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  4. Vapour pressure of benzene at 30° C is 121.8 mm. when 15 g of a non-volatile solute is dissolved in 250 g of benzene, its vapour pressure is decreased to 120.2 mm. The molecular weight of the solute is

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Q. Vapour pressure of benzene at $30^{\circ} C$ is $121.8\, mm$. when $15\, g$ of a non-volatile solute is dissolved in $250\, g$ of benzene, its vapour pressure is decreased to $120.2\, mm$. The molecular weight of the solute is

AIIMSAIIMS 1997Solutions

Solution:

As, $\frac{P^{0}-P}{P^{0}}=\frac{\frac{w}{m}}{\frac{w}{m}+\frac{W}{M}}$

$P^{0}$ = vapour pressure of pure component

P = vapour pressure in solution

w = mass of solute, $\quad$ m = mol. wt. of solute

W = mass of solvent, M = mol. wt. of solvent

$\Rightarrow \frac{121.8-120.2}{121.8}=\frac{\frac{15}{m}}{\frac{250}{78}}$

$ \Rightarrow m = 356.7 \,g$