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

Solution :

1. Molecular Structure and Coordination Geometry

The complex $[Co(NH_3)_2Cl_2(en)]^+$ features a Cobalt ($Co^{3+}$) central metal ion with a coordination number of 6, establishing an octahedral geometry. The ligands present are two ammine groups ($NH_3$), two chloride ions ($Cl^-$), and one ethylenediamine molecule ($en$), which is a bidentate ligand.

2. Determination of Geometrical Isomers

The structure can be defined by the relative positions of the $Cl^-$ ligands and the $en$ ligand. Given the bidentate nature of $en$, it must span two adjacent (cis) coordination sites. We classify isomers based on the relative arrangement of the two $Cl^-$ ligands:

  • Isomer A (trans-dichloro): The two $Cl^-$ ligands are in 180° opposition (trans).
  • Isomer B (cis-dichloro, trans-ammine): The two $Cl^-$ ligands are at 90° (cis), and the two $NH_3$ ligands are at 180° (trans).
  • Isomer C (cis-dichloro, cis-ammine): The two $Cl^-$ ligands are at 90° (cis), and the two $NH_3$ ligands are at 90° (cis).

3. Visual Representation of Geometrical Isomers

Co Cl Cl NH3 NH3 Trans-isomer Co Cl Cl NH3 NH3 Cis-isomer

4. Optical Isomerism Analysis

Optical activity arises when a molecule lacks a plane of symmetry or a center of inversion [Per the symmetry criteria for chirality].

Isomer Plane of Symmetry Chiral/Achiral
Trans-$[Co(NH_3)_2Cl_2(en)]^+$ Present (multiple) Achiral (Optically Inactive)
Cis-$[Co(NH_3)_2Cl_2(en)]^+$ Absent Chiral (Optically Active)

The cis-isomer exists as a pair of enantiomers (non-superimposable mirror images). By swapping the positions of the ligands within the cis-plane, one generates the $d$ (dextrorotatory) and $l$ (laevorotatory) forms.

5. Conclusion of Isomeric Forms

Total isomers identified:

  1. Trans-isomer: Optically inactive, geometric isomer.
  2. Cis-isomer ($d$-form): Optically active, geometric isomer.
  3. Cis-isomer ($l$-form): Optically active, geometric isomer (enantiomer of the $d$-form).

Final Solution: The complex $[Co(NH_{3})_{2}Cl_{2}(en)]^{+}$ exhibits three isomers: one optically inactive trans-geometric isomer and two optically active cis-geometric enantiomers (a racemic pair).


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