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