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5 November, 01:21

The vapor pressure of pure benzene is 750.0 torr and the vapor pressure of toluene is 300.0 torr at a certain temperature. You make a solution by pouring "some" benzene with "some" toluene. You then place this solution in a closed container and wait for the vapor to come into equilibrium with the solution. Next, you condense the vapor. You put this liquid (the condensed vapor) in a closed container and wait for the vapor to come into equilibrium with the solution. You then condense this vapor and find the mole fraction of benzene in this vapor to be 0.669. Determine the mole fraction of benzene in the original solution, assuming the solution behaves ideally. Mole fraction =

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  1. 5 November, 05:10
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    Mole fraction of benzene in pure solution is 0.4472

    Explanation:

    Vapor pressure of pure benzene = 750 torr

    Vapor pressure of pure toulene = 300 torr

    Mole fraction of benzene in vapor = 0.669

    1/P=Xa/Pa + Xb/Pb

    Where

    Xa = mole fraction of A in water

    Xb = mole fraction of B in water

    P = Total pressure

    Pa = total vapor pressure of pure A

    Pb = total vapor pressure of pure B

    Xa+Xb=1

    Let A be benzene and B be toulene

    We have Xa=0.669 and Xb = 0.331

    1/P = 0.669/750 + 0.331/300

    1/P = 0.000892/torr + 0.001103/torr

    1/P=0.001995/torr

    P = 501.25torr

    We have P = Pa + Pb

    Where Pa = XaPa0

    And Pb=XbPb0

    Where

    Xa = mole fraction of A in solution

    Xb = mole fraction of B in solution

    Now, substitute the data into the formula

    501.25torr=Xa750torr + (1 - Xa) 300 torr

    Xa450torr + 300torr

    Xa (450torr) = 201.25torr

    Xa = 0.4472

    Therefore, mole fraction of benzene in pure solution is 0.4472
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