[zerality]

Hi,

I need some assistance solving this problem:
A solution of unknow composition of Benzene and Toluene is prepared, and the mole fractions of benzene and toluene in the vapor phase at 25 degrees celsius are each .50
The vapor pressures of benzene and toulene respectively are 95 and 28 torr at 25 degrees celsius.
Calculate the mole fractions of benzene and toluene in the solution.

I know
 P_total = 95 X^liquid_benzene   + 28 (1 - X^liquid_benzene)


I know that the mole fractions of Benzene and Toluene in the vapor phase is important but don't know where to proceed from my above equation.

Thanks

[Yggdrasil]

Recall that the total pressure is the sum of the partial pressures of the components of your vapor.  Do you know how to find the partial pressure of toluene and benzene given the mole fraction in the vapor?

[zerality]

Ok,

I think I have the answer, but am not 100% sure:

P_total = 95 X^liquid_benzene   + 28 (1 - X^liquid_benzene)
         = 67 X ^l _benzene

P_total = (P_benzene) / .5
                         = [(95 X^liquid_benzene)]/.5

Using simultaneous equations: X^liquid_benzene = .2276 and X^liquid_toluene = .7724

[Yggdrasil]

Here's my solution:

P_benzene = X^gas_benzene * P_total = (95torr)X^liquid_benzene
P_toluene = X^gas_toluene * P_total = (28torr)X^liquid_toluene

Since X^gas_toluene = X^gas_benzene = 0.5 and X^liquid_toluene = 1 - X^liquid_benzene these two equations simplify to:

0.5P_t = 95X^l_b
0.5P_t = 28(1 - X^l_b)

Therefore, setting the two equations equal to eachother:

95X^l_b = 28(1 - X^l_b)
67X^l_b = 28
X^l_b = 0.418
X^l_t = 0.582

[zerality]

Thanks for your help. I see and understand where I went wrong.