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10 February, 19:54

What is the temperature of CO2 gas if the average speed (actually the root-mean-square speed) of the molecules is 750 m/s?

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  1. 10 February, 21:40
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    992.302 K

    Explanation:

    V (rms) = 750 m/s

    V (rms) = √ (3RT / M)

    V = velocity of the gas

    R = ideal gas constant = 8.314 J/mol. K

    T = temperature of the gas

    M = molar mass of the gas

    Molar mass of CO₂ = [12 + (16*2) ] = 12+32 = 44g/mol

    Molar mass = 0.044kg/mol

    From

    ½ M*V² = 3 / 2 RT

    MV² = 3RT

    K = constant

    V² = 3RT / M

    V = √ (3RT / M)

    So, from V = √ (3RT / M)

    V² = 3RT / M

    V² * M = 3RT

    T = (V² * M) / 3R

    T = (750² * 0.044) / 3 * 8.314

    T = 24750000 / 24.942

    T = 992.302K

    The temperature of the gas is 992.302K

    Note : molar mass of the gas was converted from g/mol to kg/mol so the value can change depending on whichever one you use.
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