Which of the following aqueous solutions will have the minimum freezing point ?

Options

A. 0.1 m `FeCl_(3)`
B. 0.1 m `BaCl_(2)`
C. 0.1 m NaCl
D. 0.1 m Urea

Explanation

To determine which of the given aqueous solutions will have the minimum freezing point, we can use the concept of freezing point depression. The freezing point depression is given by the formula:

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

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

### Step 1: Identify the Van't Hoff factor for each solute.

1. **For FeCl3**:
- Dissociates into: \(Fe^{3+} + 3Cl^{-}\)
- Total particles = 1 (Fe) + 3 (Cl) = 4
- Therefore, \(i = 4\).

2. **For BaCl2**:
- Dissociates into: \(Ba^{2+} + 2Cl^{-}\)
- Total particles = 1 (Ba) + 2 (Cl) = 3
- Therefore, \(i = 3\).

3. **For NaCl**:
- Dissociates into: \(Na^{+} + Cl^{-}\)
- Total particles = 1 (Na) + 1 (Cl) = 2
- Therefore, \(i = 2\).

4. **For Urea (NH2CONH2)**:
- Urea does not dissociate in solution.
- Total particles = 1
- Therefore, \(i = 1\).

### Step 2: Calculate the depression in freezing point for each solution.

Since the molality \(m\) is the same (0.1M) for all solutions, and \(K_f\) is constant for water, we can compare the values of \(i\) directly to determine which solution has the greatest depression in freezing point.

- **FeCl3**: \(i = 4\)
- **BaCl2**: \(i = 3\)
- **NaCl**: \(i = 2\)
- **Urea**: \(i = 1\)

### Step 3: Determine which solution has the maximum depression in freezing point.

The greater the value of \(i\), the greater the depression in freezing point \(\Delta T_f\). Thus, the order of depression in freezing point from highest to lowest is:

1. **FeCl3** (i = 4)
2. **BaCl2** (i = 3)
3. **NaCl** (i = 2)
4. **Urea** (i = 1)

### Conclusion:

The solution with the minimum freezing point is the one with the highest Van't Hoff factor, which is **0.1M FeCl3**.

### Final Answer:
**0.1M FeCl3 will have the minimum freezing point.**

---