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13 October, 23:01

An unknown gas at 130 celsius has a rms speed that is 0.50 that of the rms speed of N2 molecules at 50 degrees celsius. What is the molecular weight of unknown gas?

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  1. 14 October, 00:21
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    M = 613.8455 kg/mol

    Explanation:

    RMS velocity or root mean square velocity has a formula for particles:

    RMS = (3*R*T / M) ^ (1/2)

    Where R is the ideal gas constant = 8.314 (kg*m^2 / s^2) / K*mol

    T is the temperature in Kelvin

    M is the mass of a mole of the gas in kilograms (kg)

    1) Convert the temperature to Kelvin for the N2 particles

    T = * C + 273

    T = 50 + 273

    T = 323 K

    2) Find the molar mass of the particles in kg for N2

    using the periodic table: Nitrogen (N) molar mass is 14.00667 g/mol

    N2 molar mass = 2 * 14.00667 = 28.01334 g/mol

    Convert to kg/mol using dimensional analysis and conversion factor of 1 kg = 1000 g

    28.01334 g / mol * 1 kg / 1000 g = 0.02801334 kg/mol

    4) find the RMS of N2

    RMS = (3 * (8.314 (kg*m^2 / s^2) / K*mol) * (323K) / 0.02801334 kg/mol)) ^1/2

    =536.2712 m/s

    5) If we take 0.5 of N2 RMS or 1/2 we get: 268.1356 m/s for the RMS of the unknown gas

    6) Rearrange the equation to solve for M

    RMS = (3RT/M) ^1/2

    Solve for M

    We know that a^ (1/2) = sqrt (a)

    sqrt (RMS) = (3RT/M)

    sqrt (RMS) * M = 3RT

    M = 3RT / sqrt (RMS)

    5) Change the temperature to Kelvins

    T = 130 + 273 = 403 K

    6) Plug the numbers in and solve for M

    M = (3 * (8.314 (kg*m^2 / s^2) / K*mol) * (403 K)) / sqrt (268.1356 m/s)

    M = 613.8455 kg/mol
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