The vapour pressure of a solution of a non-volatile electrolyte (A) in a solvent (B) is 95% of the vapour pressure of the solvent at the same temperature. If $M_{B} = 0.3 M_{A},$ where $M_{A}$ and $M_{B}$ are molecular weights of (A) and (B) respectively, then the weight ratio of the solvent and solute are

69.8

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66.6

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5.7

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76.6

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Solution

The correct option is C 5.7
$\frac{P^{o} - P_{s}}{P^{o}} = x_{s o l u t e} = \frac{\frac{w t_{s o l u t e}}{M_{s o l u t e}}}{\frac{w t_{s o l u t e}}{M_{s o l u t e}} + \frac{w t_{s o l v e n t}}{M_{s o l v e n t}}}$

$\frac{P^{o} - 0.95 P^{o}}{P^{o}} = \frac{\frac{w t_{s o l u t e}}{M_{s o l u t e}}}{\frac{w t_{s o l u t e}}{M_{s o l u t e}} + \frac{w t_{s o l v e n t}}{0.3 M_{s o l u t e}}}$

$0.05 = \frac{0.3 w t_{s o l u t e}}{0.3 w t_{s o l u t e} + w t_{s o l v e n t}}$

$1 + \frac{w t_{s o l v e n t}}{0.3 w t_{s o l u t e}} = \frac{1}{0.05} = 20$

$\frac{w t_{s o l v e n t}}{w t_{s o l u t e}} = 19 \times 0.3 = 5.7$

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