Exhibit 10.4

RICE ACQUISITION CORP. II
RICE ACQUISITION HOLDINGS II LLC
102 East Main Street, Second Story
Carnegie, PA 15106

June 15, 2021

Rice Acquisition Sponsor II LLC

102 East Main Street, Second Story

Carnegie, PA 15106

Re: Administrative Services Agreement

Gentlemen:

This letter agreement by and between Rice Acquisition Corp. II (the “Company”), Rice Acquisition Holdings II LLC (“Opco”) and Rice Acquisition Sponsor II LLC (“Sponsor”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on the New York Stock Exchange (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

(i)       Sponsor shall make available to the Company, at 102 East Main Street, Second Story, Carnegie, PA 15106 (or any successor location of Sponsor), certain office space, utilities, secretarial support and administrative services as may be reasonably required by the Company and Opco. In exchange therefor, the Company shall cause Opco to pay Sponsor the sum of $10,000 per month on the Listing Date and continuing monthly thereafter until the Termination Date; and

(ii)       Sponsor hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public shareholders of the Company and the holders of Class A Units of Opco (other than the Company) of Opco and into which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”), and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, this letter agreement, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.

This letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

This letter agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.

No party hereto may assign either this letter agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

This letter agreement, the entire relationship of the parties hereto, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles.

[Signature page follows]

2

Very truly yours,
RICE ACQUISITION CORP. II
By:	/s/ Daniel Joseph Rice, IV
	Name:	Daniel Joseph Rice, IV
	Title:	Chief Executive Officer
RICE ACQUISITION HOLDINGS II LLC
By:	/s/ Daniel Joseph Rice, IV
	Name:	Daniel Joseph Rice, IV
	Title:	Chief Executive Officer

AGREED TO ACCEPTED BY:
RICE ACQUISITION SPONSOR II LLC
By:	/s/ Daniel Joseph Rice, IV
	Name:	Daniel Joseph Rice, IV
	Title:	Chief Executive Officer

[Signature Page to Administrative Services Agreement]