Statement (I): Molal depression constant is given by where symbols have their usual meaning. Statement (II): for benzene is less than the for water. [2025]

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Solution

Q.
Given below are two statements : [2025]

Statement (I): Molal depression constant $K_{f}$ is given by $\frac{M_{1} R T_{f}}{Δ S_{fus}},$ where symbols have their usual meaning.

Statement (II): $K_{f}$ for benzene is less than the $K_{f}$ for water.

In the light of the above statements, choose the most appropriate answer from the options given below:

1 Statement I is incorrect but Statement II is correct

2 Both Statement I and Statement II are incorrect

3 Both Statement I and Statement II are correct

4 Statement I is correct but Statement II is incorrect

Ans.
(4)

Statement I: Molal depression constant $(k_{f})$ = $= \frac{M_{1} R {(T_{f} °)}^{2}}{Δ H_{fus}},$ where $M_{1}$ is molar mass of solvent, R is gas constant, $T_{f} °$ is freezing point of solvent, $Δ H_{fus}$ is molar enthalpy of fusion of solvent.

$k_{f} = \frac{M_{1} R {(T_{f} °)}^{2}}{Δ H_{fus}} = \frac{M_{1} R T_{f} °}{Δ H_{fus} / T_{f} °} = \frac{M_{1} R T_{f} °}{Δ S_{fus}}$

Statement II:

$k_{f} (benzene) = 5.12 K kg/mol$

$k_{f} (water) = 1.86 K kg/mol$

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