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                                                                   EXHIBIT 10.31

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                           STANDBY PURCHASE AGREEMENT

                                 BY AND BETWEEN

                       STERLING CHEMICALS HOLDINGS, INC.

                                      AND

                          KOCH CAPITAL SERVICES, INC.





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                         DATED AS OF DECEMBER 15, 1998

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IN MAKING AN INVESTMENT DECISION INVESTORS MUST RELY ON THEIR OWN EXAMINATION OF
THE ISSUER AND THER TERMS OF THE OFFERING, INCLUDING THER MERITS AND RISKS
INVOLVED. THE SECURITIES PURCHASED HEREUNDER HAVE NOT BEEN RECOMMENDED OR
APPROVED BY ANY FEDERAL OR STATE SECURITIES COMMISSION OR REGULATORY AUTHORITY.
FURTHERMORE, THE FOREGOING AUTHORITIES HAVE NOT CONFIRMED THE ACCURACY OR
DETERMINED THE ADEQUACY OF THIS DOCUMENT. ANY REPRESENTATION TO THE CONTRARY IS
A CRIMINAL OFFENSE.

THE SECURITIES PURCHASED HEREUNDER ARE SUBJECT TO RESTRICTIONS ON
TRANSFERABILITY AND RESALE AND MAY NOT BEW TRANSFERRED OR RESOLD EXCEPT AS
PERMITTED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND THE APPLICABLE STATE
SECURITIES LAWS, PURSUANT TO REGISTRATION OR EXEMPTION THEREFROM, INVESTORS
SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE FINANCIAL RISKS OF THIS
INVESTMENT FOR AN INDEFINITE PERIOD OF TIME.

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                               TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                           Page
                                                                           ----
<S>            <C>                                                         <C>
Section 1      Definitions and Interpretation.............................   2

Section 2      Standby Committment........................................   5

Section 3      Closings...................................................   6

Section 4      Simultaneous Closings Under Other Purchase Agreements......   7

Section 5      Use of Proceeds............................................   7

Section 6      Representations and Warranties of the Company..............   7

Section 7      Representations and Warranties of the Purchaser............   9

Section 8      Compliance with Securities Laws and Agreements.............  10

Section 9      Changes in Capital Structure...............................  12

Section 10     Specific Performance.......................................  12

Section 11     Notices....................................................  12

Section 12     Survival...................................................  12

Section 13     Benefit and Burden.........................................  13

Section 14     No Third Party Rights......................................  13

Section 15     Amendments and Waiver......................................  13

Section 16     Severability...............................................  13

Section 17     Expenses...................................................  13

Section 18     Governing Law..............................................  13

Section 19     Entire Agreement...........................................  13

Schedule I     Purchasers
</TABLE>

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                                                                           KOCH


                           STANDBY PURCHASE AGREEMENT

        THIS STANDBY PURCHASE AGREEMENT (this "Agreement") is made and entered
into as of December 15, 1998 by and between STERLING CHEMICALS HOLDINGS, INC., a
Delaware corporation (the "Company"), and KOCH CAPITAL SERVICES, INC., a
Delaware corporation (the "Purchaser").

                             PRELIMINARY STATEMENTS

     A.   The Company and the Purchaser are entering into this Agreement to
          evidence the Purchaser's agreement to purchase up to 250,000 shares of
          common stock, par value $0.01 per share, of the Company ("Common
          Stock").

     B.   Simultaneously with the execution and delivery of this Agreement, the
          Company and Harris Trust and Savings Bank, as agent, entered into a
          Warrant Agreement dated as of the date hereof (the "Warrant
          Agreement"). In order to induce the Purchaser to enter into this
          Agreement, the Company has issued to the Purchaser on the date hereof
          warrants to purchase 30,000 shares of Common Stock (the "Initial
          Warrants"). The Initial Warrants are evidenced by a certificate in the
          form attached as Exhibit A to the Warrant Agreement and are subject to
          the terms and conditions set forth in the Warrant Agreement and such
          certificate.

     C.   The Company and the Purchaser are parties to the Stockholders
          Agreement, the Registration Rights Agreement and the Tag-Along
          Agreement (as such terms are defined below).

     D.   In connection with the issuance of the Initial Warrants, the Company,
          the Purchaser and certain other parties entered into an Amended and
          Restated Voting Agreement dated as of the date hereof (the "Voting
          Agreement").

     E.   Simultaneously with the execution and delivery of this Agreement, the
          Company is entering into separate Standby Purchase Agreements,
          substantially identical to this Agreement, with the other purchasers
          named in Schedule I (the "Other Purchasers") to evidence the Other
          Purchasers' agreement to purchase up to the number of shares of Common
          Stock set opposite their respective names in Schedule I.

        NOW, THEREFORE, in consideration of the premises and the mutual
covenants and agreements set forth herein and for other good and valuable
consideration, the receipt and sufficiency of which is hereby acknowledged, the
parties hereto, intending to be legally bound, hereby agree as follows:

<PAGE>   5

        Section 1. Definitions and Interpretation. Capitalized terms used in
this Agreement shall, except where the context otherwise requires, have the
following respective meanings:

        "Acts" has the meaning specified in Section 7(e).

        "Agreement" means this Standby Purchase Agreement, as from time to time
    amended in accordance with the terms hereof.

        "Bankruptcy Event" means that:

               (i) the Company or any Subsidiary has (A) made a general
         assignment for the benefit of creditors, (B) filed a voluntary
         bankruptcy petition, (C) become the subject of an order for relief or
         been declared insolvent in any federal or state bankruptcy or
         insolvency proceeding, (D) instituted a proceeding or filed an answer
         in a proceeding seeking to adjudicate itself insolvent or seeking
         reorganization, arrangement, composition, readjustment, protection,
         liquidation, winding-up, dissolution or similar relief of it or its
         debts under any Debtor Relief Law, (E) filed an answer or other
         pleading admitting or failing to contest the material allegations of a
         petition filed against it in a proceeding of the type described in
         subclauses (A) through (D) of this clause (i), (F) sought, consented
         to or acquiesced in an order for relief or the appointment of a
         trustee, receiver, liquidator or similar official for it or for any
         substantial part of such its assets or (G) taken any action in
         furtherance of any such actions; or

               (ii) any proceeding of the type referred to in clause (i) above
         has been filed or commenced against the Company or any Subsidiary or
         the Company or any Subsidiary by any act has indicated its approval
         thereof, consented thereto or acquiesced therein, or an order for
         relief has been entered in an involuntary case under any Debtor Relief
         Law, or an order, judgment or decree has been entered appointing a
         trustee, receiver, custodian, liquidator or similar official or
         adjudicating it insolvent, or approving the petition in any such
         proceedings.

        "Business Day" means any day which is neither a Saturday or Sunday nor a
    legal holiday on which banks are authorized or required to be closed in New
    York, New York, or Houston, Texas.

         "Closing" has the meaning specified in Section 3(a).

         "Closing Date" has the meaning specified in Section 2(b).

        "Common Shares" means the shares of Common Stock issuable to the
    Purchaser under this Agreement.

        "Common Stock" has the meaning specified in the Preliminary Statements
    of this Agreement.


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        "Company" has the meaning specified in the opening paragraph hereof.

        "Debtor Relief Laws" means the Bankruptcy Code of the United States, and
    any successor statute of similar import, and all other applicable
    dissolution, liquidation, conservatorship, bankruptcy, moratorium,
    readjustment of debt, compromise, rearrangement, receivership, insolvency,
    fraudulent transfer or conveyance, reorganization or similar debtor relief
    laws from time to time in effect affecting the rights of creditors
    generally.

        "Election Notice" has the meaning specified in Section 2(a).

        "Exchange Act" means the Securities Exchange Act of 1934.

        "Form 10-K Report" has the meaning specified in Section 6(d).

        "Governmental Authority" means (i) any nation or government, (ii) any
    federal, state, county, province, city, town, municipality, local or other
    political subdivision thereof or thereto, (iii) any court, tribunal,
    department, commission, board, bureau, instrumentality, agency, council,
    arbitrator or other entity exercising executive, legislative, judicial,
    regulatory or administrative functions of or pertaining to government and
    (iv) any other governmental entity, agency or authority having or exercising
    jurisdiction over any relevant Person, item or matter.

        "Initial Warrants" has the meaning specified in the Preliminary
    Statements of this Agreement.

        "Laws" means all laws, statutes, rules, regulations, ordinances, orders,
    writs, injunctions or decrees and other pronouncements having the effect of
    law of any Governmental Authority.

        "Material Adverse Effect" means a material adverse effect on the
    business, properties, assets, financial condition or results of operations
    of the Company and the Subsidiaries, taken as a whole.

        "Other Purchasers" has the meaning specified in the Preliminary
    Statements of this Agreement.

        "Person" means any individual, corporation, partnership, limited
    liability company, firm, association, joint venture, Governmental Authority
    or other entity or enterprise.

        "Purchaser" has the meaning specified in the opening paragraph hereof.


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        "Registration Rights Agreement" means the Registration Rights Agreement
    dated as of August 21, 1996, as amended, among the Company and the Persons
    named therein.

        "SEC" means the Securities and Exchange Commission.

        "Securities" means the Common Shares, the Warrants and the Warrant
    Shares.

        "Securities Act" means the Securities Act of 1933.

        "Stockholders Agreement" means the Sterling Chemicals Holdings, Inc.
    Stockholders Agreement dated effective as of August 21, 1996, as amended,
    among the Company and the stockholders of the Company parties thereto.

        "Subsequent Warrants" has the meaning specified in Section 3(f).

        "Subsidiary" means any subsidiary of the Company of which greater than
    50% of the outstanding shares of capital stock having ordinary voting power
    for the election of directors is owned directly or indirectly by the
    Company.

        "Tag-Along Agreement" means the Tag-Along Agreement dated effective as
    of August 21, 1996, among the Company and the stockholders of the Company
    parties thereto.

        "Transaction Documents" means, collectively, this Agreement, the
    Registration Rights Agreement, the Voting Agreement, the Tag-Along
    Agreement, the Warrant Agreement and the Stockholders Agreement.

        "Voting Agreement" means an Amended and Restated Voting Agreement dated
    as of the date hereof among the Company and the Persons named therein.

        "Warrants" means the Initial Warrants and the Subsequent Warrants.

        "Warrant Agreement" has the meaning specified in the Preliminary
    Statements of this Agreement.

        "Warrant Shares" means the shares of Common Stock issuable to the
    Purchaser upon exercise of the Warrants.

        (b) In this Agreement, unless a clear contrary intention appears:

        (i) the words "hereof," "herein" and "hereunder" and words of similar
   import refer to this Agreement as a whole and not to any particular provision
   of this Agreement;

        (ii) reference to any gender includes each other gender and the neuter;


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        (iii) all terms defined in the singular shall have the same meanings in
   the plural and vice versa;

        (iv) reference to any Person includes such Person's heirs, executors,
   personal representatives, administrators, successors and assigns; provided,
   however, that nothing contained in this clause (iv) is intended to authorize
   any assignment not otherwise permitted by this Agreement;

        (v) reference to a Person in a particular capacity or capacities
   excludes such Person in any other capacity;

        (vi) reference to any contract or agreement means such contract or
   agreement as amended, supplemented or modified from time to time in 
   accordance with the terms thereof;

        (vii) all references to Sections shall be deemed to be references to the
   Sections of this Agreement;

        (viii) all references to Exhibits and Schedules shall be deemed to be
   references to the Exhibits and Schedules attached hereto which are made a
   part hereof and incorporated herein by reference;

        (ix) the word "including" (and with correlative meaning "include") means
   including, without limiting the generality of any description preceding such
   term;

        (x) with respect to the determination of any period of time, the word
   "from" means "from and including" and the words "to" and "until" each means
   "to but excluding";

        (xi) the captions and headings contained in this Agreement shall not be
   considered or given any effect in construing the provisions hereof if any
   question of intent should arise;

        (xii) reference to any Law means such Law as amended, modified,
   codified, reenacted, supplemented or superseded in whole or in part, and in
   effect from time to time; and

        (xiii) no provision of this Agreement shall be interpreted or construed
   against any party solely because that party or its legal representative
   drafted such provision.

          Section 2. Standby Commitment. (a) Upon the terms and subject to the
satisfaction or waiver of the conditions set forth herein, the Purchaser agrees
to purchase from the Company such number of shares of Common Stock (not to
exceed 250,000 in the aggregate) as the Company may, in its sole discretion,
specify at any time or from time to time, in each case at a price per share,
payable in cash, of $6.00. If the Company desires to require the Purchaser to
purchase shares of Common Stock as aforesaid, the Company must give the
Purchaser not less than 15 days' prior written notice (an "Election Notice").
Each Election Notice shall (i) be given in 




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accordance with Section 11, (ii) refer to this Agreement, (iii) specify the
number of shares to be purchased, (iv) specify the applicable Closing Date (as
defined below), which may not be later than the third anniversary of the date
hereof, and (v) state that, in the good faith judgement of the Company, the sale
of the Common Shares referred to in such Election Notice is necessary in order
for the Company to maintain, reestablish or enhance its borrowing rights under
its revolving credit facilities and/or to satisfy any obligation under the
documentation governing its revolving credit facilities to raise additional
equity capital. Notwithstanding anything to the contrary contained herein, in no
event shall the Company be required to sell or issue any Common Shares unless
the Company has given to the Purchaser an Election Notice with respect to such
Common Shares pursuant to this paragraph (a) and then only the number of Common
Shares specified in such Election Notice. The Company may not revoke any
Election Notice given by it as aforesaid.

        (b) For purposes of this Agreement, "Closing Date" means, when used with
reference to any purchase of Common Shares, the date on which such purchase is
to be consummated; provided, however, that if such date is not a Business Day,
then the Closing Date for such purchase shall be automatically extended to the
next succeeding Business Day and, provided further, that each Closing Date shall
be at least 30 days after the immediately preceding Closing Date, if any.

        Section 3. Closings. (a) The consummation of each purchase of Common
Stock pursuant to this Agreement (a "Closing) shall take place on the applicable
Closing Date at 10:00 a.m. (Houston time) unless a different time is specified
in the applicable Election Notice. Each Closing shall be held at the corporate
offices of the Company or at such other place as may be agreed upon by the
Company and the Purchaser.

        (b) At each Closing, the Company shall deliver to the Purchaser (i) a
duly executed certificate evidencing the Common Shares being purchased at such
Closing and (ii) a duly executed certificate of the chief executive officer, the
chief financial officer or the treasurer of the Company, dated the applicable
Closing Date, stating that the representations and warranties of the Company
contained in Section 6 are true and correct on and as of such Closing Date with
the same force and effect as though made on and as of such Closing Date, except
for any representations and warranties made as of a specified date, which shall
be true and correct in all material respects as of such specified date, and
stating that (A) no Bankruptcy Event has occurred and is continuing, (B) the
Company is generally paying its debts as they become due, (C) the Company owns
property having a value greater than the amount required to pay the probable
liability on its debts and (D) the Company has no plans or intentions to
initiate a Bankruptcy Event nor is it aware that any creditor of the Company
plans or intends to initiate a Bankruptcy Event.

        (c) If the first Closing occurs before March 1, 1999, then the Company
shall issue and deliver to the Purchaser at the first Closing, for no additional
consideration, a certificate (in the form attached as Exhibit A to the Warrant
Agreement) evidencing warrants to purchase that number of shares of Common Stock
(rounded to the nearest whole number) equal to the number of Common Shares
purchased by the Purchaser at the first Closing divided by 8.3333.


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        (d) If the first Closing occurs before March 1, 1999, then the Company
shall issue and deliver to the Purchaser at the second Closing, for no
additional consideration, a certificate (in the form attached as Exhibit A to
the Warrant Agreement) evidencing warrants to purchase 30,000 shares of Common
Stock minus the number of Common Shares covered by the warrants issued to the
Purchaser at the first Closing.

        (e) If the first Closing occurs after February 28, 1999, then the
Company shall issue and deliver to the Purchaser at the first Closing, for no
additional consideration, a certificate (in the form attached as Exhibit A to
the Warrant Agreement) evidencing warrants to purchase 30,000 shares of Common
Stock.

        (f) All warrants issued to the Purchaser pursuant to this Section 3 are
collectively referred to herein as the "Subsequent Warrants". The Subsequent
Warrants shall be subject to the terms and conditions set forth in the Warrant
Agreement and the certificates evidencing the same.

        (g) At each Closing, the Purchaser shall deliver to the Company (i) an
amount (in immediately available funds) equal to the number of Common Shares
being purchased by the Purchaser times $6.00 and (ii) a duly executed
certificate of the Purchaser, dated the applicable Closing Date, stating that
the representations and warranties of the Purchaser contained in Section 7 are
true and correct on and as of such Closing Date with the same force and effect
as though made on and as of such Closing Date, except for any representations
and warranties made as of a specified date, which shall be true and correct in
all material respects as of such specified date.

        Section 4. Simultaneous Closings under Other Purchase Agreements. In no
event shall the Purchaser be obligated to consummate any Closing unless
simultaneously with such Closing (a) the Company shall sell to the Other
Purchasers shares of Common Stock numbering, in the aggregate, not less than the
amount (rounded to the nearest whole number) determined by multiplying the
number of Common Shares being purchased by the Purchaser at such Closing times
nine and (b) the Company shall have received from the Other Purchasers payments
(in immediately available funds) of the purchase price for such shares, which
shall not be less than $6.00 per share.

        Section 5 Use of Proceeds. The Company shall use the proceeds from the
sale of Common Shares at each Closing and the proceeds from each sale of Common
Stock to the Other Purchasers as contemplated by Section 4 solely for general
corporate purposes.

        Section 6. Representations and Warranties of the Company. The Company
represents and warrants to the Purchaser as follows:

        (a) The Company is a corporation duly organized, validly existing and in
   good standing under the laws of the State of Delaware, and has the corporate
   power to own its property and to carry on its business as now being
   conducted.


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        (b) The Company has all requisite corporate power to enter into and
    perform its obligations under the Transaction Documents and the Warrants and
    to consummate the transactions contemplated thereby. The Company has taken
    all corporate actions necessary to authorize it to enter into and perform
    its obligations under the Transaction Documents and the Warrants and to
    consummate the transactions contemplated thereby. The Transaction Documents
    have been duly executed and delivered by the Company and constitute legal,
    valid and binding obligations of the Company, enforceable against the
    Company in accordance with their terms, except as such enforcement may be
    limited by applicable bankruptcy, insolvency, reorganization, moratorium or
    similar Laws affecting creditors' rights generally and general equitable
    principles. Upon issuance in accordance with this Agreement and the Warrant
    Agreement, the Warrants will have been duly executed and delivered by the
    Company and will constitute legal, valid and binding obligations of the
    Company, enforceable against the Company in accordance with their terms,
    except as such enforcement may be limited by applicable bankruptcy,
    insolvency, reorganization, moratorium or similar Laws affecting creditors'
    rights generally and general equitable principles. The Common Shares have
    been duly authorized and, when issued and paid for in accordance with this
    Agreement, will be validly issued, fully paid and nonassessable. The Warrant
    Shares have been duly authorized and reserved for issuance and, when issued
    and paid for upon proper exercise of the Warrants, will be validly issued,
    fully paid and nonassessable.

        (c) Neither the execution, delivery or performance of any of the
    Transaction Documents by the Company, nor the consummation by the Company of
    the transactions contemplated thereby, will violate, or result in a breach
    of the terms of, or constitute a default under, the charter or bylaws of the
    Company or any agreement, instrument or other arrangement or obligation to
    which the Company is subject, except for such violations, breaches or
    defaults that would not have a Material Adverse Effect.

        (d) The Company has delivered to the Purchaser true and complete copies
    of (i) the Stockholders Agreement, the Registration Rights Agreement, the
    Tag-Along Agreement, the Warrant Agreement and the Company's charter and
    bylaws, in each case as in effect on the date hereof, and (ii) the Company's
    Annual Report on Form 10-K for the fiscal year ended September 30, 1998 (the
    "Form 10-K Report"). As of the date hereof, the Form 10-K Report complies in
    all material respects with all applicable requirements of the Exchange Act
    and the applicable rules and regulations promulgated thereunder and does not
    contain any untrue statement of a material fact or omit to state any
    material fact necessary in order to make the statements therein, in light of
    the circumstances under which they were made, not misleading. As of the date
    hereof, the consolidated financial statements of the Company included in the
    Form 10-K Report comply as to form in all material respects with applicable
    accounting requirements and the published rules and regulations of the SEC
    with respect thereto. Such financial statements were prepared in accordance
    with applicable generally accepted accounting principles applied on a
    consistent basis during the periods involved.


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        Section 7. Representations and Warranties of the Purchaser. The
Purchaser hereby represents and warrants to the Company as follows:

        (a) The Purchaser is a corporation duly organized, validly existing and
    in good standing under the laws of the State of Delaware. The Purchaser has
    all requisite corporate power to execute and deliver the Transaction
    Documents to which the Purchaser is a party (the "Purchaser Transaction
    Documents"), to consummate the transactions contemplated thereby and to
    perform its obligations thereunder. The Purchaser has taken all corporate
    actions necessary to authorize it to enter into and perform its obligations
    under the Purchaser Transaction Documents and to consummate the transactions
    contemplated thereby. Each of the Purchaser Transaction Documents has been
    executed and delivered by the Purchaser and constitutes the legal, valid and
    binding obligation of the Purchaser, enforceable against the Purchaser in
    accordance with its terms, except as such enforcement may be limited by
    applicable bankruptcy, insolvency, reorganization, moratorium or similar
    Laws affecting creditors' rights generally and general equitable principles.

        (b) Neither the execution, delivery and performance by the Purchaser of
    the Purchaser Transaction Documents, nor the consummation by the Purchaser
    of the transactions contemplated thereby, will violate, result in a breach
    of the terms of or constitute a default under, the charter or bylaws of the
    Purchaser or any material agreement, instrument or other arrangement or
    obligation to which the Purchaser is subject.

        (c) The Purchaser has read and understands this Agreement, including the
    Schedules and Exhibits hereto, and acknowledges and understands that
    execution and delivery of this Agreement by the Purchaser creates an
    irrevocable obligation of the Purchaser, subject to the terms and conditions
    contained in this Agreement, to purchase the Common Shares.

        (d) The Purchaser is an "accredited investor" within the meaning of
    Regulation D under the Securities Act.

        (e) The acquisition of the Securities by the Purchaser is for the
    Purchaser's own account, is for investment purposes and is not with a view
    to, or for offer or sale for the Company in connection with, the
    distribution of any Securities in violation of the Securities Act, the
    Exchange Act or any state securities laws (collectively, the "Acts"). The
    Purchaser is not participating and does not have a participation in any such
    distribution or the underwriting of any such distribution, and has no
    present intention of selling or otherwise disposing of any of the Securities
    in violation of the Acts.

        (f) The Purchaser is aware that neither the SEC nor any state securities
    commission has approved or disapproved the Securities or passed upon the
    accuracy or adequacy of this Agreement or any of the other Transaction
    Documents.

        (g) The Purchaser (i) recognizes that an investment in the Securities
    involves a high degree of risk, (ii) has such knowledge and experience in
    financial and business matters as to be 



                                      -9-
<PAGE>   13

    capable of evaluating the risks and merits of this investment and protecting
    the Purchaser's interests in connection with this investment and (iii) is
    able to bear the economic risk of an investment in the Securities, including
    the risk of the total loss of such investment.

        (h) The Purchaser has received copies of the Transactions Documents, the
    Form 10-K Report and the Company's charter and bylaws. The Purchaser has
    received all the information the Purchaser considers necessary or
    appropriate for deciding whether to enter into this Agreement or to acquire
    the Securities, and the Purchaser has had an opportunity to ask questions of
    and receive answers from the Company regarding the Company and the terms and
    conditions of the Securities.

        (i) The Purchaser understands that the Securities have not been
    registered under the Securities Act on the basis that the issuance or sale
    of the Securities is exempt from the registration provisions thereof, and
    that the Company's reliance on the exemption is predicated upon the
    representations of the Purchaser herein.

        (j) The Purchaser has read and understands the terms and provisions of
    the Transaction Documents and understands that all Common Shares and all
    Warrant Shares issued to the Purchaser will automatically become subject to
    the terms and provisions of the Stockholders Agreement, the Tag-Along
    Agreement and the Voting Agreement. The Purchaser understands that other
    shares of Common Stock currently held or subsequently acquired by the
    Purchaser may also become subject to the terms and provisions of the
    Stockholders Agreement, the Tag-Along Agreement and the Voting Agreement
    pursuant to the terms thereof.

        Section 8. Compliance with Securities Laws and Agreements. The Purchaser
acknowledges, understands and agrees that the following limitations and
restrictions are applicable to the purchase, resale and distribution of the
Securities:

        (a) The Purchaser must bear the economic risk of its investment in the
    Company for an indefinite period of time because the Securities have not
    been registered under the Acts and, therefore, may not be subsequently
    offered, sold, transferred, pledged or otherwise disposed of unless and
    until they have been registered under the Acts or exemptions from
    registration thereunder are available, and the Purchaser further understands
    that only the Company can take action to register the Securities.

        (b) The Purchaser has been advised that the Company does not expect that
    Rule 144 under the Securities Act will be available to the Purchaser with
    respect to any of the Securities unless the Purchaser is a non-affiliate of
    the Company (and has not been an affiliate of the Company for at least three
    months) and has held such Securities for at least one year from the later of
    the date that they were issued by the Company or the date that they were
    acquired from an affiliate of the Company.

        (c) The certificates representing the Warrants issued pursuant to this
    Agreement will bear the legend provided in the Warrant Agreement. The
    certificates representing the Securities 


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<PAGE>   14

    issued pursuant to this Agreement (other than the Warrants) will bear a
    legend in substantially the following form:

            THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
            REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY
            STATE SECURITIES LAW (COLLECTIVELY, THE "ACTS") AND MAY NOT BE
            OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF UNLESS
            MADE PURSUANT TO A REGISTRATION STATEMENT UNDER THE ACTS OR PURSUANT
            TO AN EXEMPTION FROM THE REGISTRATION REQUIREMENTS THEREOF. FURTHER,
            SUCH SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE
            OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF UNLESS
            AND UNTIL (1) SUCH SECURITIES HAVE BEEN REGISTERED UNDER THE ACTS OR
            (2) THE HOLDER OF SUCH SECURITIES PROVIDES THE COMPANY WITH (A) AN
            UNQUALIFIED WRITTEN OPINION OF LEGAL COUNSEL, WHICH COUNSEL AND
            OPINION (IN FORM AND SUBSTANCE) SHALL BE REASONABLY SATISFACTORY TO
            THE COMPANY, TO THE EFFECT THAT THE PROPOSED DISPOSITION OF SUCH
            SECURITIES MAY BE EFFECTED WITHOUT REGISTRATION UNDER THE ACTS OR
            (B) SUCH OTHER EVIDENCE AS MAY BE REASONABLY SATISFACTORY TO THE
            COMPANY THAT THE PROPOSED DISPOSITION OF SUCH SECURITIES MAY BE
            EFFECTED WITHOUT REGISTRATION UNDER THE ACTS.

        (d) In addition to the legends provided in paragraph (c) above, the
    certificates evidencing the Common Shares and the Warrant Shares will bear
    legends in substantially the following forms:

            BY THE TERMS OF THE STOCKHOLDERS AGREEMENT AND THE TAG-ALONG
            AGREEMENT, CERTAIN RESTRICTIONS HAVE BEEN PLACED UPON THE
            TRANSFERABILITY OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE.
            THE COMPANY WILL FURNISH A COPY OF THE STOCKHOLDERS AGREEMENT AND
            THE TAG-ALONG AGREEMENT TO THE RECORD HOLDER OF THIS CERTIFICATE
            WITHOUT CHARGE UPON WRITTEN REQUEST TO THE COMPANY AT ITS PRINCIPAL
            PLACE OF BUSINESS OR REGISTERED OFFICE. NO REGISTRATION OR TRANSFER
            OF ANY SECURITIES REPRESENTED BY THIS CERTIFICATE WILL BE MADE ON
            THE BOOKS OF THE COMPANY UNLESS AND UNTIL SUCH RESTRICTIONS HAVE
            BEEN COMPLIED WITH.

            THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO THE
            TERMS AND CONDITIONS OF AN AMENDED AND RESTATED VOTING AGREEMENT, A
            COPY OF WHICH IS ON FILE WITH THE SECRETARY OF THE COMPANY, AND ARE
            HELD AND 



                                      -11-
<PAGE>   15

            MAY BE SOLD, ASSIGNED, TRANSFERRED OR OTHERWISE DISPOSED OF ONLY IN
            ACCORDANCE WITH SUCH AGREEMENT.

        (e) Stop Transfer Instructions. The Company's stock transfer records
    will contain stop transfer instructions with respect to the Common Shares
    and the Warrant Shares to provide notice of the restrictions on the resale
    or distribution thereof imposed by the Acts and the Stockholders Agreement,
    the Tag-Along Agreement and the Voting Agreement.

        Section 9. Changes in Capital Structure. In the event of any change
after the date hereof in the number of issued shares of Common Stock by reason
of any stock dividend, split-up, recapitalization, merger, combination,
conversion, exchange of shares or other change in the corporate or capital
structure of the Company, then there shall be appropriate and equitable
adjustments made in the number and kind of shares of stock or other securities
of the Company thereafter issued to the Purchaser pursuant to this Agreement.

        Section 10. Specific Performance. The parties agree that the covenants
and obligations contained in this Agreement relate to special, unique and
extraordinary matters and that a violation of any of the terms hereof would
cause irreparable injury in an amount which would be impossible to estimate or
determine and for which any remedy at law would be inadequate. As such, the
parties agree that if either party fails or refuses to fulfill any of such
party's obligations under this Agreement or to make any payment or deliver any
instrument required hereunder, then the other party shall have the remedy of
specific performance, which remedy shall be cumulative and nonexclusive and
shall be in addition to any other rights and remedies otherwise available under
any other contract or at law or in equity and to which such party might be
entitled.

        Section 11. Notices. Any and all notices, requests or other
communications hereunder shall be given in writing and delivered by (a) regular,
overnight or registered or certified mail (return receipt requested), with first
class postage prepaid, (b) hand delivery, (c) facsimile or electronic mail
transmission or (d) overnight courier service, to the parties at addresses or
facsimile numbers set forth below their respective names on the signature pages
hereof, or at such other address or number as shall be designated by either
party in a notice to the other party given in accordance with this Section 11.
Except as otherwise provided in this Agreement, all such communications shall be
deemed to have been duly given, (i) in the case of a notice sent by regular
mail, on the date actually received by the addressee, (ii) in the case of a
notice sent by registered or certified mail, on the date receipted for (or
refused) on the return receipt, (iii) in the case of a notice delivered by hand,
when personally delivered, (iv) in the case of a notice sent by facsimile or
electronic mail, upon transmission subject to telephone confirmation of receipt,
and (v) in the case of a notice sent by overnight mail or overnight courier
service, the date delivered at the designated address, in each case given or
addressed as aforesaid.

        Section 12. Survival. All  representations, warranties and covenants
contained in this Agreement shall survive the execution and delivery of this
Agreement, the Closings and the delivery of any Securities to the Purchaser.


                                      -12-
<PAGE>   16

        Section 13. Benefit and Burden. This Agreement shall inure to the
benefit of, and shall be binding upon, the Company and the Purchaser and their
respective successors and assigns.

        Section 14. No Third Party Rights. Nothing in this Agreement shall be
deemed to create any right in any creditor or other Person not a party hereto,
and this Agreement shall not be construed in any respect to be a contract in
whole or in part for the benefit of any third party.

        Section 15. Amendments and Waiver. No amendment, modification,
restatement or supplement of this Agreement shall be valid unless the same is in
writing and signed by the parties. No waiver of any provision of this Agreement
shall be valid unless in writing and signed by the party against whom that
waiver is sought to be enforced. No failure or delay on the part of any of the
parties in exercising any right, power or privilege hereunder, and no course of
dealing between or among the parties, shall operate as a waiver of any right,
power or privilege hereunder. No single or partial exercise of any right, power
or privilege hereunder shall preclude any other or further exercise thereof or
the exercise of any other right, power or privilege hereunder. No notice to or
demand on either party in any case shall entitle such party to any other or
further notice or demand in similar or other circumstances or constitute a
waiver of the rights of any party to any other or further action in any
circumstances without notice or demand.

        Section 16. Severability. Should any clause, sentence, paragraph,
subsection or Section of this Agreement be judicially declared to be invalid,
unenforceable or void, such decision will not have the effect of invalidating or
voiding the remainder of this Agreement, and the parties agree that the part or
parts of this Agreement so held to be invalid, unenforceable or void will be
deemed to have been stricken herefrom as if such stricken part or parts had
never been included herein.

        Section 17. Expenses. The Company will pay, or reimburse the Purchaser
for the payment of, all reasonable expenses incurred by the Purchaser prior to
the date hereof in connection with this Agreement, including all legal and
accounting fees and disbursements. Except as aforesaid, each of the parties
shall pay its own expenses incident to this Agreement, including all legal and
accounting fees and disbursements.

        Section 18. Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY,
CONSTRUED UNDER, AND ENFORCED IN ACCORDANCE WITH THE LAWS OF THE STATE OF
DELAWARE, WITHOUT REFERENCE TO THE CONFLICT-OF-LAWS PROVISIONS THEREOF.

        Section 19. Entire Agreement. This Agreement sets forth all of the
promises, agreements, conditions, understandings, warranties and representations
of the parties with respect to the transactions contemplated hereby, and
supersedes all prior agreements, arrangements and understandings between the
parties, whether written, oral or otherwise, with respect to the subject matter
hereof. There are no promises, agreements, conditions, understandings,
warranties or representations, oral or written, express or implied, between the
parties concerning the subject matter hereof except as set forth herein.


                                      -13-
<PAGE>   17

        IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
executed as of the date first above written.


                                  STERLING CHEMICALS HOLDINGS, INC.



                                  By:
                                     -------------------------------------------
                                  Printed Name:
                                               ---------------------------------
                                  Title:
                                        ----------------------------------------

                                  Address: Sterling Chemicals Holdings, Inc.
                                           1200 Smith, Suite 1900
                                           Houston, Texas 77002
                                           Attention: General Counsel
                                  Facsimile No.: (713) 654-9577
                                  E-Mail: Delkins@sterlingchemicals.com


                                  PURCHASER:

                                  KOCH CAPITAL SERVICES, INC.



                                  By:
                                     -------------------------------------------
                                  Printed Name:
                                               ---------------------------------
                                  Title:
                                        ----------------------------------------

                                  Address:
                                          --------------------------------------

                                          --------------------------------------

                                          --------------------------------------

                                          --------------------------------------
                                  Facsimile No.:
                                                --------------------------------
                                  E-Mail:
                                         ---------------------------------------




                                      -14-
<PAGE>   18

                                   SCHEDULE I
                                   PURCHASERS


<TABLE>
<CAPTION>
PURCHASER                                                 NUMBER OF SHARES     PERCENTAGE ALLOCATION
---------                                                 ----------------     ---------------------
<S>                                                       <C>                  <C>   
Gordon A. Cain........................................        1,333,333                53.33%
William A. McMinn.....................................          333,333                13.33%
James Crane...........................................          250,000                10.00%
Frank P. Diassi.......................................          166,667                 6.67%
Frank J. Hevrdejs.....................................          166,667                 6.67%
Koch Capital Services, Inc............................          250,000                10.00%
                                                              ---------               ------
            Total.....................................        2,500,000               100.00%
</TABLE>




                                      -15-