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14 May, 05:54

A 2.10-mole sample of an ideal gas is allowed to expand at a constant temperature of 278 K. The initial volume is 14.5 L and the gas performs 945 J of work. What is the final volume of the container? Let the ideal-gas constant R = 8.314 J / (mol • K).

Answers:

22.3 L

19.5 L

17.6 L

28.4 L

+2
Answers (1)
  1. 14 May, 06:21
    0
    Given that,

    Number of mole

    n = 2.1mole

    Temperature

    T = 278 K

    Initial volume

    V1 = 14.5L

    Work done

    W = 945J

    R = 8.314 J/mol•K

    Work done is given as at constant temperature is

    W = - P1•V1 In (V2/V1)

    Now, let know the pressure using is ideal gas law

    PV = nRT

    P = nRT/V

    P = 2.1 * 8.314 * 278 / 14.5

    P = 334.74 N/L

    Then,

    W = - P1•V1 In (V1/V2)

    945 = - 334.74*14.5 In (V1/V2)

    -945 / (334.74*14.5) = In (V1/V2)

    In (V1/V2) = - 0.1947

    Take exponential of both sides

    V1/V2 = exp (-0.1947)

    14.5/V2 = 0.823

    14.5 = 0.823V2

    V2 = 14.5/0.823

    V2 = 17.62 L

    The third option is correct
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