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Q5.11(i):
Draw all the isomers (geometrical and optical) of: \([CoCl_{2}(en)_{2}]^{+}\)

Solution :

Given Molecular Configuration

The complex is $[CoCl_{2}(en)_{2}]^{+}$, where $Co^{3+}$ is the central metal ion. The ligand $en$ (ethylenediamine, $NH_2CH_2CH_2NH_2$) is a bidentate ligand, and $Cl^-$ is a monodentate ligand. The coordination number is 6, indicating an octahedral geometry. The total charge of the complex is $+1$.

Step 1: Identification of Geometric Isomers

The complex follows the formula $MA_2B_2$ type (where $A = Cl$ and $B = en$). There are two possible geometric arrangements for the monodentate ligands ($Cl$):

  • Cis-isomer: The two $Cl$ ligands occupy adjacent positions (angle $90^\circ$).
  • Trans-isomer: The two $Cl$ ligands occupy opposite positions (angle $180^\circ$).

Step 2: Analysis of Optical Isomers

  • Cis-isomer: This isomer lacks a plane of symmetry and a center of inversion. Therefore, it is chiral and exists as a pair of enantiomers (non-superimposable mirror images).
  • Trans-isomer: This isomer possesses a plane of symmetry (the plane containing the $Cl-Co-Cl$ axis). Therefore, it is achiral and optically inactive.

Visual Representation of Isomers

Co Cl Cl en en Cis (Chiral) Co Cl Cl en en Trans (Achiral)

Summary Table of Isomers

Isomer Type Configuration Optical Activity
Geometric Cis Optically Active (Pair of $d$ and $l$ forms)
Geometric Trans Optically Inactive

Final Solution: The complex $[CoCl_{2}(en)_{2}]^{+}$ exhibits two geometric isomers (cis and trans). The cis-isomer is optically active and exists as a pair of enantiomers, while the trans-isomer is optically inactive due to the presence of a plane of symmetry. Total isomers: 3 (cis-$d$, cis-$l$, and trans).


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