Assertion (A): `0.1 M` solution of glucose has same increment in freezing point than has `0.1 M` solution of urea.
Reason (R ): `K_(f)` for both has different value.

Options

A. If both `(A)` and `(R )` are correct, and `(R )` is the correct explanation of `(A)`.
B. If both `(A)` and `(R )` are correct, but `(R )` is not the correct explanation of `(A)`.
C. If `(A)` is correct, but `(R )` is incorrect.
D. If `(A)` is correct, but `(R )` is correct.

Explanation

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion (A)
The assertion states that a `0.1 M` solution of glucose has the same increment in freezing point as a `0.1 M` solution of urea.

**Explanation**:
- The freezing point depression (ΔTf) can be calculated using the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \(i\) = van 't Hoff factor (which is 1 for both glucose and urea since they do not dissociate in solution),
- \(K_f\) = freezing point depression constant of the solvent (water in this case),
- \(m\) = molality of the solution.

For both glucose and urea:
- \(i = 1\)
- The molarity (M) is given as `0.1 M`, which can be approximated to molality (m) for dilute solutions.

### Step 2: Calculate ΔTf for Both Solutions
For glucose:
\[ \Delta T_f (\text{glucose}) = 1 \cdot K_f \cdot 0.1 \]

For urea:
\[ \Delta T_f (\text{urea}) = 1 \cdot K_f \cdot 0.1 \]

Since both calculations yield the same result, we conclude:
\[ \Delta T_f (\text{glucose}) = \Delta T_f (\text{urea}) \]
Thus, the assertion (A) is **true**.

### Step 3: Understand the Reason (R)
The reason states that \(K_f\) for both solutions has different values.

**Explanation**:
- The freezing point depression constant \(K_f\) depends on the solvent, not the solute. Since both solutions are in the same solvent (water), \(K_f\) will be the same for both solutions.

### Step 4: Conclusion on Reason (R)
Since the reason (R) claims that \(K_f\) values are different for glucose and urea, which is incorrect because they are both in the same solvent (water), we conclude that the reason (R) is **false**.

### Final Answer
- Assertion (A) is **true**.
- Reason (R) is **false**.

Thus, the correct option is **C**: Assertion A is correct, but Reason R is incorrect.

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