Problem 160 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following compounds shows optical isomerism? (a) \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) (b) \(\left[\mathrm{ZnCl}_{4}\right]^{2}\) (c) \(\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3}-\) (d) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3}-\)

Step-by-Step Solution

Answer

Compound (c) \( \left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]^{3}- \) shows optical isomerism.

Step 1: Understand Optical Isomerism

Optical isomerism occurs in compounds that can form non-superimposable mirror images. This is common in complexes that lack a plane of symmetry or a center of symmetry, often involving chiral centers.

Step 2: Examine Each Compound for Elements of Chirality

Analyze each compound to see if it can exist as non-superimposable mirror images. This involves checking the coordination complex's geometry and its symmetry.

Step 3: Analyze Compound (a): \( \left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} \)

Compound (a) forms a square planar or tetrahedral complex with four similar ligands. Both geometries are symmetrical, with no element of chirality, thus not showing optical isomerism.

Step 4: Analyze Compound (b): \( \left[\mathrm{ZnCl}_{4}\right]^{2} \)

Compound (b) forms a tetrahedral complex but has identical ligands, which means it has a plane of symmetry and cannot possess chirality, so it does not show optical isomerism.

Step 5: Analyze Compound (c): \( \left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]^{3}- \)

Compound (c) has a metal surrounded by oxalate ions in a three-dimensional arrangement with no plane of symmetry. The bidentate nature of oxalate can lead to chirality, allowing for non-superimposable mirror images, hence optical isomerism is possible.

Step 6: Analyze Compound (d): \( \left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3}- \)

Compound (d) is an octahedral complex with six identical cyanide ligands, leading to complete symmetry with a center of symmetry, making optical isomerism impossible.

Key Concepts

Coordination Compounds

Coordination compounds play a central role in the field of inorganic chemistry. These compounds consist of a central metal atom bonded to a surrounding array of molecules or ions. These surrounding entities are known as ligands. The interaction between the metal and the ligands involves coordinate covalent bonds, which differ from normal covalent bonds as the electrons come from the ligand.

Coordination compounds exhibit diverse geometries, such as octahedral, tetrahedral, and square planar. The geometry plays a crucial role in determining the properties and functions of these compounds. In the context of optical isomerism, the arrangement of ligands around the central metal can lead to the formation of non-superimposable mirror images, if asymmetry is present.

• **Octahedral complexes** can sometimes show optical isomerism if they lack symmetry, especially when bidentate ligands are involved.
• **Square planar complexes** are generally symmetrical, typically not showing optical isomerism.
• **Tetrahedral complexes** with different ligands can be chiral and show optical isomerism, though not when all ligands are identical.

Understanding the coordination number, which indicates how many ligands directly bond to a metal, is also essential. This not only influences the geometry but also the potential for optical activity.

Chirality in Chemistry

Chirality is a fascinating concept in chemistry, referring to an object's ability to have non-superimposable mirror images, much like left and right hands. In molecules, chirality arises when a carbon atom or other central atom has four different groups attached, creating a chiral center.

In coordination chemistry, chirality can occur in metal complexes, especially those with asymmetric ligand arrangements. When a coordination compound has chiral centers, its mirror images cannot be superimposed on one another. These mirror images are called enantiomers, and they have identical physical properties but can behave differently in biological and chemical environments.

• **Bidentate ligands**, such as oxalate ions, can lead to chiral complexes by creating an environment that isn't symmetric.
• If a complex has a **plane of symmetry** or **center of symmetry**, it generally won't show chirality and, therefore, cannot exhibit optical isomerism.
• Enantiomers can rotate plane-polarized light in different directions, a phenomenon known as optical activity.

Exploring chirality helps in understanding how different structures interact with light and other chiral substances. It's essential for fields like pharmaceuticals, where the function of a drug can be heavily dependant on its chirality.

Symmetry in Molecules

Symmetry plays a significant role in determining whether a molecule can exhibit optical isomerism. In molecular terms, symmetry involves an object's invariance under certain transformations. The more symmetrical a molecule is, the less likely it will be chiral.

Key symmetry elements in molecules include:

• **Planes of symmetry**: These divide a molecule into two mirrored halves. If present, they rule out the possibility of optical isomerism.
• **Centers of symmetry**: These imply that moving from any part of the molecule through this center leads to an identical segment on the opposite side.
• **Axes of symmetry**: Allow rotation of the molecule so that it appears the same, which again reduces the chances of chirality.

In coordination chemistry, these principles of symmetry help identify which compounds might exhibit optical isomerism. Compounds lacking a plane of symmetry or a center of symmetry, especially those with multiple and varied ligands, are prime candidates to be optically active.

Therefore, understanding symmetry not only assists in predicting physical properties but also in designing and manipulating coordination compounds for desired chiral features.