Which one of the following aqueous solution has the highest freezing point at 1 atm:

Options

A. `0.1M `urea
B. `0.1M` acetic acid
C. `0.1M NaCI`
D. `0.1M BaCI_(2)`

Explanation

To determine which aqueous solution has the highest freezing point at 1 atm, we can use the concept of freezing point depression, which is given by the formula:

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

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

Since the question involves comparing different solutions, we can assume that the molality (\(m\)) and the \(K_f\) value for water (the solvent) are constant for all solutions. Therefore, the depression in freezing point (\(\Delta T_f\)) will depend primarily on the Van't Hoff factor (\(i\)).

### Step-by-Step Solution:

1. **Identify the solutes and their properties:**
- **Urea (NH₂CONH₂)**: A non-electrolyte, does not dissociate in solution. Thus, \(i = 1\).
- **Acetic Acid (CH₃COOH)**: A weak electrolyte, partially dissociates in solution. The value of \(i\) is between 1 and 2 (approximately \(i \approx 1.2\)).
- **Sodium Chloride (NaCl)**: A strong electrolyte, dissociates completely into 2 ions (Na⁺ and Cl⁻). Thus, \(i = 2\).
- **Barium Chloride (BaCl₂)**: A strong electrolyte, dissociates completely into 3 ions (Ba²⁺ and 2 Cl⁻). Thus, \(i = 3\).

2. **Compare the Van't Hoff factors (\(i\)):**
- Urea: \(i = 1\)
- Acetic Acid: \(i \approx 1.2\)
- Sodium Chloride: \(i = 2\)
- Barium Chloride: \(i = 3\)

3. **Determine the effect on freezing point:**
- The higher the value of \(i\), the greater the depression in freezing point (\(\Delta T_f\)).
- Therefore, the solution with the lowest \(i\) will have the highest freezing point.

4. **Conclusion:**
- Since urea has the lowest \(i\) value (1), it will have the highest freezing point among the given solutions.

### Final Answer:
**Urea (NH₂CONH₂) has the highest freezing point at 1 atm.**