A solution of sucrose ( molar mass $$ = 342g\,mo{l^{ - 1}}$$   ) has been prepared by dissolving $$68.5\,g$$  of sucrose in $$1000\,g$$  of water. The freezing point of the solution obtained will be $$\left( {{k_f}\,{\text{for water}} = 1.86\,K\,kg\,mo{l^{ - 1}}} \right)$$

Solution :
$$\eqalign{ & {\text{Depression in freezing point,}} \cr & \Delta {T_f} = {k_f} \times m \cr & {\text{where,}}\,m = {\text{molality}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{W_B} \times 1000}}{{{M_B}.{W_A}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{68.5 \times 1000}}{{342 \times 1000}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{68.5}}{{342}} \cr & \Delta {T_f} = 1.86 \times \frac{{68.5}}{{342}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {0.372^ \circ }C \cr & {T_f} = T_F^0 - \Delta {T_f} \cr & \,\,\,\,\,\,\, = 0 - {0.372^ \circ }C \cr & \,\,\,\,\,\,\, = - {0.372^ \circ }C \cr} $$