Which of the following aqueous solutions has the highest freezing point ?

Options

A. `0.1M" sucrose"`
B. `0.01MNaCl`
C. `0.1MNaCl`
D. `0.01MNa_(2)SO_(4)`

Explanation

To determine which of the given aqueous solutions has the highest freezing point, we need to analyze the freezing point depression (ΔTf) for each solution. The freezing point depression is given by the formula:

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

Where:
- \( \Delta T_f \) = change in freezing point
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( m \) = molality of the solution
- \( K_f \) = freezing point depression constant (specific to the solvent, which is water in this case)

Since we are interested in the freezing point, a higher \( \Delta T_f \) means a lower freezing point. Therefore, we want to find the solution with the lowest \( i \cdot m \) value, as this will correspond to the smallest depression in freezing point and thus the highest freezing point.

### Step-by-Step Solution:

1. **Identify the Solutions**:
- Solution 1: 0.1 M Sucrose (non-electrolyte)
- Solution 2: 0.01 M NaCl (strong electrolyte)
- Solution 3: 0.1 M NaCl (strong electrolyte)
- Solution 4: 0.01 M Na₂SO₄ (strong electrolyte)

2. **Calculate \( i \) for Each Solution**:
- **Solution 1 (Sucrose)**:
- \( i = 1 \) (does not dissociate)
- **Solution 2 (NaCl)**:
- \( i = 2 \) (dissociates into Na⁺ and Cl⁻)
- **Solution 3 (NaCl)**:
- \( i = 2 \) (same as above)
- **Solution 4 (Na₂SO₄)**:
- \( i = 3 \) (dissociates into 2 Na⁺ and SO₄²⁻)

3. **Calculate \( i \cdot m \) for Each Solution**:
- **Solution 1**:
\[ i \cdot m = 1 \cdot 0.1 = 0.1 \]
- **Solution 2**:
\[ i \cdot m = 2 \cdot 0.01 = 0.02 \]
- **Solution 3**:
\[ i \cdot m = 2 \cdot 0.1 = 0.2 \]
- **Solution 4**:
\[ i \cdot m = 3 \cdot 0.01 = 0.03 \]

4. **Compare \( i \cdot m \) Values**:
- Solution 1: 0.1
- Solution 2: 0.02
- Solution 3: 0.2
- Solution 4: 0.03

5. **Determine the Highest Freezing Point**:
- The lowest \( i \cdot m \) value corresponds to the highest freezing point.
- The lowest value is from Solution 2 (0.02), which means it has the highest freezing point.

### Conclusion:
The aqueous solution with the highest freezing point is **0.01 M NaCl**.

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