Problem 24 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which of the following complex species is not expected to exhibit optical isomerism ? (a) \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) (b) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\) (d) \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}\)

Step-by-Step Solution

Answer

(c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\) is not optically active.

Step 1: Understand the Concept of Optical Isomerism

Optical isomerism occurs when a compound cannot be superimposed onto its mirror image, typically due to the presence of chiral centers. For complexes, this often requires a non-planar or asymmetric geometry, such as octahedral complexes with certain arrangements of ligands.

Step 2: Analyze Each Complex for Optical Isomerism

Examine each given complex: (a) \([Co(en)_{3}]^{3+}\) is an octahedral complex with three bidentate ethylenediamine (en) ligands, allowing for chirality and optical isomerism. (b) \([Co(en)_{2}{Cl}_{2}]^{+}\) is also an octahedral complex with two bidentate en ligands and two chloro ligands in cis configuration, which can exhibit optical isomerism. (c) \([Co(NH_{3})_{3}{Cl}_{3}]\) is an octahedral complex but with three ammonia and three identical chlorides, allowing only for geometric isomerism (fac and mer), not optical. (d) \([Co(en)(NH_{3})_{2}{Cl}_{2}]^{+}\) could have a chiral arrangement if the en, NH3, and Cl ligands allow it under certain geometries.

Step 3: Identify the Non-Optical Isomerism Complex

From the analysis, \([Co(NH_{3})_{3}{Cl}_{3}]\) (option c) stands out as the complex that cannot be chiral, because it consists of three identical ammonia ligands and three identical chloro ligands arranged symmetrically, leading to geometric isomers but not optical ones.

Key Concepts

Chirality in Coordination Complexes

Chirality is an important aspect of coordination chemistry, especially when it comes to understanding the optical isomerism of coordination complexes. In simple terms, chirality involves a molecule that cannot be superimposed on its mirror image, much like our left and right hands are mirror images, but cannot perfectly fit over each other. This inability to superimpose is what gives rise to optical isomerism, a type of stereoisomerism.

In coordination complexes, chirality often arises in octahedral complexes where the ligands—the atoms or groups of atoms surrounding the central metal—are arranged in a way that results in non-superimposable mirror images. An excellent example is when a central metal atom is surrounded by three bidentate ligands such as ethylenediamine (en). This type of arrangement breaks the symmetry required for achiral complexes.

• Bidentate ligands: Ligands that form two bonds with the central metal atom. These ligands increase the likelihood of a complex being chiral due to their "grabbing" capability on the metal center on two opposite sides.
• Asymmetry: For a complex to be chiral, it must lack symmetry, meaning it cannot be divided into two mirror-image halves.

Considering these principles, chirality and the potential for optical isomerism arise in cases like \([Co(en)_{3}]^{3+}\) where the tri-ethylene-diamine configuration leads to chirality.

Geometric Isomerism

Geometric isomerism is a form of stereoisomerism that occurs due to the different spatial arrangements of ligands around the central atom. Unlike chirality which involves non-superimposable mirror images, geometric isomerism merely involves rearranging the relative positions of ligands. This kind of isomerism typically occurs in octahedral and square planar complexes.

In octahedral complexes, typical geometric isomers include "cis" and "trans" configurations, as well as "fac" (facial) and "mer" (meridional) for complexes with at least three similar ligands.

• Cis-Trans: "Cis" isomers have similar ligands grouped closely on adjacently across or near each other, while in "trans" isomers, they are positioned opposite each other across the central metal.
• Fac-Mer: "Facial" isomers have three identical ligands forming the face of an octahedron, while "meridional" isomers arrange them across an axis.

For a complex like \([Co(NH_{3})_{3}Cl_{3}]\), geometric isomerism is the key point as it exhibits differentiation based on ligand positioning, resulting in fac and mer isomers, but not optical isomerism due to its inherent symmetry.

Coordination Chemistry

Coordination chemistry deals with the study of complexes that consist of a central metal atom or ion, bonded to surrounding molecules or ions called ligands. These ligands can greatly influence the properties and reactions of the metal center, creating a rich field of study.

A coordination complex is denoted by brackets such as \([Co(en)_{3}]^{3+}\). The central atom, usually a transition metal, coordinates with ligands through coordinate bonds, which involve the donation of an electron pair from the ligand to the metal.

• Coordination Number: The number of ligand donor atoms to which the metal is directly bonded. For octahedral complexes, this number is typically six.
• Ligands: Can be monodentate (one-point attachment) or polydentate (multiple-point attachments like bidentate "en" ligands), influencing stability and isomerism potential.

The study of coordination complexes involves various concepts including isomerism, electronic structure, and the energetics of complex formation. Understanding these elements helps to comprehend why certain complexes exhibit specific types of isomerism such as optical or geometric.