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Q5.10 (iii):
Draw the structures of optical isomers of: ([Cr(NH_{3})_{2}Cl_{2}(en)]^{+})

Solution :

Step 1: Analyzing the Coordination Entity

The complex ion given is $[Cr(NH_{3})_{2}Cl_{2}(en)]^{+}$.

  • Central Metal: Chromium ($Cr^{3+}$).
  • Coordination Number: $6$ (Octahedral geometry).
  • Ligands: Two ammine ($NH_3$), two chloro ($Cl^-$), and one ethylenediamine ($en$, a bidentate ligand).
[Per IUPAC nomenclature and coordination theory, the ethylenediamine ligand acts as a chelate occupying two adjacent coordination sites.]

Step 2: Determining Geometric Isomers

To identify optical isomers, we must first establish the configuration of the geometric isomers. For $[M(AA)(a)_2(b)_2]$, there are several possible geometric arrangements. Optical activity in octahedral complexes requires the absence of a plane of symmetry ($POS$) and a center of inversion. The cis-cis configuration (where similar ligands are adjacent) is chiral.

Step 3: Visualizing the Optical Isomers

The optical isomers are non-superimposable mirror images of the cis-dichloro-cis-diammine configuration. We represent the $en$ ligand as an arc connecting two adjacent vertices.

Cl NH3 NH3 Cl en Isomer I (d-form) NH3 Cl Cl NH3 en Isomer II (l-form)

Step 4: Theoretical Justification

The optical isomerism in this complex arises because the cis-isomer lacks a plane of symmetry. When we place the mirror plane between the two structures shown above, they are non-superimposable.

  • d-isomer: Rotates plane-polarized light to the right.
  • l-isomer: Rotates plane-polarized light to the left.
[As per the Criteria for Chirality in Coordination Compounds, an octahedral complex is optically active if it lacks both an improper axis of rotation ($S_n$) and a center of inversion ($i$).]

Final Solution: The optical isomers of $[Cr(NH_{3})_{2}Cl_{2}(en)]^{+}$ consist of a pair of enantiomers (dextro and levo) corresponding to the cis-geometric configuration, where the mirror-image relationship confirms non-superimposability.


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