The two isomers X and Y with the formula `Cr(H_(2)O)_(5)CIBr_(2)` were taken for experiment on depression in freezing point. It was found that one mole of X gave depression corresponding to 2 moles of particles and one mole of Y gave depression due to 3 moles of particels . The structural formulae of x and Y respectively are

Options

A. ` [Cr(H_(2)O)_(5)CI]Br_(2) , [Cr(H_(2)O)_(4)Br_(2)] CI.H_(2)O`
B. `[Cr(H_(2)O)_(5)CI]Br_(2),[Cr(H_(2)O)_(3)CIBr_(2)].2H_(2)O`
C. `[Cr(H_(2)O)_(5)Br]BrCI , [Cr(H_(2)O)_(4)CIBr] Br.H_(2)O`
D. `[Cr(H_(2)O)_(4)Br_(2)]CI.H_(2)O , [Cr(H_(2)O)_(5)CI]Br_(2)`

Answer

To determine the structural formulas of isomers X and Y with the formula `Cr(H₂O)₅ClBr₂`, we need to analyze the information provided regarding their behavior in freezing point depression experiments.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have two isomers, X and Y, both with the formula `Cr(H₂O)₅ClBr₂`.
- Isomer X corresponds to a depression in freezing point that indicates it produces 2 moles of particles when 1 mole is dissolved.
- Isomer Y corresponds to a depression in freezing point that indicates it produces 3 moles of particles when 1 mole is dissolved.

2. **Analyzing Isomer X**:
- Since X produces 2 moles of particles, it suggests that it dissociates into one complex ion and one neutral species.
- A possible structure for X could be: `Cr(H₂O)₄Br₂Cl·H₂O`.
- When this complex ion dissociates, it can be represented as:
\[ [Cr(H₂O)₄Br₂]^+ + H₂O \]
- Here, the complex ion contributes 1 particle, and the water contributes another, leading to a total of 2 particles.

3. **Analyzing Isomer Y**:
- Since Y produces 3 moles of particles, it suggests that it dissociates into one complex ion and two ions.
- A possible structure for Y could be: `Cr(H₂O)₅ClBr₂`.
- When this complex ion dissociates, it can be represented as:
\[ [Cr(H₂O)₅Cl]^2+ + 2Br^- \]
- Here, the complex ion contributes 1 particle, and the two bromide ions contribute 2 more, leading to a total of 3 particles.

4. **Conclusion**:
- The structural formula for isomer X is `Cr(H₂O)₄Br₂Cl·H₂O`.
- The structural formula for isomer Y is `Cr(H₂O)₅ClBr₂`.

### Final Answer:
- Structural formula of X: `Cr(H₂O)₄Br₂Cl·H₂O`
- Structural formula of Y: `Cr(H₂O)₅ClBr₂`