Solutions of benzene and toluene obey Raoult's law.The vapor pressures at 20°C are: benzene,76 torr;toluene,21 torr.
-A benzene-toluene solution is allowed to come to equilibrium with its vapor.The vapor is then condensed and found to contain 50.0 mole percent of each component.Calculate the composition (mole percent)of the original solution.The vapor pressures of pure benzene and toluene at this temperature are: 750.torr and 300.torr,respectively.

Question

Quizplus · Accepted Answer

Let x be the mole fraction of benzene in the original solution.
According to Raoult's law, the vapor pressure of the solution is:
P = x*76 + (1-x)*21
In equilibrium, the vapor should have the same composition as the solution:
0.5 = P_benzene/P = x*76/P + (1-x)*21/P
0.5*P = x*76 + (1-x)*21
Substitute P = 750 torr and solve for x:
375 = 55x + 21 - 21x
354 = 34x
x = 10.4
Therefore, the original solution had a mole fraction of benzene of 10.4/100 = 0.104, or 10.4 mole percent.
The composition in mole percent is 10.4% benzene and 89.6% toluene.
The best choice is B.

Solutions of Benzene and Toluene Obey Raoult's Law