Problem 57 - A Complete Resource Book in Chemistry for JEE Main

Question

Optical isomerism is not shown by the complex (a) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\)(cis-form) (b) \(\left[\mathrm{Cr}\left(\mathrm{en}_{3}\right)\right]^{3+}\) (c) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\)(trans- form) (d) \(\left[\mathrm{Cr}(\mathrm{ox})_{3}\right]^{3-}\)

Step-by-Step Solution

Answer

The complex (c) trans-[b ext{Co}( ext{en})_{2} ext{Cl}_{2}d]^{+} does not show optical isomerism.

Step 1: Identify optically active complex

For optical isomerism, a complex must be able to exist as non-superimposable mirror images. This typically occurs when there is no plane of symmetry.

Step 2: Analyze each option

(a)  ext{cis-} ext{[b ext{Co}( ext{en})_{2} ext{Cl}_{2}d]^{+}} - In cis-form, this complex is not superimposable on its mirror image, hence it shows optical isomerism. (b)  ext{[b ext{Cr}( ext{en}_{3})d]^{3+}} - This complex has the structure of a chiral center with three bidentate ligands, so it can show optical isomerism. (c)  ext{trans-} ext{[b ext{Co}( ext{en})_{2} ext{Cl}_{2}d]^{+}} - In trans-form, this complex has a plane of symmetry and does not show optical isomerism. (d)  ext{[b ext{Cr}( ext{ox})_{3}d]^{3-}} - This complex is capable of existing as non-superimposable mirror images and shows optical isomerism.

Step 3: Conclude the answer

Based on the analysis, the trans-form of  ext{[b ext{Co}( ext{en})_{2} ext{Cl}_{2}d]^{+}} does not show optical isomerism due to the presence of a plane of symmetry.

Key Concepts

Coordination Compounds

Coordination compounds are fascinating entities in chemistry that involve metal atoms or ions surrounded by molecules or ions called ligands. These ligands can donate pairs of electrons to form coordinate bonds with the metal center. A well-known example of a coordination compound is \([\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}]^{+}\), where cobalt (Co) is the central metal and the ligands include ethylenediamine (en) and chloride ions (Cl).

Coordination compounds have several interesting properties, making them crucial in various fields:

• They can show different colors depending on the ligands attached and their arrangements.
• They often exhibit unique magnetic properties.
• They can demonstrate various types of isomerism, including structural and stereochemical.

The versatility and complexity of coordination compounds arise from the ability of metal atoms to form bonds with multiple ligands, often leading to various geometrical arrangements and interesting chemical behavior.

Chirality in Chemistry

Chirality is a crucial concept in chemistry and concerns the geometric arrangements of atoms within molecules, which leads to non-superimposable mirror images. These mirror-image forms are called enantiomers. To visualize this, imagine your hands: they are mirror images but can't be perfectly overlapped.

In coordination chemistry, chirality often arises when ligands arrange in a way around the central metal that lacks symmetry. Take for instance the molecule \([\mathrm{Cr}(\mathrm{en}_{3})]^{3+}\), which contains bidentate ligands. These ligands "bite" the metal at two points, creating complex structures that can show chirality if no symmetry plane divides them into equal halves.

• Chiral molecules are important because they can rotate plane-polarized light, a property that is useful in various scientific applications.
• In biosystems, many molecules are chiral, which affects how they interact within biological systems, impacting drug design and synthesis.

Symmetry in Molecules

Symmetry in molecules is a pivotal concept that helps determine the optical activity of compounds. Symmetry refers to various elements such as planes, axes, and points that describe how a molecule can be divided into mirror image parts. The presence or absence of symmetry can dramatically influence a compound's physical properties.

For the compound \([\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}]^{+}\), understanding its symmetry helps predict its optical behavior.

• **Cis-form:** In this form, the arrangement of ligands creates asymmetry, allowing it to exist as non-superimposable mirror images that are capable of optical isomerism.
• **Trans-form:** Here, the symmetry is dominant, as there is a plane of symmetry dividing the complex. This symmetry renders the molecule non-chiral, and it does not exhibit optical isomerism.

Employing symmetry concepts is essential to predict the likelihood of optical isomerism in any given coordination compound.