Question

Two liquids $A$ and $B$ have vapour pressure in the ratio $P_{A}^{\circ}: P_{B}^{\circ}=1: 2$ at a certain temperature. Suppose that we have an ideal solution of $A$ and $B$ in the mole fraction ratio $A: B=1: 2,$ the mole fraction of $A$ in the vapour in equilibrium with the solution at the given temperature is

• A. 0.25
• B. 0.2
• C. 0.5
• D. 0.33

Answer 1

Answer: (B)

Since the ratio of $P_{A}^{\circ}$ and $P_{B}^{\circ}$ is 1: 2 and mole fraction is 1: 2 therefore,

partial pressure of $A\left(P_{A}'\right)=P_{A}^{\circ} x_{A}$ and

partial pressure of $B\left(P_{B}'\right)=P_{B}^{\circ} x_{B}$ are related as

$P_{B}'=4 P_{A}'$

$P=P_{A}'+P_{B}'=P_{A}'+4 P_{A}'=5 P_{A}'$

The mole fraction of $A$ in the vapour in equilibrium with solution (according to Dalton's law of partial pressure) is

$x_{A}'=\frac{P_{A}'}{P}=\frac{P_{A}'}{5 P_{A}'}=\frac{1}{5}=0.2$