Diethyl ether has a vapor pressure of 400.0 torr at 18°C. When a sample of benzoic acid is dissolved in ether, the vapor pressure of the solution is 342 torr. What is the mole fraction of benzoic acid in the solution?
A) 0.0169
B) 0.0197
C) 0.145
D) 0.855
E) 0.045

Question

Quizplus · Accepted Answer

We can use Raoult's law to solve for the mole fraction of benzoic acid:

P_total = P_A + P_B

where P_total is the vapor pressure of the solution, P_A is the vapor pressure of pure diethyl ether, and P_B is the vapor pressure of benzoic acid.

We can rearrange this equation to solve for the mole fraction of benzoic acid:

X_B = P_B / P_total

We are given P_A = 400.0 torr and P_total = 342 torr, so we can solve for P_B:

P_B = P_total - P_A
     = 342 torr - 400.0 torr
     = -58 torr (Note: This negative vapor pressure implies that benzoic acid is not volatile at the given temperature and pressure.)

Since P_B is negative, X_B must also be negative, so the only possible answer is D) 0.855, which is the absolute value of X_B.

Diethyl Ether Has a Vapor Pressure of 400