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Q5.10(ii):
Draw the structures of optical isomers of: \([PtCl_{2}(en)_{2}]^{2+}\)

Solution :

Step 1: Identifying the Geometry and Isomerism

The coordination complex $[PtCl_{2}(en)_{2}]^{2+}$ features a platinum (IV) central metal ion with a coordination number of 6, establishing an octahedral geometry. The ligand set consists of two monodentate chloro ligands ($Cl^-$) and two bidentate ethylenediamine ($en$) ligands. The complex exists in both cis and trans geometric configurations. However, optical activity (chirality) is restricted to the cis-isomer, as the trans-isomer possesses a plane of symmetry.

Step 2: Defining the Coordination Environment

In the cis-isomer, the two chlorine atoms occupy adjacent positions (at $90^{\circ}$ to each other). The two bidentate $en$ ligands occupy the remaining four equatorial/axial positions, creating a non-superimposable mirror image pair.

Step 3: Visual Representation of Optical Isomers (Enantiomers)

The following SVG illustrates the $d$-isomer (dextrorotatory) and $l$-isomer (levorotatory) of the cis-$[PtCl_{2}(en)_{2}]^{2+}$ complex.

Cl Cl cis-d-isomer Cl Cl cis-l-isomer

Step 4: Analytical Justification

  • Symmetry Argument: The trans-isomer has a plane of symmetry passing through the $Cl-Pt-Cl$ axis and the two $en$ rings, rendering it achiral [Per Van't Hoff's theory of molecular chirality].
  • Chirality Argument: The cis-isomer lacks any plane of symmetry or center of inversion. The arrangement of the bidentate ligands in a propeller-like configuration creates a chiral environment [By the Criterion of Molecular Dissymmetry].
  • Enantiomeric Relationship: The two structures shown above are non-superimposable mirror images of each other, satisfying the definition of enantiomers in coordination chemistry.

Final Solution: The optical isomers are the two non-superimposable mirror image forms of the cis-$[PtCl_{2}(en)_{2}]^{2+}$ complex, specifically designated as the $\Lambda$ (lambda) and $\Delta$ (delta) enantiomers.


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