`PtCl_(4).6H_(2)O`can exist as hydrated complex `1` molal aq.solution has depression in freezing point of `3.72^(@)C`Assume `100%` ionisation and `K_(f)(H_(2)O=1.86^(@)Cmol^(-1)Kg)` then complex is

Options

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

Answer

To solve the problem, we need to determine the complex formed by `PtCl4.6H2O` based on the given information about the depression in freezing point of a 1 molal aqueous solution.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Depression in freezing point (ΔTf) = 3.72 °C
- Molality (m) = 1 molal
- Freezing point depression constant (Kf) for water = 1.86 °C kg/mol

2. **Use the Freezing Point Depression Formula:**
The formula for freezing point depression is given by:
\[ \Delta T_f = K_f \cdot m \cdot i \]
where:
- ΔTf = depression in freezing point
- Kf = freezing point depression constant
- m = molality of the solution
- i = Van't Hoff factor (number of particles the solute dissociates into)

3. **Rearranging the Formula to Find i:**
Rearranging the formula to solve for the Van't Hoff factor (i):
\[ i = \frac{\Delta T_f}{K_f \cdot m} \]

4. **Substituting the Values:**
Now, substitute the known values into the equation:
\[ i = \frac{3.72}{1.86 \cdot 1} \]
\[ i = \frac{3.72}{1.86} = 2 \]

5. **Interpret the Value of i:**
The value of i = 2 indicates that the complex dissociates into 2 particles in solution.

6. **Identify the Possible Complexes:**
Now, we need to analyze the possible complexes of `PtCl4.6H2O`:
- **Option A:** \( \text{[Pt(H}_2\text{O)}_6]^{4+} + 4 \text{Cl}^- \) → i = 5
- **Option B:** \( \text{[Pt(H}_2\text{O)}_5\text{Cl}]^{+} + 2 \text{Cl}^- \) → i = 3
- **Option C:** \( \text{[Pt(H}_2\text{O)}_3\text{Cl}_3]^{+} + \text{Cl}^- \) → i = 2
- **Option D:** \( \text{[Pt(H}_2\text{O)}_2\text{Cl}_4]^{+} \) → i = 1

7. **Conclusion:**
Since we found that i = 2, the correct complex is the one that dissociates into 2 particles, which corresponds to **Option C**: \( \text{[Pt(H}_2\text{O)}_3\text{Cl}_3]^{+} + \text{Cl}^- \).

### Final Answer:
The complex is **Option C: \( \text{[Pt(H}_2\text{O)}_3\text{Cl}_3]^{+} + \text{Cl}^- \)**.