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:
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:
Show Hint
- Statement I is incorrect but Statement II is correct
- Both Statement I and Statement II are incorrect
- Both Statement I and Statement II are correct
- Statement I is correct but Statement II is incorrect
The Correct Option is D
Approach Solution - 1
To solve this question, we must assess the correctness of both statements in light of the principles of chemistry involved in molal depression constants.
- 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
- 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.
Approach Solution -2
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).
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