Assuming complete ionisation, the solution having maximum freezing point will be:

Options

A. 1 M `CaF_(2)`
B. 1.5 M`Al_(2)(SO_(4))_(3)`
C. 2 M NaCl
D. 1 M `AgNO_(3)`

Answer

To solve the question of which solution has the maximum freezing point assuming complete ionization, we will follow these steps:

### Step 1: Understand the Concept of Freezing Point Depression
The freezing point depression (\( \Delta T_f \)) is given by the formula:
\[ \Delta T_f = K_f \cdot m \cdot i \]
where:
- \( K_f \) is the molal freezing point depression constant (a property of the solvent),
- \( m \) is the molality of the solution,
- \( i \) is the Van't Hoff factor (the number of particles the solute dissociates into).

### Step 2: Relate Freezing Point Depression to Freezing Point
The freezing point of the solution (\( T_f \)) is related to the freezing point of the pure solvent (\( T_f^0 \)) by:
\[ T_f = T_f^0 - \Delta T_f \]
This means that a higher \( \Delta T_f \) results in a lower freezing point of the solution.

### Step 3: Identify the Requirement
To find the solution with the maximum freezing point, we need to minimize \( \Delta T_f \). This can be achieved by minimizing the product \( m \cdot i \).

### Step 4: Calculate \( m \cdot i \) for Each Solution
1. **Calcium Fluoride (CaF₂)**:
- Dissociates into \( Ca^{2+} \) and \( 2F^{-} \) → \( i = 3 \)
- Given \( m = 1 \) molal
- \( m \cdot i = 1 \cdot 3 = 3 \)

2. **Aluminum Sulfate (Al₂(SO₄)₃)**:
- Dissociates into \( 2Al^{3+} \) and \( 3SO₄^{2-} \) → \( i = 5 \)
- Given \( m = 1.5 \) molal
- \( m \cdot i = 1.5 \cdot 5 = 7.5 \)

3. **Sodium Chloride (NaCl)**:
- Dissociates into \( Na^{+} \) and \( Cl^{-} \) → \( i = 2 \)
- Given \( m = 2 \) molal
- \( m \cdot i = 2 \cdot 2 = 4 \)

4. **Silver Nitrate (AgNO₃)**:
- Dissociates into \( Ag^{+} \) and \( NO₃^{-} \) → \( i = 2 \)
- Given \( m = 1 \) molal
- \( m \cdot i = 1 \cdot 2 = 2 \)

### Step 5: Compare the Products
Now, we compare the values of \( m \cdot i \):
- CaF₂: \( 3 \)
- Al₂(SO₄)₃: \( 7.5 \)
- NaCl: \( 4 \)
- AgNO₃: \( 2 \)

### Step 6: Determine the Solution with Maximum Freezing Point
The solution with the lowest product \( m \cdot i \) is AgNO₃ with a value of \( 2 \). Therefore, it will have the maximum freezing point.

### Final Answer
The solution with the maximum freezing point is **1 molar AgNO₃**.

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