Problem 140 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of geomatrical isomers exhibited by \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\) is

Step-by-Step Solution

Answer

There are 2 geometrical isomers.

Step 1: Understanding the Compound

The compound \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \) is a coordination complex where chromium (Cr) is the central metal atom. The coordination number of the chromium atom is 6, as it is surrounded by six ligands comprising three ammonia ( \( \mathrm{NH}_3 \) ) molecules and three chloride ( \( \mathrm{Cl}^- \) ) ions.

Step 2: Evaluating Ligand Arrangement

The ligands in the complex can be arranged around the chromium atom in an octahedral geometry. Due to this geometry, there are two distinct ways to arrange three ammonia molecules and three chloride ions: either all chlorides can be adjacent to each other (facial, or ‘fac’ arrangement) or they can be opposite each other (meridional, or ‘mer’ arrangement).

Step 3: Identifying Isomers

The fac and mer arrangements represent two different geometrical isomers. In the fac isomer, the three chloride ions occupy one face of the octahedron, and the three ammonia molecules occupy the remaining positions. In the mer isomer, the chloride ions are aligned along the meridian line (two are opposite, and one is adjacent).

Step 4: Counting the Isomers

Since there are only two possible distinct geometrical arrangements of the ligands around the chromium center that result in different spatial orientations relative to one another, the number of geometrical isomers for \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \) is two.

Key Concepts

Coordination Complexes

Coordination complexes are fascinating structures formed by central metal atoms or ions bonded to surrounding molecules or ions, called ligands. Picture a metal atom as the center of a complex system, embraced by ligands that attach themselves through coordinate covalent bonds. In the compound \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), chromium (Cr) is the central metal atom involved in forming the coordination complex.
Crucially, coordination complexes can exhibit unique properties dependent on their structure and the nature of the ligands involved. Ligands can either be neutral molecules such as water \( \mathrm{H}_2\mathrm{O} \) or ammonia \( \mathrm{NH}_3 \), or can be charged species like chloride \( \mathrm{Cl}^- \). The ligands encircle the central metal atom, often creating intricate geometrical arrangements that influence the chemical behavior of the complex.

• Coordination Number: This term refers to the number of ligand atoms directly bonded to the central metal. For \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), the coordination number is 6.
• Coordinate Covalent Bonds: These are a type of chemical bond where both electrons in the bond originate from the same atom, typically from the ligand.

Octahedral Geometry

Octahedral geometry is a common shape for coordination complexes, especially when the central metal is surrounded by six ligands. It forms elegantly, with each ligand positioned at the corners of an imaginary octahedron. This setup gives the complex distinct 3-D spatial properties and plays a significant role in determining the complex's chemical characteristics.
In the case of \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), the six positions around the central chromium atom are occupied by three ammonia molecules and three chloride ions. Their arrangement forms the basis for the different isomers of the compound.

• Ligand Positioning: In an octahedral complex, ligands can occupy any of the six positions, meaning various geometric isomers can arise due to different spatial arrangements.
• Bond Angles and Symmetry: The bond angles in octahedral geometry are 90 degrees between adjacent ligands and 180 degrees between opposite ligands, providing a high degree of symmetry.

Isomerism in Coordination Compounds

Isomerism is a fascinating concept in coordination chemistry where compounds with the same formula have different arrangements of atoms, leading to different properties. Geometrical isomers, specifically, differ in the spatial positioning of ligands.
In the context of an octahedral complex like \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), geometrical isomerism manifests as two distinct forms: the fac (facial) and mer (meridional) isomers.

• Facial Isomers (fac): Here, three identical ligands (like \(\mathrm{Cl}^-\)) are grouped together on one face of the octahedron. This creates a distinctive plane that separates it from the rest of the complex.
• Meridional Isomers (mer): These occur when a set of identical ligands sits around the central metal in a meridian line (like a line on a globe connecting the North and South poles), balancing with two opposite each other and one adjacent.

By realizing and identifying these isomers, chemists can better understand and predict the interactions and reactions of coordination complexes, which is crucial in fields ranging from catalysis to pharmaceutical design.