$\displaystyle 18$ g of a non-volatile solute is dissolved in $\displaystyle 200$ g of $\displaystyle \mathrm{H}_{2} \mathrm{O}$ freezes at $\displaystyle 272.07$ K. Calculate the molecular mass of solute ( $\displaystyle \mathrm{K}_{\mathrm{f}}$ for water $\displaystyle =1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ ) $\displaystyle 2$

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