Question

A solution at ${20^ \circ }$ is composed of 1.5 mol of benzene and 3.5 mol of toluene. At the same temperature, if the vapour pressure of pure benzene and toluene are 74.7 and 22.3 (torrs), then total vapour pressure of solution and the benzene mole fraction in equilibrium with it is going to be respectively:
A.) 35.0 torr and 0.480
B.) 30.5 torr and 0.389
C.) 38.0 torr and 0.589
D.) 35.8 torr and 0.280

Answer 1

Hint: First we will be recalling Raoult’s law and as we know, Raoult’s law is used to state that, for a solution of volatile liquids, the partial vapour pressure of each liquid present in the solution is directly proportional to its mole fraction. And by keeping this in mind, we will be solving this question.

Complete step-by-step answer:
Raoult’s law: It states that the freezing and boiling points of an ideal solution are respectively depressed and elevated relative to that of the pure solvent by an amount proportional to the mole fraction of the solute.
A law stating that vapour pressure of an ideal solution is proportional to the mole fraction of solvent.
Partial vapour pressure: The pressure of a component in a mixture is calculated as the vapour pressure of pure component at the temperature multiplied by its mole fraction in the mixture.
In a mixture of different gases, each gas exerts its own pressure. This is called its partial pressure and it is independent of the other gases present.
${X_B} = \dfrac{{1.5}}{{1.5 + 3.5}} = 0.3$

The mole fraction of benzene is

The partial pressure of benzene is ${P_B} = 0.3 \times 74.7 = 22.4$ torr

The partial pressure of toluene is ${X_T} = 0.7 \times 22.3 = 15.6$ torr

The total pressure is ${P_T} = 22.4 + 15.6 = 38.0$ torr

The mole fraction of benzene in vapour form is, $Y = \dfrac{{22.4}}{{38.0}} = 0.589$

Hence, the correct answer is C) 38.0 torr and 0.589

Note - Raoult’s law is true to solutions having non-volatile solute only, whereas it is not applicable to solutes that dissociate or associate in a particular solution. This law also plays an important role on the phase diagram of a solvent.