A solution containing $2.5 \times 10^{- 3} kg$ of a solute dissolved in $75 \times 10^{- 3} kg$ of water boils at $373.535 K$ . The molar mass of the solute is ______ g mol^-1. [nearest integer] (Given: $K_{b} (H_{2} O) = 0.52 K Kg$ ${mol}^{- 1}$ , boiling point of water =373.15 K )

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answer is 45.

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Detailed Solution

The molar mass of the solute is 45 g mol^-1.

$\begin{array}{l} w = 2.5 g, & K_{b} = 0.52 \\ w_{solvent} = 75 g, & M = Mol. Wt. of solute \\ T_{B}^{'} = 373.535 K \end{array}$

$T_{B}^{o} = 373.15 K$
$Δ T_{B} = K_{b} m = 0.385$
$0.385 = 0.52 \times (\frac{2.5}{M} \times \frac{1000}{75})$
$M = 45 g {mol}^{- 1}$

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