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 =

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