18 g of a non-volatile solute is dissolved in 200 g of H_2 O freezes at 272.07 K. Calculate the molecular mass of solute ( K_f for water =1.86 K kg…

\[\begin{aligned} & \Delta \mathrm{T}_{\mathrm{f}}=\mathrm{K}_{\mathrm{f}} \mathrm{~m} \\ & \mathrm{M}_{\mathrm{B}}=\frac{\mathrm{K}_{\mathrm{f}} \times \mathrm{w}_{\mathrm{B}} \times 1000}{\mathrm{w}_{\mathrm{A}} \times \Delta \mathrm{T}_{\mathrm{f}}} \\ & \Delta \mathrm{~T}_{\mathrm{f}}=\mathrm{T}_{\mathrm{f}}^{\mathrm{o}}-\mathrm{T}_{\mathrm{f}} \\ & \Delta \mathrm{~T}_{\mathrm{f}}=273 \cdot 15-272 \cdot 07=1 \cdot 08 \mathrm{~K} \\ & \mathrm{M}_{\mathrm{B}}=\frac{1 \cdot 86 \times 18 \times 1000}{200 \times 1 \cdot 08} \\ & =155 \mathrm{~g} \mathrm{~mol}^{-1} \end{aligned} \]