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 \([\mathrm{cis-Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}]\) shows optical isomerism.

Step 1: Identify Optical Isomerism

Optical isomerism occurs when a molecule is non-superimposable on its mirror image, often occurring in a molecule with chiral centers and no plane of symmetry.

Step 2: Analyze Option (a)

The complex \(\mathrm{cis}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) involves ethylenediamine (en), which is a bidentate ligand, creating a chiral coordination complex without a plane of symmetry, allowing for optical isomerism.

Step 3: Analyze Option (b)

The complex \(\mathrm{trans}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) is not optically active. In the trans form, the ligands are positioned opposite each other, creating a plane of symmetry which does not support optical isomers.

Step 4: Analyze Option (c)

In \(\left[\mathrm{Co}(\mathrm{NH}_{3})_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\), Co has a coordination number of 6 with a cis-configuration of \(\mathrm{NH}_{3}\) and Cl ligands, but it has a plane of symmetry and is thus not optically active.

Step 5: Analyze Option (d)

The complex \(\left[\mathrm{Co}(\mathrm{NH}_{3})_{3} \mathrm{Cl}_{3}\right]\), with a coordination number of 6, is not chiral due to the presence of a plane of symmetry with \(\mathrm{Cl}\) ligands, thus not showing optical isomerism.

Step 6: Conclusion

Among the given options, only \(\mathrm{Cis}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) is capable of optical isomerism.

Key Concepts

Chiral Coordination Complex

In the realm of coordination chemistry, a chiral coordination complex is a fascinating topic. Chiral complexes do not share the same shape as their mirror images, much like your left and right hands. This is known as being non-superimposable.
The presence of chiral centers, usually arising from the 3D arrangement of atoms in the complex, is the key. Often, a lack of a plane of symmetry contributes to this property. A chiral coordination complex can rotate plane-polarized light, which is the fundamental aspect of optical isomerism. Not all molecules have this property; it's the unique arrangement of ligands around a central atom that creates chirality.
Understanding chirality is crucial, as it affects how complexes interact with biological molecules, impacting their chemical behavior and properties in various reactions.

Ethylenediamine (en) Ligand

Ethylenediamine, often abbreviated as en, is a popular bidentate ligand in coordination chemistry. But what exactly does that mean? "Bidentate" refers to a ligand that can form two bonds with a central metal atom in a complex. Ethylenediamine achieves this through its two nitrogen atoms, each of which has a lone pair of electrons ready to donate.
The ability of ethylenediamine to form stable chelate rings is particularly important. These rings enhance the stability of the complexes they form. Moreover, their geometry can result in cis and trans isomers.
When arranged around a metal ion like cobalt, ethylenediamine can lead to chiral structures capable of exhibiting optical isomerism. Thus, understanding the unique properties of ethylenediamine is vital for grasping how coordination complexes obtain their optical activity.

Coordination Chemistry

Coordination chemistry is a broad and fascinating area of inorganic chemistry focused on the behavior of complex molecules. These molecules consist of a central metal ion surrounded by a set of molecules or ions known as ligands.
The way these ligands coordinate to the metal center impacts the physical and chemical properties of the whole complex. By using different types of ligands, one can modify the complex's reactivity, color, magnetic properties, and more.
Understanding the spatial arrangement of these ligands and the resulting geometrical structures helps in predicting and explaining phenomena such as optical isomerism. In our current discussion, coordination chemistry provides the backdrop to decipher which complexes are optically active and understand why chirality and optical isomers emerge.

Non-superimposable Mirror Images

A vital element in the concept of optical isomerism is non-superimposable mirror images. This refers to two molecules that are mirror reflections of each other but cannot be aligned or superimposed perfectly. Think of the way your hands are mirror images but can never stack perfectly on top of one another.
For coordination complexes, this non-superimposability typically arises due to the spatial arrangement of ligands around the central atom. When a complex lacks a plane of symmetry or a center of inversion, it has the potential to be optically active.

• This property is utilized in examining how different isomers might interact differently with polarized light.
• Also, non-superimposable mirror images can have diverse biological activities, making them crucial in the fields of pharmaceuticals and materials science.

Recognizing when complexes present non-superimposable mirror images is essential in predicting which complexes will display optical isomerism.