Which of the following solutions `(1 molal)` will have the maximum freezing point, assuming equal ionization in each case?

Options

A. `[Fe(H_(2)O)_(6)Cl]Cl_(3)`
B. `[Fe(H_(2)O)_(5)Cl]Cl_(2).H_(2)O`
C. `[Fe(H_(2)O)_(4)Cl_(2)]Cl.2H_(2)O`
D. `[Fe(H_(2)O)_(3)Cl_(3)].3H_(2)O`

Answer

To determine which of the given 1 molal solutions will have the maximum freezing point, we need to analyze the van 't Hoff factor (I) for each solution. The van 't Hoff factor represents the number of particles the solute dissociates into when dissolved in a solvent. The relationship between the freezing point depression (ΔTf) and the van 't Hoff factor is given by the formula:

\[ \Delta Tf = K_f \cdot m \cdot I \]

Where:
- ΔTf is the depression in freezing point.
- Kf is the cryoscopic constant (a property of the solvent).
- m is the molality of the solution.
- I is the van 't Hoff factor.

Since we are looking for the maximum freezing point of the solution, we need to find the solution with the smallest ΔTf, which corresponds to the smallest van 't Hoff factor (I).

### Step-by-step Solution:

1. **Identify the Solutions and Their Ionization**:
- **Solution A**: Fe(H2O)6Cl3
- Dissociates into 1 Fe(H2O)6^3+ and 3 Cl^− ions.
- Total particles (I) = 1 + 3 = 4.
- **Solution B**: Fe(H2O)5Cl2
- Dissociates into 1 Fe(H2O)5^2+ and 2 Cl^− ions.
- Total particles (I) = 1 + 2 = 3.
- **Solution C**: Fe(H2O)4Cl2
- Dissociates into 1 Fe(H2O)4^2+ and 2 Cl^− ions.
- Total particles (I) = 1 + 2 = 3.
- **Solution D**: Fe(H2O)3Cl3
- Dissociates into 1 Fe(H2O)3^3+ and 3 Cl^− ions.
- Total particles (I) = 1 + 3 = 4.

2. **Calculate the van 't Hoff Factor (I)**:
- For **Solution A**: I = 4
- For **Solution B**: I = 3
- For **Solution C**: I = 3
- For **Solution D**: I = 4

3. **Determine the Solution with the Lowest van 't Hoff Factor**:
- The solutions with the lowest I value will have the least freezing point depression (ΔTf).
- Solutions B and C both have I = 3, which is the lowest among the options.

4. **Conclusion**:
- Since both Solutions B and C have the same van 't Hoff factor, they will have the same freezing point. However, they have a higher freezing point than Solutions A and D, which have I = 4.
- Therefore, the solutions with the maximum freezing point are Solutions B (Fe(H2O)5Cl2) and C (Fe(H2O)4Cl2).

### Final Answer:
The solutions with the maximum freezing point are **Fe(H2O)5Cl2** and **Fe(H2O)4Cl2**.