Below is a P-x-y diagram for mixtures of n-pentane and methanol at a temperature of 422.6 K (it also appears as Figure 10-4 in your book). Use the information in the figure to answer the following questions.

Question

A) What are the vapor pressures of pure pentane and pure methanol at this temperature?

B) A mixture of 30 mol% pentane and 70 mol% methanol is in the vapor phase at 422.6 K. Its pressure is increased isothermally until it begins to condense. What is the pressure at which condensation begins, and the composition of the first drop of liquid?

C) As the pressure of the mixture in part B continues to increase isothermally, at what pressure does the last bubble of vapor disappear? What is the composition of the last bubble of vapor?

D) What WOULD be the answers to part C be if this mixture followed Raoult’s Law?

E) List the assumptions made in the derivation of Raoult’s Law and discuss how well or how poorly each of them is reflected in this system.

F) It has been stated that Raoult’s Law is a good model for a compound that has x>0.99, even if the compound is not chemically similar to the other components of the liquid phase. What is the rationale for this statement?

Answer 1

A)

The vapor pressure of pure pentane at this temperature corresponds to the pressure at which the pentane mole fraction is 1.0, while the vapor pressure of pure methanol at this temperature corresponds to the pressure at which the pentane mole fraction is 0. According to the given graph: