Which of the following aqueous molal solution have highest freezing point

Options

A. Urea
B. Barium chloride
C. Potassium bromide
D. Alluminimum sulphate

Explanation

To determine which of the following aqueous molal solutions has the highest freezing point, we need to analyze the freezing point depression (ΔTf) for each solution. The freezing point depression can be calculated using the formula:

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

Where:
- \( Kf \) is the cryoscopic constant (a property of the solvent, which remains constant for all solutions in this case).
- \( m \) is the molality of the solution (which is the same for all options).
- \( i \) is the van 't Hoff factor, which represents the number of particles the solute breaks into when dissolved.

Since \( Kf \) and \( m \) are constant for all solutions, the freezing point depression will depend solely on the value of \( i \). The lower the value of \( i \), the smaller the freezing point depression, and thus the higher the freezing point of the solution.

### Step-by-Step Solution:

1. **Identify the solutes and their dissociation**:
- **Option A**: Urea (NH₂CONH₂) - does not dissociate, so \( i = 1 \).
- **Option B**: Barium chloride (BaCl₂) - dissociates into \( Ba^{2+} \) and \( 2Cl^{-} \), so \( i = 3 \).
- **Option C**: Potassium bromide (KBr) - dissociates into \( K^{+} \) and \( Br^{-} \), so \( i = 2 \).
- **Option D**: Aluminum sulfate \((Al_2(SO_4)_3)\) - dissociates into \( 2Al^{3+} \) and \( 3SO_4^{2-} \), so \( i = 5 \).

2. **Calculate the van 't Hoff factor (i)**:
- For Urea: \( i = 1 \)
- For Barium Chloride: \( i = 3 \)
- For Potassium Bromide: \( i = 2 \)
- For Aluminum Sulfate: \( i = 5 \)

3. **Determine the freezing point depression**:
- The freezing point depression is directly proportional to \( i \). Therefore, the solution with the lowest \( i \) will have the highest freezing point.
- Urea has the lowest \( i \) value of 1.

4. **Conclusion**:
- Since Urea has the lowest van 't Hoff factor, it will result in the least freezing point depression, meaning it has the highest freezing point among the options provided.

### Final Answer:
**Option A (Urea) has the highest freezing point.**