Which one of the following complexes will have six isomers ?

Options

A. `[Co(en)NH_(3)Cl_(2)]Cl`
B. `[Cr(PPh_(3))_(2)(H_(2)O)_(2)Cl_(2)]Cl `
C. `[Co(o x)_(3)]^(3-)`
D. `[Co(en)_(2)Br]Cl`

Answer

To determine which complex has six isomers, we need to analyze the coordination compounds based on their ligands and geometrical arrangements. The key is to identify the type of complex and the arrangement of its ligands.

### Step-by-Step Solution:

1. **Identify the Type of Complex**:
We are looking for a complex of the type \( MA_2B_2C_2 \), where M is the metal center and A, B, C are different ligands.

2. **Understanding Isomerism**:
- **Geometrical Isomers**: These arise from different arrangements of ligands around the metal center. For a complex with two pairs of identical ligands, geometrical isomers can be cis (same side) or trans (opposite sides).
- **Optical Isomers**: These are non-superimposable mirror images, which occur when the arrangement of ligands creates chirality.

3. **Counting Geometrical Isomers**:
For the complex \( MA_2B_2C_2 \):
- **Trans Isomers**: There are three types of trans isomers:
- \( A \) trans (A ligands opposite each other)
- \( B \) trans (B ligands opposite each other)
- \( C \) trans (C ligands opposite each other)
- **Cis Isomers**: There are two types of cis isomers:
- All ligands are cis to each other (all A, B, and C are adjacent).
- One pair of ligands is cis while the other pair is trans.

4. **Identifying Optical Isomers**:
- The all-cis arrangement \( (A, A, B, B, C, C) \) can lead to optical isomers because it creates a chiral environment.
- Therefore, the all-cis form has two optical isomers.

5. **Total Count of Isomers**:
- We have 3 trans isomers + 2 cis isomers + 1 all-cis isomer (which has 2 optical forms) = 6 isomers in total.

6. **Conclusion**:
The complex that fits this description and has six isomers is of the type \( MA_2B_2C_2 \).

### Final Answer:
The complex that will have six isomers is of the type \( MA_2B_2C_2 \).