Problem 81 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following octahedral complexes will not show geometric isomerism? (A and B are monodentate ligands) (a) \(\left[\mathrm{MA}_{4} \mathrm{~B}_{2}\right]\) (b) \(\left[\mathrm{MA}_{5} \mathrm{~B}\right]\) (c) \(\left[\mathrm{MA}_{2} \mathrm{~B}_{4}\right]\) (d) \(\left[\mathrm{MA}_{3} \mathrm{~B}_{3}\right]\)

Step-by-Step Solution

Answer

The complex [ ext{MA}_{5} ext{B}] does not show geometric isomerism.

Step 1: Understanding Geometric Isomerism

Geometric isomerism occurs in octahedral complexes when a compound can have different spatial arrangements of its ligands. Not all octahedral complexes can exhibit geometric isomerism. It largely depends on how many different types of ligands are present and their arrangement around the central metal atom.

Step 2: Examine the Complex [ ext{MA}_{4} ext{B}_{2}]

The formula [ ext{MA}_{4} ext{B}_{2}] has four identical A ligands and two identical B ligands. This complex can form geometric isomers: **cis** configurations (where both B ligands are adjacent) and **trans** configurations (where they are opposite). Therefore, it shows geometric isomerism.

Step 3: Examine the Complex [ ext{MA}_{5} ext{B}]

The formula [ ext{MA}_{5} ext{B}] has five identical A ligands and one B ligand. There cannot be an alternate spatial arrangement for the ligands around the central atom, so this complex does not exhibit geometric isomerism.

Step 4: Examine the Complex [ ext{MA}_{2} ext{B}_{4}]

The formula [ ext{MA}_{2} ext{B}_{4}] has two identical A ligands and four identical B ligands. This complex can form geometric isomers: **cis** configurations (where both A's are adjacent) and **trans** configurations (where they are opposite). Thus, it exhibits geometric isomerism.

Step 5: Examine the Complex [ ext{MA}_{3} ext{B}_{3}]

The formula [ ext{MA}_{3} ext{B}_{3}] has three A ligands and three B ligands. This complex can form different spatial arrangements: **facial** (where ligands form a face of the octahedron) and **meridional** (where ligands are along a central line) isomers. Therefore, it does display geometric isomerism.

Key Concepts

Octahedral Complexes

In chemistry, octahedral complexes refer to coordination compounds where six ligands are symmetrically arranged around a central metal atom, forming an octahedral geometry. This configuration is quite common in transition metal complexes and plays a vital role in determining the properties of the compound. The octahedral shape allows for a variety of possible arrangements of ligands, leading to interesting forms of isomerism such as geometric isomerism.

An octahedral complex can be visualized as a central atom bonded to six points that form an imaginary symmetrical octahedron. The spatial geometry significantly influences the chemical behavior and properties of the compound. For instance, octahedral complexes can show different electronic transitions, leading to varied colors of solutions of these complexes.

• Common examples include \[ \left[ \text{Fe(H}_2\text{O)}_6 \right]^{3+} \] and \[ \left[ \text{Co(NH}_3\text{)}_6 \right]^{3+} \].
• In octahedral complexes, ligands can be of the same type or different, influencing the possible isomeric forms.

Ligand Arrangements

Ligand arrangement in octahedral complexes is crucial in understanding isomerism. Ligands are ions or molecules that donate one or more pairs of electrons to the central metal atom. Their arrangement determines whether a compound can exhibit isomerism. In an octahedral complex, the ligands can occupy different positions around the metal center, leading to various spatial configurations.

The possible arrangements primarily include the following isomers:

• **Cis arrangement**: Where similar ligands are adjacent.
• **Trans arrangement**: Where similar ligands are opposite to each other.
• **Facial (fac) isomers**: When three identical ligands occupy one face of the octahedron.
• **Meridional (mer) isomers**: When three identical ligands are in a line around the central atom, connecting through one vertex.

Different arrangements affect the complex's properties, such as dipole moment, reactivity, and color. Understanding these arrangements is critical for grasping concepts such as geometric isomerism.

Chemical Isomerism

Chemical isomerism refers to compounds with the same molecular formula but different arrangements of atoms in space, leading to distinct properties. It is a broad concept in chemistry and includes several types, such as structural isomerism and stereoisomerism. Specifically for coordination compounds like octahedral complexes, geometric isomerism is a subtype of stereoisomerism.

Geometric isomerism occurs due to the different possible spatial arrangements of the ligands in the complex. Not every coordination complex exhibits geometric isomerism; it depends on the specific ligand arrangements and the symmetry of the complex.

• For example, an octahedral complex \( [ ext{MA}_4 ext{B}_2] \) can have cis and trans isomers.
• Complexes like \( [ ext{MA}_5 ext{B}] \) do not show geometric isomerism because there's only one B ligand and no scope for different spatial arrangements.

The isomerism leads to variations in physical and chemical properties, such as solubility, melting points, and reactivity, which are significant in their applications in fields like pharmacology and materials science.