Which of the following will have maximum depression in freezing point ?

Options

A. `0.5 M Li_(2)SO_(4)`
B. 1 M KCI
C. `0.5 M BaCI_(2)`
D. `1 M Al_(2)(SO_(4))_(3)`

Explanation

To determine which of the given compounds will have the maximum depression in freezing point, we need to analyze the van 't Hoff factor (I), the cryoscopic constant (Kf), and the molality of each solution. The formula for depression in freezing point (ΔTf) is given by:

\[ \Delta Tf = I \times Kf \times m \]

Where:
- \( \Delta Tf \) = depression in freezing point
- \( I \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( Kf \) = cryoscopic constant (depends on the solvent)
- \( m \) = molality of the solution

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds given are:
- A) \( Li_2SO_4 \)
- B) \( KCl \)
- C) \( BaCl_2 \)
- D) \( Al_2(SO_4)_3 \)

2. **Determine the Van 't Hoff Factor (I)**:
- For \( Li_2SO_4 \):
- Dissociation: \( Li_2SO_4 \rightarrow 2Li^+ + SO_4^{2-} \)
- Total particles = 2 + 1 = 3
- \( I = 3 \)
- For \( KCl \):
- Dissociation: \( KCl \rightarrow K^+ + Cl^- \)
- Total particles = 1 + 1 = 2
- \( I = 2 \)
- For \( BaCl_2 \):
- Dissociation: \( BaCl_2 \rightarrow Ba^{2+} + 2Cl^- \)
- Total particles = 1 + 2 = 3
- \( I = 3 \)
- For \( Al_2(SO_4)_3 \):
- Dissociation: \( Al_2(SO_4)_3 \rightarrow 2Al^{3+} + 3SO_4^{2-} \)
- Total particles = 2 + 3 = 5
- \( I = 5 \)

3. **Calculate the Effective Value of \( I \times m \)**:
- Assuming the molality (m) is the same for all options (let's say \( m = 1 \) for simplicity):
- For \( Li_2SO_4 \): \( I \times m = 3 \times 1 = 3 \)
- For \( KCl \): \( I \times m = 2 \times 1 = 2 \)
- For \( BaCl_2 \): \( I \times m = 3 \times 1 = 3 \)
- For \( Al_2(SO_4)_3 \): \( I \times m = 5 \times 1 = 5 \)

4. **Compare the Values**:
- \( Li_2SO_4 \) = 3
- \( KCl \) = 2
- \( BaCl_2 \) = 3
- \( Al_2(SO_4)_3 \) = 5

5. **Conclusion**:
- The compound with the highest value of \( I \times m \) is \( Al_2(SO_4)_3 \) with a value of 5. Therefore, it will have the maximum depression in freezing point.

### Final Answer:
The compound that will have the maximum depression in freezing point is **D) \( Al_2(SO_4)_3 \)**.