The depression of freezing points of `0.05` molal aqueous solution of the following compounds are measured.
`1. `NaCl` 2. `K_(2)SO_(4)` 3. `C_(6)H_(12)O_(6)` 4. `Al_(2)(SO_(4))_(3)`
Which one of the above compounds will exhibit the maximum depression of freezing point ?

Options

A. 3
B. 2
C. 4
D. 1

Explanation

To determine which compound exhibits the maximum depression of freezing point, we will use the concept of colligative properties, specifically the depression of freezing point, which is influenced by the number of particles (ions or molecules) in solution.

### Step-by-Step Solution:

1. **Understanding Colligative Properties**:
- Colligative properties depend on the number of solute particles in a solution rather than the identity of the solute. The depression of freezing point (ΔTf) is directly proportional to the number of solute particles.

2. **Formula for Depression of Freezing Point**:
- The formula for depression of freezing point is given by:
\[ \Delta T_f = i \cdot K_f \cdot m \]
- Where:
- \( \Delta T_f \) = depression of freezing point
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( K_f \) = freezing point depression constant (for water, it is a constant)
- \( m \) = molality of the solution

3. **Calculate the van 't Hoff Factor (i)**:
- **For NaCl**:
- NaCl dissociates into Na⁺ and Cl⁻.
- \( i = 2 \)
- **For K₂SO₄**:
- K₂SO₄ dissociates into 2K⁺ and SO₄²⁻.
- \( i = 3 \)
- **For C₆H₁₂O₆ (Glucose)**:
- Glucose does not dissociate in solution.
- \( i = 1 \)
- **For Al₂(SO₄)₃**:
- Al₂(SO₄)₃ dissociates into 2Al³⁺ and 3SO₄²⁻.
- \( i = 5 \)

4. **Comparing the van 't Hoff Factors**:
- Now we compare the values of \( i \) for each compound:
- NaCl: \( i = 2 \)
- K₂SO₄: \( i = 3 \)
- C₆H₁₂O₆: \( i = 1 \)
- Al₂(SO₄)₃: \( i = 5 \)

5. **Conclusion**:
- The compound with the highest van 't Hoff factor will exhibit the maximum depression of freezing point. Here, Al₂(SO₄)₃ has the highest \( i \) value of 5.
- Therefore, **Al₂(SO₄)₃ will exhibit the maximum depression of freezing point**.

### Final Answer:
**Al₂(SO₄)₃** will exhibit the maximum depression of freezing point.

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