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1 January, 10:17

A gas has a density of 2.22 g/L at 1.04 atm and a molar mass of 51.7 g/mol.

What is the temperature of the gas in Kelvin?

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Answers (1)
  1. 1 January, 10:24
    0
    295.4K

    Explanation:

    Step 1:

    Obtaining an expression which relates density, pressure and temperature together.

    This is can done by using the ideal gas equation as shown below:

    PV = nRT ... (1)

    Recall:

    Number of mole (n) = mass (m) / Molar Mass (M) i. e

    n = m/M

    Substituting the m/M for n in equation 1 above

    PV = nRT

    PV = mRT/M

    Divide both side by P

    V = mRT/MP

    Divide both side by m

    V/m = RT/MP

    Invert the above equation

    m/V = MP/RT ... (2)

    Density (D) = mass (m) / volume (V)

    D = m/V

    Replacing m/V with D in equation 2.

    m/V = MP/RT

    D = MP/RT

    Step 2:

    Data obtained from the question. This includes the following:

    Density (D) = 2.22 g/L

    Pressure (P) = 1.04 atm

    Molar Mass of (M) = 51.7 g/mol.

    Temperature (T) =.?

    Gas constant (R) = 0.082atm. L/Kmol

    Step 3:

    Determination of the temperature.

    D = MP/RT

    2.22 = 51.7 x 1.04 / 0.082 x T

    Cross multiply to express in linear form

    2.22 x 0.082 x T = 51.7 x 1.04

    Divide both side by 2.22 x 0.082

    T = (51.7 x 1.04) / (2.22 x 0.082)

    T = 295.4K

    Therefore, the temperature of the gas is 295.4K
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