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28 February, 01:10

5. At 20 °C the vapor pressure of pure benzene (C6H6) is 75.0 torr, and that of toluene (C7H8) is 22.0 torr. Assume that benzene and toluene form ideal solutions. What is the mole fraction of benzene in a solution that has a (total) vapor pressure of 55.0 torr at 20 °C? A) 1.764 B) 0.623 C) 0.106 D) - 0.362 E) 4.451

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  1. 28 February, 03:55
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    B) 0.623

    Explanation:

    In an ideal solution of benzene and toluene, vapor pressure is:

    Total Pressure = Xbenzene * P°benzene + Xtoluene * P°toluene

    Where X is mole fraction of each compound, and P° is vapor pressure of pure compound

    Replacing with given values:

    55.0 torr = Xbenzene * 75.0 torr + Xtoluene * 22.0 torr (1)

    Also, the sum of moles fraction is = 1:

    1 = Xbenzene + Xtoluene (2)

    Replacing (2) in (1):

    55.0 torr = Xbenzene * 75.0 torr + (1 - Xbenzene) * 22.0 torr

    55.0 torr = Xbenzene*75.0 torr + 22.0 torr - Xbenzene*22.0 torr

    33.0 torr = Xbenzene*53.0torr

    0.623 = Xbenzene

    Mole fraction of benzene is B) 0.623
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