Statement I: 0.1 m aqueous solution of glucose has higher depression in freezing point than 0.1 m aqueous solution of urea.

Statement II: k_f has the same value in both.

If Statement I is INCORRECT, but Statement II is CORRECT

Statement I: 0.1 m aqueous solution of glucose has higher depression in freezing point than 0.1 m aqueous solution of urea.

This statement is incorrect. The depression in the freezing point of a solution is directly proportional to the molality of the solute. Glucose has a higher molecular mass than urea, so a 0.1 m aqueous solution of glucose will have a higher molality than a 0.1 m aqueous solution of urea. However, the molality is not the only factor that affects depression in the freezing point. The other factor is the freezing point depression constant, which is different for different solvents. The freezing point depression constant for water is 1.86 K kg/mol. This means that the depression in the freezing point of a solution will be different for different solvents, even if the molality of the solute is the same.

Statement II: \(\) has same value in both.

This statement is correct. The freezing point depression constant is a property of the solvent, and it does not depend on the solute. Therefore, the freezing point depression constant will be the same for 0.1 m aqueous solution of glucose and 0.1 m aqueous solution of urea.

Therefore, Statement I is incorrect, but Statement II is correct.

Here is a table summarizing the two statements: