`0.2` molal solution each of glucose (I) , magnesium chloride (II) and Aluminium sulphate (III) is taken . The correct order freezing point of the solutions will be :

Options

A. all same
B. `("freezing point")_(I) lt ("freezing point")_(II) lt ("freezing point")_(III)`
C. `("freezing point")_(III) lt ("freezing point")_(I) lt ("freezing point")_(II)`
D. `("freezing point")_(I) gt ("freezing point")_(II) gt ("freezing point")_(III)`

Answer

To determine the correct order of the freezing points of the given solutions, we need to consider the van 't Hoff factor (i) for each solute, which indicates the number of particles the solute dissociates into when dissolved in a solvent. The freezing point depression (ΔTf) is given by the formula:

\[ \Delta T_f = i \cdot K_f \cdot m \]

Where:
- \( \Delta T_f \) = depression in freezing point
- \( i \) = van 't Hoff factor
- \( K_f \) = cryoscopic constant (depends on the solvent, usually water)
- \( m \) = molality of the solution

### Step-by-Step Solution:

1. **Identify the van 't Hoff factor (i) for each solute:**
- For **Glucose (C6H12O6)**: It does not dissociate in solution, so \( i = 1 \).
- For **Magnesium Chloride (MgCl2)**: It dissociates into 3 ions (1 Mg²⁺ and 2 Cl⁻), so \( i = 3 \).
- For **Aluminium Sulfate (Al2(SO4)3)**: It dissociates into 5 ions (2 Al³⁺ and 3 SO₄²⁻), so \( i = 5 \).

2. **Calculate the freezing point depression for each solution:**
- For **Glucose**:
\[ \Delta T_f = 1 \cdot K_f \cdot 0.2 \]
- For **Magnesium Chloride**:
\[ \Delta T_f = 3 \cdot K_f \cdot 0.2 \]
- For **Aluminium Sulfate**:
\[ \Delta T_f = 5 \cdot K_f \cdot 0.2 \]

3. **Determine the order of freezing point depression:**
- The greater the value of \( i \), the greater the freezing point depression.
- Therefore:
- Glucose has the least depression (i = 1).
- Magnesium Chloride has a moderate depression (i = 3).
- Aluminium Sulfate has the greatest depression (i = 5).

4. **Order the freezing points based on depression:**
- The solution with the least depression (highest freezing point) is Glucose.
- The next is Magnesium Chloride.
- The solution with the greatest depression (lowest freezing point) is Aluminium Sulfate.

5. **Final Order of Freezing Points:**
- **Glucose > Magnesium Chloride > Aluminium Sulfate**

### Conclusion:
The correct order of freezing points for the solutions is:
\[ \text{Glucose} > \text{Magnesium Chloride} > \text{Aluminium Sulfate} \]