An ideal solution of liquid ApA∗=100mmHg and liquid BpB∗=30mmHg has 0.6 mole fraction of A in the vapour phase. The mole fraction of A in the liquid phase will be

An ideal solution of liquid $A (p_{A}^{} = 100 mmHg)$ and liquid $B (p_{B}^{} = 30 mmHg)$ has 0.6 mole fraction of A in the vapour phase. The mole fraction of A in the liquid phase will be

A
0.21
B
0.25
C
0.31
D
0.41

Solution:

We have $y_{A} = \frac{p_{A}}{p_{A} + p_{B}} = \frac{x_{A} p_{A}^{*}}{x_{A} p_{A}^{*} + (1 - x_{A}) p_{B}^{*}} = \frac{x_{A} p_{A}^{*}}{p_{B}^{*} + (p_{A}^{*} - p_{B}^{*}) x_{A}}$

This gives $x_{A} = \frac{y_{A} p_{B}^{*}}{p_{A}^{*} + (p_{B}^{*} - p_{A}^{*}) y_{A}} = \frac{(0.69) (30)}{100 + (30 - 100) (0.60)} = 0.31$

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