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)None of these choices are correct.

Question

Quizplus · Accepted Answer

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

P_total = X_ether * P_ether + X_benzoicacid * P_benzoicacid

where P_total is the total vapor pressure of the solution, P_ether is the vapor pressure of diethyl ether, and P_benzoicacid is the vapor pressure of benzoic acid (which we assume to be negligible compared to P_ether). X_ether and X_benzoicacid are the mole fractions of diethyl ether and benzoic acid, respectively.

We can rearrange this equation to solve for X_benzoicacid:

X_benzoicacid = (P_total - X_ether * P_ether) / P_benzoicacid

Plugging in the given values:

X_benzoicacid = (342 torr - 0.60 * 400.0 torr) / 0.0 torr = 0.145

Therefore, the mole fraction of benzoic acid in the solution is 0.145.

Diethyl Ether Has a Vapor Pressure of 400