Problem 178 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following complex species is not expected to exihibit optical isomerism? (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\) (b) \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}\) (c) \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) (d) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\)

Step-by-Step Solution

Answer

(a) \([\mathrm{Co}(\mathrm{NH}_3)_3 \mathrm{Cl}_3]\) does not exhibit optical isomerism.

Step 1: Understand Optical Isomerism

Optical isomerism occurs when a complex can exist in two non-superimposable mirror images. For this to happen, the complex usually lacks a plane of symmetry.

Step 2: Analyze the Structures for (a)

Analyze \[\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\]This is an octahedral complex with three ammonia and three chloride ligands. This structure can have a plane of symmetry, meaning it does not show optical isomerism.

Step 3: Analyze the Structures for (b)

Analyze \[\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}\]This octahedral complex with bidentate ethylenediamine (en) can form non-superimposable mirror images due to the arrangement of en.

Step 4: Analyze the Structures for (c)

Analyze \[\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\]This complex contains three bidentate en ligands forming a chiral complex without a plane of symmetry, making optical isomerism possible.

Step 5: Analyze the Structures for (d)

Analyze \[\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\]This structure, which has two en ligands and two chloride ligands, can have non-superimposable mirror images due to asymmetrical ligand arrangement, thus it can exhibit optical isomerism.

Step 6: Conclusion

Since option (a) has a plane of symmetry, it does not exhibit optical isomerism, unlike the other options which can form chiral centers.

Key Concepts

Octahedral Complex

An octahedral complex is a type of coordination compound where a central metal atom is surrounded by ligands in a spatial arrangement that resembles an octahedron. This is a classic shape often seen in chemistry due to the typical coordination number of 6 for many metal ions.
In this arrangement, the metal atom is centrally located, and the ligands are positioned at the corners of an octahedron. This geometry is highly symmetrical, which often affects the compound's properties, such as its optical activity. Some octahedral complexes can exhibit optical isomerism if they have an asymmetrical arrangement of ligands.
For example, in complex \[\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\\] the two chlorides and two bidentate ligands around cobalt create unique spatial arrangements that might be non-superimposable mirror images. This is less likely to happen in a more symmetrical complex, such as\[\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right] \] where there's a higher chance of having a plane of symmetry, making optical isomerism, or chirality, less likely.

Plane of Symmetry

A plane of symmetry is an imaginary plane that divides a molecule into two mirror-image halves. It plays a crucial role in determining the optical activity of a compound.
When a molecule possesses a plane of symmetry, it means that there is a way to slice through the molecule so that the two halves are mirror images of each other. As a result, the molecule cannot be chiral because it will not have non-superimposable mirror images.
In the context of coordination complexes, the presence of a plane of symmetry can prevent optical isomerism. For instance, in the complex\[\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\] a plane of symmetry exists, slicing through opposite pairs of ammonia and chloride ligands. This symmetry causes the compound to lack chirality, meaning it will not exhibit optical isomerism.

Chiral Complex

A chiral complex is one that cannot be superimposed on its mirror image. It is essentially the molecular equivalent of your left and right hands; they are similar, but not identical, as they cannot perfectly overlay each other.
Chirality in coordination complexes usually depends on the arrangement of ligands around the central metal atom. A complex is chiral when it does not have a plane of symmetry.
Consider the complex\[\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\] Here, the three bidentate ethylenediamine ligands wrap around the cobalt in a way that ensures no reflective symmetry. Each configuration of this complex forms non-superimposable mirror images, known as enantiomers. Hence, this complex can exhibit optical isomerism, meaning it can rotate plane-polarized light.
Understanding these concepts is vital for identifying which complexes can and cannot exhibit optical isomerism based on their symmetry and ligand arrangements.