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:
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The molal depression constant depends on the solvent. Water has a lower \( k_f \) than benzene, which is why Statement II is incorrect.
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
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The Correct Option isD
Solution and Explanation
To address this problem, we must evaluate the accuracy of both declarations concerning the chemical principles of molal depression constants.
Declaration (I): The molal depression constant \( k_f \) is calculated using the formula \( \frac{M_1 R T_f}{\Delta S_{\text{fus}}} \), where:
\( M_1 \) signifies the molar mass of the solvent
\( R \) represents the universal gas constant
\( T_f \) denotes the freezing point of the pure solvent
\( \Delta S_{\text{fus}} \) is the entropy change of fusion
Declaration (II): The \( k_f \) for benzene is lower than that for water.
Generally, the molal depression constant, \( k_f \), is contingent upon the unique characteristics of the substance, such as its latent heat of fusion.
The \( k_f \) value for water is approximately 1.86 K kg/mol, while for benzene, it is approximately 5.12 K kg/mol. This indicates that the \( k_f \) for benzene is higher, not lower, than that for water.
Based on this analysis:
Declaration I is accurate.
Declaration II is inaccurate.
Therefore, the most fitting conclusion is: Declaration I is accurate, but Declaration II is inaccurate.
