JEE MAIN - Chemistry (2025 - 4th April Evening Shift - No. 7)
Given below are two statements:
Statement (I) : Molal depression constant $\mathrm{K}_f$ is given by $\frac{\mathrm{M}_1 \mathrm{RT}_f}{\Delta \mathrm{~S}_{\mathrm{fus}}}$, where symbols have their usual meaning.
Statement (II) : $\mathrm{K}_f$ for benzene is less than the $\mathrm{K}_f$ for water.
In the light of the above statements, choose the most appropriate answer from the options given below :
Explanation
Statement-I
Molar depression constant $\mathrm{k}_f=\frac{\mathrm{M}_1 \mathrm{RT}_f^2}{\Delta \mathrm{H}_{\text {fus }}}$
$$\begin{aligned} & \mathrm{k}_f=\frac{\mathrm{M}_1 \mathrm{RT}_{\mathrm{f}}}{\left[\frac{\Delta \mathrm{H}_{\mathrm{fus}}}{\mathrm{~T}_{\mathrm{f}}}\right]} \\ & \mathrm{k}_f=\frac{\mathrm{M}_1 \mathrm{RT}_f}{\Delta \mathrm{~S}_{\text {fus }}} \end{aligned}$$
Hence statement-I is correct
but $\mathrm{k}_{\mathrm{f}}$ for benzene $=5.12 \frac{{ }^{\circ} \mathrm{C}}{\text { molal }}$
$\mathrm{k}_{\mathrm{f}}$ for water $=1.86 \frac{{ }^{\circ} \mathrm{C}}{\text { molal }}$ Hence statement- II is incorrect
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