Which of the following are coordination isomers of `[Co(NH_(3))_(6)][Cr(CN)_(6)]` ?

Options

A. `[Cr(NH_(3))_(6)][Co(CN)_(6)]`
B. `[Cr(NH_(3))_(4)(CN)_(2)][Co(CN)_(4)(NH_(3))_(2)]`
C. `[Cr(NH_(3))_(3)(CN)_(3)][Co(NH_(3))_(3)(CN)_(3)]`
D. none of these

Answer

To determine the coordination isomers of the complex `[Co(NH₃)₆][Cr(CN)₆]`, we need to understand the concept of coordination isomers. Coordination isomers are compounds that have the same molecular formula but differ in the distribution of ligands around the central metal ions in their respective coordination spheres.

### Step-by-Step Solution:

1. **Identify the Coordination Complexes**:
- The given complex consists of two metal centers: cobalt (Co) and chromium (Cr).
- The cobalt complex is `[Co(NH₃)₆]`, which has 6 ammonia (NH₃) ligands.
- The chromium complex is `[Cr(CN)₆]`, which has 6 cyanide (CN⁻) ligands.

2. **Understand Coordination Isomers**:
- Coordination isomers arise when the ligands can be redistributed between the two metal centers while maintaining the same overall coordination number for each metal.
- In this case, both Co and Cr have a coordination number of 6.

3. **Possible Ligand Redistribution**:
- The ligands can be interchanged between the two metal centers. For example:
- Cobalt can take some cyanide ligands from chromium, and chromium can take some ammonia ligands from cobalt.
- This results in different arrangements of ligands around each metal.

4. **Example of Coordination Isomers**:
- One possible coordination isomer could be `[Co(NH₃)₄(CN)₂][Cr(CN)₄(NH₃)₂]`, where cobalt has 4 ammonia and 2 cyanide ligands, and chromium has 4 cyanide and 2 ammonia ligands.
- Another possible coordination isomer could be `[Co(NH₃)₃(CN)₃][Cr(NH₃)₃(CN)₃]`, where both metals have a mix of ligands.

5. **Eliminate Non-Isomers**:
- If both metal centers have the same distribution of ligands (e.g., both having 3 ammonia and 3 cyanide), they do not qualify as coordination isomers because there is no difference in ligand arrangement.

6. **Conclusion**:
- The coordination isomers of `[Co(NH₃)₆][Cr(CN)₆]` are those where the ligands are distributed differently between the two metal centers. Thus, options that show different arrangements of ligands between cobalt and chromium qualify as coordination isomers.

### Final Answer:
The coordination isomers of `[Co(NH₃)₆][Cr(CN)₆]` are those where the ligands have been redistributed, such as:
- `[Co(NH₃)₄(CN)₂][Cr(CN)₄(NH₃)₂]`
- `[Co(NH₃)₃(CN)₃][Cr(NH₃)₃(CN)₃]`