Geometrical isomerism occurs in coordination compounds with specific coordination numbers and ligand arrangements, typically in square planar (coordination number 4) or octahedral (coordination number 6) complexes. It is observed when ligands can occupy different spatial positions, such as cis (adjacent) and trans (opposite) arrangements. Let’s analyze each option:
- (1) \( [\text{Co}(\text{NH}_3)_6]\text{Cl}_3 \): This is an octahedral complex with six identical ligands (\( \text{NH}_3 \)). Since all ligands are the same, no geometrical isomerism is possible.
- (2) \( [\text{Co}(\text{NH}_3)_4\text{Cl}_2]\text{Cl} \): This is an octahedral complex with four \( \text{NH}_3 \) and two \( \text{Cl} \) ligands, having the formula \( \text{MA}_4\text{B}_2 \). In an octahedral complex, the two \( \text{Cl} \) ligands can be:
- Cis: Adjacent to each other (90° apart),
- Trans: Opposite each other (180° apart).
These distinct arrangements result in geometrical isomerism.
- (3) \( [\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2 \): This is an octahedral complex with five \( \text{NH}_3 \) and one \( \text{Cl} \) ligand (\( \text{MA}_5\text{B} \)). Since there is only one \( \text{Cl} \) ligand, different spatial arrangements are not possible, so it does not exhibit geometrical isomerism.
- (4) \( [\text{Co}(\text{Cl})_4]^{2-} \): This is a tetrahedral complex with four identical \( \text{Cl} \) ligands. Tetrahedral complexes with four identical ligands do not show geometrical isomerism due to the symmetry of the tetrahedral geometry.
Thus, the compound that exhibits geometrical isomerism is \( [\text{Co}(\text{NH}_3)_4\text{Cl}_2]\text{Cl} \).