Diethyl ether has a vapor pressure of 400.0 torr at 18$\degree$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 is correct.

Question

Quizplus · Accepted Answer

Using Raoult's law, we can relate the vapor pressure of the solution to the mole fraction of benzoic acid:

Psolution = Xbenzoic acid * Pbenzoic acid + Xether * Pether

where Xbenzoic acid is the mole fraction of benzoic acid, Xether is the mole fraction of ether, and Pbenzoic acid and Pether are the vapor pressures of pure benzoic acid and ether, respectively.

Since we know the vapor pressures of ether and the solution, we can solve for the mole fraction of benzoic acid:

342 torr = Xbenzoic acid * 760 torr + (1 - Xbenzoic acid) * 400.0 torr

Xbenzoic acid = (342 torr - 400.0 torr) / (760 torr - 400.0 torr) = 0.145

Therefore, the mole fraction of benzoic acid in the solution is 0.145. The answer is (C).

Diethyl Ether Has a Vapor Pressure of 400 °\degree° C When a Sample of Benzoic Acid Is Dissolved in 18

Diethyl Ether Has a Vapor Pressure of 400 $\degree$ C When a Sample of Benzoic Acid Is Dissolved in 18