Which of the following complex(s) can not exhibit both geometrical and optical isomerism?

Options

A. `[Ru(en)_(3)]^(3+)`
B. `[Co(H_(2)O)Cl_(3)]`
C. `[PtBrCl(H_(2)O)NH_(3)]`
D. `[FeBr_(2)(en)_(2)]^(+)`

Answer

To determine which complex cannot exhibit both geometrical and optical isomerism, we need to analyze the given complexes one by one.

### Step-by-Step Solution:

1. **Understanding Geometrical and Optical Isomerism**:
- **Geometrical Isomerism**: This occurs when ligands can be arranged in different spatial orientations, leading to cis and trans forms.
- **Optical Isomerism**: This occurs when a compound can exist in two forms that are non-superimposable mirror images of each other, known as enantiomers.

2. **Analyzing the First Complex: Ruthenium(III) Ethylenediamine**:
- The complex is [Ru(en)3]³⁺ where ethylenediamine (en) is a bidentate ligand.
- Since there are three bidentate ligands, they can only arrange themselves in a certain way, leading to one form (cis) and it can exhibit optical isomerism.
- **Conclusion**: This complex can exhibit optical isomerism but not geometrical isomerism.

3. **Analyzing the Second Complex: Cobalt(III) Chloride with Water**:
- The complex is [Co(H2O)3Cl3].
- In this case, there are three identical ligands (water) and three identical chloride ions.
- This arrangement does not allow for any geometrical isomerism (no cis/trans forms) since all ligands are the same.
- Additionally, since the arrangement is symmetrical, it cannot have non-superimposable mirror images, hence it does not exhibit optical isomerism either.
- **Conclusion**: This complex cannot exhibit either geometrical or optical isomerism.

4. **Analyzing the Third Complex: Iron(II) Bromide with Ethylenediamine**:
- The complex is [FeBr2(en)2]²⁺.
- Here, we have two different types of ligands (bromide and ethylenediamine), allowing for both cis and trans arrangements.
- This complex can also exhibit optical isomerism due to the possibility of forming non-superimposable mirror images.
- **Conclusion**: This complex can exhibit both geometrical and optical isomerism.

5. **Final Answer**:
- The complex that cannot exhibit both geometrical and optical isomerism is **Cobalt(III) Chloride with Water** ([Co(H2O)3Cl3]).

### Summary of Findings:
- **Ruthenium(III) Ethylenediamine**: Can exhibit optical isomerism but not geometrical.
- **Cobalt(III) Chloride with Water**: Cannot exhibit either geometrical or optical isomerism.
- **Iron(II) Bromide with Ethylenediamine**: Can exhibit both geometrical and optical isomerism.