For 1 molal solution of each compound minimum freezing point will be assuming compound ionisation in each case :
(a)`[Fe(H_(2)O)_(6)]Cl_(3)`
(b)`[Fe(H_(2)O)_(5)Cl]Cl_(2) . H_(2)O`
(c)`[Fe(H_(2)O)_(4)Cl_(2)]Cl .2 H_(2)O`
(d)`[Fe(H_(2)O)_(3)Cl_(3)] .3 H_(2)O`

Options

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

Answer

To determine the minimum freezing point of 1 molal solutions of each compound, we will analyze the ionization of each compound and calculate the van 't Hoff factor (i) for each. The freezing point depression is directly proportional to the van 't Hoff factor, so the compound with the highest i value will have the lowest freezing point.

### Step-by-Step Solution:

1. **Identify the Compounds and Their Ionization:**
- (a) `[Fe(H₂O)₆]Cl₃`
- (b) `[Fe(H₂O)₅Cl]Cl₂ . H₂O`
- (c) `[Fe(H₂O)₄Cl₂]Cl . 2 H₂O`
- (d) `[Fe(H₂O)₃Cl₃] . 3 H₂O`

2. **Calculate the van 't Hoff factor (i) for each compound:**
- **(a) `[Fe(H₂O)₆]Cl₃`:**
- Ionization: 1 `[Fe(H₂O)₆]³⁺` and 3 `Cl⁻` ions.
- Total ions = 1 + 3 = 4.
- Therefore, i = 4.

- **(b) `[Fe(H₂O)₅Cl]Cl₂ . H₂O`:**
- Ionization: 1 `[Fe(H₂O)₅Cl]²⁺` and 2 `Cl⁻` ions.
- Total ions = 1 + 2 = 3.
- Therefore, i = 3.

- **(c) `[Fe(H₂O)₄Cl₂]Cl . 2 H₂O`:**
- Ionization: 1 `[Fe(H₂O)₄Cl₂]⁺` and 1 `Cl⁻` ion.
- Total ions = 1 + 1 = 2.
- Therefore, i = 2.

- **(d) `[Fe(H₂O)₃Cl₃] . 3 H₂O`:**
- Ionization: 1 `[Fe(H₂O)₃]³⁺` and 3 `Cl⁻` ions.
- Total ions = 1 + 3 = 4.
- Therefore, i = 4.

3. **Determine the freezing point depression (ΔTf):**
- The freezing point depression is given by the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
- Since we are considering 1 molal solutions and the Kf value is constant for all solutions, we can conclude that ΔTf is directly proportional to i.

4. **Compare the i values:**
- For (a) and (d), i = 4 (maximum).
- For (b), i = 3.
- For (c), i = 2 (minimum).

5. **Conclusion:**
- The compounds with the highest van 't Hoff factor (i) will have the lowest freezing point due to maximum depression in freezing point.
- Therefore, both compounds (a) `[Fe(H₂O)₆]Cl₃` and (d) `[Fe(H₂O)₃Cl₃] . 3 H₂O` will have the minimum freezing point, but since we need to choose one, we can state that either could be considered correct based on the highest ionization.

### Final Answer:
The minimum freezing point will be for the compounds:
- (a) `[Fe(H₂O)₆]Cl₃` or (d) `[Fe(H₂O)₃Cl₃] . 3 H₂O` (both have i = 4).