Two liquids A and B have vapour pressure in the ratio $P_{A}^{\circ} : P_{B}^{\circ} = 1 : 3$ at a certain temperature. Assume A and B form an ideal solution and the ratio of mole fractions of A to B in the vapour phase is 4 : 3. Then the mole fraction of B in the solution at the same temperature is :

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$\frac{1}{5}$

$\frac{2}{3}$

$\frac{4}{5}$

$\frac{1}{4}$

answer is A.

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Detailed Solution

$y_{A} = \frac{P_{A}}{P} \Rightarrow \frac{P_{A}^{\circ} x_{A}}{P} and y_{B} = \frac{P_{B}^{\circ} x_{B}}{P} \frac{y_{A}}{y_{B}} = \frac{P_{A}^{\circ}}{P_{B}^{\circ}} \times \frac{x_{A}}{x_{B}} \Rightarrow \frac{4}{3} = \frac{1}{3} \times \frac{x_{A}}{(1 - x_{A})} x_{A} = \frac{4}{5} or x_{B} = \frac{1}{5}$