EX-10.5





 Exhibit 10.5 

Execution Version 
 PRIVATE
PLACEMENT WARRANTS PURCHASE AGREEMENT 
 THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT (as it may from time to time be amended and
including all exhibits referenced herein, this “Agreement”), dated as of January 11, 2021, is entered into by and between Adit EdTech Acquisition Corp., a Delaware corporation
(the “Company”), and Adit EdTech Sponsor, LLC, a Delaware limited liability company (the “Purchaser”). 

WHEREAS, the Company intends to consummate an initial public offering of the Company’s units (the “Public
Offering”), each unit consisting of one share of common stock of the Company, par value $0.0001 per share (each, a “Share”), and one-half of one warrant, each whole warrant
entitling the holder to purchase one Share at an exercise price of $11.50 per Share, as set forth in the Company’s Registration Statement on Form S-1, filed with the U.S. Securities and Exchange
Commission (the “SEC”) (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”); and 

WHEREAS, the Purchaser has agreed to purchase an aggregate of 6,550,000 warrants (and up to 720,000 additional warrants if the
underwriters (the “Underwriters”) in the Public Offering exercise their option to purchase additional units in full) (the “Private Placement Warrants”), each Private Placement Warrant entitling the
holder to purchase one Share at an exercise price of $11.50 per Share, at a price of $1.00 per Warrant. 
 NOW THEREFORE, in
consideration of the mutual promises contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as
follows: 
 AGREEMENT 

Section 1. Authorization, Purchase and Sale; Terms of the Private Placement Warrants. 

A. Authorization of the Private Placement Warrants. The Company has duly authorized the issuance and sale of the Private Placement
Warrants to the Purchaser. 
 B. Purchase and Sale of the Private Placement Warrants. 

a) On the date of the consummation of the Public Offering (the “IPO Closing Date”), the Company shall issue and sell to
the Purchaser, and the Purchaser shall purchase from the Company, 6,550,000 Private Placement Warrants at a price of $1.00 per Warrant for an aggregate purchase price of $6,550,000 (the “Purchase Price”). On the IPO Closing
Date, subject to the receipt of funds pursuant to Section 1.B.d) below, the Company, at its option, shall deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the Purchaser’s name to the
Purchaser or effect such delivery in book-entry form. 
 b) On the date of the closing (the “Option Closing”) of the
option to purchase additional units, if any, in connection with the Public Offering or on such earlier time and date as may be mutually agreed by the Purchaser and the Company (the “Option Closing Date”, and each Option
Closing Date (if any) and the IPO Closing Date, a “Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to 720,000 Private Placement Warrants (or, to the
extent the option to purchase additional units is not exercised in full, a lesser number of Private Placement Warrants in proportion to the portion of the option that is exercised) at a price of $1.00 per













 
warrant for an aggregate purchase price of up to $720,000 (the “Option Purchase Price”). On the Option Closing Date, subject to the receipt of funds pursuant to
Section 1.B.e) below, the Company shall, at its option, deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the Purchaser’s name to the Purchaser or effect such delivery in book-entry
form. 
 c) At least twenty-four (24) hours prior to the effective date of the Registration Statement, the undersigned will cause the
Purchase Price and the maximum amount of the Option Purchase Price (i.e., $720,000) to be delivered to Continental Stock Transfer and Trust Company (“CST”), escrow agent for the Company, by wire transfer as set forth in the
instructions to be provided to it by the Company to hold in a non-interest bearing account (the “Escrow Account”) until the Company consummates the Public Offering. 

d) Simultaneously with the consummation of the Public Offering, the Purchaser shall cause CST to deposit on behalf of the Purchaser the
Purchase Price, without interest or deduction, by wire transfer of immediately available funds from the Escrow Account as follows: (i) $1,750,000 to the Company at a financial institution to be chosen by the Company, and (ii) $4,800,000 to the trust
account maintained by CST, acting as trustee (the “Trust Account”), in each case in accordance with the Company’s wiring instructions. If the Company does not complete the Public Offering within ten (10) days from
the date of this Agreement, the Purchase Price (without interest or deduction) in the Escrow Account will be returned to the Purchaser. 
 e)
Simultaneously with the Option Closing, the Purchaser shall cause CST to deposit on behalf of the Purchaser the Option Purchase Price, without interest or deduction, by wire transfer of immediately available funds from the Escrow Account to the
Trust Account, in accordance with the Company’s wiring instructions. If the Option Closing does not occur, or if the Option Closing occurs but the Option Purchase Price is less than $720,000, the balance of the Option Purchase Price in the
Escrow Account will promptly be returned to the Purchaser. 
 f) Each of the Company and the Purchaser acknowledges and agrees that CST is
serving hereunder solely as a convenience to the parties to facilitate the purchase of the Private Placement Warrants, and CST’s sole obligation with respect to this Agreement is to hold and disburse the Purchase Price and the Option Purchase
Price for the Private Placement Warrants, as described above. CST shall not be liable to the Company, the Underwriters or the Purchaser or any other person or entity in respect of any act or failure to act hereunder or otherwise in connection with
performing its services hereunder unless CST has acted in a manner constituting gross negligence or willful misconduct. The Company shall indemnify CST against any claim made against it (including reasonable attorney’s fees) by reason of it
acting or failing to act in connection with this Agreement except as a result of its gross negligence or willful misconduct. CST may rely and shall be protected in acting or refraining from acting upon any written notice, instruction or request
furnished to it hereunder and believed by it to be genuine and to have been signed or presented by the proper party or parties. 
 C.
Terms of the Private Placement Warrants. 
 a) Each Private Placement Warrant shall have the terms set forth in a warrant agreement to
be entered into by the Company and a warrant agent on the IPO Closing Date, in connection with the Public Offering (the “Warrant Agreement”). 

  
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 b) On the IPO Closing Date, the Company and the Purchaser shall enter into a registration
rights agreement (the “Registration Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private Placement Warrants and the Shares underlying the Private
Placement Warrants. 
 Section 2. Representations and Warranties of the Company. As a material inducement to
the Purchaser to enter into this Agreement and purchase the Private Placement Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall survive each Closing Date) that: 

A. Incorporation and Corporate Power. The Company is a corporation duly incorporated, validly existing and in good standing under the
laws of the State of Delaware and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, operating results or assets of the
Company. The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement. 

B. Authorization; No Breach. 

a) The execution, delivery and performance of this Agreement and the Private Placement Warrants have been duly authorized by the Company as of
the Closing Date. This Agreement constitutes the valid and binding obligation of the Company, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general
applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law). Upon issuance in accordance with, and payment pursuant to, the terms of the Warrant Agreement
and this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Date. 

b) The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of the Private
Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment of and compliance with the respective terms hereof and thereof by the Company, do not and will not as of the Closing Date
(i) conflict with or result in a breach of the terms, conditions or provisions of, (ii) constitute a default under, (iii) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s share
capital or assets under, (iv) result in a violation of, or (v) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or
agency pursuant to the memorandum and articles of association of the company (in effect on the date hereof or as may be amended prior to completion of the Public Offering) or any material law, statute, rule or regulation to which the Company is
subject, or any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof under federal or state securities laws. 

C. Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, the
Shares issuable upon exercise of the Private Placement Warrants will be duly and validly issued, fully paid and nonassessable. On the date of issuance of the Private Placement Warrants, the Shares issuable upon exercise of the Private Placement
Warrants shall have been reserved for issuance. Upon issuance in accordance with, and payment pursuant to, the terms hereof and 

  
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the Warrant Agreement, the Purchaser will have good title to the Private Placement Warrants purchased by it and the Shares issuable upon exercise of such Private Placement Warrants, free and
clear of all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and under the other agreements contemplated hereby, (ii) transfer restrictions under federal and state securities laws, and
(iii) liens, claims or encumbrances imposed due to the actions of the Purchaser. 
 D. Governmental Consents. No permit, consent,
approval or authorization of, or declaration to or filing with, any governmental authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other
transactions contemplated hereby. 
 E. Regulation D Qualification. Neither the Company nor, to its actual knowledge, any of its
affiliates, officers, directors or beneficial stockholders of 20% or more of its outstanding securities, has experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 

Section 3. Representations and Warranties of the Purchaser. As a material inducement to the Company to enter
into this Agreement and issue and sell the Private Placement Warrants to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties shall survive each Closing Date) that: 

A. Organization and Requisite Authority. The Purchaser possesses all requisite power and authority necessary to carry out the
transactions contemplated by this Agreement. 
 B. Authorization; No Breach. 

a) This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to bankruptcy,
insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law). 

b) The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by the Purchaser
does not and shall not as of each Closing Date (i) conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of, (ii) constitute a default under, (iii) result in the creation of any lien, security
interest, charge or encumbrance upon the Purchaser’s equity or assets under, (iv) result in a violation of, or (v) require authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any
court or administrative or governmental body or agency pursuant to the Purchaser’s organizational documents in effect on the date hereof or as may be amended prior to completion of the contemplated Public Offering, or any material law, statute,
rule or regulation to which the Purchaser is subject, or any agreement, instrument, order, judgment or decree to which the Purchaser is subject, except for any filings required after the date hereof under federal or state securities laws. 

C. Investment Representations. 

a) The Purchaser is acquiring the Private Placement Warrants and, upon exercise of the Private Placement Warrants, the Shares issuable upon
such exercise (collectively, the “Securities”) for its own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution thereof. 

  
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 b) The Purchaser is an “accredited investor” as such term is defined
in Rule 501(a)(3) of Regulation D, and the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 

c) The Purchaser understands that the Securities are being offered and will be sold to it in reliance on specific exemptions from the
registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the representations and warranties of the Purchaser set forth
herein in order to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities. 
 d) The
Purchaser did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under the Securities Act. 

e) The Purchaser has been furnished with all materials relating to the business, finances and operations of the Company and materials relating
to the offer and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions of the executive officers and directors of the Company. The Purchaser understands that its
investment in the Securities involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed investment decision with respect to the acquisition of the Securities. 

f) The Purchaser understands that no United States federal or state agency or any other government or governmental agency has passed on or made
any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Securities. 

g) The Purchaser understands that: (i) the Securities have not been and are not being registered under the Securities Act or any state
securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold in reliance on an exemption therefrom, and (ii) except as specifically set forth in the
Registration Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder.
In this regard, the Purchaser understands that the SEC has taken the position that promoters or affiliates of a blank check company and their transferees, both before and after an initial Business Combination, are deemed to be
“underwriters” under the Securities Act when reselling the securities of a blank check company. Based on that position, Rule 144 adopted pursuant to the Securities Act would not be available for resale transactions of the
Securities despite technical compliance with the requirements of such Rule, and the Securities can be resold only through a registered offering or in reliance upon another exemption from the registration requirements of the Securities Act. 

h) The Purchaser has such knowledge and experience in financial and business matters, knowledge of the high degree of risk associated with
investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to bear the economic risk of an investment in the Securities in the
amount contemplated hereunder for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies and will have no current or anticipated future needs for liquidity which would be
jeopardized by the investment in the Securities. The Purchaser can afford a complete loss of its investments in the Securities. 

  
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 Section 4. Conditions of the Purchaser’s Obligations. The
obligations of the Purchaser to purchase and pay for the Private Placement Warrants are subject to the fulfillment, on or before each Closing Date, of each of the following conditions: 

A. Representations and Warranties. The representations and warranties of the Company contained in Section 2 shall be true and
correct at and as of the Closing Date as though then made. 
 B. Performance. The Company shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before such Closing Date. 

C. No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted,
entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the
transactions contemplated by this Agreement or the Warrant Agreement. 
 D. Warrant Agreement and Registration Rights Agreement. The
Company shall have entered into the Warrant Agreement and the Registration Rights Agreement in each case on terms reasonably satisfactory to the Purchaser. 

Section 5. Conditions of the Company’s Obligations. The obligations of the Company to the Purchaser under this
Agreement are subject to the fulfillment, on or before each Closing Date, of each of the following conditions: 
 A. Representations and
Warranties. The representations and warranties of the Purchaser contained in Section 3 shall be true and correct at and as of such Closing Date as though then made. 

B. Performance. The Purchaser shall have performed and complied with all agreements, obligations and conditions contained in this
Agreement that are required to be performed or complied with by the Purchaser on or before such Closing Date. 
 C. No Injunction. No
litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization
having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement. 

D. Warrant Agreement. The Company shall have entered into the Warrant Agreement. 

Section 6. Miscellaneous. 

A. Successors and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or
on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign
this Agreement, other than assignments by the Purchaser to affiliates thereof (including, without limitation one or more of its members). 

  
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 B. Severability. Whenever possible, each provision of this Agreement shall be
interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective only to the extent of such
prohibition or invalidity, without invalidating the remainder of this Agreement. 
 C. Counterparts. This Agreement may be executed
simultaneously in two or more counterparts, none of which need contain the signatures of more than one party, but all such counterparts taken together shall constitute one and the same agreement. Signatures to this Agreement transmitted via
facsimile or e-mail shall be valid and effective to bind the party so signing. 
 D. Descriptive
Headings; Interpretation. The descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive part of this Agreement. The use of the word “including” in this Agreement shall be by way of
example rather than by limitation. 
 E. Governing Law. This Agreement shall be deemed to be a contract made under the laws of the
State of New York and for all purposes shall be construed in accordance with the internal laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the laws of another jurisdiction.

 F. Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument
executed by the parties hereto. 
 [Remainder of Page Intentionally Left Blank; Signature page follows] 

  
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 IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date
first set forth above. 
  

			
	COMPANY:
	
	ADIT EDTECH ACQUISITION CORP.
		
	By:	 	 /s/ David Shrier

		 	Name: David Shrier
		 	Title: Chief Executive Officer
	
	PURCHASER:
	
	ADIT EDTECH SPONSOR, LLC
		
	By:	 	 /s/ Eric L. Munson

		 	Name: Eric L. Munson
		 	Title: Chairman


 [Signature Page to Private Placement Warrants Purchase Agreement]