Problem 154 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following has largest number of isomers? (a) \(\left[\mathrm{Ru}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\) (b) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right]^{2+}\) (c) \(\left[\mathrm{Ir}\left(\mathrm{PR}_{3}\right)_{2} \mathrm{H}(\mathrm{CO})\right]^{2+}\) (d) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\) \([\mathrm{R}=\) alkyl group, en \(=\) ethylenediamine \(]\)

Step-by-Step Solution

Answer

(d) \([\text{Co(en)}_2\text{Cl}_2]^+\) has the largest number of isomers.

Step 1: Identify the Type of Complexes

All given complexes are coordination compounds. Determine whether they are octahedral, square planar, or other types of complexes. Most of these are octahedral due to the coordination numbers.

Step 2: Analyze the Ligand Configuration

For (a) \([\text{Ru(NH}_3)_4\text{Cl}_2]^+\), the possible isomers are based on the four \(\text{NH}_3\) groups and two \(\text{Cl}\) anions arranged around a central metal in an octahedral geometry. This can lead to cis-trans isomerism.For (b) \([\text{Co(NH}_3)_5\text{Cl}]^{2+}\), there is one geometric change possible around the octahedral complex, considering the position of the single \(\text{Cl}\) ligand.For (c) \([\text{Ir(PR}_3)_2\text{H(CO)}]^{2+}\), the ligands \(\text{PR}_3\), \(\text{H}\), and \(\text{CO}\) don't allow for much variation in arrangement.For (d) \([\text{Co(en)}_2\text{Cl}_2]^+\), it can have cis-trans isomers due to two equivalent \(\text{en}\) ligands and two \(\text{Cl}\) anions.

Step 3: Determine Potential Isomers for Each Complex

(a) \([\text{Ru(NH}_3)_4\text{Cl}_2]^+\): 2 different geometrical isomers (cis and trans).(b) \([\text{Co(NH}_3)_5\text{Cl}]^{2+}\): No geometric isomers as there is no free rotation or arrangement possible with only one \(\text{Cl}\) ligand.(c) \([\text{Ir(PR}_3)_2\text{H(CO)}]^{2+}\): This complex does not exhibit geometric isomerism due to its linear ligand arrangement.(d) \([\text{Co(en)}_2\text{Cl}_2]^+\): 2 geometrical isomers (cis and trans), and potentially optical isomerism due to the chiral centers of the \(\text{en}\) ligands.

Step 4: Identify the Largest Number of Isomers

Compare the number of isomers for all the complexes. Complex (d) exhibits more isomer possibilities (2 geometric isomers and potentially optical isomerism), leading to a larger total number of isomers compared to the other complexes.

Key Concepts

Geometric Isomerism

Geometric isomerism is often seen in certain coordination complexes. It occurs when the ligands bonded to a central metal can be arranged in different spatial orientations. In an octahedral complex, this isomerism mainly occurs due to the position of specific ligands around the metal center.

Imagine an octahedron as two pyramids sharing a base where ligands can attach at the vertices. When identical ligands are adjacent to each other, they form a cis-isomer. Conversely, when they are positioned opposite to one another, they form a trans-isomer. For example, in the complex \(\left[\mathrm{Ru(NH}_3)_4\mathrm{Cl}_2\right]^+\), located in an octahedral geometry, the \(\mathrm{NH}_3\) groups and \(\mathrm{Cl}^-\) ions can be arranged as either cis or trans, leading to two possible geometric isomers.

Keep in mind, not all ligand arrangements allow for geometric isomerism. The arrangement of ligands and their type significantly determine the existence of such isomers.

Optical Isomerism

Optical isomerism is another fascinating aspect of coordination compounds. This type of isomerism occurs when the complex cannot be superimposed on its mirror image, much like left and right hands. These types of isomers are also referred to as enantiomers, which have identical physical and chemical properties in the absence of chiral influences but rotate plane-polarized light in different directions.

Optical isomerism is common in octahedral complexes, mainly when the complex involves bidentate ligands (ligands that can attach to the central metal at two points). In the complex \(\left[\text{Co(en)}_2\text{Cl}_2\right]^+\), ethylenediamine (\(\text{en}\)) is a bidentate ligand, and this formation may cause optical isomers. These mirror-image structures make the complex chiral and allow the optical isomer to rotate light.

However, to exhibit optical isomerism, a compound must be free of elements of symmetry such as planes, centers, or improper axes of rotation.

Octahedral Complexes

Octahedral complexes are some of the most common and key structures in coordination chemistry, with the central atom usually surrounded by six ligands at the vertices of an octahedron. This type of complex is essential for understanding different isomerisms due to its spatial arrangement.

The octahedral geometry results from a coordination number of six. This means the metal atom forms bonds with six ligands, which could be any molecule or ion, like ammonia or chloride. The spatial configuration in octahedral complexes allows for a varied combination of ligands, influencing both geometric and optical isomerism.

In the context of the example \(\left[\text{Co(en)}_2\text{Cl}_2\right]^+\), we see important implications of octahedral geometry. Here, ethylenediamine \((\text{en})\) acts as a bidentate ligand and can achieve either a cis or trans configuration around the cobalt center, showing geometric isomerism. Additionally, the possible chiral nature of these configurations may result in optical isomerism. This multi-dimensional aspect of octahedral complexes underlines their complexity and fascinating role in coordination chemistry.