Exhibit 5.1

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

September 20, 2024

Arq, Inc.

8051 E. Maplewood Ave, Suite 210

Greenwood Village, CO 80111

Ladies and Gentlemen:

We have acted as counsel to Arq, Inc., a Delaware corporation (the “Company”), in connection with the public offering (a) by the Company of up to 5,485,500 shares of common stock, par value $0.001 per share (the “Shares”), including up to 715,500 Shares that may be sold pursuant to the exercise of an option to purchase additional Shares. The Shares are being offered pursuant to the Registration Statement on Form S-3 (File No. 333-281762) (the “Registration Statement”), filed by the Company with the Securities and Exchange Commission (the “Commission”) on September 4, 2024 under the Securities Act of 1933, as amended (the “Act”), the base prospectus dated August 23, 2024 included in the Registration Statement at the time it became effective (the “Base Prospectus”) and a prospectus supplement dated September 20, 2024 filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”). This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

In this capacity, we have examined originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments as we have deemed necessary for the purposes of this opinion, including (i) the Registration Statement and Prospectus, (ii) the Underwriting Agreement dated as of September 20, 2024 entered into by and among the underwriters named therein (the “Underwriters”) and the Company, to be filed as Exhibit 1.1 to the Company’s Current Report on Form 8-K to be filed on September 20, 2024 (the “Underwriting Agreement”), (iii) the Company’s Second Amended and Restated Certificate of Incorporation, as in effect on the date hereof, (iv) the Company’s Amended and Restated Bylaws, as in effect on the date hereof, and (v) resolutions of the Board of Directors and of the Pricing Committee of the Board of Directors.

In all cases, we have assumed the legal capacity of each natural person signing any of the documents and corporate records examined by us, the genuineness of signatures, including electronic signatures, the authenticity of documents submitted to us as originals, the conformity to authentic original documents of documents submitted to us as copies and the accuracy and completeness of all corporate records and other information made available to us by the Company. We have not independently established or verified any facts relevant to the opinion expressed herein, but have relied upon statements and representations of officers and other representatives of the Company and others as to factual matters.

Based upon and subject to the foregoing qualifications, assumptions and limitations and the further limitations set forth below, we are of the opinion that (i) when delivered to and paid

Arq, Inc.    -2-

for by the Underwriters in accordance with the Underwriting Agreement, the Shares to be issued and sold by the Company will be validly issued, fully paid and non-assessable.

This opinion is limited to the General Corporation Law of the State of Delaware. We express no opinion as to any other matters, including without limitation any matters relating to the securities or blue sky laws of any jurisdiction or any rules or regulations thereunder.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Company’s Current Report on Form 8-K to be filed on September 20, 2024, which Current Report on Form 8-K will be incorporated by reference into the Registration Statement. We also consent to the reference to our firm under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not admit that we come within the categories of persons whose consent is required under Section 7 of the Act or under the rules and regulations of the Commission issued thereunder.

    This letter is given as of the date hereof, and we assume no responsibility for updating this letter or the opinions or statements 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 any of such opinions or statements.

Very truly yours,

/s/ Faegre Drinker Biddle & Reath LLP

FAEGRE DRINKER BIDDLE & REATH LLP