Step 1: Understanding the Concept:
Geometrical isomerism in octahedral coordination complexes involves the spatial arrangement of ligands around the central metal ion. For a complex of the type \([M(AA)_2a_2]\), the bidentate ligands (\(en\)) and monodentate ligands (\(Cl\)) can be arranged in specific ways.
Step 2: Key Formula or Approach:
The complex \([Co(en)_2Cl_2]^+\) can exhibit two geometrical isomers based on the position of the \(Cl^-\) ligands:
- Cis-isomer: The two \(Cl\) ligands are adjacent to each other (\(90^\circ\) angle).
- Trans-isomer: The two \(Cl\) ligands are opposite to each other (\(180^\circ\) angle).
Step 3: Detailed Explanation:
The cis-isomer is optically active (chiral) and exists as two enantiomers, while the trans-isomer is optically inactive (achiral). However, the question specifically asks for the number of "geometrical isomers," which refers to the distinct structural arrangements (cis and trans), resulting in a count of 2.
Step 4: Final Answer:
The number of geometrical isomers possible for this complex is 2.