Problem 19 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following does not have an optical isomer? (a) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{3}\right]\) (b) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\) (d) \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\)

Step-by-Step Solution

Answer

The compound \([\mathrm{Co}( ext{NH}_{3})_{3} \mathrm{Cl}_{3}]\) does not have an optical isomer.

Step 1: Understanding Optical Isomerism

Optical isomers are stereoisomers that are mirror images of each other and are non-superimposable. For a compound to exhibit optical isomerism, it must lack a plane of symmetry, meaning no internal mirror plane exists that divides the molecule into two equivalent halves.

Step 2: Evaluating Option (a)

The compound \([\mathrm{Co}( ext{en})_{2} \mathrm{Cl}_{3}]\) forms a coordination complex with two ethylenediamine (en) ligands. Ethylenediamine is a bidentate ligand, and with the arrangement of ligands, it can form optical isomers due to asymmetric distribution around the metal center.

Step 3: Evaluating Option (b)

The compound \([\mathrm{Co}( ext{en})_{2} \mathrm{Cl}_{2}] \mathrm{Cl}\) contains two ethylenediamine ligands and two chloride ions directly bonded to the cobalt center. The placement of bidentate ligands and chlorides allows for the possibility of optical isomerism.

Step 4: Evaluating Option (c)

The compound \([\mathrm{Co}( ext{NH}_{3})_{3} \mathrm{Cl}_{3}]\) has three ammonia ligands and three chloride ions. This is an octahedral complex with fac/mer possibilities, leading to geometric isomerism, but no optical isomers because it has a plane of symmetry.

Step 5: Evaluating Option (d)

The compound \([\mathrm{Co}( ext{en})( ext{NH}_{3})_{2} \mathrm{Cl}_{2}] \mathrm{Cl}\) involves ethylenediamine ligands and a mixture of chlorides and ammonia on the coordination sphere. This non-uniform ligand distribution can lead to optical isomerism.

Key Concepts

Coordination Complex

A coordination complex is a unique chemical structure formed when a central metal atom or ion is surrounded by a set of molecules or ions known as ligands. This central entity is known as the coordination center. In the realm of chemistry, coordination complexes are fascinating because they exhibit various properties like color, magnetism, and especially, their stereochemistry. This stereochemistry gives rise to different isomers, and in particular, optical isomers can emerge from certain symmetric configurations of the central metal and its ligands.

• The metal ion acts as the core, typically a transition metal, providing a space for ligands to attach.
• Ligands are molecules or ions that donate a pair of electrons to bond with the metal ion.

These complexes are fundamental in understanding optical isomerism because their specific arrangements can lead to very different chemical behavior.

Stereoisomers

Stereoisomers are compounds that have the same chemical formula and the same bond connectivity but differ in the three-dimensional orientation of their atoms. This is an essential concept in understanding coordination chemistry as the spatial arrangement significantly affects a compound's properties and reactivity. For coordination complexes:

• Stereoisomers include both geometric and optical isomers.
• Geometric isomers differ by the relative positions of the ligands in space, while optical isomers are non-superimposable mirror images.

This distinction is crucial when analyzing complexes such as in our original exercise, where some compounds might exhibit optical isomerism based on their symmetry and spatial arrangement.

Chirality

Chirality is a fundamental concept in chemistry that describes a property of a molecule that makes it non-superimposable on its mirror image. It is often compared to human hands—left and right are mirror images, but they cannot perfectly overlap. To determine whether a coordination complex is chiral (and thus has optical isomerism), you need to assess the symmetry:

• A chiral coordination complex lacks a plane of symmetry.
• Such molecules usually exist in pairs known as enantiomers, which are mirror images of each other.

Understanding chirality helps explain why only certain complexes in the exercise exhibit optical isomerism, as those lacking symmetry allow for non-superimposable mirror images to exist.

Bidentate Ligand

Bidentate ligands are fascinating because they bind to a central metal atom at two distinct sites. This type of bonding enhances stability and alters the three-dimensional arrangement of the coordination complex. In studying optical isomers, bidentate ligands play a crucial role:

• Their dual-attachment points constrain the ligand's spatial orientation, influencing the overall geometry of the complex.
• Common bidentate ligands, like ethylenediamine ('en'), are often involved in forming chelate rings within the complex.

These attributes of bidentate ligands are significant when predicting the existence of optical isomers, as seen in some options from the original exercise, where the presence of bidentate ligands allows for an asymmetric arrangement around the metal center.