Which of the following complex species is not expected to exhibit optical isomerism ?

Options

A. `[Co(en)_(2)Cl_(2)]^(+)`
B. `[Co(NH_(3))_(3)Cl_(3)]`
C. `[Co(en)(NH_(3))_(2)Cl_(2)]^(+)`
D. `[Co(en)_(3)]^(3+)`

Answer

To determine which complex species is not expected to exhibit optical isomerism, we need to analyze the given coordination compounds and their structures. Optical isomerism occurs when a compound lacks any element of symmetry, allowing for non-superimposable mirror images (enantiomers).

### Step-by-Step Solution:

1. **Identify the Complex Species**: The question presents four coordination compounds, all involving cobalt as the central metal ion. We will analyze each one for symmetry.

2. **Analyze the First Complex**:
- **Complex**: [Co(en)₂Cl₂]⁺
- **Structure**: The central cobalt is coordinated by two ethylene diamine (en) ligands and two chloride (Cl) ligands.
- **Symmetry**: This complex can exist in both cis and trans forms. In both forms, there is no plane of symmetry, which means it can exhibit optical isomerism.

**Conclusion**: This complex can exhibit optical isomerism.

3. **Analyze the Second Complex**:
- **Complex**: [Co(NH₃)Cl₃]
- **Structure**: Cobalt is coordinated by three ammonia (NH₃) ligands and three chloride (Cl) ligands.
- **Symmetry**: This complex can exist in facial and meridional isomers. Both forms have a plane of symmetry due to the arrangement of identical ligands, making them optically inactive.

**Conclusion**: This complex does not exhibit optical isomerism.

4. **Analyze the Third Complex**:
- **Complex**: [Co(en)(NH₃)₂Cl₂]⁺
- **Structure**: Cobalt is coordinated by one ethylene diamine, two ammonia ligands, and two chloride ligands.
- **Symmetry**: This complex can have different geometrical isomers, and all of them lack symmetry, allowing for optical isomerism.

**Conclusion**: This complex can exhibit optical isomerism.

5. **Analyze the Fourth Complex**:
- **Complex**: [Co(en)₃]³⁺
- **Structure**: Cobalt is coordinated by three ethylene diamine ligands.
- **Symmetry**: This complex has no plane of symmetry and can exist as enantiomers, thus exhibiting optical isomerism.

**Conclusion**: This complex can exhibit optical isomerism.

### Final Answer:
The complex species that is not expected to exhibit optical isomerism is **[Co(NH₃)Cl₃]** (Option B).