collaboration agreement. Relief’s complaint seeks several remedies, including damages for alleged breaches of the terms of the collaboration agreement. The Company believes the lawsuit is baseless and without merit. However, the parties to the lawsuit have agreed to engage in an effort to amicably resolve the litigation and have agreed to hold a mediation in early January 2022. If the mediation does not resolve the dispute, the Company intends to defend itself vigorously and to prosecute significant counterclaims against Relief. 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 thus preventing its usage. 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 were 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. As of December 31, 2020, the Company recognized a contingent liability for its obligation to issue to GEM certain equity instruments at a discounted per share price. Specifically, as the amount was deemed probable and estimable at December 31, 2020, NeuroRx recorded a liability and settlement expense of $39,486,139 to reflect the fair value of the expected GEM Warrant to be issued. On March 28, 2021, when the GEM Warrant was issued, the Company recorded an additional charge of $21,365,641 to reflect the increased fair value of the GEM Warrant on its grant date. Upon issuance, the GEM Warrant was equity classified and was determined to be within the scope of ASC 718, Share-Based Payments (“ASC 718”). 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. The GEM Warrants that were not exercised as of the Merger were modified and became Substitute Warrants (1,833,596 shares, adjusted for the Merger as discussed in Note 11). These Substitute Warrants were liability classified (see Note 11). The changes in fair value of these Substitute Warrants were recognized as a gain or loss in the statement of operations until these Substitute Warrants were exercised in July 2021, at which time they were reclassified to additional paid-in capital.

Equity

Equity	9 Months Ended
	Sep. 30, 2021
Equity
Equity	11. 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 5, 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 3,238,338 and 3,642,515 shares of common stock during the three and nine months ended September 30, 2021, respectively, generating gross proceeds of $31,134,816 and $39,624,175, respectively. Of the 511,065 shares of common stock issued for the exercise of stock options, 185,472 shares of common stock are contingently issuable Earnout Shares and are excluded from the weighted average shares outstanding for computing EPS until the contingent conditions are satisfied. There are 1,044,453 shares of common stock issued pursuant to the GEM warrants which are contingently issuable Earnout Shares and are excluded from the weighted average shares outstanding for computing EPS until the contingent conditions are satisfied. The Company issued 2,334,370 and 3,830,586 shares of common stock pursuant to warrants and Unit Purchase Options exercised during the three and nine months ended September 30, 2021, and received gross proceeds from the warrant exercise of $9,199,471 and $16,699,489, respectively. The Company issued 634,045 and 834,045 shares of common stock for consulting services during the three and nine months ended September 30, 2021, and recognized non-cash consulting expense in general and administrative expenses of $7,925,511 and $12,775,511, respectively. The Company sold 292,534 and 343,378 shares of common stock during the three and nine months ended September 30, 2020, and received gross proceeds of $1,412,067 and $1,589,092, respectively. The Company issued 1,138,199 shares of common stock to settle the notes conversion during the three and nine months ended September 30, 2020 and recorded a loss of $306,641. 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 nine months ended September 30, 2021. Refer to Note 13 for discussion of fair value measurement of the warrant liabilities. 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 5), 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 5), 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 As discussed in Note 10, 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. 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. As further discussed below, upon the Merger the remaining unexercised GEM Warrants were modified to become Substitute Warrants in July 2021, GEM exercised their Substitute Warrants for the purchase of 1,833,596 shares for gross proceeds of $9,186,316 and the GEM Warrant was extinguished. Substitute Warrants As discussed in Note 5, 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 5, 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 $2.45 per share. 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. For the portion of the warrants subject to the base Exchange Ratio (3.16:1), the warrants were fully vested and therefore the incremental fair value of these Substitute Warrants at the date of the modification date was immediately recognized as compensation expense. For the incremental portion of the warrants with performance-based vesting conditions (i.e., the achievement of the Earnout Cash Milestone and/or Earnout Shares Milestone) the Company determined it was not probable that the Earnout Cash Milestone or Earnout Shares Milestone would be met on the Effective Date and at September 30, 2021 and therefore no expense has been recognized for this portion. The Company will reevaluate the probability of the Earnout Cash Milestone and/or Earnout Shares Milestone 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 nine months ended September 30, 2021. Unamortized compensation costs related to performance-based vesting conditions of these Substitute Warrants as of the modification date was $23,760,993. For any remaining outstanding warrants, as the warrant holders were no longer providing services at the date of the modification, in accordance with ASC 815, the Company concluded that the provisions in the Merger Agreement related to the Earnout Shares Milestone and the Earnout Cash Milestone and the contingent right to receive additional shares for these provisions precluded these the Substitute Warrants from being accounted for as components of equity. As the Substitute Warrants meet the definition of a derivative as contemplated in ASC 815, the Substitute Warrants should be recorded as derivative liabilities on the balance sheet and measured at fair value at inception (on the date of the Merger) and at each reporting date in accordance with ASC 820, Fair Value Measurement, with changes in fair value recognized in the Statements of Operations in the period of change. On May 24, 2021, the Company recorded a warrant liability of $53,337,336 for the Substitute Warrants, reclassified out of additional paid-in capital $38,220,448 representing fair value of these NeuroRx warrants, immediately before the modifications as a result of the Merger, and recognized a loss of $15,116,888 for the incremental fair value of these Substitute Warrants which is recorded in the Change in fair value of warrant liabilities on the Condensed Consolidated Statement of Operations. The Company recognized a loss on the change in fair value of the Substitute Warrants for the three months ended September 30, 2021 and 2020 of $16,276,232 and $0, respectively. The Company recognized a loss on the change in fair value of the Substitute Warrants for the nine months ended September 30, 2021 and 2020 of $385,873 and $0, respectively. Refer to Note 13 for discussion of fair value measurement of the warrant liabilities. As discussed above the GEM Substitute Warrants were exercised in July 2021, and changes in fair value of the warrant liability through the date of exercise were recognized in the statement of operations and upon exercise any remaining instruments were reclassified to additional paid-in capital and includes associated escrow shares for the contingent earnouts. The fair value of the original NeuroRx warrants and Substitute Warrants as of the Merger Date 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 ​ 0.57-3.69 ​ 0.57-3.69 ​ Dividend yield ​ — ​ — ​ ​ 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. During the three months ended September 30, 2021, 1,144 Public Warrants were exercised for gross proceeds of $13,156. 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 September 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 loss on the change in fair value of the Placement Warrants for the three months ended September 30, 2021 and 2020 of $260,238 and $0, respectively. The Company recognized a gain on the change in fair value for the nine months ended September 30, 2021 and 2020 of $1,208,412 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 5) ​ 2,455,415 ​ — ​ ​ (13.53) ​ ​ — Outstanding as of December 31, 2020, effect of Merger (Note 5) ​ 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 ​ $ 6.63 ​ $ 42,385,824 Issued ​ 2,863,637 ​ 3.00 ​ ​ 12.08 ​ ​ 4,858,637 Exercised (1,834,740) — ​ (3.19) ​ (17,498,538) Forfeited ​ (218,423) ​ — ​ ​ (1.53) ​ ​ (1,500,566) Outstanding as of September 30, 2021 9,305,790 3.87 ​ $ 9.09 ​ $ 17,770,340 ​ 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 at the Effective Time. Each Unit consists of one one one five On July 23, 2021, the outstanding 600,000 Units were converted on a cashless basis into 499,630 shares of the Company’s common stock. 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 paid at the Effective Time, as the consideration related thereto had been included in the original unit purchase price paid for by investors in the Company's Initial Public Offering or the concurrent private placement, as applicable. ​ August 2021 Private Placement On August 23, 2021, the Company completed a Private Placement and issued 2,727,273 shares of common stock for a purchase price of $11.00 per share and the Preferred Investment Options (warrants) to purchase up to an aggregate of 2,727,273 shares of common stock for a purchase price of $12.00 per share until they expire on August 23, 2024. The aggregate gross proceeds to the Company from the Private Placement were approximately $30.0 million, before deducting placement agent fees and other offering expenses. In connection with the Private Placement, the Company entered into a Registration Rights Agreement with the purchasers of the Securities. The Company’s registration statement on Form S-1 to register the Securities became effective on September 15, 2021. Transaction costs incurred related to the Private Placement include the following: (i) placement fees of $2,250,000 (ii) issuance of Preferred Investment Options to the placement agent to purchase up to an aggregate of 136,364 shares with an exercise price of $13.75 per share and a three-year term with a fair value of $1,026,957, and (iii) legal, professional and printing fees of $391,781. Preferred Investment Options (included in above warrants table) The form of the Preferred Investment Option is a warrant. The measurement of fair value was determined utilizing a Black-Scholes model considering all relevant assumptions current at the date of issuance (i.e., share price of $13.78, exercise price of $12.00, term of three years, volatility of 85.9%, risk-free rate of 0.43%, and expected dividend rate of 0%). The grant date fair value of these Preferred Investment Options was estimated to be $21,695,457 on August 23, 2021 and is reflected within additional paid-in capital as of September 30, 2021. As noted above, the Company issued fully vested Preferred Investment Options to the placement agent with an exercise price of $13.75. As these Preferred Investment Options were issued for services provided in facilitating the Private Placement, the Company recorded the fair value of such Preferred Investment Options as a cost of capital on the issuance date. The measurement of fair value was determined utilizing a Black-Scholes model considering all relevant assumptions current at the date of issuance (i.e., share price of $13.78, exercise price of $13.75, term of three years, volatility of 85.9%, risk-free rate of 0.43%, and expected dividend rate of 0%).

Stock-Based Compensation

Stock-Based Compensation	9 Months Ended
	Sep. 30, 2021
Stock-Based Compensation
Stock-Based Compensation	12. 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 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 an option to acquire an adjusted number of shares of Common Stock at an adjusted exercise price per share (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 5, 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 $5.10 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 Milestone and/or Earnout Shares Milestone). The Company determined it was not probable that the Earnout Cash Milestone or Earnout Shares Milestone would be met on the Effective Date and at September 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 Milestone and/or Earnout Shares Milestone 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 nine months ended September 30, 2021. 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 Milestone and/or Earnout Shares Milestone. 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 September 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. The Substitute Options do not reduce the number of shares authorized for grant under the 2021 Plan. As of September 30, 2021, 732,460 shares have been awarded and 4,640,589 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 FDA 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: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, 2021 December 31, 2020 Exercise price ​ $10.03-$23.41 ​ ​ $2.22-$3.07 ​ Risk-free rate of interest ​ 0.69%-1.24% ​ 0.79% ​ Expected term (years) ​ 5.25-6.5 ​ 4.69-5.9 ​ Expected stock price volatility ​ 80.0%-85.9% ​ 80.0% ​ 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 granted ​ 82,890 ​ ​ 13.68 ​ 9.9 ​ ​ — Forfeited ​ (102,507) ​ ​ (3.07) ​ — ​ ​ (635,543) Exercised ​ (511,065) ​ ​ (2.22) ​ — ​ ​ (3,602,645) Outstanding as of September 30, 2021 ​ 2,388,811 ​ $ 6.04 ​ 8.1 ​ $ 12,447,723 Options vested and exercisable as of September 30, 2021 ​ 1,250,340 ​ $ 1.86 ​ 6.2 ​ $ 9,418,169 ​ 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 nine months ended September 30, 2021, respectively was $9.80 and $16.53. The weighted average grant date fair value per share for employee stock and non-employee option grants during the three months ended and nine months ended September 30, 2020, respectively was $11.62 and $4.44. At September 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 $32,644,383, of which the Company expects to recognize $8,152,105 over a weighted-average period of approximately 1.23 years. The following table summarizes the Company’s recognition of stock-based compensation for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three months ended September 30, ​ Nine months ended September 30, ​ 2021 2020 2021 2020 Stock-based compensation expense ​ ​ ​ ​ General and administrative ​ $ 1,340,023 ​ $ 64,604 ​ $ 5,778,606 ​ $ 182,073 Regulatory and process development ​ 219,802 ​ 126,146 ​ 436,247 ​ 190,945 Total stock-based compensation expense ​ $ 1,559,825 ​ $ 190,750 ​ $ 6,214,853 ​ $ 373,018 ​

Fair Value Measurements

Fair Value Measurements	9 Months Ended
	Sep. 30, 2021
Fair Value Measurements
Fair Value Measurements	13. 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 nine months ended September 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 nine months ended September 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 September 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 September 30, 2021 (As restated) December 31, 2020 Liabilities: ​ ​ ​ ​ ​ ​ ​ ​ Warrant liabilities (Note 11) ​ 3 ​ $ 1,261,550 ​ $ — Earnout Cash liability (Note 5) 3 ​ $ 26,283,238 ​ $ — ​ 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 Company uses a modified Black-Scholes model approach for the Substitute Warrants which applies a probability factor based on the probabilities of achievement of the Earnout Cash Milestone and/or Earnout Shares Milestone 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 Black Scholes 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 and peer company 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 inputs used in the Black-Scholes model to measure the warrant liabilities that are categorized within Level 3 of the fair value hierarchy are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, 2021 At Effective Time ​ ​ (As restated) ​ Expected life ​ 1.77 - 4.65 ​ 0.3 - 5.0 ​ Volatility ​ 82.5% - 85.9% ​ 39.0% - 80.0% ​ Risk-free rate ​ 0.15% - 0.32% ​ 0.03% - 0.82% ​ Dividend yield ​ — % — % Fair value of warrants ​ ​ $4.26 - $7.40 ​ ​ $14.56 - $22.72 ​ ​ A reconciliation of warrant liabilities is included below: ​ ​ ​ ​ ​ Fair Value (As restated) Balance as of December 31, 2020 ​ $ — Additions pursuant to Merger ​ 40,204,122 Gain upon re-measurement ​ (17,359,009) Balance as of June 30, 2021 ​ ​ 22,845,113 Loss upon re-measurement ​ ​ 16,536,469 Reclassification to additional paid-in capital upon exercise ​ ​ (38,120,032) Balance as of September 30, 2021 ​ $ 1,261,550 ​ 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, including the probability of achievement, 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 Loss upon re-measurement ​ ​ 408,342 Balance as of September 30, 2021 ​ $ 26,283,238 ​ 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 3 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 was recognized as a deemed dividend. Upon closing of the Merger, the estimated fair value of the contingent Earnout Shares was $255,822,071 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

Income Taxes	9 Months Ended
	Sep. 30, 2021
Income Taxes
Income Taxes	14. Income Taxes The Company recorded no provision or benefit for income tax expense for the nine months ended September 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 nine months ended September 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 September 30, 2021.

Related Party Transactions

Related Party Transactions	9 Months Ended
	Sep. 30, 2021
Related Party Transactions
Related Party Transactions	15. Related Party Transactions All related party transactions are governed by and implemented in accordance with the Company’s Related Person Transactions Policy which relates to the review, approval, ratification and disclosure of transactions or arrangements between the Company and its directors, executive officers and other related persons, All Related Person Transactions are submitted to the General Counsel of the Company and the Chair of the Audit Committee for approval. The Company licenses patents that are owned by Glytech, LLC (“Glytech”), pursuant to a license agreement (the “Glytech Agreement”). Glytech 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 September 30, 2021 and 2020 the Company paid a co-founder $0 and $0, respectively, and during the nine months ended September 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 aggregate the value of NRx Pharmaceuticals equity held by Glytech exceeds $50,000,000 on any date prior to August 6, 2022, based on the average daily value of the equity held by Glytech during a period of 20 consecutive days prior to such date. 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 $68,750 and $128,750 during the three months ended September 30, 2021 and 2020, respectively, and $355,000 and $250,625 during the nine months ended September 30, 2021 and 2020, respectively. The services are ongoing. Zachary Javitt 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. The Company paid this family member a total of $28,580 and $19,585 during the three months ended September 30, 2021 and 2020, respectively, and $58,320 and $60,355 during the nine months ended September 30, 2021 and 2020, respectively. In addition, the Company pays PillTracker for digital health product development required to track the use of Aviptadil in clinical trials. FDA guidance recommends such solutions and the FDA specifically directed the Company to implement a digital health tracking solution. Zachary Javitt and Jonathan Javitt are the chief executive officer and board chairman, respectively, of PillTracker. As PillTracker is a Related Person, all PillTracker agreements and transactions are submitted to the General Counsel of the Company and the Chair of the Audit Committee for approval in accordance with the terms of the Company’s Related Person Transactions Policy. On July 26, 2021, the Company and PillTracker entered into a statement of work (“SOW”) under the Master Service Agreement dated April 1, 2020 (“MSA”). Under this SOW, PillTracker provides support for the inhaled ZYESAMI Phase 2/3 clinical trials by monitoring SP02 and Heart Rate in patients in a sub-study of the AVICOVID-2 clinical trial in the U.S. to determine the physiological effects of ZYESAMI vs. a placebo. PillTracker’s responsibilities include set-up, patient monitoring, and the provision of tablets and other necessary hardware. The total cost under the SOW is $157,110. NRx Pharmaceuticals paid PillTracker $289,308 and $118,642 during the three months ended September 30, 2021 and 2020, respectively, and $685,066 and $118,642 during the nine months ended September 30, 2021 and 2020, respectively. Included in accounts payable were $138,501 and $149,067 due to the above related parties as of September 30, 2021 and December 31, 2020, respectively.

Subsequent Events

Subsequent Events	9 Months Ended
	Sep. 30, 2021
Subsequent Events
Subsequent Events	16. Subsequent Events VaccineCo Agreement and Issuance of Additional Shares On October 15, 2021, the Company entered into a Shareholder Agreement (“Agreement”) TM – take any and all necessary actions to support the negotiation and execution of an exclusive license agreement to the Company and/or VaccineCo for the development and marketing of the Vaccine; – assist in obtaining all permits, licenses and approvals from all local, regional and national governmental departments and other regulatory health authorities, including the European Medicines Agency and the World Health Organization, as applicable, which are necessary for the Company and/or VaccineCo to advance the current clinical trials of the Vaccine in the nation of Georgia and to commence clinical trials of the Vaccine in Ukraine and such other countries as the parties shall agree; – assist the Company and/or VaccineCo in furthering, organizing and/or commencing clinical trials of the Vaccine in each of the above mentioned countries; – market and sell the Vaccine, once approved, in all countries of the Caucasus region, Russia, Peru, and such other countries as the parties shall agree; and – pay 40% of all costs of developing, marketing, and selling the Vaccine. In consideration for the Shareholders’ commencement of work under the Agreement, the Agreement provides that the Company will grant the Shareholders 4,000,000 shares of the Company’s Common Stock. On October 20, 2021, the Shares were issued by the Company to the Shareholders under the Company’s 2021 Omnibus Incentive Plan. ​ ​

Summary of Significant Accoun_2

Summary of Significant Accounting Policies (Policies)	9 Months Ended
	Sep. 30, 2021
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 the 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 presentation of the balance sheet, statements of operations and cash flows for the interim 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 was accounted for as a reverse recapitalization in accordance with GAAP (the “Reverse Recapitalization”). Under this method of accounting, BRPA is 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	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	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 13)
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.
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.
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.
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. For a Type 1 (probable-to-probable) modification, incremental stock-based compensation cost is measured as the excess, if any, of the fair value of the modified option/warrant over the fair value of the original option/warrant immediately before its terms are modified, measured based on the fair value of the 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	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 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 liability classified and recorded at their initial fair value on the date of issuance and remeasured at fair value 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 and the fair value of the Substitute Warrants was estimated using a modified Black Scholes valuation approach which applies a probability factor based on the probabilities of achieving the Earnout Cash Milestone and/or Earnout Shares Milestone at each reporting period (see Notes 11 and 13).
Income Taxes	Income Taxes Income taxes are recorded in accordance with ASC 740, Income Taxes
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 separation models required under current GAAP. The ASU removes certain settlement conditions that are required for equity contracts to qualify for the derivative scope exception and it also simplifies the diluted earnings per share calculation in certain areas. The ASU is effective for fiscal years beginning after December 15, 2023, including interim periods within those fiscal years. Early adoption is permitted, but no earlier than fiscal years beginning after December 15, 2020 and adoption must be as of the beginning of the Company’s annual fiscal year. We adopted ASU 2020-06 on January 1, 2021, with no material impact on our financial statements. 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

Summary of Significant Accoun_3

Summary of Significant Accounting Policies (Tables)	9 Months Ended
	Sep. 30, 2021
Summary of Significant Accounting Policies
Schedule of Outstanding Shares of Common Stock Equivalents Excluded From Diluted Net Loss Per Share	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three Months Ended September 30, ​ Nine Months Ended September 30, ​ 2021 2020 2021 2020 Stock options 2,388,811 — 2,388,811 1,754,623 Common stock warrants 9,305,790 — 9,305,790 1,690,192 Earnout Shares ​ 22,209,280 ​ — ​ 22,209,280 ​ — Earnout Shares from exercised Substitute Options and Substitute Warrants ​ 1,229,925 ​ — ​ 1,229,925 ​ —

Restatement of Previously Iss_2

Restatement of Previously Issued Financial Statements (Tables)	9 Months Ended
	Sep. 30, 2021
Restatement of Previously Issued Financial Statements
Summary of the effect of the restatement on financial statement line items	The tables summarize the effect of the restatement on each financial statement line item as of the dates, and for the period, indicated: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Balance Sheet as of September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Warrant liabilities $ 775,263 $ 486,287 $ 1,261,550 Total current liabilities ​ ​ 36,282,975 ​ ​ 486,287 ​ ​ 36,769,262 Total liabilities ​ ​ 36,282,975 ​ ​ 486,287 ​ ​ 36,769,262 Additional paid-in capital ​ ​ 161,362,260 ​ ​ (100,415) ​ ​ 161,261,845 Accumulated deficit ​ ​ (152,449,666) ​ ​ (385,872) ​ ​ (152,835,538) Total stockholders' equity (deficit) ​ ​ 8,967,404 ​ ​ (486,287) ​ ​ 8,481,117 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Operations for the three months ended September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Change in fair value of warrant liabilities $ 260,238 $ 16,276,232 $ 16,536,470 Total other (income) expenses ​ ​ 673,948 ​ ​ 16,276,232 ​ ​ 16,950,180 Loss before tax ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) Net loss ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) Net loss attributable to common stockholders ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) Net loss per share, basic and diluted ​ $ (0.40) ​ ​ (0.32) ​ ​ (0.72) Net loss per share attributable to common stockholders, basic and diluted ​ $ (0.40) ​ ​ (0.32) ​ ​ (0.72) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Operations for the nine months ended September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Change in fair value of warrant liabilities $ (1,208,412) $ 385,873 $ (822,539) Total other (income) expenses ​ ​ (550,523) ​ ​ 385,873 ​ ​ (164,650) Loss before tax ​ ​ (62,269,946) ​ ​ (385,873) ​ ​ (62,655,819) Net loss ​ ​ (62,269,946) ​ ​ (385,873) ​ ​ (62,655,819) Net loss attributable to common stockholders ​ ​ (318,092,017) ​ ​ (385,873) ​ ​ (318,477,890) Net loss per share, basic and diluted ​ $ (1.44) ​ ​ (0.01) ​ ​ (1.45) Net loss per share attributable to common stockholders, basic and diluted ​ $ (7.35) ​ ​ (0.01) ​ ​ (7.36) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Stockholders' Equity (Deficit) for the nine months ended September 30, 2021 (unaudited) ​ As Reported ​ Adjustment ​ As Restated Effect of Merger and recapitalization, net of redemptions and issuance costs of $1,412,846 $ (26,615,796) $ (38,220,448) $ (64,836,244) Issuance of common stock for exercise of warrants and Unit Purchase Options ​ ​ 9,199,471 ​ ​ 38,120,033 ​ ​ 47,319,504 Net loss for the three months ended September 30, 2021 ​ ​ (20,773,099) ​ ​ (16,276,232) ​ ​ (37,049,331) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Condensed Consolidated Statement of Cash Flows for the nine months ended September 30, 2021 (unaudited) As Reported Adjustment As Restated CASH FLOWS FROM OPERATING ACTIVITIES: ​ ​ ​ ​ ​ ​ ​ ​ Net Loss ​ $ (62,269,946) ​ $ (385,873) ​ $ (62,655,819) Adjustments to reconcile net loss to net cash and used in operating activities: ​ ​ ​ ​ ​ ​ ​ ​ ​ Change in fair value of warrant liabilities ​ ​ (1,208,412) ​ ​ 385,873 ​ ​ (822,539) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Supplemental disclosure of cash flow information: ​ ​ ​ ​ ​ ​ ​ ​ ​ Non-cash investing and financing activities ​ ​ ​ ​ ​ ​ ​ ​ ​ Reclassification of legacy NeuroRx warrants to warrant liabilities ​ ​ - ​ ​ 38,220,448 ​ ​ 38,220,448 Reclassification of warrant liability upon exercise of warrant ​ ​ - ​ ​ 38,120,032 ​ ​ 38,120,032 ​

Reverse Recapitalization (Table

Reverse Recapitalization (Tables)	9 Months Ended
	Sep. 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 nine months ended September 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 nine months ended September 30, 2021: ​ ​ ​ ​ ​ Recapitalization (As restated) 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 legacy NeuroRx Warrants ​ ​ (38,220,448) 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 ​ $ (64,836,244) ​

Prepaid Expenses and Other Cu_2

Prepaid Expenses and Other Current Assets (Tables)	9 Months Ended
	Sep. 30, 2021
Prepaid Expenses and Other Current Assets
Schedule of prepaid expenses and other current assets	​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, 2021 December 31, 2020 ​ ​ ​ (Unaudited) ​ ​ ​ Prepaid expenses and other current assets: ​ ​ ​ Prepaid insurance ​ $ 3,767,488 ​ $ 49,029 Prepaid manufacturing expenses ​ 1,407,500 ​ — Prepaid clinical development expenses ​ ​ 720,686 ​ ​ — Other prepaid expenses ​ 455,215 ​ 164,772 Other current assets ​ — ​ $ 26,551 Total prepaid expenses and other current assets ​ $ 6,350,889 ​ $ 240,352

Accrued and Other Current Lia_2

Accrued and Other Current Liabilities (Tables)	9 Months Ended
	Sep. 30, 2021
Accrued and Other Current Liabilities
Schedule of accrued and other current liabilities	​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Accrued and other current liabilities: ​ ​ ​ ​ ​ ​ Accrued research and development expenses $ 625,139 $ 586,426 Accrued employee expenses ​ ​ — ​ ​ 530,500 Professional services ​ 685,802 ​ 606,553 Accrued insurance expenses ​ ​ 651,835 ​ ​ — Other accrued expenses ​ 33,185 ​ 5,004 Total accrued and other current liabilities ​ $ 1,995,961 ​ $ 1,728,483

Notes Payable (Tables)

Notes Payable (Tables)	9 Months Ended
	Sep. 30, 2021
Notes Payable.
Schedule of Notes Payable and Accrued Interest	​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, December 31, ​ ​ 2021 ​ 2020 ​ ​ (Unaudited) ​ ​ ​ Relief Therapeutics loan ​ $ 500,000 ​ $ 500,000 Paycheck Protection Program loan ​ — ​ 119,842 Note payable — vendor ​ ​ — ​ ​ 154,190 Carrying value of notes payable ​ 500,000 ​ 774,032 Accrued interest ​ ​ 15,059 ​ ​ 22,656 Note payable ​ ​ 515,059 ​ ​ 796,688 Notes payable and accrued interest, current ​ $ 515,059 ​ $ 248,861 Notes payable and accrued interest, non-current ​ $ — ​ $ 547,827

Equity (Tables)

Equity (Tables)	9 Months Ended
	Sep. 30, 2021
Equity
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 ​ 0.57-3.69 ​ 0.57-3.69 ​ Dividend yield ​ — ​ — ​
Summary of activity for 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 5) ​ 2,455,415 ​ — ​ ​ (13.53) ​ ​ — Outstanding as of December 31, 2020, effect of Merger (Note 5) ​ 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 ​ $ 6.63 ​ $ 42,385,824 Issued ​ 2,863,637 ​ 3.00 ​ ​ 12.08 ​ ​ 4,858,637 Exercised (1,834,740) — ​ (3.19) ​ (17,498,538) Forfeited ​ (218,423) ​ — ​ ​ (1.53) ​ ​ (1,500,566) Outstanding as of September 30, 2021 9,305,790 3.87 ​ $ 9.09 ​ $ 17,770,340

Stock-Based Compensation (Table

Stock-Based Compensation (Tables)	9 Months Ended
	Sep. 30, 2021
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 ​ — ​ — ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, 2021 December 31, 2020 Exercise price ​ $10.03-$23.41 ​ ​ $2.22-$3.07 ​ Risk-free rate of interest ​ 0.69%-1.24% ​ 0.79% ​ Expected term (years) ​ 5.25-6.5 ​ 4.69-5.9 ​ Expected stock price volatility ​ 80.0%-85.9% ​ 80.0% ​ Dividend yield ​ — ​ — ​
Schedule of share-based compensation arrangements by share-based payment award	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 granted ​ 82,890 ​ ​ 13.68 ​ 9.9 ​ ​ — Forfeited ​ (102,507) ​ ​ (3.07) ​ — ​ ​ (635,543) Exercised ​ (511,065) ​ ​ (2.22) ​ — ​ ​ (3,602,645) Outstanding as of September 30, 2021 ​ 2,388,811 ​ $ 6.04 ​ 8.1 ​ $ 12,447,723 Options vested and exercisable as of September 30, 2021 ​ 1,250,340 ​ $ 1.86 ​ 6.2 ​ $ 9,418,169
Summary of recognition of stock-based compensation	The following table summarizes the Company’s recognition of stock-based compensation for the following periods: ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Three months ended September 30, ​ Nine months ended September 30, ​ 2021 2020 2021 2020 Stock-based compensation expense ​ ​ ​ ​ General and administrative ​ $ 1,340,023 ​ $ 64,604 ​ $ 5,778,606 ​ $ 182,073 Regulatory and process development ​ 219,802 ​ 126,146 ​ 436,247 ​ 190,945 Total stock-based compensation expense ​ $ 1,559,825 ​ $ 190,750 ​ $ 6,214,853 ​ $ 373,018

Fair Value Measurements (Tables

Fair Value Measurements (Tables)	9 Months Ended
	Sep. 30, 2021
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Summary of fair value hierarchy	​ ​ ​ ​ ​ ​ ​ ​ ​ ​ Description Level September 30, 2021 (As restated) December 31, 2020 Liabilities: ​ ​ ​ ​ ​ ​ ​ ​ Warrant liabilities (Note 11) ​ 3 ​ $ 1,261,550 ​ $ — Earnout Cash liability (Note 5) 3 ​ $ 26,283,238 ​ $ —
Schedule of significant unobservable inputs	The significant inputs used in the Black-Scholes model to measure the warrant liabilities that are categorized within Level 3 of the fair value hierarchy are as follows: ​ ​ ​ ​ ​ ​ ​ ​ ​ September 30, 2021 At Effective Time ​ ​ (As restated) ​ Expected life ​ 1.77 - 4.65 ​ 0.3 - 5.0 ​ Volatility ​ 82.5% - 85.9% ​ 39.0% - 80.0% ​ Risk-free rate ​ 0.15% - 0.32% ​ 0.03% - 0.82% ​ Dividend yield ​ — % — % Fair value of warrants ​ ​ $4.26 - $7.40 ​ ​ $14.56 - $22.72 ​
Common stock warrants
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 (As restated) Balance as of December 31, 2020 ​ $ — Additions pursuant to Merger ​ 40,204,122 Gain upon re-measurement ​ (17,359,009) Balance as of June 30, 2021 ​ ​ 22,845,113 Loss upon re-measurement ​ ​ 16,536,469 Reclassification to additional paid-in capital upon exercise ​ ​ (38,120,032) Balance as of September 30, 2021 ​ $ 1,261,550 ​
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 Loss upon re-measurement ​ ​ 408,342 Balance as of September 30, 2021 ​ $ 26,283,238

Organization (Details)

Organization (Details) $ in Millions	9 Months Ended
	Sep. 30, 2021 USD ($)
Reimbursements from Relief Therapeutics Holding AG
Related Party Transaction [Line Items]
Payment to related party	$ 10.9

Liquidity (Details)

Liquidity (Details) - USD ($)		3 Months Ended	9 Months Ended
	Aug. 23, 2021	Sep. 30, 2021	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
Schedule of Liquidity [Line Items]
Cash		$ 38,883,569	$ 38,883,569		$ 1,858,513
Common stock issued (in shares)		511,065
Proceeds from issuance of common stock			$ 9,623,899	$ 1,589,103
Private Placement
Schedule of Liquidity [Line Items]
Common stock issued (in shares)	2,727,273
Price per share	$ 11
Proceeds from issuance of common stock	$ 30,000,000
Preferred Investment Options
Schedule of Liquidity [Line Items]
Price per share	$ 12
Preferred Investment Options | Maximum
Schedule of Liquidity [Line Items]
Common stock issued (in shares)	2,727,273

Summary of Significant Accoun_4

Summary of Significant Accounting Policies (Details) - shares	3 Months Ended	9 Months Ended
	Sep. 30, 2021	Sep. 30, 2021	Sep. 30, 2020
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	2,388,811	2,388,811	1,754,623
Common stock warrants
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	9,305,790	9,305,790	1,690,192
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
Earnout Shares from exercised Substitute Options and Substitute Warrants
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Shares excluded from computation of diluted net loss per share	1,229,925	1,229,925

Restatement of Previously Iss_3

Restatement of Previously Issued Financial Statements (Details) - USD ($)	3 Months Ended						9 Months Ended
	Sep. 30, 2021	Jun. 30, 2021	Mar. 31, 2021	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Condensed Consolidated Balance Sheet
Warrant liabilities	$ 1,261,550						$ 1,261,550
Total current liabilities	36,769,262						36,769,262		$ 46,164,225
Total liabilities	36,769,262						36,769,262		46,712,052
Additional paid-in capital	161,261,845						161,261,845		46,365,863
Accumulated deficit	(152,835,538)						(152,835,538)		(90,179,720)
Total stockholders' equity (deficit)	8,481,117	$ (39,767,431)	$ 6,390,824	$ (2,828,954)	$ (5,921,867)	$ (6,117,620)	8,481,117	$ (2,828,954)	$ (43,770,883)	$ (4,843,405)
Condensed Consolidated Statement of Operations
Change in fair value of warrant liabilities	16,536,470						(822,539)
Total other (income) expenses	16,950,180			12,513			(164,650)	385,118
Loss before tax	(37,049,331)			(5,161,712)			(62,655,819)	(6,649,481)
Net loss	(37,049,331)	(117,613)	(25,488,874)	(5,161,712)	102,287	(1,590,056)	(62,655,819)	(6,649,481)
Net loss attributable to common stockholders	$ (37,049,331)			$ (5,161,712)			$ (318,477,890)	$ (6,649,481)
Net loss per share:
Basic	$ (0.72)			$ (0.15)			$ (1.45)	$ (0.20)
Diluted	(0.72)			(0.15)			(1.45)	(0.20)
Net loss per share attributable to common stockholders:
Basic	(0.72)			(0.15)			(7.36)	(0.20)
Diluted	$ (0.72)			$ (0.15)			$ (7.36)	$ (0.20)
Condensed Consolidated Statement of Stockholders' Equity (Deficit)
Effect of Merger and recapitalization, net of redemptions and issuance costs		(64,836,244)					$ (64,836,244)
Merger and recapitalization, redemptions and issuance costs		1,412,846					1,412,846
Issuance of common stock for exercise of warrants and Unit Purchase Options	$ 47,319,504						47,319,504
Net income (loss)	(37,049,331)	(117,613)	(25,488,874)	$ (5,161,712)	102,287	(1,590,056)	(62,655,819)	$ (6,649,481)
CASH FLOWS FROM OPERATING ACTIVITIES:
Net Loss	(37,049,331)	$ (117,613)	$ (25,488,874)	$ (5,161,712)	$ 102,287	$ (1,590,056)	(62,655,819)	$ (6,649,481)
Adjustments to reconcile net loss to net cash used in operating activities:
Change in fair value of warrant liabilities							(822,539)
Non-cash investing and financing activities
Reclassification of legacy NeuroRx warrants to warrant liability							38,220,448
Reclassification of warrant liability upon exercise of warrant							38,120,032
As previously reported
Condensed Consolidated Balance Sheet
Warrant liabilities	775,263						775,263
Total current liabilities	36,282,975						36,282,975
Total liabilities	36,282,975						36,282,975
Additional paid-in capital	161,362,260						161,362,260
Accumulated deficit	(152,449,666)						(152,449,666)
Total stockholders' equity (deficit)	8,967,404						8,967,404
Condensed Consolidated Statement of Operations
Change in fair value of warrant liabilities	260,238						(1,208,412)
Total other (income) expenses	673,948						(550,523)
Loss before tax	(20,773,099)						(62,269,946)
Net loss	(20,773,099)						(62,269,946)
Net loss attributable to common stockholders	$ (20,773,099)						$ (318,092,017)
Net loss per share:
Basic	$ (0.40)						$ (1.44)
Diluted	(0.40)						(1.44)
Net loss per share attributable to common stockholders:
Basic	(0.40)						(7.35)
Diluted	$ (0.40)						$ (7.35)
Condensed Consolidated Statement of Stockholders' Equity (Deficit)
Effect of Merger and recapitalization, net of redemptions and issuance costs							$ (26,615,796)
Issuance of common stock for exercise of warrants and Unit Purchase Options							9,199,471
Net income (loss)	$ (20,773,099)						(62,269,946)
CASH FLOWS FROM OPERATING ACTIVITIES:
Net Loss	(20,773,099)						(62,269,946)
Adjustments to reconcile net loss to net cash used in operating activities:
Change in fair value of warrant liabilities							(1,208,412)
Adjustment
Condensed Consolidated Balance Sheet
Warrant liabilities	486,287						486,287
Total current liabilities	486,287						486,287
Total liabilities	486,287						486,287
Additional paid-in capital	(100,415)						(100,415)
Accumulated deficit	(385,872)						(385,872)
Total stockholders' equity (deficit)	(486,287)						(486,287)
Condensed Consolidated Statement of Operations
Change in fair value of warrant liabilities	16,276,232						385,873
Total other (income) expenses	16,276,232						385,873
Loss before tax	(16,276,232)						(385,873)
Net loss	(16,276,232)						(385,873)
Net loss attributable to common stockholders	$ (16,276,232)						$ (385,873)
Net loss per share:
Basic	$ (0.32)						$ (0.01)
Diluted	(0.32)						(0.01)
Net loss per share attributable to common stockholders:
Basic	(0.32)						(0.01)
Diluted	$ (0.32)						$ (0.01)
Condensed Consolidated Statement of Stockholders' Equity (Deficit)
Effect of Merger and recapitalization, net of redemptions and issuance costs							$ (38,220,448)
Issuance of common stock for exercise of warrants and Unit Purchase Options							38,120,033
Net income (loss)	$ (16,276,232)						(385,873)
CASH FLOWS FROM OPERATING ACTIVITIES:
Net Loss	$ (16,276,232)						(385,873)
Adjustments to reconcile net loss to net cash used in operating activities:
Change in fair value of warrant liabilities							385,873
Non-cash investing and financing activities
Reclassification of legacy NeuroRx warrants to warrant liability							38,220,448
Reclassification of warrant liability upon exercise of warrant							$ 38,120,032

Reverse Recapitalization (Detai

Reverse Recapitalization (Details)			3 Months Ended					9 Months Ended
	May 24, 2021 $ / shares shares	May 23, 2021	Sep. 30, 2021 USD ($) $ / shares shares	Jun. 30, 2021 USD ($)	Mar. 31, 2021 USD ($)	Sep. 30, 2020 USD ($)	Mar. 31, 2020 USD ($)	Sep. 30, 2021 USD ($) $ / shares shares
Business Acquisition [Line Items]
Deemed dividend - Earnout Shares | $								$ 255,822,071
Stock Issued During Period, Shares, New Issues			511,065
Aggregate purchase price | $			$ 1,134,816	$ 1,562,272	$ 6,927,086	$ 1,412,067	$ 177,025
Merger agreement
Business Acquisition [Line Items]
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
Aggregate purchase price | $								$ 10,000,000
Merger agreement | Stockholders of NeuroRx
Business Acquisition [Line Items]
Consideration (in 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	9 Months Ended
	Sep. 30, 2021 USD ($)
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 legacy NeuroRx Warrants	(38,220,448)
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	(64,836,244)
Effect of Merger, net of redemptions and transaction costs	$ 11,049,628

Reverse Recapitalization - Cons

Reverse Recapitalization - Consummation of the merger (Details) - shares		3 Months Ended	9 Months Ended
	May 24, 2021	Sep. 30, 2021	Sep. 30, 2021	Dec. 31, 2020
Business Acquisition [Line Items]
Merger and PIPE Financing shares - common stock		511,065
Total shares of common stock immediately after Merger		0	0	42,973,462
Merger agreement
Business Acquisition [Line Items]
Common stock, outstanding prior to Merger		552,412	552,412
Less: redemption of BRPA shares			(216)
Common stock of BRPA		552,196	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
Merger and PIPE Financing shares - common stock			3,729,730
Total shares of common stock immediately after Merger		48,603,585	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	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 ($)	Sep. 30, 2021	Dec. 31, 2020
Prepaid Expenses and Other Current Assets
Prepaid insurance	$ 3,767,488	$ 49,029
Prepaid manufacturing expenses	1,407,500
Prepaid clinical development expenses	720,686
Other prepaid expenses	455,215	164,772
Other current assets		26,551
Total prepaid expenses and other current assets	$ 6,350,889	$ 240,352

Accrued and Other Current Lia_3

Accrued and Other Current Liabilities (Details) - USD ($)	Sep. 30, 2021	Dec. 31, 2020
Accrued and other current liabilities:
Accrued research and development expenses	$ 625,139	$ 586,426
Accrued employee expenses		530,500
Professional services	685,802	606,553
Accrued insurance expenses	651,835
Other accrued expenses	33,185	5,004
Total accrued and other current liabilities	$ 1,995,961	$ 1,728,483

Convertible Notes Payable - Add

Convertible Notes Payable - Additional Information (Details) - USD ($)					3 Months Ended		4 Months Ended	9 Months Ended
	Feb. 12, 2020	Apr. 25, 2018	Nov. 19, 2017	Nov. 16, 2017	Sep. 30, 2021	Sep. 30, 2020	Apr. 25, 2018	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
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				$ 15,059			$ 15,059		$ 22,656
Common stock fair value						$ 0			$ 306,641
Interest paid					0	0		0	0
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%
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
Two Thousand And Eighteen Note [Member]
Schedule of Convertible Notes [Line Items]
Interest rate		6%					6%
Principal and interest maturity date		4 years
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.
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	$ 16,475
Two Thousand Seventeen And Eighteen Convertible Notes Payable[Member]
Schedule of Convertible Notes [Line Items]
Recognized gain (loss)at fair value					$ 0	$ 0
Two Thousand Eighteen Convertible Notes Payable [Member]
Schedule of Convertible Notes [Line Items]
Convertible notes gross proceeds							$ 300,000

Notes Payable - Notes payable a

Notes Payable - Notes payable and Accrued Interest (Details) - USD ($)	9 Months Ended	12 Months Ended
	Sep. 30, 2021	Dec. 31, 2020	Feb. 12, 2020	Jul. 01, 2019
Carrying value of notes payable	$ 500,000	$ 774,032
Accrued interest	15,059	22,656	$ 369,660
Note payable	515,059	796,688
Notes payable and accrued interest, current	515,059	248,861
Notes payable and accrued interest, non-current		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
Vendor
Note Payable - Related Party		$ 154,190		$ 154,190

Notes Payable - Additional Info

Notes Payable - Additional Information (Details) - USD ($)			9 Months Ended
	Apr. 28, 2020	Apr. 06, 2020	Sep. 30, 2021	Dec. 31, 2019
Loan term	2 years
Loan forgiveness, description	The PPP Loan amount may be eligible for forgiveness in the event that (1) at least 75% of the PPP 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 PPP 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%
Related party loan		$ 500,000
Debt Instrument, Maturity Date		Apr. 06, 2022
Vendor
Interest rate				6%
Pay Check Protection Program [Member]
Loan funding	$ 119,842
Outstanding principal rate	1%
Principal and interest due	$6,744
Gain on extinguishment of debt			$ 120,810

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($)				3 Months Ended		9 Months Ended
	Jul. 01, 2021	Mar. 28, 2021	Aug. 25, 2020	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020	Oct. 09, 2020
Commitments and Contingencies [Line Items]
Rent expense				$ 9,162	$ 14,174	$ 64,555	$ 32,076
Percentage of company's annual requirements			100%
Allowance for doubtful accounts								$ 257,463
Accrued settlement expense								39,486,139
Additional settlement liability						21,365,641
Proceeds from issuance of common stock for exercise of warrant						16,699,489
Prepaid expenses and other current assets				6,350,889		6,350,889		$ 240,352
GEM 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 were 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.
Reimbursements from Relief Therapeutics Holding AG
Commitments and Contingencies [Line Items]
Reimbursable expenses						13,800,000
Payment to related party						$ 10,900,000
Phase II Inhaled clinical trial of Aviptadil
Commitments and Contingencies [Line Items]
Research commitments	$ 7,400,000
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									$ 5,255,000
Prepaid expenses and other current assets				1,407,500		1,407,500
Sponsored Research Agreement [Member]
Commitments and Contingencies [Line Items]
Research commitments						399,320
Research commitments paid				$ 90,112		$ 216,269

Equity - Additional Information

Equity - Additional Information (Details)			3 Months Ended					9 Months Ended		12 Months Ended
	May 24, 2021 shares	May 23, 2021	Sep. 30, 2021 USD ($) $ / shares shares	Jun. 30, 2021 USD ($) $ / shares shares	Mar. 31, 2021 USD ($) $ / shares shares	Sep. 30, 2020 USD ($) shares	Mar. 31, 2020 USD ($) shares	Sep. 30, 2021 USD ($) D $ / shares shares	Sep. 30, 2020 USD ($) shares	Dec. 31, 2020 $ / shares shares	Jul. 23, 2021 shares
Stockholders Equity [Line Items]
Common stock, shares authorized			500,000,000					500,000,000		500,000,000
Common stock, par value | $ / shares			$ 0.001					$ 0.001		$ 0.001
Merger and PIPE Financing shares - common stock			511,065
Issuance of common stock for exercise of warrants and Unit Purchase Options | $			$ 47,319,504					$ 47,319,504
Contingently issuable Earnout Shares Excluded from EPS computation			185,472
Common stock issued for consulting services (in shares)			634,045					834,045
Non-cash consulting expense | $			$ 7,925,511					$ 12,775,511
Common stock issued | $			1,134,816	$ 1,562,272	$ 6,927,086	$ 1,412,067	$ 177,025
Proceeds from issuance of common stock | $								9,623,899	$ 1,589,103
Loss on conversion of convertible notes payable | $									$ 306,641
Common stock issued to settle note conversion (in shares)									1,138,199
Awarded to employees as bonus for services provided					210,800
Compensation expenses | $			$ 1,559,825			190,750		6,214,853	$ 373,018
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
Number of shares outstanding			0					0		0
Warrant issued			2,863,637	3,586,250	3,329,812
Warrant, exercise price per share | $ / shares			$ 9.09	$ 6.63	$ 1.78			$ 9.09		$ 1.09
Proceeds from exercise of warrant | $								$ 16,699,489
Number of shares issued upon exercise of warrants | $					$ 7,500,018
Net impact to additional paid-in capital | $					$ 60,851,779
Number of outstanding warrants			9,305,790	8,495,316	4,909,066			9,305,790		3,075,470
Change in fair value of the warrants | $								$ (822,539)
Number of units outstanding			600,000					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 | $			$ 32,644,383					$ 32,644,383
Substitute Warrants
Stockholders Equity [Line Items]
Warrant, exercise price per share | $ / shares			$ 2.45					$ 2.45
Warrants exercised			4,909,066					4,909,066
Public Warrants
Stockholders Equity [Line Items]
Warrant, exercise price per share | $ / shares			$ 11.50					$ 11.50
Warrants exercised			1,144					1,144
Gross proceeds from exercise of warrants | $			$ 13,156
Number of outstanding warrants			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]
Number of outstanding warrants			136,250					136,250
Change in fair value of the warrants | $						0			0
Public Right
Stockholders Equity [Line Items]
Number of outstanding warrants			6,900,000					6,900,000
Number of shares per unit								1
Number of shares per right								1
Placement Rights
Stockholders Equity [Line Items]
Number of outstanding warrants			272,500					272,500
Merger agreement
Stockholders Equity [Line Items]
Merger and PIPE Financing shares - common stock								3,729,730
Merger agreement | Stockholders of NeuroRx
Stockholders Equity [Line Items]
Exchange Ratio	3.16	4.96
General and administrative
Stockholders Equity [Line Items]
Compensation expenses | $			$ 1,340,023			$ 64,604		$ 5,778,606	$ 182,073
Common Stock
Stockholders Equity [Line Items]
Merger and PIPE Financing shares - common stock			3,238,338			292,534		3,642,515	343,378
Issuance of common stock for exercise of warrants and Unit Purchase Options (in shares)			2,334,370					3,830,586
Proceeds from issuance of common stock | $			$ 31,134,816			$ 1,412,067		$ 39,624,175	$ 1,589,092
Awarded to employees as bonus for services provided						200,000		200,000
Common Stock | General and administrative
Stockholders Equity [Line Items]
Compensation expenses | $								$ 4,850,000
Legacy NeuroRx Preferred Stock | Convertible Series A Preferred Stock
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
Number of shares outstanding	2,367,543
Shares issued upon conversion	7,480,836
Legacy NeuroRx Preferred Stock | Convertible Series B-1 Preferred Stock
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
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
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
Number of shares outstanding	4,167
Shares issued upon conversion	13,168

Equity - Schedule of Assumption

Equity - Schedule of Assumptions (Details) - $ / shares		9 Months Ended	12 Months Ended
	Aug. 23, 2021	Sep. 30, 2021	Dec. 31, 2020
Class of Warrant or Right [Line Items]
Volatility rate			80%
Risk-free rate, minimum		0.69%	0.79%
Risk-free rate, maximum		1.24%
Dividend yield		0%	0%
Preferred Investment Options
Class of Warrant or Right [Line Items]
Strike price	$ 12
Volatility rate	85.90%
Risk-free rate	0.43%
Expected term	3 years
Dividend yield	0%
Private Placement
Class of Warrant or Right [Line Items]
Strike price	$ 13.78
Volatility rate	85.90%
Risk-free rate	0.43%
Expected term	3 years
Dividend yield	0%
Minimum
Class of Warrant or Right [Line Items]
Strike price		$ 10.03	$ 2.22
Expected term		5 years 3 months	4 years 8 months 8 days
Minimum | Substitute Warrants
Class of Warrant or Right [Line Items]
Strike price		$ 1.53
Risk-free rate, minimum		0.03%
Expected term		6 months 26 days
Minimum | Common stock warrants
Class of Warrant or Right [Line Items]
Strike price		$ 7.58
Risk-free rate, minimum		0.03%
Expected term		6 months 26 days
Maximum
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
Maximum | Substitute Warrants
Class of Warrant or Right [Line Items]
Strike price		$ 3.19
Risk-free rate, maximum		0.32%
Expected term		3 years 8 months 9 days
Maximum | Common stock warrants
Class of Warrant or Right [Line Items]
Strike price		$ 15.84
Risk-free rate, maximum		0.32%
Expected term		3 years 8 months 9 days

Equity - Schedule of Warrants (

Equity - Schedule of Warrants (Details) - USD ($)	3 Months Ended			12 Months Ended
	Sep. 30, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020
Total Warrants
Outstanding at the beginning	8,495,316	4,909,066	3,075,470
Issued	2,863,637	3,586,250	3,329,812
Exercised	(1,834,740)		(1,496,216)
Forfeited	(218,423)
Outstanding at the end	9,305,790	8,495,316	4,909,066	3,075,470
Weighted Average Remaining Term
Outstanding	3 years 10 months 13 days	4 years 1 month 2 days	3 years 8 months 26 days	4 years 4 months 2 days
Issued (in years)	3 years	5 years	3 years
Forfeited (in years)	0 years
Exercised (in years)	0 years
Weighted Average Exercise Price
Outstanding at the beginning (in dollars per share)	$ 6.63	$ 1.78	$ 1.09
Issued (in dollars per share)	12.08	11.50	3.19
Forfeited (in dollars per share)	(1.53)
Exercised (in dollars per share)	(3.19)		(3.19)
Outstanding at the end (in dollars per share)	$ 9.09	$ 6.63	$ 1.78	$ 1.09
Aggregate Intrinsic Value
Outstanding at the beginning (in dollars)	$ 42,385,824	$ 244,574,345	$ 150,955,963
Issued (in dollars)	4,858,637	45,724,688	111,082,528
Exercised (in dollars)	(17,498,538)		(49,913,766)
Forfeited (in dollars)	(1,500,566)
Outstanding at the end (in dollars)	$ 17,770,340	$ 42,385,824	$ 244,574,345	$ 150,955,963
Substitute Warrants
Weighted Average Exercise Price
Outstanding at the end (in dollars per share)	$ 2.45
Public Warrants
Total Warrants
Outstanding at the end	3,450,000
Weighted Average Exercise Price
Outstanding at the end (in dollars per share)	$ 11.50
Placement Warrants
Total Warrants
Outstanding at the end	136,250
As previously reported
Total Warrants
Outstanding at the beginning			620,055
Outstanding at the end				620,055
Weighted Average Remaining Term
Outstanding				11 years 29 days
Weighted Average Exercise Price
Outstanding at the beginning (in dollars per share)			$ 14.61
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
Outstanding at the beginning			2,455,415
Outstanding at the end				2,455,415
Weighted Average Remaining Term
Exercised (in years)				0 years
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) - USD ($)		9 Months Ended
	Jul. 23, 2021	Sep. 30, 2021
Class of Warrant or Right [Line Items]
Number of units outstanding	600,000	600,000
Shares of common stock issued through conversion	499,630
Price per unit		$ 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, August 2021 Private Placement and Preferred Investment Options (Details) - USD ($)		9 Months Ended
	Aug. 23, 2021	Sep. 30, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020
Class of Warrant or Right [Line Items]
Number of outstanding right		9,305,790	8,495,316	4,909,066	3,075,470
Number of shares per right		1
Fractional shares issued upon conversion of rights		0
Price per unit		$ 10
Aggregate exercise price		$ 6,000,000
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
Private Placement
Class of Warrant or Right [Line Items]
Common stock and warrants issued in private placement, net of issuance costs (in shares)	2,727,273
Price per unit	$ 11
Placement fees	$ 2,250,000
Legal, professional and printing fees	$ 391,781
Private Placement | Maximum
Class of Warrant or Right [Line Items]
Issuance of Common Stock to holders of rights	136,364
Common stock and warrants issued in private placement, net of issuance costs (in shares)	1,026,957
Price per unit	$ 13.75
Preferred Investment Options
Class of Warrant or Right [Line Items]
Common stock and warrants issued in private placement, net of issuance costs (in shares)	2,727,273
Price per unit	$ 12
Aggregate exercise price	$ 30,000,000
Fair value on the date of issuance	$ 21,695,457
Preferred Investment Options | Maximum
Class of Warrant or Right [Line Items]
Price per unit	$ 13.78
Merger agreement
Class of Warrant or Right [Line Items]
Issuance of Common Stock to holders of rights		717,250

Stock Based Compensation - Addi

Stock Based Compensation - Additional Information (Details)			3 Months Ended		9 Months Ended
	May 24, 2021 $ / shares shares	May 23, 2021	Sep. 30, 2021 USD ($) $ / shares shares	Sep. 30, 2020 USD ($) $ / shares	Sep. 30, 2021 USD ($) $ / shares shares	Sep. 30, 2020 USD ($) $ / shares	Jun. 30, 2021 $ / shares shares	Mar. 31, 2021 $ / shares shares	Dec. 31, 2020 $ / shares shares
Equity Incentive Plan [Line Items]
Options to purchase shares of common Stock | shares							2,919,493		2,414,303
Exercise price | $ / shares							$ 5.25		$ 2.17
Expected dividend yield					0%
Weighted average grant date fair value | $ / shares			$ 9.80	$ 11.62	$ 16.53	$ 4.44
Unrecognized compensation			$ 32,644,383		$ 32,644,383
Weighted-average period					1 year 2 months 23 days
Stock-based compensation expense allocated			1,559,825	$ 190,750	$ 6,214,853	$ 373,018
Merger agreement | Stockholders of NeuroRx
Equity Incentive Plan [Line Items]
Exchange Ratio	3.16	4.96
Substitute Options
Equity Incentive Plan [Line Items]
Share-based Payment Arrangement, Plan Modification, Incremental Cost					25,877,473
General and administrative
Equity Incentive Plan [Line Items]
Stock-based compensation expense allocated			1,340,023	64,604	5,778,606	182,073
Research and development
Equity Incentive Plan [Line Items]
Stock-based compensation expense allocated			$ 219,802	$ 126,146	$ 436,247	$ 190,945
2016 Omnibus Inventive Plan [Member]
Equity Incentive Plan [Line Items]
Share-based compensation arrangement by share-based payment award, number of shares authorized | shares			3,472,000		3,472,000
Options to purchase shares of common Stock | shares	2,895,423		2,388,811		2,388,811			2,426,703
Exercise price | $ / shares	$ 5.10		$ 6.04		$ 6.04			$ 14.58

Stock Based Compensation - Lega

Stock Based Compensation - Legacy NeuroRx 2016 Omnibus Incentive Plan - Stock option (Details) - $ / shares	9 Months Ended	12 Months Ended
	Sep. 30, 2021	Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Volatility rate		80%
Risk-free rate, minimum	0.69%	0.79%
Risk-free rate, maximum	1.24%
Dividend yield	0%	0%
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%
Risk-free rate, 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%
Risk-free rate, minimum	0.07%
Minimum
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 10.03	$ 2.22
Expected term	5 years 3 months	4 years 8 months 8 days
Minimum | 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	2 months 4 days
Minimum | 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	2 months 4 days
Maximum
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]
Strike price	$ 23.41	$ 3.07
Expected term	6 years 6 months	5 years 10 months 24 days
Maximum | 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	5 years 11 months 26 days
Maximum | 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	5 years 11 months 26 days

Stock Based Compensation - Le_2

Stock Based Compensation - Legacy NeuroRx 2016 Omnibus Incentive Plan (Details)	9 Months Ended
	Sep. 30, 2021 USD ($)
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
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
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	9 Months Ended
	Sep. 30, 2021 shares
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	732,460
Number of shares remain available for issuance	4,640,589

Stock Based Compensation - Summ

Stock Based Compensation - Summary of grant date of stock option award (Details) - $ / shares	9 Months Ended	12 Months Ended
	Sep. 30, 2021	Dec. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Risk-free rate of interest, minimum	0.69%	0.79%
Risk-free rate of interest, maximum	1.24%
Expected stock price volatility		80%
Dividend yield	0%	0%
Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price	$ 10.03	$ 2.22
Expected term (years)	5 years 3 months	4 years 8 months 8 days
Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Exercise price	$ 23.41	$ 3.07
Expected term (years)	6 years 6 months	5 years 10 months 24 days

Share based compensation - Summ

Share based compensation - Summary of stock option activity (Details) - USD ($)	3 Months Ended			9 Months Ended	12 Months Ended
	Sep. 30, 2021	Jun. 30, 2021	Mar. 31, 2021	Sep. 30, 2021	Dec. 31, 2020
Number of shares
Outstanding at the beginning	2,919,493		2,414,303	2,414,303
Granted			210,800
Forfeited			(198,400)
Outstanding at the end		2,919,493			2,414,303
Weighted average exercise price
Outstanding at the beginning (in dollars per share)	$ 5.25		$ 2.17	$ 2.17
Granted (in dollars per share)			11.69
Forfeited (in dollars per share)			$ (2.22)
Outstanding at the end (in dollars per share)		$ 5.25			$ 2.17
Weighted average remaining remaining term (in years)
Outstanding		9 years			8 years 2 months 12 days
Granted (in years)			9 years 9 months 18 days
Aggregate intrinsic value
Outstanding at the beginning (in dollars)	$ 20,558,299		$ 53,659,966	$ 53,659,966
Granted (in dollars)			3,825,276
Forfeited			$ (6,587,328)
Outstanding at the end (in dollars)		$ 20,558,299			$ 53,659,966
2016 Omnibus Inventive Plan [Member]
Number of shares
Outstanding at the beginning		2,426,703
Granted	82,890	587,030
Exercised	(511,065)	(4,960)
Forfeited	(102,507)	(89,280)
Outstanding at the end	2,388,811		2,426,703	2,388,811
Weighted average exercise price
Outstanding at the beginning (in dollars per share)		$ 14.58
Granted (in dollars per share)	$ 13.68	14.94
Exercised (in dollars per share)	(2.22)	(3.07)
Forfeited (in dollars per share)	(3.07)	$ (7.86)
Outstanding at the end (in dollars per share)	$ 6.04		$ 14.58	$ 6.04
Weighted average remaining remaining term (in years)
Outstanding	8 years 1 month 6 days		8 years 8 months 12 days
Granted (in years)	9 years 10 months 24 days	9 years 10 months 24 days
Forfeited (in years)	0 years
Exercised (in years)	0 years
Aggregate intrinsic value
Outstanding at the beginning (in dollars)		$ 30,388,510
Exercised (in dollars)	$ (3,602,645)	(42,385)
Forfeited	(635,543)	$ (339,082)
Outstanding at the end (in dollars)	$ 12,447,723		$ 30,388,510	$ 12,447,723
2021 Omnibus Incentive Plan
Number of shares
Options vested and exercisable	1,250,340			1,250,340
Weighted average exercise price
Options vested and exercisable	$ 1.86			$ 1.86
Weighted average remaining remaining term (in years)
Options vested and exercisable	6 years 2 months 12 days
Aggregate intrinsic value
Options vested and exercisable	$ 9,418,169			$ 9,418,169
As previously reported
Number of shares
Outstanding at the beginning (as previously reported)					486,755
Weighted average exercise price
Outstanding at the beginning (as previously reported)					$ 10.79
Weighted average remaining remaining term (in years)
Outstanding at the beginning (as previously reported) (in years)					8 years 9 months 18 days
Aggregate intrinsic value
Outstanding at the beginning (as previously reported) (in dollars)					$ 19,571,655
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		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation expense allocated	$ 1,559,825	$ 190,750	$ 6,214,853	$ 373,018
Unrecognized compensation costs expected to be recognized	8,152,105		8,152,105
General and administrative
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation expense allocated	1,340,023	64,604	5,778,606	182,073
Research and development
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation expense allocated	$ 219,802	$ 126,146	$ 436,247	$ 190,945

Fair Value Measurements (Detail

Fair Value Measurements (Details) - Level 3 - USD ($)	Sep. 30, 2021	Dec. 31, 2020
Liabilities:
Warrant liabilities (Note 10)	$ 1,261,550	$ 0
Earnout Cash liability (Note 4)	$ 26,283,238	$ 0

Fair Value Measurements - Recon

Fair Value Measurements - Reconciliation of warrant liabilities (Details) - Common stock warrants - USD ($)	3 Months Ended	6 Months Ended
	Sep. 30, 2021	Jun. 30, 2021
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Balance at the beginning balance	$ 22,845,113
Additions pursuant to Merger		$ 40,204,122
(Gain) loss upon re-measurement	16,536,469	(17,359,009)
Balance at the ending balance	$ 1,261,550	$ 22,845,113

Fair Value Measurements - Rec_2

Fair Value Measurements - Reconciliation of Earnout Cash liability (Details) - Earnout Cash liability - USD ($)	3 Months Ended	6 Months Ended
	Sep. 30, 2021	Jun. 30, 2021
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Balance at the beginning balance	$ 25,874,896
Additions pursuant to Merger		$ 25,520,195
Loss upon re-measurement	408,342	354,701
Balance at the ending balance	$ 26,283,238	$ 25,874,896

Fair Value Measurements - Fair

Fair Value Measurements - Fair value on a Recurring Basis (Details)	9 Months Ended
	Sep. 30, 2021 USD ($) $ / shares
Fair Value Measurements
Trading price | $ / shares	$ 24.25
Deemed dividend - Earnout Shares	$ 255,822,071
Net impact to additional paid-in capital	$ 0

Income Taxes (Details)

Income Taxes (Details)	9 Months Ended
	Sep. 30, 2021 USD ($)
Income Taxes
Provision or benefit for income tax expense	$ 0

Related Party Transactions (Det

Related Party Transactions (Details) - USD ($)		3 Months Ended		9 Months Ended
	Jul. 26, 2021	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
Related Party Transaction [Line Items]
Accounts payable due to related parties		$ 138,501		$ 138,501		$ 149,067
CEO
Related Party Transaction [Line Items]
Compensation amount received related to related party transaction		68,750	$ 128,750	355,000	$ 250,625
PillTracker SOW
Related Party Transaction [Line Items]
Payment to related party		289,308	118,642	685,066	118,642
Total cost under SOW	$ 157,110
Neuro Rx | Chief Commercial Officer
Related Party Transaction [Line Items]
Payment to related party		28,580	19,585	58,320	60,355
Neuro Rx | Glytech Agreement
Related Party Transaction [Line Items]
Continuing technology support services and reimbursed expenses		$ 0	$ 0	$ 125,000	$ 82,569
Related party transaction description				The Excluded Technology will transfer to the Company for no additional consideration if aggregate the value of NRx Pharmaceuticals equity held by Glytech exceeds $50,000,000 on any date prior to August 6, 2022, based on the average daily value of the equity held by Glytech during a period of 20 consecutive days prior to such date.

Subsequent Events (Details)

Subsequent Events (Details) - shares		3 Months Ended
	Oct. 15, 2021	Sep. 30, 2021
Subsequent Event [Line Items]
Common stock issued (in shares)		511,065
Subsequent Event | VaccineCo
Subsequent Event [Line Items]
Percentage of equity interest held by Company	60%
Percentage of equity interest remaining with Shareholders	40%
Percentage of development, marketing and sales costs the Company is responsible for	40%
Common stock issued (in shares)	4,000,000