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) \(\mathrm{Cr}\left[\left(\mathrm{NH}_{3}\right)\right] \mathrm{Cl}_{3}\) (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), \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]\), shows optical isomerism due to chiral bidentate ligands.

Step 1: Understanding Optical Isomerism

Optical isomerism occurs in compounds that can exist as non-superimposable mirror images, similar to 'left-handed' and 'right-handed' configurations. This is typically possible in complexes with an asymmetric or chiral structure, often seen in complexes with bidentate ligands forming non-planar structures.

Step 2: Analyzing Option (a)

Option (a) is \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\). This complex contains the ligand cyanide (\(\mathrm{CN}^{-}\)), which is monodentate, and forms an octahedral geometry around the central atom. Monodentate ligands in symmetrical octahedral complexes typically do not exhibit optical isomerism as they can be superimposed on their mirror images.

Step 3: Analyzing Option (b)

Option (b) is \(\mathrm{Cr}\left[\left(\mathrm{NH}_{3}\right)\right] \mathrm{Cl}_{3}\). This is incorrectly denoted, likely meant to be \([\mathrm{Cr}(\mathrm{NH}_{3})_6]^{3+}\). Assuming that, it contains only monodentate ligands, ammonia, which also form an octahedral geometry. Such symmetrical complexes do not show optical isomerism.

Step 4: Analyzing Option (c)

Option (c) is \(\mathrm{FeSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\). This is a simple salt hydrate with no complex ion structure, as the water molecules are associated as crystal water. Simple salts or hydrates like this generally do not exhibit optical isomerism.

Step 5: Analyzing Option (d)

Option (d) is \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\). This complex contains the bidentate ligand oxalate (\(\mathrm{C}_2\mathrm{O}_4^{2-}\)). Bidentate ligands in an octahedral geometry can form chiral complexes depending on their spatial arrangement, making this complex capable of showing optical isomerism.

Key Concepts

Chirality in Chemistry

Optical isomerism is a fascinating aspect of chirality in chemistry, which occurs when molecules or compounds can exist in two forms that are mirror images of each other, yet cannot be superimposed. This non-superimposability is akin to how your left and right hands are mirror images but cannot perfectly overlay each other. In chemistry, this concept is crucial for understanding the behavior of many molecules, especially in coordination compounds. These non-superimposable mirror images are referred to as enantiomers.

Enantiomers have the same molecular formula and connectivity of atoms but differ in the arrangement of atoms in space. This unique arrangement leads to significant differences in chemical and physical properties, such as the direction in which they rotate plane-polarized light. These properties play a central role in fields such as pharmaceuticals, where one enantiomer of a drug might be beneficial, while the other could be harmful. Understanding the principles of chirality in coordination compounds helps chemists design specific molecules for desired purposes, highlighting the significance of chirality in practical applications.

Bidentate Ligands

Bidentate ligands are a fascinating type of ligand in coordination chemistry. The term 'bidentate' comes from Latin, where 'bi-' means two and 'dentate' means tooth-like, suggesting that these ligands attach to a central metal atom using two 'teeth' or points of attachment. This dual attachment allows the ligand to form a more stable complex with the metal atom. A classic example is the oxalate ion ( abla ) found in the compound abla .

Bidentate ligands are significant because they help form stable and stereochemically non-rigid complexes. By creating "bridges" over the central atom, they increase the complexity of the three-dimensional structure, making it possible for the compound to exhibit optical isomerism. The spatial configuration achieved through these ligands can lead to chiral complexes, especially in octahedral arrangements, as they constrain and define the spatial orientation of the entire complex. Understanding the role of bidentate ligands aids in predicting the formation and properties of such isomeric complexes, important in both natural systems and industrial applications.

Octahedral Complexes

Octahedral complexes are widespread in coordination chemistry and typically involve a central metal atom surrounded by six ligands. These ligands could be ions or neutral molecules. The classic geometry of octahedral complexes is akin to an octahedron - a polyhedron with eight equilateral triangular faces. The arrangement is highly symmetrical and can accommodate a wide range of ligand types, including bidentate ligands.

In octahedral complexes, the spatial arrangement of the ligands around the central atom plays a pivotal role in determining whether a compound can exhibit chirality. When symmetrical, with monodentate ligands, these complexes tend not to be chiral, as in the case of abla . However, when ligands like bidentate oxalate are involved, the asymmetric spatial arrangement can lead to chiral forms.

Understanding octahedral geometry is crucial for predicting the behavior and properties of coordination compounds, especially in detecting potential for optical isomerism. This geometry's ability to twist and turn into different orientations makes it a critical study area in designing compounds with desired chemical properties for various applications.