Problem 68 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following can show optical isomerism? (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) (b) \(\mathrm{Cr}\left[\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) (c) \(\mathrm{FeSO}_{4^{-}} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\)

Step-by-Step Solution

Answer

Option (d) \(\mathrm{K}_{3}\left[\mathrm{Cr}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}\right]\) can show optical isomerism.

Step 1: Understanding Optical Isomerism

Optical isomerism occurs in compounds that can exist as non-superimposable mirror images due to the presence of chirality. In coordination chemistry, this often involves complexes where a central metal atom is bonded to chiral ligands or a coordination geometry that allows for such isomerism.

Step 2: Examining Option (a)

The compound \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) contains the \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) complex ion, which is octahedral and symmetrical. Symmetrical octahedral complexes do not exhibit optical isomerism as they have a plane of symmetry.

Step 3: Examining Option (b)

The compound \(\mathrm{Cr}\left[\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) consists of an \(\left[\mathrm{Cr}(\mathrm{NH}_{3})_{6}\right]^{3+}\) complex ion. The ammine ligands are symmetrical around the chromium center, and such a complex is octahedral and saturated with symmetrical ligands, which means it cannot show optical isomerism.

Step 4: Examining Option (c)

The compound \(\mathrm{FeSO}_{4^{-}} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) is a hydrated salt where optical isomerism is not applicable. Optical isomerism usually involves complex ions or organic molecules with chiral centers, not simple hydrated salts.

Step 5: Examining Option (d)

The compound \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]\) includes the \(\left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]^{3-}\) complex. This is an octahedral complex with bidentate oxalate ligands arranged asymmetrically. The presence of three bidentate ligands in an octahedral arrangement creates chirality, allowing for optical isomers known as 'dark green' complex salts.

Step 6: Conclusion

After analyzing each option, it's clear that option (d), the compound \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]\), is the only one that can exhibit optical isomerism due to its asymmetrical arrangement of bidentate ligands.

Key Concepts

Coordination Complexes

In the realm of chemistry, coordination complexes are fascinating structures made up of a central metal atom or ion surrounded by molecules or anions called ligands. These complexes form through coordinate covalent bonds, where both electrons in the bond come from the ligand. The central metal atom can bond with multiple ligands, and the number and arrangement often determine the properties of the complex, including its shape and potential optical properties.

• Chelation Effect: When ligands form more than one bond with the central atom, they create very stable structures known as chelates.
• Different Geometries: Common coordination geometries include tetrahedral, square planar, and octahedral, each affecting the complex’s symmetry and reactivity.

Coordination complexes are crucial in various applications, from catalysis to the development of new materials and medicines.

Chirality in Chemistry

Chirality is a fundamental concept that extends to several areas, including coordination chemistry, where it plays a key role in the optical isomerism of certain complexes. In simple terms, chirality refers to a property of asymmetry where an object is not superimposable on its mirror image, much like left and right hands. In coordination complexes, chirality arises when a complex can exist in two non-superimposable forms. These are called enantiomers, and they differ in their interaction with plane-polarized light.

• Impact on Light: Chiral molecules rotate plane-polarized light, a property used in identifying optical isomers, a process known as optical activity.
• Biological Significance: Many biomolecules are chiral, and this characteristic is vital in biochemical processes, making chirality essential in drug design.

Understanding chirality helps us grasp why only certain arrangements of atoms cause optical isomerism.

Bidentate Ligands

Bidentate ligands are unique because they can form two bonds with a central metal atom in a coordination complex, creating a more stable arrangement called a chelate. This feature makes them distinct from monodentate ligands that form only a single bond.The presence of bidentate ligands often leads to the formation of more complex and stable structures. When these ligands arrange asymmetrically around a metal center, they can induce chirality, leading to the possibility of optical isomers.

• Common Examples: Oxalate (\[C_2O_4^{2-}\]) and ethylenediamine are popular bidentate ligands known for their coordinating abilities.
• Applications: Bidentate ligands are used extensively in catalysis and synthesis of coordination compounds with specific optical properties needed for particular applications.

Their ability to create asymmetric complexes is a fundamental reason why certain coordination compounds, like the one provided in option (d), can show optical isomerism.