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Q5.11(ii):
Draw all the isomers (geometrical and optical) of: \([Co(NH_{3})Cl(en)_{2}]^{2+}\)

Solution :

Step 1: Analyzing the Coordination Sphere

The complex ion is $\left[Co(NH_{3})Cl(en)_{2}\right]^{2+}$.

  • Central Metal: Cobalt ($Co^{3+}$), which is $d^6$ and typically octahedral in coordination number 6.
  • Ligands:
    • One ammine ligand ($NH_3$), unidentate.
    • One chloride ligand ($Cl^-$), unidentate.
    • Two ethylenediamine ($en$) ligands, bidentate ($NH_2CH_2CH_2NH_2$).
  • General Formula: $[M(AA)_2bc]$, where $AA$ is the bidentate ligand, and $b, c$ are unidentate ligands.

Step 2: Determining Geometrical Isomers

The complex exhibits two geometrical isomers based on the relative position of the two unidentate ligands ($NH_3$ and $Cl$) with respect to each other and the bidentate ligands.

Isomer Type Description
cis-Isomer The $NH_3$ and $Cl$ ligands are adjacent to each other (90° angle).
trans-Isomer The $NH_3$ and $Cl$ ligands are opposite each other (180° angle).

Step 3: Evaluating Optical Activity

Optical activity requires the absence of a plane of symmetry (chirality). [Per the Criterion for Optical Activity].

  • cis-Isomer: Does not possess a plane of symmetry. Therefore, the cis-isomer exists as a pair of enantiomers (non-superimposable mirror images).
  • trans-Isomer: Possesses a plane of symmetry passing through the $Cl-Co-NH_3$ axis and the two $en$ rings. Therefore, it is achiral and optically inactive.

Step 4: Visualizing the Isomers

cis-Isomer (d) NH3 Cl trans-Isomer NH3 Cl

Step 5: Summary of Isomeric Forms

The total number of isomers identified is three:

  1. $cis$-isomer (d-form): Optically active.
  2. $cis$-isomer (l-form): Optically active (enantiomer of 1).
  3. $trans$-isomer: Optically inactive.

Final Solution: The complex $[Co(NH_{3})Cl(en)_{2}]^{2+}$ exhibits two geometrical isomers (cis and trans), where the cis-isomer is further resolved into two optical enantiomers, resulting in a total of three distinct isomeric structures.


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