The vapour pressure of pure benzene and methyl benzene at 27°C is given as 80 Torr and 24 Torr, respectively. The mole fraction of methyl benzene in vapour phase, in equilibrium with an equimolar mixture of those two liquids (ideal solution) at the same t

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Solution

Q.
The vapour pressure of pure benzene and methyl benzene at 27°C is given as 80 Torr and 24 Torr, respectively. The mole fraction of methyl benzene in vapour phase, in equilibrium with an equimolar mixture of those two liquids (ideal solution) at the same temperature is _____ $\times 10^{- 2}$ (nearest integer). [2024]

Ans.
(23)

Mole fraction of benzene in liquid,

$x_{C_{6} H_{6}} = \frac{n_{C_{6} H_{6}}}{n_{C_{6} H_{6}} + n_{C_{6} H_{5} {CH}_{3}}} = \frac{n_{C_{6} H_{6}}}{n_{C_{6} H_{6}} + n_{C_{6} H_{6}}} = \frac{1}{2}$

Mole fraction of methyl benzene in liquid,

$x_{C_{6} H_{5} {CH}_{3}} = \frac{n_{C_{6} H_{5} {CH}_{3}}}{n_{C_{6} H_{6}} + n_{C_{6} H_{5} {CH}_{3}}} = \frac{n_{C_{6} H_{6}}}{n_{C_{6} H_{6}} + n_{C_{6} H_{6}}} = \frac{1}{2}$

$\frac{y_{C_{6} H_{5} {CH}_{3}}}{y_{C_{6} H_{6}}} = \frac{P_{C_{6} H_{5} {CH}_{3}}^{°} x_{C_{6} H_{5} {CH}_{3}}}{P_{C_{6} H_{6}}^{°} x_{C_{6} H_{6}}} = \frac{24 \times 1 / 2}{80 \times 1 / 2} = \frac{3}{10}$

$y_{C_{6} H_{5} {CH}_{3}} = \frac{3}{3 + 10} = 23 \times 10^{- 2}$

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