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

Solution :

Step 1: Analyzing the Coordination Entity

The complex ion given is $[PtCl_{2}(en)_{2}]^{2+}$. We first identify the coordination geometry and ligand arrangement:

  • Central Metal: Platinum ($Pt^{4+}$).
  • Coordination Number: $6$ (Octahedral geometry).
  • Ligands: Two chloride ions ($Cl^-$) and two ethylenediamine ($en$) molecules. Since $en$ is a bidentate ligand, it occupies two coordination sites each ($2 \times 2 = 4$).
  • Geometric Isomers: The complex exhibits cis-trans isomerism. Only the cis-isomer is optically active, as the trans-isomer possesses a plane of symmetry [Per the principle of molecular chirality in coordination chemistry].

Step 2: Defining the Optical Isomers

The cis-isomer of $[PtCl_{2}(en)_{2}]^{2+}$ lacks a plane of symmetry and a center of inversion, existing as a pair of non-superimposable mirror images (enantiomers), labeled as $\Delta$ (delta) and $\Lambda$ (lambda) isomers.

Step 3: Visualization of Geometric Structures

Cl Cl en Cis-Delta Isomer Cl Cl en Cis-Lambda Isomer

Step 4: Theoretical Justification

The chirality arises due to the helical arrangement of the bidentate ethylenediamine ligands around the $Pt$ center. By applying the Cahn-Ingold-Prelog (CIP) priority rules for coordination compounds:

  • In the $\Delta$ isomer, the skew lines formed by the $en$ ligands describe a right-handed helix.
  • In the $\Lambda$ isomer, the skew lines formed by the $en$ ligands describe a left-handed helix [By the IUPAC nomenclature rules for chiral coordination compounds].

The trans-isomer is excluded from optical isomerism because it contains a plane of symmetry passing through the $Cl-Pt-Cl$ axis, making it achiral.

Final Solution: The optical isomers of $[PtCl_{2}(en)_{2}]^{2+}$ are the pair of enantiomers derived from the cis-geometric configuration, represented as the $\Delta$ and $\Lambda$ forms which are non-superimposable mirror images of each other.


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