Mass of glucose required to be dissolved to prepare one litre of its solution which is isotonic with 15 g solution of urea is (Given: Molar mass in g C : 12, H : 1, O : 16, N : 14) [2024]

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Solution

Q.
Mass of glucose $(C_{6} H_{12} O_{6})$ required to be dissolved to prepare one litre of its solution which is isotonic with 15 g $L^{- 1}$ solution of urea $({NH}_{2} {CONH}_{2})$ is

(Given: Molar mass in g ${mol}^{- 1}$ C : 12, H : 1, O : 16, N : 14) [2024]

1 55 g

2 15 g

3 30 g

4 45 g

Ans.
(4)

As the two solutions of glucose and urea are isotonic, it means they have the same osmotic pressure at a given temperature.

$π_{1} (Glucose) = π_{2} (Urea)$

$C_{1} R T = C_{2} R T (∵ π = C R T)$

$\frac{n_{1}}{V_{1}} R T = \frac{n_{2}}{V_{2}} R T$ $\Rightarrow \frac{n_{1}}{V_{1}} = \frac{n_{2}}{V_{2}}$ $\Rightarrow \frac{w_{1}}{M_{1} V_{1}} = \frac{w_{2}}{M_{2} V_{2}}$

$w_{1} = \frac{15 \times 180}{60} = 45$ $g$

(Molar mass; glucose = 180 g ${mol}^{- 1}$ , urea = 60 g ${mol}^{- 1}$ )

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