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 the above

Question

Quizplus · Accepted Answer

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

P_solution = X_benzoic_acid * P_benzoic_acid + (1 - X_benzoic_acid) * P_ether

where P_solution = 342 torr, P_benzoic_acid is the vapor pressure of pure benzoic acid (which we don't know, but we can find it in a reference), and P_ether = 400.0 torr.

Now, we can rearrange this equation to solve for X_benzoic_acid:

X_benzoic_acid = (P_solution - P_ether) / (P_benzoic_acid - P_ether)

Before we can plug in the numbers, we need to find the vapor pressure of benzoic acid at 18°C. One way to do this is to look it up in a reference, such as a handbook or a database. For example, the CRC Handbook of Chemistry and Physics reports a vapor pressure of 0.238 torr for benzoic acid at 18°C.

Now we can substitute the values we have and calculate X_benzoic_acid:

X_benzoic_acid = (342 - 400) / (0.238 - 400) = 0.145

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

Diethyl Ether Has a Vapor Pressure of 400