Liquids A and B form an ideal solution. The total vapour pressure at a fixed temperature is $440 torr$ when $x_{A} = 0.20$ and $520 torr$ when $x_{A} = 0.60$ (liquid-phase mole fractions). For a liquid with $x_{A} = 0.30$ at the same temperature, find the mole fraction of A in the vapour. Give the answer to three decimal places.

Numerical answer type, tolerance 0.001.

Answer: 0.391

For an ideal solution

P = p_{B}^{0} + x_{A} (p_{A}^{0} - p_{B}^{0})

, which is linear in

x_{A}

. The slope is

(520 - 440) / (0.60 - 0.20) = 200 torr

, so

p_{B}^{0} = 440 - 0.20 \times 200 = 400

and

p_{A}^{0} = 600 torr

. At

x_{A} = 0.30

P = 460 torr

and

p_{A} = 0.30 \times 600 = 180 torr

. Hence

y_{A} = 180/460 = 0.3913 \approx 0.391