Q22 / 75 · JEE Main 2025 (4 Apr Shift 2) · Chemistry

Given below are two statements :
Statement (I) : Molal depression constant $\mathrm{K}_{\mathrm{f}}$ is given by $\frac{M_1 R T_f}{\Delta S_{f u s}}$, where symbols have their usual meaning.
Statement (II) : $\mathrm{K}_{\mathrm{f}}$ for benzene is less than the $\mathrm{K}_{\mathrm{f}}$ for water.
In the light of the above statements, choose the most appropriate answer from the options given below :

  • A
    Statement I is incorrect but Statement II is correct
  • B
    Both Statement I and Statement II are incorrect
  • C
    Both Statement I and Statement II are correct
  • Correct answer
    D
    Statement I is correct but Statement II is incorrect

Solution

Statement-I
Molar depression constant $\mathrm{k}_f=\frac{\mathrm{M}_1 \mathrm{RT}_{\mathrm{f}}^2}{\Delta \mathrm{H}_{\text {fus }}}$
$\begin{aligned}<br />& \mathrm{k}_f=\frac{\mathrm{M}_1 \mathrm{RT}_{\mathrm{f}}}{\left[\frac{\Delta \mathrm{H}_{\text {fus }}}{\mathrm{T}_{\mathrm{f}}}\right]} \\<br>& \mathrm{k}_f=\frac{\mathrm{M}_1 \mathrm{RT}_f}{\Delta \mathrm{~S}_{\text {fus }}}<br />\end{aligned}$
Hence statement-I is correct
$\text { but } \mathrm{k}_{\mathrm{f}} \text { for benzene }=5.12 \frac{{ }^{\circ} \mathrm{C}}{\mathrm{molal}}$
$\mathrm{k}_{\mathrm{f}}$ for water $=1.86 \frac{{ }^{\circ} \mathrm{C}}{\text { molal }}$ Hence statement- II is incorrect

Hence, the correct answer is option: 'D'.

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