In coparison to a 0.01 M solution of glucose, the depression in freezing point of a 0.01 M `MgCl_(2)` solution is……

Options

A. the same
B. about twice
C. about three times
D. about six times

Explanation

To determine the depression in freezing point of a 0.01 M solution of MgCl₂ in comparison to a 0.01 M solution of glucose, we will use the concept of the van 't Hoff factor (i) and the formula for freezing point depression.

### Step-by-Step Solution:

1. **Understand the Freezing Point Depression Formula**:
The depression in freezing point (ΔTf) is given by the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- ΔTf = depression in freezing point
- i = van 't Hoff factor (number of particles the solute dissociates into)
- Kf = freezing point depression constant (depends on the solvent)
- m = molality of the solution

2. **Determine the van 't Hoff Factor for Glucose**:
Glucose (C₆H₁₂O₆) is a non-electrolyte, meaning it does not dissociate into ions in solution. Therefore, the van 't Hoff factor (i) for glucose is:
\[ i_{\text{glucose}} = 1 \]

3. **Determine the van 't Hoff Factor for MgCl₂**:
Magnesium chloride (MgCl₂) is an electrolyte and dissociates in water into three ions:
\[ \text{MgCl}_2 \rightarrow \text{Mg}^{2+} + 2\text{Cl}^- \]
Therefore, the total number of particles (ions) produced is 3. Hence, the van 't Hoff factor for MgCl₂ is:
\[ i_{\text{MgCl}_2} = 3 \]

4. **Calculate the Depression in Freezing Point for Each Solution**:
Since both solutions have the same molality (0.01 M), we can express the depression in freezing point for both solutions:
- For glucose:
\[ \Delta T_f^{\text{glucose}} = 1 \cdot K_f \cdot 0.01 \]
- For MgCl₂:
\[ \Delta T_f^{\text{MgCl}_2} = 3 \cdot K_f \cdot 0.01 \]

5. **Compare the Depression in Freezing Points**:
The depression in freezing point for the MgCl₂ solution is three times that of the glucose solution:
\[ \Delta T_f^{\text{MgCl}_2} = 3 \cdot \Delta T_f^{\text{glucose}} \]

### Conclusion:
The depression in freezing point of a 0.01 M MgCl₂ solution is **3 times** that of a 0.01 M glucose solution.