JEE Chemistry 2025 Question with Solution

Given: Two statements about the molal depression constant $k_f$.

Find: Which option correctly identifies the truth value of Statement (I) and Statement (II).

For Statement (I), the relation given is

$$k_f = \frac{M_1 R T_f}{\Delta S_{\text{fus}}}$$

This matches the stated formula, so Statement (I) is correct.

For Statement (II), compare the known values of $k_f$ for the two solvents:

$$k_f(\text{water}) \approx 1.86 \; \text{K kg mol}^{-1}$$ $$k_f(\text{benzene}) \approx 5.12 \; \text{K kg mol}^{-1}$$

Since the value for benzene is greater than the value for water, the statement "$k_f$ for benzene is less than the $k_f$ for water" is false. Therefore, Statement (II) is incorrect.

Thus, the correct option is D: Statement I is correct but Statement II is incorrect.

Given:

1. Statement (I) gives a formula for $k_f$.
2. Statement (II) compares $k_f$ of benzene and water.

Find: The most appropriate option.

The solution text states that the molal depression constant depends on the solvent.

For Statement (I), the formula provided is

$$k_f = \frac{M_1 R T_f}{\Delta S_{\text{fus}}}$$

Hence, Statement (I) is taken as correct according to the provided solution.

For Statement (II), the given comparison is checked using standard values:

$$k_f(\text{water}) \approx 1.86$$ $$k_f(\text{benzene}) \approx 5.12$$

So benzene has a higher molal depression constant than water. Therefore the statement saying benzene has a lower value is incorrect.

Therefore, the final conclusion is that Statement (I) is correct and Statement (II) is incorrect, so the correct option is D.