A solution of nonvolatile solute is obtained by dissolving $1 \mathrm{~g}$ in $100 \mathrm{~g}$ solvent,…

A solution of nonvolatile solute is obtained by dissolving $1 \mathrm{~g}$ in $100 \mathrm{~g}$ solvent, decreases its freezing point by $0.3 \mathrm{~K}$. Calculate cryoscopic constant of solvent if molar mass of solute is $60 \mathrm{~g} \mathrm{~mol}^{-1}$.
  1. $1.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  2. $1.4 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  3. $2.4 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  4. $1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \Delta \mathrm{T}_{\mathrm{f}} & =\frac{1000 \mathrm{~K}_{\mathrm{f}} \mathrm{W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \\ \therefore \quad \mathrm{K}_{\mathrm{f}} & =\frac{\Delta \mathrm{T}_{\mathrm{f}} \mathrm{M}_2 \mathrm{~W}_1}{1000 \mathrm{~W}_2} \\ & =\frac{0.3 \mathrm{~K} \times 60 \mathrm{~g} \mathrm{~mol}^{-1} \times 100 \mathrm{~g}}{1000 \times 1 \mathrm{~g}} \\ & =1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2023 (09 May Shift 2)

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