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30 January, 04:26

The composition of planetary atmospheres is determined in part by the speeds of the molecules of the constituent gases because the faster-moving molecules can reach escape velocity and leave the planet. Calculate the mean speed of CH4 molecules at 77K and 1500K.

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  1. 30 January, 04:43
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    At T = 77k, V = 2.69m/a

    At T = 1500K, V = 11.86m/s

    Explanation:

    Hello,

    We're required to find the root mean speed (RMS) of a gas and to do that, we'll have to relate the energy of a gas and its kinetic energy

    Ek = 3/2 RT

    Ek = ½mv²

    ½mv² = 3/2 RT

    Solve for V

    MV² = 3RT

    V² = 3RT / M

    V = √ (3RT/M)

    V = velocity or speed of the gas

    R = ideal gas constant

    T = temperature of the gas

    M = molarmass mass of the gas

    Molar mass of CH4 = 12 + 4 = 16g/mol

    At T = 77k

    V = √[ ((3/2) * 77) / 16]

    V = √7.216

    V = 2.69m/s

    At T = 1500K

    V = √[ ((3/2) * 1500) / 16]

    V = √140.625

    V = 11.86m/s
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