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29 November, 15:26

A mixture of h2 and n2 has a density of 0.216 at 300k and 500 torr. what is the mole fraction composition of the mixture

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  1. 29 November, 18:42
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    We know that:

    number of moles (n) = mass / molar mass

    Now, from the general law of gases:

    PV = nRT

    where:

    P is the pressure = 500 torr = 0.65 atm

    V is the volume

    n is the number of moles

    R is the gas constant = 0.082

    T is the temperature = 300 k

    We will just rearrange this equation as follows:

    P = nRT / V

    Then we will substitute n with its equivalent equation mentioned at the beginning:

    P = (mass x R x T) / (volume x molar mass) ... > equation I

    Now, we know that:

    density = mass / volume

    We will substitute (mass/volume) in equation I with density as follows:

    P = (density x R x T) / molar mass

    Rearrange this equation to get the mass as follows:

    molar mass = dRT/P = (0.216 x 0.082 x 300) / 0.65 = 8.4738 grams

    From the periodic table:

    molecular mass of hydrogen = 1 grams

    molecular mass of nitrogen = 14 grams

    Therefore:

    molar mass of hydrogen = 2 x 1 = 2 grams

    molar mass of nitrogen = 2 x 14 = 28 grams

    We can assume that the number of moles of of each element is y.

    We can thus build up the following equation:

    2y + 28y = 8.4738

    30y = 8.4738

    y = 0.28246

    Therefore:

    mole fraction of hydrogen = 2 x 0.28246 = 0.56492

    mole fraction of nitrogen = 28 x 0.28246 = 7.90888
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