An ideal solution of benzene (p* = 75 mmHg) and toluene (p* = 22 mmHg) has a vapour pressure of 50 mmHg. The mole fraction of benzene in liquid and vapour phases, respectively are

A
0.53, 0.795
B
0.795, 0.53
C
0.47, 0.205
D
0.205, 0.47

Solution:

We have $p_{total} = x_{b} p_{b}^{*} + x_{t} p_{t}^{*} = x_{b} p_{b}^{*} + (1 - x_{b}) p_{t}^{*} = p_{t}^{*} + (p_{b}^{*} - p_{t}^{*}) x_{b}$

Hence, $x_{b} = \frac{p_{total} - p_{t}^{*}}{p_{b}^{*} - p_{t}^{*}} = \frac{(50 - 22) mmHg}{(75 - 22) mmHg} = 0.53$

$\begin{array}{l} p_{b} = x_{b} p_{b}^{*} = (0.53) (75 mmHg) = 39.75 mmHg \\ y_{b} = \frac{p_{b}}{p_{total}} = \frac{39.75 mmHg}{50 mmHg} = 0.795 \end{array}$

Solution:

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