Geometrical isomerism in coordination compounds arises from distinct spatial arrangements of ligands, typically in square planar or octahedral geometries. Ligands can be adjacent (cis) or opposite (trans). Evaluating each option:
- (1) \( [\text{Co}(\text{NH}_3)_6]\text{Cl}_3 \): An octahedral complex with six identical \( \text{NH}_3 \) ligands. No geometrical isomerism is possible.
- (2) \( [\text{Co}(\text{NH}_3)_4\text{Cl}_2]\text{Cl} \): An octahedral complex (formula \( \text{MA}_4\text{B}_2 \)) with four \( \text{NH}_3 \) and two \( \text{Cl} \) ligands. The two \( \text{Cl} \) ligands can occupy cis (adjacent) or trans (opposite) positions, demonstrating geometrical isomerism.
- (3) \( [\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2 \): An octahedral complex (formula \( \text{MA}_5\text{B} \)) with one \( \text{Cl} \) ligand. With only one of a particular ligand type, different spatial arrangements are not possible, thus no geometrical isomerism.
- (4) \( [\text{Co}(\text{Cl})_4]^{2-} \): A tetrahedral complex with four identical \( \text{Cl} \) ligands. Tetrahedral complexes with identical ligands do not exhibit geometrical isomerism due to the inherent symmetry.
Consequently, \( [\text{Co}(\text{NH}_3)_4\text{Cl}_2]\text{Cl} \) is the compound exhibiting geometrical isomerism.