Exhibit 5.1

Troutman Pepper Hamilton Sanders LLP 875 Third Avenue New York, New York 10022   troutman.com

January 11, 2021

Adit EdTech Acquisition Corp.

1345 Avenue of the Americas, 33rd Floor

New York, New York 10105

Ladies and Gentlemen:

We have acted as counsel to Adit EdTech Acquisition Corp., a Delaware corporation (the “Company”), in connection with the preparation of the Company’s registration statement on Form S-1 (the “462(b) Registration Statement”), filed with the U.S. Securities and Exchange Commission (the “Commission”) on January 11, 2021 under the Securities Act of 1933, as amended (the “Securities Act”), which relates to the Company’s Registration Statement on Form S-1, as amended (File No. 333-251641) (the “Registration Statement”), initially filed by the Company on December 23, 2020 and declared effective by the Commission on January 11, 2021.

The 462(b) Registration Statement relates to the offer and sale by the Company of up to (A) an additional 4,600,000 units of the Company (the “Units”), each Unit consisting of (i) one share of the Company’s common stock, par value $0.0001 per share (“Common Stock,” and the shares of Common Stock underlying the Units, the “Shares”), for an aggregate of up to 4,600,000 Shares; and (ii) one-half of one redeemable warrant (each whole warrant, a “Warrant”) with each Warrant entitling the holder to purchase one share of Common Stock, for an aggregate of up to 2,300,000 Warrants to be issued under a Warrant Agreement (the “Warrant Agreement”) to be entered into by the Company and Continental Stock Transfer & Trust Company, as Warrant Agent, pursuant to the terms of an underwriting agreement (the “Underwriting Agreement”) to be executed by the Company and EarlyBirdCapital, Inc., as representative of the several underwriters named therein (the “Underwriters”); and (B) an aggregate of 2,300,000 additional shares (the “Warrant Shares”) of Common Stock that may be issued upon exercise of the Warrants included in the Units.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

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We have examined originals or copies, certified or otherwise identified to our satisfaction, of such corporate records, agreements, and other instruments, certificates, orders, opinions, correspondence with public officials, certificates provided by the Company’s officers and representatives, and other documents as we have deemed necessary or advisable for the purposes of rendering the opinion set forth herein, including (i) the corporate and organizational documents of the Company, including the Certificate of Incorporation, as amended to date, and the Bylaws of the Company, (ii) the resolutions of the Board of Directors of the Company with respect to the 462(b) Registration Statement and the registration of the Units, the Shares, the Warrants and the Warrant Shares, (iii) a specimen certificate representing the Common Stock, (iv) a specimen certificate representing the Warrants, (iv) the Underwriting Agreement, and (v) the 462(b) Registration Statement and the Registration Statement and exhibits thereto, including the prospectus (the “Prospectus”) contained therein.

For purposes of the opinions expressed below, we have assumed (i) the authenticity of all documents submitted to us as originals, (ii) the conformity to the originals of all documents submitted as certified, photostatic or electronic copies and the authenticity of the originals thereof, (iii) the legal capacity of natural persons, (iv) the genuineness of signatures not witnessed by us, (v) the due authorization, execution and delivery of all documents by all parties, other than the Company, and the validity, binding effect and enforceability thereof, and (vi) the truth, accuracy and completeness of the information, representations and warranties contained in the records, documents, instruments and certificates we have reviewed. In rendering the opinions set forth below, we have further assumed that, before the issuance of the Units, the Shares, the Warrants and the Warrant Shares, the conditions to consummating the transactions contemplated by the Underwriting Agreement will have been satisfied or duly waived and such transactions are consummated.

Based upon the foregoing, and subject to all of the other assumptions, limitations and qualifications set forth herein, we are of the opinion as follows:

1. When the Units are delivered to the Underwriters against payment of the agreed consideration therefor in accordance with the Underwriting Agreement, such Units will be validly issued, fully paid and non-assessable and will be legally binding obligations of the Company, enforceable against the Company in accordance with their terms, except to the extent that enforcement thereof may be limited by (i) bankruptcy, insolvency, reorganization, fraudulent conveyance, moratorium or other similar laws now or hereafter in effect relating to creditors’ rights generally, and (ii) general principles of equity (regardless of whether enforceability is considered in a proceeding at law or in equity).

2. The Shares included in the Units have been duly authorized and, when the Units are delivered to the Underwriters against payment of the agreed consideration therefor in accordance with the Underwriting Agreement, the Shares included in the Units will be validly issued, fully paid and non-assessable.

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3. When the Units are delivered to the Underwriters against payment of the agreed consideration therefor in accordance with the Underwriting Agreement, the Warrants included in the Units will be validly issued, fully paid and non-assessable will be legal binding obligations of the Company, enforceable against the Company in accordance with their terms, except to the extent that enforcement thereof may be limited by (i) bankruptcy, insolvency, reorganization, fraudulent conveyance, moratorium or other similar laws now or hereafter in effect relating to creditors’ rights generally, and (ii) general principles of equity (regardless of whether enforceability is considered in a proceeding at law or in equity).

4. The Warrant Shares that may be issued upon exercise of the Warrants have been duly authorized and when the Warrant Shares have been issued and paid for in accordance with the terms of the Warrant Agreement and the Warrants, will be validly issued, fully paid and nonassessable.

We express no opinion as to the laws of any jurisdiction other than (i) the laws of the State of New York and (ii) the General Corporation Law of the State of Delaware. As used herein, the term “General Corporation Law of the State of Delaware” includes the statutory provisions contained therein and all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting these laws.

This opinion is limited to the matters expressly opined on herein, and no opinion may be implied or inferred beyond those expressly stated. This opinion is rendered as of the date hereof, and we make no undertaking and expressly disclaim any duty to supplement or update such opinion, if, after the date hereof, facts or circumstances come to our attention or changes in the law occur which could affect such opinion.

We hereby consent to the filing of this opinion as an exhibit to the 462(b) Registration Statement and to the use of our name under the caption “Legal Matters” in the Prospectus and Registration Statement. In giving this consent, we do not hereby admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act, or the rules or regulations of the Commission promulgated thereunder.