Exhibit 5.1

	Faegre Drinker Biddle & Reath LLP 1144 15th Street, Suite 3400 Denver, Colorado 80202 +1 215 988 3330 main

August 23, 2024

Arq, Inc.

8051 E. Maplewood Ave., Suite 210

Greenwood Village, CO 80111

Ladies and Gentlemen:

We have acted as counsel for Arq, Inc., a Delaware corporation (the “Company”), in connection with the preparation of a Registration Statement on Form S-3 (the “Registration Statement”) of the Company filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the issuance and sale from time to time by the Company, pursuant to Rule 415 of the Securities Act, of the following securities of the Company having an aggregate initial offering price of up to $100,000,000: (i) shares of common stock, $0.001 par value per share (“Common Stock”); (ii) shares of preferred stock, having a par value as determined by the Company’s Board of Directors (“Preferred Stock”), in one or more classes or series; (iii) warrants to purchase shares of Common Stock or shares of Preferred Stock (collectively, “Warrants”); and (iv) units, consisting of Common Stock, Preferred Stock or Warrants in any combination (the “Units”). The Common Stock, Preferred Stock, Warrants and Units are collectively referred to herein as the “Securities.”

The Securities may be offered separately or together with other Securities, in one or more series, and in amounts, at prices and on terms to be set forth in the prospectus and one or more supplements to the prospectus (collectively, the “Prospectus”) constituting a part of the Registration Statement.

This opinion letter is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K.

Any series of Preferred Stock is to be issued under the Second Amended and Restated Certificate of Incorporation, as amended, of the Company (the “Certificate of Incorporation”) and one or more statements of designations (each, a “Certificate of Designations”) to be approved by the Board of Directors of the Company or a committee thereof and filed with the Office of the Secretary of State of the State of Delaware. Any Common Stock is to be issued under the Certificate of Incorporation. Any Warrants are to be issued under a warrant agreement (including, if applicable, a form of certificate evidencing the Warrants) in a form to be filed as an exhibit to and incorporated by reference into the Registration Statement (the “Warrant Agreement”). Any Units are to be issued pursuant to a unit agreement (including, if applicable, a form of certificate evidencing the Units) in a form to be filed as an exhibit to and incorporated by reference into the Registration Statement (the “Unit Agreement”). The Certificate of Incorporation, each Certificate of Designations, each Warrant Agreement and each Unit Agreement are referred to herein individually as a “Governing Document” and collectively as the “Governing Documents.”

As part of the corporate actions taken and to be taken (the “Corporate Proceedings”) in connection with the issuance of any Securities to be issued and sold from time to time under the Registration Statement, the Board of Directors of the Company (the “Board of Directors”), or a committee thereof or officers of the Company to whom such authority has been properly delegated by the

Board of Directors, will be required to, before such Securities are issued under the Registration Statement, duly authorize the issuance.

As counsel for the Company, we have examined or are otherwise familiar with the Certificate of Incorporation, the Amended and Restated Bylaws of the Company, as amended to the date hereof (the “Bylaws”), the Registration Statement and the Corporate Proceedings taken by the Company to date in connection with the authorization of the Securities. We have also examined originals, or copies certified or otherwise authenticated to our satisfaction, of such corporate records of the Company and other instruments, certificates of public officials and representatives of the Company, and other documents as we have deemed necessary as a basis for the opinions hereinafter expressed and have made such examination of statutes and decisions and reviewed such questions of law as we have deemed necessary or appropriate for the purposes of this opinion letter

Based on and subject to the foregoing and to the other assumptions, qualifications and limitations set forth herein, we are of the opinion that:

1with respect to any series of Preferred Stock, including Preferred Stock issuable upon the exercise of Warrants or as a component of Units (the “Offered Preferred Stock”), upon (a) the completion of all required Corporate Proceedings with respect to the issuance and terms of such Offered Preferred Stock, (b) the due authorization, execution, acknowledgment, delivery and filing with, and recording by, the Office of the Secretary of State of the State of Delaware of a Certificate of Designations in respect of such Offered Preferred Stock, (c) unless issued without certificates, the due execution, registration of issuance and delivery of certificates evidencing such Offered Preferred Stock (or, in the case of shares of Offered Preferred Stock issued without certificates, the due registration of issued and constructive delivery through book entry of such shares), (d) the payment of the agreed upon consideration therefor in accordance with any relevant agreements and the Corporate Proceedings, and (e) in the case of Offered Preferred Stock issuable upon the exercise of, or constituting a component of, any other Securities, completion of all actions in respect of such other Securities referred to in the applicable paragraph hereof, such Offered Preferred Stock will be duly and validly issued, fully paid and nonassessable;

2with respect to any Common Stock, including Common Stock issuable upon conversion of Preferred Stock, upon the exercise of Warrants or as a component of Units (the “Offered Common Stock”), upon (a) the completion of all required Corporate Proceedings with respect to the issuance of such Offered Common Stock, (b) unless issued without certificates, the due execution, registration of issuance and delivery of certificates representing such Offered Common Stock (or, in the case of shares of Offered Common Stock issued without certificates, the due registration of issuance and constructive delivery through book entry of such shares), (c) the payment of the agreed upon consideration therefor in accordance with any relevant agreements and the Corporate Proceedings, and (d) in the case of Offered Common Stock issuable upon the conversion or exercise of, or constituting a component of, any other Securities, completion of all actions in respect of such other Securities referred to in the applicable paragraph hereof, such Offered Common Stock will be duly and validly issued, fully paid and nonassessable; and

3with respect to any Warrants, including Warrants issuable as a component of Units, upon (a) the completion of all required Corporate Proceedings with respect to the authorization of the form, terms, execution and delivery of a Warrant Agreement (including, if applicable, a form of certificate evidencing such Warrants) and the issuance of the Warrants, (b) the due execution and delivery by the Company and the warrant agent of the Warrant Agreement pursuant to which such Warrants are to be issued, (c) if applicable, the due execution, issuance and delivery of warrant certificates evidencing such Warrants pursuant to such Warrant Agreement, countersigned by the warrant agent pursuant to such Warrant Agreement, (d) the payment of the

agreed upon consideration therefor in accordance with the Warrant Agreement and any other relevant agreements and the Corporate Proceedings, and (e) in the case of Warrants constituting a component of any Units, completion of all actions in respect of such Units referred to in paragraph 4 hereof, such Warrant Agreement will constitute a valid and binding obligation of the Company and the warrant certificates evidencing such Warrants will be valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms, and will entitle the holders thereof to the rights specified in such Warrant Agreement.

4With respect to any Units, upon (a) the completion of all required Corporate Proceedings with respect to the authorization of the form, terms, execution and delivery of a Unit Agreement (including, if applicable, a form of certificate evidencing such Units) and the issuance of the Units, (b) the due execution and delivery by the Company and the unit agent of the Unit Agreement pursuant to which such Units are to be issued, (c) if applicable, the due execution, issuance and delivery of unit certificates evidencing such Units pursuant to such Unit Agreement, countersigned by the unit agent pursuant to such Unit Agreement, (d) the payment of the agreed upon consideration therefor in accordance with the Unit Agreement and any other relevant agreements and the Corporate Proceedings, and (e) the actions in respect of any Common Stock, Preferred Stock and/or Warrants comprising such Units referred to in paragraphs 1, 2 and 3 hereof (as the case may be) have been completed, such Unit Agreement will constitute a valid and binding obligation of the Company and the unit certificates evidencing such Units will be valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms, and will entitle the holders thereof to the rights specified in such Unit Agreement.

The foregoing opinions are subject to the limitation that the validity, binding effect or enforceability of the provisions of any agreement or instrument is limited by (i) applicable bankruptcy, insolvency, reorganization, assignment for the benefit of creditors, moratorium, fraudulent conveyance, fraudulent transfer, voidable transaction, receivership and other laws of general application affecting the enforcement of creditors’ rights, (ii) general principles of equity, including, without limitation, concepts of materiality, reasonableness, good faith, fair dealing and the possible unavailability of specific performance, injunctive relief or other equitable remedies, whether considered in a proceeding at law or in equity, (iii) public policy considerations that may limit the rights of parties to obtain specific remedies or enforce specific terms, and (iv) governmental authority to limit, delay or prohibit the making of payments outside the United States.

The foregoing opinions assume that (a) the Registration Statement and any amendments relating thereto shall have become effective under the Securities Act and will continue to be effective, (b) the Company will remain duly organized, validly existing and in good standing under the laws of the State of Delaware, (c) at the time any Securities or Governing Documents are authorized, issued, executed, acknowledged, delivered or filed (as the case may be), there will not have occurred any change in the law or in the Certificate of Incorporation or Bylaws affecting the authorization, issuance, execution, acknowledgement, delivery, filing, validity or enforceability of such Securities or Governing Documents, and no relevant Corporate Proceedings will have been modified or rescinded, (d) none of the particular terms of any Securities or Governing Documents established after the date hereof will violate, or be void or voidable under, any applicable law, (e) neither the authorization, issuance, execution, acknowledgement, delivery or filing of any Securities or Governing Documents, nor the compliance by the Company with the terms of such Securities or Governing Documents, will result in a violation of or default under any agreement or instrument then binding upon the Company or any order of any court or governmental body having jurisdiction over the Company then in effect, (f) the Securities will be issued in accordance with, and in compliance with any limitations on issuance contained in, the Corporate

Proceedings related thereto, (g) the Company shall have received legally sufficient consideration for all Securities, (h) each party to any Securities or Governing Documents (other than the Company) will have duly authorized, executed and delivered such agreements or instruments and complied with all legal requirements pertaining to its status as such status relates to the right to enforce such agreements or instruments against the Company and will have satisfied those legal requirements applicable to it to the extent necessary to make such agreements or instruments enforceable against it, (i) the terms of the Securities will be established in conformity with the applicable Governing Documents and the Securities will be issued within the limits of the then remaining authorized but unreserved and unissued amounts of such Securities under the Governing Documents, (j) a prospectus supplement and any other offering material describing each class or series of Securities offered pursuant to the Registration Statement, to the extent required by applicable law, will be timely filed with the Commission, (k) any Securities issued upon conversion, exercise of, or constituting a component of, any other Securities will have been duly authorized and reserved for issuance (in each case, within the limits of the then remaining authorized but unreserved and unissued amounts of such Securities), and any issuance of such Securities will be effected in accordance with the terms and conditions set forth in such other Securities and the Governing Documents related thereto, (l) all certificates evidencing any Securities will be in the form required by law and approved for issuance by the Company, (m) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities will be obtained, (n) the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the Delaware General Corporation Law, and (o) the Securities will be duly registered on the books of the transfer agent and registrar thereof in the name and on behalf of the holders thereof.

We have relied upon certificates of public officials as to the accuracy of all matters addressed therein and, with respect to certain factual matters, upon certificates of and information provided by officers and employees of the Company as to the accuracy of such factual matters, in each case without independent verification thereof or other investigation. We have assumed, without investigation, the following: (a) the genuineness of signatures, including electronic signatures, appearing upon certifications, documents and proceedings, (b) each document submitted to us for review is accurate and complete, each such document that is an original is authentic and each such document that is a copy conforms to an authentic original, (c) the legal capacity of natural persons who are involved on behalf of the Company to enter into and perform the referenced instrument or agreement or to carry out their role in the transactions contemplated thereby, (d) the truth, accuracy and completeness of the information, representations and warranties contained in the documents, instruments, certificates and records we have reviewed, (e) the absence of any undisclosed modifications to the agreements and instruments reviewed by us, and (f) that New York law has or will be chosen to govern the each Warrant Agreement, each Unit Agreement and all Securities issued thereunder and/or certificates evidencing such Securities.

Without limiting any other qualifications set forth herein, the opinions expressed herein are subject to the effect of generally applicable laws that (a) provide for the enforcement of oral waivers or modifications where a material change of position in reliance thereon has occurred or provide that a course of performance may operate as a waiver, (b) limit the enforcement of provisions of instruments or agreements that purport to require waiver of the obligations of good faith, fair dealing, diligence and reasonableness, (c) limit the availability of a remedy under certain circumstances where another remedy has been elected, (d) limit the enforceability of provisions releasing, exculpating or exempting a party from, or requiring indemnification of or contribution to a party for, liability for its own action or inaction, to the extent the action or inaction involves negligence, recklessness, willful misconduct or unlawful conduct or insofar as such provisions otherwise contravene public policy, (e) may, where less than all of an instrument or agreement may be unenforceable, limit the enforceability of the balance of the instrument or agreement to circumstances in which the unenforceable portion is not an essential part of the agreed exchange, (f) govern and afford judicial discretion regarding the determination of damages and

entitlement to attorneys’ fees and other costs, (g) may permit a party who has materially failed to render or offer performance required by a contract to cure that failure unless either permitting a cure would unreasonably hinder the aggrieved party from making substitute arrangements for performance or it is important under the circumstances to the aggrieved party that performance occur by the date stated in the instrument or agreement, (h) may require mitigation of damages, (i) may limit the enforceability of certain waivers, and (j) provide a time limitation after which a remedy may not be enforced, including statutes of limitation and statutes of repose.

Our opinions set forth herein are limited to the Delaware General Corporation Law and the laws of the State of New York, and we express no opinion as to the effect of any other laws.

This opinion is rendered as of the date first written above, and we assume no responsibility for updating this opinion letter or the opinions set forth herein to take into account any event, action, interpretation or change in law occurring subsequent to the date hereof that may affect the validity of such opinions. This opinion letter is expressly limited to the matters set forth above, and we render no opinion, whether by implication or otherwise, as to any other matters relating to the Company, the Securities or the Governing Documents.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to being named in the Registration Statement under the caption “Legal Matters” with respect to the matters stated therein without implying or admitting that we are “experts” within the meaning of the Securities Act, or other rules and regulations of the Commission issued thereunder with respect to any part of the Registration Statement, including this exhibit.

Very truly yours,

/s/ Faegre Drinker Biddle & Reath LLP

FAEGRE DRINKER BIDDLE & REATH LLP