A coordination complex has only two stereo isomers, having octahedral coordination geometry. Identify the complex(es) among the following:
`[Cr(H_(2)O_5 Cl]Cl_(2)]Cl_(2),[Cr(H_2O)_(3)Cl_(3)],[Ni(NH_3)_(4)Cl_(2)],[NH_4]_(2)[NiCl_6]`

Options

A. only `[Cr(H_2O)_(5)Cl]Cl_(2)`
B. `[Cr(H_2O)_(3)Cl_3] and [NH_4]_(4)[NiCl_(6)]`
C. `[Cr(H_2O)_(3)Cl_3] and [Ni(NH_3)_(4)Cl_(2)]`
D. only `[Ni(NH_3)_(4)Cl_(2)]`

Explanation

To determine which coordination complexes have only two stereoisomers with octahedral coordination geometry, we need to analyze each of the given complexes for geometrical isomerism.

### Step 1: Analyze the first complex `[Cr(H₂O)₅Cl]Cl₂`
- This complex can be rewritten as `[Cr(H₂O)₅Cl]²⁺` with 2 Cl⁻ ions outside the coordination sphere.
- The ligands consist of five water molecules and one chloride ion. Since all water molecules are identical, this complex does not exhibit geometrical isomerism (cis/trans) but can show hydration isomerism.
- **Conclusion**: This complex does not have geometrical isomers.

### Step 2: Analyze the second complex `[Cr(H₂O)₃Cl₃]`
- This complex can be represented as `[Cr(H₂O)₃Cl₃]`.
- It has three water molecules and three chloride ions. This type of complex (MA₃B₃) can exhibit geometrical isomerism.
- **Cis Isomer**: All three water molecules on one side and three chloride ions on the opposite side.
- **Trans Isomer**: The three water molecules and three chloride ions are arranged such that they are opposite each other.
- **Conclusion**: This complex has two geometrical isomers (cis and trans).

### Step 3: Analyze the third complex `[Ni(NH₃)₄Cl₂]`
- This complex can be represented as `[Ni(NH₃)₄Cl₂]`.
- It consists of four ammonia ligands and two chloride ions. This type of complex (MA₄B₂) can also exhibit geometrical isomerism.
- **Cis Isomer**: Two chloride ions are adjacent to each other, and the ammonia ligands are on the opposite side.
- **Trans Isomer**: The two chloride ions are opposite each other, with the ammonia ligands filling the remaining positions.
- **Conclusion**: This complex also has two geometrical isomers (cis and trans).

### Step 4: Analyze the fourth complex `[NH₄]₂[NiCl₆]`
- This complex can be represented as `[NiCl₆]²⁻` with two ammonium ions outside.
- All six chloride ions are identical, and thus, this complex cannot exhibit geometrical isomerism.
- **Conclusion**: This complex does not have geometrical isomers.

### Final Conclusion:
The complexes that have only two stereoisomers with octahedral coordination geometry are:
- `[Cr(H₂O)₃Cl₃]`
- `[Ni(NH₃)₄Cl₂]`

### Summary of Results:
- Complexes with geometrical isomers:
- `[Cr(H₂O)₃Cl₃]` (cis and trans)
- `[Ni(NH₃)₄Cl₂]` (cis and trans)
- Complexes without geometrical isomers:
- `[Cr(H₂O)₅Cl]Cl₂`
- `[NH₄]₂[NiCl₆]`