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Q.

A solution containing 10g per $d m^{3}$ of urea (molecular mass = $60 g m o l^{- 1})$ is isotonic with a 5% solution of a non-volatile solute. The molecular mass of this non-volatile solute is

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a

$350 g m o l^{- 1}$

b

$200 g m o l^{- 1}$

c

$250 g m o l^{- 1}$

d

$300 g m o l^{- 1}$

answer is B.

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Detailed Solution

Isotonic means osmotic pressures are equal.

$\begin{array}{l} ∴ π_{1} = π_{2} \\ \frac{n_{1}}{v_{1}} R T = \frac{n_{2}}{v_{1}} R T \\ \frac{w_{1}}{m_{1}} \frac{R T}{V_{1}} = \frac{w_{2}}{m_{2}} \frac{R T}{V_{2}} \\ \frac{10}{60} \times \frac{1}{1000} = \frac{5}{m_{2}} \times \frac{1}{100} \\ ∴ m_{2} = 300 g m o l^{- 1} \end{array}$

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