FORM OF COMMON STOCK PURCHASE WARRANT

Exhibit 10.40

EXHIBIT A

COMMON STOCK PURCHASE WARRANT

ALEXZA PHARMACEUTICALS, INC.

     THIS COMMON STOCK PURCHASE WARRANT (the “ Warrant ”) certifies that, for value received, Biomedical Sciences Investment Fund Pte Ltd (the “ Holder ”), is entitled, upon the terms and subject to the limitations on exercise and the conditions hereinafter set forth, at any time during the Exercise Period (as defined below), to subscribe for and purchase from Alexza Pharmaceuticals, Inc., a Delaware corporation (the “ Company ”), up to a number of shares of Common Stock, par value $0.0001 per share, of the Company (the “ Common Stock ”) as provided for in Section 2(c) (the “ Warrant Shares ”). The purchase price of one share of Common Stock under this Warrant shall be equal to the Exercise Price, as defined in Section 2(b).

      Section 1 . Definitions . Capitalized terms used and not otherwise defined herein shall have the meanings set forth in that certain Stock and Warrant Purchase Agreement (the “ Purchase Agreement ”), dated March 26, 2008, by and between the Company and the Holder.

      Section 2 . Exercise .

          a) Exercise of Warrant . Exercise of the purchase rights represented by this Warrant may be made, in whole or in part, at any time or times during the Exercise Period by delivery to the Company of a duly executed facsimile copy of the Notice of Exercise Form annexed hereto (or such other office or agency of the Company as it may designate by notice in writing to the registered Holder at the address of such Holder appearing on the books of the Company); provided , however , within 5 Trading Days of the date said Notice of Exercise is delivered to the Company, the Holder shall have surrendered this Warrant to the Company and the Company shall have received payment of the aggregate Exercise Price of the shares thereby purchased by wire transfer or cashier’s check drawn on a United States bank.

          b) Exercise Price . The exercise price of the Common Stock under this Warrant shall be $8.00 (such price to be adjusted for stock splits, stock dividends and the like) per share; provided , however , that if (i) the Pricing Adjustment Point is not triggered, or (ii) a binding agreement to acquire substantially all of the assets or a majority of the outstanding voting securities of the Company (through merger, acquisition, consolidation or otherwise) in which the aggregate purchase price is less than $8.00 (such price to be adjusted for stock splits, stock dividends and the like) per share is entered into prior to the earlier of (a) the triggering of a Pricing Adjustment Point or (b) the end of the Pricing Period (a “ Pricing Change in Control Event ”), then the exercise price of the Common Stock under this Warrant shall be $7.22 (such price to be adjusted for stock splits, stock dividends and the like) per share (the “ Exercise Price ”); provided , further that if this Warrant is exercised prior to December 31, 2008 other than in connection with a Pricing Change in Control Event the Exercise Price shall be $8.00 (such

price to be adjusted for stock splits, stock dividends and the like) per share. The Exercise Price shall be subject to adjustment pursuant to Section 3 hereof.

          c) Number of Warrant Shares . The number of shares of Common Stock that the Holder may purchase by exercising this Warrant shall equal the number of whole shares of Common Stock equal to $3,000,000 divided by the Exercise Price determined pursuant to Section 2(b).

          d) Exercise Period . This Warrant shall not become exercisable unless and until an Exercise Trigger Event (as defined below) occurs. If an Exercise Trigger Event occurs, this Warrant shall be exercisable for the period commencing on the date of the Exercise Trigger Event and ending on the close of business on the fifth year anniversary of the date hereof (the “ Exercise Period ”). For purposes of this Warrant, “ Exercise Trigger Event ” shall mean each of the following events:

               i. The failure by the Company, including any of its Affiliates or a joint venture of which the Company is stockholder or member, to achieve a milestone set forth on Exhibit A hereto (each a “ Milestone ”, and collectively, the “ Milestones ”); provided , however , that the Company shall have forty five (45) days after the date on which the Company receives a Cure Notice (as defined on Exhibit A) to cure any alleged failure before any such failure shall be deemed an Exercise Trigger Event; and provided further that with respect to any Milestone, the Company may request the written consent of the Holder for the modification of such Milestone, or the modification of the timing for the performance of such Milestone, and the Holder hereby agrees that it will not unreasonably withhold consent to such modification; and

               ii. The termination by the Company of its operations in Singapore or the transfer of all, or substantially all, of the Company’s Singapore operations outside of Singapore without the prior written consent of the Holder.

          e) Cashless Exercise . This Warrant may also be exercised during the Exercise Period by means of a “cashless exercise” in which the Holder shall be entitled to receive a certificate for the number of Warrant Shares equal to the quotient obtained by dividing [(A-B)*(X)] by (A), where:

          (A) = the VWAP on the Trading Day immediately preceding the date of such election;

          (B) = the Exercise Price of this Warrant, as adjusted; and

          (X) = the number of Warrant Shares issuable upon exercise of this Warrant in accordance with the terms of this Warrant by means of a cash exercise rather than a cashless exercise.

     For purposes of this Section 2(e), “ VWAP ” shall mean the daily volume weighted average price of the Company on the Principal Market as reported by Bloomberg Financial L.P. using the AQR function.

          f) Mechanics of Exercise .

               i.  Authorization of Warrant Shares . The Company covenants that all Warrant Shares which may be issued upon the exercise of the purchase rights represented by this Warrant will, upon exercise of the purchase rights represented by this Warrant, be duly authorized, validly issued, fully paid and nonassessable and free from all taxes, liens and charges in respect of the issue thereof (other than taxes in respect of any transfer occurring contemporaneously with such issue).

               ii.  Delivery of Certificates Upon Exercise . Certificates for shares purchased hereunder shall be transmitted by the transfer agent of the Company to the Holder by crediting the account of the Holder’s prime broker with the Depository Trust Company through its Deposit Withdrawal Agent Commission (“ DWAC ”) system if the Company is a participant in such system and such system is available for transmitting such certificates, or otherwise by physical delivery to the address specified by the Holder in the Notice of Exercise within 5 Trading Days from the delivery to the Company of the Notice of Exercise Form, surrender of this Warrant and payment of the aggregate Exercise Price as set forth above (“ Warrant Share Delivery Date ”). This Warrant shall be deemed to have been exercised on the date the aggregate Exercise Price is received by the Company. The Warrant Shares shall be deemed to have been issued, and Holder or any other person so designated to be named therein shall be deemed to have become a holder of record of such shares for all purposes, as of the date the Warrant has been exercised by payment to the Company of the aggregate Exercise Price and all taxes required to be paid by the Holder, if any, pursuant to Section 2(f)(vi) prior to the issuance of such shares, have been paid.

               iii.  Delivery of New Warrants Upon Exercise . If this Warrant shall have been exercised in part, the Company shall, at the time of delivery of the certificate or certificates representing Warrant Shares, deliver to the Holder a new Warrant evidencing the rights of the Holder to purchase the unpurchased Warrant Shares called for by this Warrant, which new Warrant shall in all other respects be identical with this Warrant.

               iv.  Rescission Rights . If the Company fails to cause its transfer agent to transmit to the Holder a certificate or certificates representing the Warrant Shares pursuant to Section 2(f)(ii) by the date that is two business days after the Warrant Share Delivery Date, then the Holder will have the right to rescind such exercise.

               v.  No Fractional Shares or Scrip . No fractional shares or scrip representing fractional shares shall be issued upon the exercise of this Warrant. As to any fraction of a share which the Holder would otherwise be entitled to purchase upon such exercise, the Company shall pay a cash adjustment in respect of such final fraction in an amount equal to such fraction multiplied by the Exercise Price.

               vi.  Charges, Taxes and Expenses . Issuance of certificates for Warrant Shares shall be made without charge to the Holder for any issue or transfer tax or other incidental expense in respect of the issuance of such certificate, all of which taxes and expenses shall be paid by the Company, and such certificates shall be issued in the name of the Holder or in such name or names as may be directed by the Holder; provided , however , that in the event

certificates for Warrant Shares are to be issued in a name other than the name of the Holder, this Warrant when surrendered for exercise shall be accompanied by the Assignment Form attached hereto duly executed by the Holder; and the Company may require, as a condition thereto, the payment of a sum sufficient to reimburse it for any transfer tax incidental thereto.

      Section 3 . Certain Adjustments; Early Termination .

          a) Stock Dividends and Splits . If the Company, at any time while this Warrant is outstanding: (A) pays a stock dividend or otherwise make a distribution or distributions on shares of its Common Stock or any other equity or equity equivalent securities payable in shares of Common Stock (which, for avoidance of doubt, shall not include any shares of Common Stock issued by the Company pursua