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27 May, 22:02

The volume of a gas is 27.5 mL at 22.0°C and 0.974 atm. What will the volume be at 15.0°C and 0.993 atm? Use Ideal Gas Law (PV = nRT) to find the appropriate gas law for this problem.

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  1. 28 May, 00:05
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    26.3 mL

    Explanation:

    Step 1:

    Obtaining an appropriate gas law from the ideal gas equation.

    This is illustrated below:

    From the ideal gas equation:

    PV = nRT

    Divide both side by T

    PV/T = nR

    At this stage, we'll assume the number of mole (n) to be constant.

    Note: R is the gas constant.

    PV/T = constant.

    We can thus, write the above equation as:

    P1V1/T1 = P2V2/T2

    The above equation is called the general gas equation.

    Step 2:

    Data obtained from the question. This includes the following:

    Initial volume (V1) = 27.5 mL

    Initial temperature (T1) = 22.0°C = 22.0°C + 273 = 295K

    Initial pressure (P1) = 0.974 atm.

    Final temperature (T2) = 15.0°C = 15.0°C + 273 = 288K

    Final pressure (P2) = 0.993 atm

    Final volume (V2) = ... ?

    Step 3:

    Determination of the final volume of the gas using the general gas equation obtained. This is illustrated below:

    P1V1 / T1 = P2V2/T2

    0.974 x 27.5/295 = 0.993 x V2/288

    Cross multiply to express in linear.

    295x0.993xV2 = 0.974x27.5x288

    Divide both side by 295 x 0.993

    V2 = (0.974x27.5x288) / (295x0.993)

    V2 = 26.3 mL

    Therefore, the new volume of the gas is 26.3 mL
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