EXHIBIT 5.1

Faegre Drinker Biddle & Reath LLP

1144 15th Street, Suite 3400

Denver, Colorado 80202

+1 303 607 3500 main

July 1, 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 preparation and filing with the Securities and Exchange Commission (the “Commission”) of the Company’s Registration Statement on Form S-8 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Act”), registering the offer and sale of up to an aggregate of 2,609,028 shares (the “Shares”) of the Company’s common stock, par value $0.001 per share (the “Common Stock”), consisting of (a) 2,500,000 shares of Common Stock newly reserved for issuance under the 2024 Omnibus Incentive Plan (the “Incentive Plan”), and (b) 109,028 shares of Common Stock that remained available for issuance under the Advanced Emissions Inc. 2022 Omnibus Plan as of June 10, 2024 and are available for issuance under the Incentive Plan.

For purposes of this opinion letter, we have examined the Incentive Plan, the Registration Statement, the Company’s Second Amended and Restated Certificate of Incorporation, as amended to date, the Company’s Amended and Restated Bylaws, as amended to date, and the resolutions of the Company’s board of directors authorizing the issuance of the Shares. We have also examined a certificate of the Secretary of the Company dated the date hereof (the “Certificate”) and originals, or copies certified or otherwise authenticated to our satisfaction, of such corporate and other records, agreements, instruments, certificates of public officials and documents as we have deemed necessary as a basis for the opinions hereinafter expressed and have made such examination of law as we have deemed relevant and necessary in connection with the opinions hereinafter expressed. As to facts material to this opinion letter, we have relied upon certificates, statements or representations of public officials, of officers and representatives of the Company (including the Certificate) and of others, without any independent verification thereof.

In our examination, we have assumed: (i) the legal capacity of all natural persons; (ii) the genuineness of all signatures, including electronic signatures; (iii) the authenticity of all documents submitted to us as originals; (iv) the conformity to authentic original documents of all documents submitted to us as certified, conformed, photostatic or facsimile copies; (v) the truth, accuracy and completeness of the information, representations and warranties contained in the agreements, documents, instruments, certificates and records we have reviewed; and (vi) the absence of any undisclosed modifications to the agreements and instruments reviewed by us.

Based upon such examination and review, and subject to the foregoing and the other qualifications, assumptions and limitations set forth herein, we are of the opinion that all necessary corporate action on the part of the Company has been taken to authorize the issuance and sale of the Shares to be issued in accordance with the Incentive Plan and that, when (a) the Shares have been issued and sold as contemplated in the Registration Statement and related prospectus and in accordance with the Incentive Plan and any applicable award agreement, and (b) where applicable, the consideration for the Shares specified in the Incentive Plan and any applicable award agreement has been received by the Company, the Shares will be validly issued, fully paid and nonassessable.

We do not express any opinion herein with respect to the laws of any jurisdiction other than, subject to the limitations and assumptions contained herein, the General Corporation Law of the State of Delaware.

This opinion speaks only as of the date the Registration Statement becomes effective under the Act, and we assume no obligation to revise or supplement this opinion thereafter. This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving such consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Faegre Drinker Biddle & Reath LLP

FAEGRE DRINKER BIDDLE & REATH LLP