Problem 181 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following complexe shows optical isomerism (a) \(\operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (b) \(\operatorname{trans}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (d) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\)

Step-by-Step Solution

Answer

The complex (a) Cis[Co(en)_2Cl_2]Cl shows optical isomerism.

Step 1: Understanding Optical Isomerism

Optical isomerism occurs in complexes that have non-superimposable mirror images, typically those without a center of symmetry or a plane of symmetry. It is often found in complexes with bidentate ligands like ethylenediamine (en). Therefore, the first step is identifying which of the given complexes has a geometric arrangement that can have a non-superimposable mirror image.

Step 2: Analyzing the Complexes

Inspect each complex: (a) \([\text{Cis}\ [\mathrm{Co}(\mathrm{en})_{2}\mathrm{Cl}_{2}]]\mathrm{Cl}\) is a cis form, suggesting no plane of symmetry, making optical isomerism possible. (b) \([\text{trans}\ [\mathrm{Co}(\mathrm{en})_{2}\mathrm{Cl}_{2}]]\mathrm{Cl}\) is a trans form and has a plane of symmetry, disallowing optical isomers. (c) and (d) have monodentate ligands and do not possess the required asymmetry for optical isomerism.

Step 3: Confirming the Optical Isomer

Based on the analysis, the complex \([\text{Cis}\ [\mathrm{Co}(\mathrm{en})_{2}\mathrm{Cl}_{2}]]\mathrm{Cl}\) provides a configuration where left and right-handed isomers are possible, i.e., they have chiral centers without a symmetry plane, allowing optical isomerism.

Key Concepts

Chiral Centers

Chiral centers are crucial in understanding optical isomerism. A chiral center usually refers to a carbon atom bonded to four different groups, leading to non-superimposable mirror images. This means that the structure can exist in two mirror image forms, called enantiomers. In coordination complexes, a similar idea applies to metal ions that bind with different ligands.
While organic molecules often focus on carbon atoms when discussing chiral centers, this concept also applies to other molecules. These can include metal ions coordinated with ligands around them.
For example, in the complex \([ ext{Cis} extrm{Co}( extrm{en})_2 extrm{Cl}_2] extrm{Cl}\), the arrangement of ethylenediamine (en) and chlorine around the cobalt atom can lead to asymmetry, resulting in chiral centers. Once the structure lacks a plane of symmetry, these chiral centers can lead to optical isomerism.

Geometric Isomerism

Geometric isomerism, a subset of stereoisomerism, arises when ligands around a central atom are variably positioned, unlike structural isomers where different atoms or bonds form. Typically observed in square planar and octahedral complexes, geometric isomerism signifies different arrangements.
Consider the complexes cis-\([ extrm{Co}( extrm{en})_2 extrm{Cl}_2] extrm{Cl}\)\ and trans-\([ extrm{Co}( extrm{en})_2 extrm{Cl}_2] extrm{Cl}\). In cis isomers, identical ligands appear next to each other, while in trans isomers, they're opposite each other. Such arrangements cause different physical and chemical properties and opportunities for isomerization, including optical isomerism in the cis form, as it lacks symmetry planes.
Understanding geometric isomerism is crucial, as it informs the partial structural asymmetry necessary for optical isomerism, especially when chiral centers are present.

Bidentate Ligands

Bidentate ligands play a vital role in the formation of complexes that display optical isomerism. These ligands can form two bonds with a central metal atom, enhancing the stability and formation of stereoisomers. A common example of a bidentate ligand is ethylenediamine (en), which has the ability to occupy two coordination sites on the metal center.
Bidentate ligands contribute significantly to the structural rigidity necessary for optical isomerism by effectively capturing the metal ion within a specific geometric framework.
In the complex \([ ext{Cis} extrm{Co}( extrm{en})_2 extrm{Cl}_2] extrm{Cl}\), ethylenediamine's dual bonding encourages non-superimposable mirror image formations. This unique bonding ability facilitates the creation of chiral centers and the resulting optical activity. By holding metal ions in a configuration without a symmetry plane, bidentate ligands open up possibilities for enantiomer formation, thus playing a key role in optical isomerism.