Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

The possible numbers of isomers for the complex \(\left[\mathrm{MCl}_{2} \mathrm{Br}_{2}\right] \mathrm{SO}_{4}\) will be (a) 5 (b) 4 (c) 3 (d) 2

Step-by-Step Solution

Answer

The possible number of isomers is 2.

Step 1: Identify Coordinate Geometry

Determine the coordination geometry of the complex \([ ext{MCl}_2 ext{Br}_2]\). In this exercise, we will assume the central metal M forms a coordination number of 4, often leading to a square planar or tetrahedral arrangement.

Step 2: Consider Different Arrangements

For a square planar coordination, Cl and Br can be arranged in a variety of ways around M, given that they are different ligands.

Step 3: Analyze Square Planar Arrangements

Consider the square planar geometry for \([ ext{MCl}_2 ext{Br}_2]\): 1. Cis-isomer: Two chloride ions and two bromide ions are adjacent.2. Trans-isomer: Two chloride ions and two bromide ions are opposite to each other.

Step 4: Count Isomers

For the complex \([ ext{MCl}_2 ext{Br}_2]\) in square planar geometry:- There is 1 cis-isomer where Cl and Br are adjacent to each other.- There is 1 trans-isomer where Cl and Br are on opposite sides.Thus, there are 2 possible isomers.

Key Concepts

Isomers

In coordination chemistry, isomers are molecules that have the same chemical formula but differ in the arrangement of their atoms or the orientation of their ligands in space.
These differences can significantly affect the physical and chemical properties of the complexes.
Understanding isomers is crucial for predicting the behavior of these compounds in various chemical reactions and environments. Isomerism in coordination chemistry can be categorized into **structural** and **stereoisomerism**.
Structural isomers are those that differ in connectivity of atoms. On the other hand, stereoisomers have the same connectivity but differ in spatial arrangement. Some key points to remember about isomers include:

• Isomers can exhibit different chemical reactivities.
• Their physical properties, such as melting point and solubility, can also vary.
• Even a slight change in atom arrangement can lead to drastic changes in functionality.

Complexes like \([\text{MCl}_2\text{Br}_2]\) exemplify how different ligands can lead to isomer formation.

Coordination Geometry

Coordination geometry refers to the geometric arrangement of ligands around a central metal atom in a complex.
In coordination complexes, the central atom (often a metal) is bonded to a number of surrounding molecules or ions known as ligands.
This arrangement, known as the coordination geometry, can vary based on the coordination number and the type of ligands involved.In the case of a coordination number of 4, some typical geometries include:

• **Square planar**: Four ligands positioned in the same plane 90° apart. Commonly seen in d8 metal ions.
• **Tetrahedral**: Four ligands positioned at the vertices of an imaginary tetrahedron, approximately 109.5° apart.

The geometry can influence the number and types of isomers possible.
For example, in the complex \(\left[\mathrm{MCl}_{2} \mathrm{Br}_{2}\right]\), the geometry directly affects how we can arrange the Cl and Br atoms around the central M.

Cis-Trans Isomers

Cis-trans isomers are a type of stereoisomerism that occurs mostly in square planar and octahedral complexes.
Cis-trans isomerism involves the geometric positioning of ligands in the complex.In a cis configuration:

• Similar ligands are positioned adjacent to each other.
• This configuration can influence the dipole moment and solubility of the complex.

In a trans configuration:

• Similar ligands are positioned opposite to each other.
• This typically leads to a more symmetrical molecule.

For the complex \(\left[\mathrm{MCl}_{2}\mathrm{Br}_{2}\right]\), this type of isomerism is observed due to its square planar geometry.
The complex can exhibit both cis and trans isomers, resulting in different physical properties and chemical behaviors.