Which of the following solutions has the minimum freezing point

Options

A. 1 molal NaCl solution
B. 1 molal KCl solution
C. `1 molal CaCl_(2)` solution
D. 1 molal urea solution

Explanation

To determine which solution has the minimum freezing point, we will use the concept of freezing point depression. The freezing point depression can be calculated using the formula:

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

Where:
- \(\Delta T_f\) is the depression in freezing point,
- \(K_f\) is the freezing point depression constant (which is constant for a given solvent),
- \(m\) is the molality of the solution,
- \(i\) is the van 't Hoff factor (the number of particles the solute breaks into when dissolved).

### Step-by-Step Solution:

1. **Identify the Solutions**:
- Solution A: 1 molal NaCl
- Solution B: 1 molal KCl
- Solution C: 1 molal CaCl2
- Solution D: 1 molal Urea

2. **Determine the van 't Hoff Factor (i)**:
- For NaCl: NaCl dissociates into Na\(^+\) and Cl\(^-\), so \(i = 2\).
- For KCl: KCl dissociates into K\(^+\) and Cl\(^-\), so \(i = 2\).
- For CaCl2: CaCl2 dissociates into Ca\(^{2+}\) and 2 Cl\(^-\), so \(i = 3\).
- For Urea: Urea does not dissociate in solution, so \(i = 1\).

3. **Calculate the Effective Molality (m × i)**:
- For NaCl: \(m \cdot i = 1 \cdot 2 = 2\)
- For KCl: \(m \cdot i = 1 \cdot 2 = 2\)
- For CaCl2: \(m \cdot i = 1 \cdot 3 = 3\)
- For Urea: \(m \cdot i = 1 \cdot 1 = 1\)

4. **Compare the Effective Molalities**:
- NaCl: 2
- KCl: 2
- CaCl2: 3
- Urea: 1

5. **Determine the Minimum Freezing Point**:
- The solution with the highest effective molality (m × i) will have the lowest freezing point.
- CaCl2 has the highest effective molality of 3, therefore it will have the minimum freezing point.

### Conclusion:
The solution with the minimum freezing point is **1 molal CaCl2**.

---