Question

The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are) (A) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2}\) and \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (B) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\) and \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}\right]^{+}\) (C) \(\left[\mathrm{CoBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\) and \(\left[\mathrm{PtBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\) (D) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{NO}_{3}\right)\right] \mathrm{Cl}\) and \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}\right] \mathrm{Br}\)

Short answer

The pair of coordination complexes/ions that exhibit the same kind of isomerism is pair C: \(\left[\mathrm{CoBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\) and \(\left[\mathrm{PtBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\).

Step-by-step solution

Identify Isomerism Types

First, determine the types of isomerism each pair of complexes can exhibit. Isomerism in coordination complexes includes geometrical and optical isomerism. Geometrical isomers differ in the arrangement of ligands around the metal center, while optical isomers are non-superimposable mirror images of each other.

Analyze Pair A

For pair A, both complexes have a chromium metal center with six coordination sites. \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2}\) can exhibit geometrical isomerism (cis and trans forms), based on the position of chloride. Likewise, \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) can show geometrical isomerism, with different arrangements (cis and trans) of the chloride ligands.

Analyze Pair B

For pair B, the cobalt complex can exist in cis and trans forms due to geometrical isomerism, while the platinum complex does not allow for geometrical isomers because the platinum center has a coordination number of four, creating a square planar geometry which can't have cis or trans forms with the given ligands.

Analyze Pair C

Examining pair C, both complexes feature a metal center with four different ligands, leading to potential geometrical isomerism (where positions of bromide and chloride can vary). Both \(\left[\mathrm{CoBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\) and \(\left[\mathrm{PtBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\) can exhibit geometrical isomerism.

Analyze Pair D

In pair D, both platinum complexes cannot exhibit geometrical isomerism as they have a coordination number of four in a square planar geometry, and while they could exhibit optical isomerism, both of the given complexes are not chiral (they don't have a non-superimposable mirror image), thus neither geometrical nor optical isomerism is displayed in this pair.

Conclusion

From the analysis, the only pair of complexes that exhibit the same kind of geometrical isomerism is pair C (\(\left[\mathrm{CoBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\) and \(\left[\mathrm{PtBr}_{2} \mathrm{Cl}_{2}\right]^{2-}\)).

Key concepts

Geometrical Isomerism

Understanding geometrical isomerism is crucial when exploring the structural diversity of coordination complexes. This form of isomerism arises due to the different possible layouts of ligands around a central metal atom within the same coordination sphere.

Consider a metal center bonded to various ligands. If the ligands can switch places, leading to distinct arrangements, we have a scenario ripe for geometrical isomerism. This phenomenon is most commonly witnessed in complexes with coordination numbers of four or six. In the case of four, a square planar configuration can lead to 'cis' and 'trans' isomers, where ligands are adjacent or across from each other, respectively. Similarly, in an octahedral complex with six coordination sites, as seen with chromium in the provided example, ligands may arrange in multiple distinct ways, resulting in isomers with unique spatial arrangements.

Optical Isomerism

Diving into the concept of optical isomerism reveals a fascinating aspect of coordination chemistry. Optical isomers, or enantiomers, are molecules that are mirror images of one another yet cannot be superimposed. This non-superimposability is a hallmark of chirality—a concept that we'll discuss shortly.

In coordination complexes, optical isomerism occurs when there is an asymmetric arrangement of ligands around the central metal, bestowing the complex with a 'handedness.' It's akin to your left and right hands—mirror images but not the same. Such isomers can rotate the plane of polarized light in different directions, one to the left (levorotatory) and the other to the right (dextrorotatory). However, optical activity requires the presence of a chiral center; without it, as noted in pair D of the problem, the complex will not exhibit optical isomerism.

Ligand Arrangement

The term ligand arrangement refers to the spatial distribution of ligands—molecules or ions that donate at least one electron pair to bind to a central metal atom or ion. It significantly influences the properties and reactivity of the complex.

The arrangement can vary widely: linear for a coordination number of two, trigonal planar or T-shaped for three, tetrahedral or square planar for four, trigonal bipyramidal or square pyramidal for five, and octahedral for six. It's this variability in ligand placement that leads to the different types of isomerism, which can include not just the geometrical and optical but also linkage isomerism and coordination isomerism among others.

Chiral Centers

The concept of chiral centers is intertwined with the occurrence of optical isomerism in chemistry. A chiral center in a molecule is an atom that bears groups of substituents in such a manner that it creates a non-superimposable mirror image of the molecule. Most commonly, it is a carbon atom with four different substituents.

It is essential to note that the existence of a chiral center is not enough to ensure optical activity; the molecule as a whole must lack an internal plane of symmetry. In coordination complexes, a chiral center leads to the potential of having two enantiomers, which was not the case with pair D in the exercise. There, the platinum complexes do not possess the requisite chiral centers to result in optical isomerism.