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17 March, 11:29

The pressure of sulfur dioxide (SO2) is 2.27 x 104 Pa. There are 418 moles of this gas in a volume of 57.9 m3. Find the translational rms speed of the sulfur dioxide molecules.

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  1. 17 March, 13:01
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    The translational rms speed of the sulfur dioxide molecules. vrms = 52.8 m/s

    Explanation:

    The root-mean-square speed is the measure of the speed of particles in a gas. It is given by the formula below;

    vrms=√3RT/M

    where vrms is the root-mean-square of the velocity, M is the molar mass of the gas in kilograms per mole, R is the molar gas constant, and T is the temperature in Kelvin.

    Molar mass of SO₂ in Kg / mole = (64/1000) Kg/mol = 0.064 kg/mol

    R = 8.314 m³. Pa/K*mol

    T = ?

    Using PV = nRT to find T

    T = PV/nR

    Substituting for T in the rms formula

    vrms = √ (3R*PV/nR) / M

    vrms = √3PV/nM

    vrms = √3 * 2.27 * 10⁴ * 57.9) / 418 * 0.064

    vrms = 52.8 m/s
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