Which one of the following aqueous solutions will have the lowest freezing point ?

Options

A. 0.1 molal solution of urea
B. 0.1 molal solution of acetic acid
C. 0.1 molal solution of sodium chloride
D. 0.1 molal solution of calcium chloride

Explanation

To determine which aqueous solution has the lowest freezing point, we can use the formula for freezing point depression:

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

Where:
- \(\Delta T_f\) = freezing point depression
- \(K_f\) = freezing point depression constant (specific to the solvent)
- \(m\) = molality of the solution
- \(i\) = van 't Hoff factor (number of particles the solute breaks into)

### Step-by-Step Solution:

1. **Identify the given solutions**:
We need to compare the freezing points of the following solutions:
- Urea (non-electrolyte)
- Acetic acid (weak electrolyte)
- Sodium chloride (strong electrolyte)
- Calcium chloride (strong electrolyte)

2. **Determine the van 't Hoff factor (i)**:
- Urea: Since it does not dissociate in solution, \(i = 1\).
- Acetic acid: It partially dissociates, but for simplicity, we can approximate \(i \approx 1.2\) (as it is a weak acid).
- Sodium chloride (NaCl): It dissociates into two ions (Na\(^+\) and Cl\(^-\)), so \(i = 2\).
- Calcium chloride (CaCl\(_2\)): It dissociates into three ions (Ca\(^{2+}\) and 2 Cl\(^-\)), so \(i = 3\).

3. **Calculate the freezing point depression for each solution**:
Since all solutions have the same molality (0.1 molal) and \(K_f\) is constant for water, we can focus on the \(i\) values:
- Urea: \(\Delta T_f = K_f \cdot 0.1 \cdot 1\)
- Acetic acid: \(\Delta T_f = K_f \cdot 0.1 \cdot 1.2\)
- Sodium chloride: \(\Delta T_f = K_f \cdot 0.1 \cdot 2\)
- Calcium chloride: \(\Delta T_f = K_f \cdot 0.1 \cdot 3\)

4. **Compare the freezing point depressions**:
The freezing point depression is directly proportional to \(i\):
- Urea: \(\Delta T_f = K_f \cdot 0.1 \cdot 1\)
- Acetic acid: \(\Delta T_f = K_f \cdot 0.1 \cdot 1.2\)
- Sodium chloride: \(\Delta T_f = K_f \cdot 0.1 \cdot 2\)
- Calcium chloride: \(\Delta T_f = K_f \cdot 0.1 \cdot 3\)

The highest value of \(i\) corresponds to the greatest freezing point depression.

5. **Conclusion**:
Since calcium chloride has the highest \(i\) value (3), it will produce the greatest freezing point depression, leading to the lowest freezing point of the solution.

Thus, the aqueous solution with the lowest freezing point is **Calcium Chloride**.