AMENDMENT NO. 2 TO EMPLOYMENT AGREEMENT

Exhibit 10.5

AMENDMENT NO. 2 TO EMPLOYMENT AGREEMENT

This AMENDMENT NO. 2 (the “Amendment”) by and between TPC Group LLC (formerly known as Texas Petrochemicals LP) (the “Partnership”), TPC Group Inc. (formerly known as Texas Petrochemicals Inc.) (the “Company”), and Christopher A. Artzer (the “Executive”), effective as of January 1, 2009, is an amendment to that certain Employment Agreement by and among the Partnership, the Company and the Executive dated as of July 1, 2006 (the “Employment Agreement”).

RECITALS

The Partnership, the Company and the Executive have previously entered into the Employment Agreement to provide for terms and conditions of the Executive’s employment by the Company; and

The Partnership, the Company and the Executive desire to make certain changes to the Employment Agreement to ensure that the Employment Agreement complies with the applicable requirements of Section 409A of the Internal Revenue Code; and

Internal Revenue Service Notice 2010-6 permits this Amendment to be effective as of January 1, 2009 and for the Employment Agreement to be treated as being corrected on January 1, 2009.

NOW, THEREFORE, IT IS HEREBY AGREED AS FOLLOWS:

1. Section 4(d) of the Employment Agreement is hereby amended to read as follows:

“(d) Termination without Cause. The Company may terminate Artzer’s employment hereunder at any time without cause; provided, however, that Artzer shall, subject to the timing rules of Section 11, be entitled to: (i) accrued but unpaid base salary and accrued vacation, less deductions required by law; (ii) continued payment of Artzer’s Section 3(a)(i) base compensation until the date that is twelve (12) months following the date of Artzer’s termination of employment (the ‘Severance Amount’), with such salary continuation payments continuing in accordance with the normal payroll practices of the Company; and (iii) his Section 3(c) benefits until the date that is twelve (12) months following the date of Artzer’s termination of employment.”

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2. The last sentence of Section 4(f) of the Employment Agreement is hereby amended to read as follows:

“Under such circumstances, Artzer shall be entitled to (i) the severance benefits set forth in Section 4(d) and paid at the time provided therein, subject to the timing rules of Section 11 and (ii) any benefits granted him in the Equity Plan.”

3. A new Section 11 is hereby added to the Employment Agreement to read as follows:

“11. Section 409A.

(a) Notwithstanding anything in this Agreement to the contrary, if any provision hereof would result in the imposition of an additional tax under Section 409A of the Internal Revenue Code of 1986, as amended, (the ‘Code’) and related regulations and Treasury pronouncements (‘Section 409A’), that provision will be reformed to avoid imposition of the applicable tax to the extent permissible under Section 409A and no action so taken shall be deemed to adversely affect Artzer’s rights under this Agreement. The benefits under this Agreement are intended to be exempt from or in compliance with the requirements of Section 409A, and this Agreement shall be interpreted in accordance with such intent.

(b) Each payment under this Agreement, including each payment in a series of installment payments, is intended to be a separate payment for purposes of Treas. Reg. § 1.409A-2(b), and is intended to be: (i) exempt from Section 409A, including, but not limited to, by compliance with the short-term deferral exemption as specified in Treas. Reg. § 1.409A-1(b)(4), or (ii) in compliance with Section 409A, including, but not limited to, being paid pursuant to a fixed schedule or specified date pursuant to Treas. Reg. § 1.409A-3(a) and the provisions of this Agreement will be administered, interpreted and construed accordingly.

(c) All reimbursements or provision of in-kind benefits pursuant to this Agreement shall be made in accordance with Treas. Reg. § 1.409A-3(i)(1)(iv) such that the reimbursement or provision will be deemed payable at a specified time or on a fixed schedule relative to a permissible payment event. Specifically, the reimbursement of an eligible expense shall be made on or before the last day of Artzer’s taxable year following the taxable year in which the expense was incurred.

(d) Notwithstanding any provision of this Agreement to the contrary, Artzer and the Company agree that any benefit or benefits under this Agreement or any other agreement or arrangement that provides for deferred compensation subject to Section 409A payable upon Artzer’s separation from service with the Company that are subject to the six-month delay under Section 409A(a)(2)(B) of the Code shall not be paid or

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commence until the earliest of: (i) the first business day following the expiration of six months from Artzer’s separation from service, (ii) the date of Artzer’s death, or (iii) such earlier date as complies with the requirements of Section 409A, provided that in no event shall any such delayed payment be made prior to July 1, 2010.”

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The parties have executed this Amendment this 24th day of May, 2010, effective as of the date specified herein.

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