Problem 72 - A Complete Resource Book in Chemistry for JEE Main

Question

Tetrahedral complexes of the types of \(\left[\mathrm{Ma}_{4}\right]\) and \(\left[\mathrm{Ma}_{3} \mathrm{~b}\right]\) (here \(\mathrm{M}=\) Metal, \(\mathrm{a}, \mathrm{b}=\) Achiral ligands) are not able to show optical isomerism because (a) these molecules/ions have non super imposable mirror images (b) these molecules possess a centre of symmetry (c) these molecules/ions possess a plane of symmetry and hence are achiral (d) these molecules/ions possess \(\mathrm{C}_{\mathrm{n}}\) axis of symmetry

Step-by-Step Solution

Answer

(c) These molecules/ions possess a plane of symmetry and hence are achiral.

Step 1: Understanding the Problem

The problem is asking why tetrahedral complexes of the type \([\mathrm{Ma}_4]\) and \([\mathrm{Ma}_3\mathrm{b}]\) do not exhibit optical isomerism. Optical isomerism requires molecules to be chiral, which means they cannot have an internal plane of symmetry.

Step 2: Analyzing Tetrahedral Complexes

Analyze the structures of \([\mathrm{Ma}_4]\) and \([\mathrm{Ma}_3\mathrm{b}]\):- \([\mathrm{Ma}_4]\) complex has four identical ligands attached to the metal, forming a symmetrical tetrahedral shape.- \([\mathrm{Ma}_3\mathrm{b}]\) complex has three identical ligands and one different ligand, which still forms a tetrahedral geometry that can be bisected through a mirror plane.

Step 3: Understanding Symmetry in Complexes

Optical isomerism in molecules is impossible if the molecule has any symmetry element like a plane of symmetry, center of symmetry, or a rotational symmetry axis (\(\mathrm{C}_n\) axis). - For \([\mathrm{Ma}_4]\), the complex is symmetrical with a \(\mathrm{C}_n\) axis and a mirror plane, rendering it achiral.- For \([\mathrm{Ma}_3\mathrm{b}]\), the presence of one distinct ligand still allows collection of symmetry since it's not a complete set of different ligands, allowing for a mirror plane.

Step 4: Identifying the Correct Answer

Optical isomerism is hindered by planes of symmetry, which make the molecules achiral. Since both \([\mathrm{Ma}_4]\) and \([\mathrm{Ma}_3\mathrm{b}]\) possess such planes, they cannot exhibit optical isomerism.

Key Concepts

Tetrahedral Complexes

Tetrahedral complexes are a fascinating part of coordination chemistry, featuring a central metal atom surrounded by four ligands. These ligands are positioned at the corners of a tetrahedron, creating a three-dimensional structure. The geometry of these complexes leads to interesting properties, especially regarding symmetry and chirality.

Understanding the spatial arrangement of a tetrahedral complex begins with recognizing its basic symmetrical nature. In complexes like \([\mathrm{Ma}_4]\), the four ligands are identical and equidistant from one another, resembling a symmetrical object like a pyramid with triangular faces. This symmetry plays a crucial role in determining whether a molecule can exhibit optical isomerism.

Chiral Molecules

Chirality in chemistry is linked to the idea that an object or a molecule cannot be superimposed on its mirror image. When discussing tetrahedral complexes, chirality becomes critical when considering optical isomerism. For a molecule to be chiral, it must lack any internal plane of symmetry or any other type of symmetry like rotational axis or center.

Imagine your hands as mirror images—they cannot be exactly superimposed over each other. Similarly, a chiral molecule will have this property where its mirror image is distinct and non-superimposable, leading to the possibility of enantiomers, which are pairs of optical isomers. In metal complexes like \([\mathrm{Ma}_3\mathrm{b}]\), the presence of different ligands can potentially create chirality, though this is not the case if there's symmetry allowing a mirror plane.

Symmetry in Molecules

Symmetry in molecules refers to the balanced distribution of identical elements or parts. In tetrahedral complexes, symmetry can include planes of symmetry, rotational axes, and centers of symmetry. Each type plays a role in how the molecule's 3D arrangement looks and behaves.

For \([\mathrm{Ma}_4]\) complexes, the symmetrical arrangement of ligands means that any line through the metal can act as an axis of symmetry, and any plane can bisect the structure symmetrically, highlighting its overall balanced nature. This inherent symmetry means it cannot be chiral, as chirality demands asymmetry. When considering optical activity or lack thereof, it's the presence of such symmetry that decides the behavior of the molecules.

Ligand Arrangement

Ligands are ions or molecules attached to a central metal atom in a complex. Their arrangement in a tetrahedral complex significantly impacts the molecule's properties, especially concerning its symmetry and potential to be chiral.

In a \([\mathrm{Ma}_4]\) tetrahedral complex, having four identical ligands creates a highly symmetrical arrangement, preventing optical isomerism. Meanwhile, in \([\mathrm{Ma}_3\mathrm{b}]\), although one ligand differs, the arrangement still allows for a plane of symmetry if three of the four ligands are identical.

• The identical nature of three ligands ensures that, despite one differing ligand, the structure is still sufficiently symmetrical to inhibit chirality.
• Achieving optical isomerism requires a full set of different ligands, breaking any planes of symmetry.

Careful analysis of ligand arrangement helps determine complex behavior and whether these structures have the potential for optical activity.