Question

Given below are two statements: 
Statement (I): Molal depression constant $ k_f $ is given by $ \frac{M_1 R T_f}{\Delta S_{\text{fus}}} $, where symbols have their usual meaning.
Statement (II): $ k_f $ for benzene is less than the $ k_f $ for water.  
In 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
• D. Statement I is correct but Statement II is incorrect

Hint:

The molal depression constant depends on the solvent. Water has a lower \( k_f \) than benzene, which is why Statement II is incorrect.

Answer 1

The Correct Option is D

To solve this question, we must assess the correctness of both statements in light of the principles of chemistry involved in molal depression constants.

1. Statement (I): Molal depression constant \( k_f \) is given by \( \frac{M_1 R T_f}{\Delta S_{\text{fus}}} \), where:
   • \( M_1 \) = molar mass of the solvent
   • \( R \) = universal gas constant
   • \( T_f \) = freezing point of the pure solvent
   • \( \Delta S_{\text{fus}} \) = entropy change of fusion
2. Statement (II): \( k_f \) for benzene is less than the \( k_f \) for water.
   • Typically, the molal depression constant, \( k_f \), depends on the specific properties of the substance, such as its latent heat of fusion.
   • The \( k_f \) value for water is known to be approximately 1.86 K kg/mol, whereas for benzene, it is about 5.12 K kg/mol. This means the \( k_f \) for benzene is higher, not lower, than that for water.

Now, based on the above evaluation:

• Statement I is indeed correct.
• Statement II is incorrect.

Thus, the most appropriate answer is: Statement I is correct but Statement II is incorrect.

Answer 2

1. Statement I: The formula for the molal depression constant is correctly given by: \[ k_f = \frac{M_1 R T_f}{\Delta S_{\text{fus}}} \] Here, \( M_1 \) represents the molality of the solution, \( R \) is the gas constant, \( T_f \) is the freezing point depression, and \( \Delta S_{\text{fus}} \) is the enthalpy of fusion.
Therefore, Statement I is correct.
2. Statement II: The molal depression constant \( k_f \) for benzene is greater than for water, not less. Specifically, \( k_f \) for water is 1.86 °C/molal and for benzene is 5.12 °C/molal. Hence, Statement II is incorrect.
Thus, the correct answer is (4).