$\textbf{Number of complexes which show optical isomerism among the following is \_\_\_\_\_\_.}$ \[ \text{cis}-[\text{Cr(ox)}_2\text{Cl}_2]^{3-}, \quad [\text{Co(en)}_3]^{3+}, \] \[ \text{cis}-[\text{Pt(en)}_2\text{Cl}_2]^{2+}, \quad \text{cis}-[\text{Co(en)}_2\text{Cl}_2]^{+}, \] \[ \text{trans}-[\text{Pt(en)}_2\text{Cl}_2]^{2+}, \quad \text{trans}-[\text{Cr(ox)}_2\text{Cl}_2]^{3-} \]
To determine the number of complexes that exhibit optical isomerism, it is important to understand the structural features and symmetry elements that influence chirality in coordination compounds. Optical isomerism arises when a compound has non-superimposable mirror images, or enantiomers, typically due to the absence of a plane of symmetry (POS) or a center of symmetry (COS).
Analysis of the Given Complexes:
cis−[Cr(ox)2Cl2]3−: This complex can exhibit optical isomerism due to its lack of both POS and COS. The cis configuration allows for chirality, as the two oxalate ligands and two chloride ligands create a structure capable of forming non-superimposable mirror images.
[Co(en)3]3+: Optical isomerism is possible because the complex contains three bidentate ethylenediamine (en) ligands, creating a chiral coordination environment without POS or COS.
cis−[Pt(en)2Cl2]2+: The cis arrangement of the two ethylenediamine ligands and two chloride ions gives rise to optical isomerism due to the lack of POS and COS.
cis−[Co(en)2Cl2]+: This complex also shows optical isomerism, as it does not have POS or COS and the cis configuration enables chirality.
trans−[Pt(en)2Cl2]2+: Optical isomerism is not possible because the trans configuration introduces symmetry, including POS or COS, eliminating the possibility of forming enantiomers.
trans−[Cr(ox)2Cl2]3−: This complex cannot show optical isomerism due to the presence of POS or COS, making it symmetric.
Conclusion: Based on the analysis, four complexes can exhibit optical isomerism: cis−[Cr(ox)2Cl2]3−, [Co(en)3]3+, cis−[Pt(en)2Cl2]2+, and cis−[Co(en)2Cl2]+. Final Answer: (4)
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Determine the number of given coordination complexes that exhibit optical isomerism (chirality).
Concept Used:
A complex will show optical isomerism if it is chiral (non-superimposable on its mirror image) and lacks a plane of symmetry, center of inversion, or improper rotation axis. Key geometries and cases:
Octahedral M(bidentate)3: Chiral (exists as Λ and Δ enantiomers).
Octahedral M(bidentate)2X2: cis isomer is chiral; trans isomer is achiral.
Square planar M(bidentate)2: Can exhibit optical isomerism if the chelate rings prevent a plane of symmetry.
Step-by-Step Solution:
Step 1: Analyze cis-[Cr(ox)2Cl2]3–. Octahedral complex with two bidentate oxalate ligands and two Cl ligands in cis positions. The cis geometry lacks a plane of symmetry. Yes, optically active.
Step 2: Analyze [Co(en)3]3+. Octahedral complex with three bidentate ethylenediamine ligands. This is chiral (Λ and Δ enantiomers). Yes, optically active.
Step 3: Analyze cis-[Pt(en)2Cl2]2+. Square planar complex with two bidentate en ligands. Despite being square planar, the ethylenediamine chelate rings create a non-planar "propeller" arrangement, making the complex chiral. Yes, optically active.
Step 4: Analyze cis-[Co(en)2Cl2]+. Octahedral complex with two bidentate en ligands and two Cl ligands in cis positions. The cis geometry is chiral. Yes, optically active.
Step 5: Analyze trans-[Pt(en)2Cl2]2+. Square planar complex in trans configuration. This has a plane of symmetry. No, not optically active.
Step 6: Analyze trans-[Cr(ox)2Cl2]3–. Octahedral complex in trans configuration. This has a plane of symmetry. No, not optically active.
Thus, the complexes showing optical isomerism are: cis-[Cr(ox)2Cl2]3–, [Co(en)3]3+, cis-[Pt(en)2Cl2]2+, and cis-[Co(en)2Cl2]+.
The number of complexes which show optical isomerism is 4.
