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A solvent freezes at $17^{\circ} \mathrm{C}$ and it has latent heat of fusion $180 \mathrm{~J} \mathrm{~g}^{-1}$. The molal depression constant of the solvent is [units of $\mathrm{K}_{\mathrm{f}}=\mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}$ ]
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3.88
$\begin{aligned} & \mathrm{K}_{\mathrm{f}}=\frac{\mathrm{RT}_{\mathrm{f}}^2 \mathrm{M}_1}{1000 \Delta \mathrm{H}_{\mathrm{f}}} ; \Delta \mathrm{H}_{\mathrm{f}}=\text { latent heat of fusion }=180 \mathrm{~J} / \mathrm{g} \\ & =\frac{8.314 \times(290)^2 \times 1}{1000 \times 180} \mathrm{~T}_{\mathrm{f}}=\text { Freezing temperature }=290 \mathrm{~K} \\ & =3.88 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}-1 \mathrm{M}_1=\text { concentration }=1(\mathrm{M}) \\ & \text { (considering) }\end{aligned}$
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