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 when a compound can exist in two non-superimposable mirror image forms, known as enantiomers. This type of isomerism is typically found in chiral molecules, usually tetrahedral or octahedral complexes that do not have a plane of symmetry.

Step 2: Analyze Compound Structure (a)

The compound (a) \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is a tetraammine copper(II) cation. It has a square planar or tetrahedral geometry. This type of compound is generally not chiral because it is either symmetric or has a plane of symmetry.

Step 3: Analyze Compound Structure (b)

Compound (b) \(\left[\mathrm{ZnCl}_{4}\right]^{2-}\) is a tetrahedral complex. However, for tetrahedral complexes to show optical isomerism, they must have four different ligands, which is not the case here as all four ligands (chlorides) are identical.

Step 4: Analyze Compound Structure (c)

The compound (c) \(\left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]^{3-}\) is an octahedral complex with three bidentate \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\) (oxalate) ligands. This structure can form two non-superimposable mirror images due to the specific arrangement of bidentate ligands, exhibiting optical isomerism.

Step 5: Analyze Compound Structure (d)

Compound (d) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\) is also an octahedral complex but with six identical cyanide ligands. The symmetry of six identical ligands in an octahedral coordination prevents it from being chiral.

Step 6: Conclusion

Considering the analyses in steps 2 to 5, only compound (c) \(\left[\mathrm{Cr}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]^{3-}\) has a structure capable of showing optical isomerism.

Key Concepts

Chirality

Chirality is a fascinating concept found in chemistry, which denotes a molecule's characteristic of having a non-superimposable mirror image. To understand chirality, think of your hands. They are mirror images of each other but cannot be perfectly aligned when superimposed - this is chirality in a nutshell.

In chemical terms, a chiral molecule often contains a carbon atom bonded to four different substituents. This unique arrangement makes it impossible for the molecule and its mirror image to overlap completely. Such molecules are known as enantiomers, which can significantly affect properties like smell or biological activity. For a molecule to be chiral, it must lack an internal plane of symmetry - a feature allowing its mirror image to be distinct and non-superimposable.

• Enantiomers: Pairs of chiral molecules that are mirror images.
• Molecular Symmetry: Chiral molecules must not have a plane of symmetry.

Chirality is not only vital for organic molecules but also plays a key role in inorganic systems like coordination complexes.

Coordination Complexes

Coordination complexes are compounds formed by the association of metal ions with ligands, where ligands donate pairs of electrons to the metallic center. These complexes exhibit various geometries, including linear, square planar, tetrahedral, and octahedral configurations.

A coordination complex becomes a fascinating subject when it shows optical isomerism, as seen in some chiral complexes. Optically active complexes must have a chiral arrangement of ligands around the central metal atom. The variety of shapes that coordination complexes can take often determines whether or not they are chiral.

• Square Planar: Generally symmetric, often non-chiral.
• Tetrahedral: Can be chiral if all four ligands are different.
• Octahedral: Chiral complexes often involve non-identical, mutually oriented bidentate ligands.

The true intrigue of coordination complexes lies in their geometry, which can drastically affect their chemical properties and reactivity.

Molecular Symmetry

Molecular symmetry is a critical element when determining whether a compound will have optical isomerism. Symmetry refers to how a molecule can be transformed into itself through various operations, like reflection, rotation, or inversion.

A molecule with high symmetry, often represented by identical ligands evenly distributed around a central atom, will likely not exhibit optical isomerism. This is because such symmetrical arrangements result in the molecule's mirror image being superimposable onto the original. Only when a molecule lacks symmetrical alignment can chirality, hence optical isomerism, be possible.

• Planes of Symmetry: Presence usually indicates non-chirality.
• Asymmetrical Arrangement: Needed for chirality and optical isomerism.
• Inversion Centers: Often prevent a molecule from being chiral.

Understanding molecular symmetry can help predict the optical activity of organic and inorganic compounds, guiding chemists in designing substances with desired properties.