Problem 123 - A Complete Resource Book in Chemistry for JEE Main

Question

The coordination compound is a complex substance which contains a central metal atom or ion surrounded by oppositely charged ions or neutral molecules. These compounds exhibit structural as well as stereoisomerism. Hybridisation theory explains the geometry of the complex. Crystal field theory explains the colour of complexes and magnetic properties. Which one of the following does not show optical activity? (a) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\) (b) \(\left[\mathrm{Pt}(\mathrm{Br})(\mathrm{Cl})(\mathrm{I})\left(\mathrm{NO}_{2}\right)\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{~N}\right)\left(\mathrm{NH}_{3}\right)\right]^{-}\) (c) \(\operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}\) (d) \(\operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\)

Step-by-Step Solution

Answer

Compound (a) does not show optical activity.

Step 1: Understand Optical Activity

Optical activity refers to a compound's ability to rotate plane-polarized light. It is typically shown by molecules that do not possess a plane of symmetry and are chiral. In coordination compounds, optical activity is often observed in chiral complexes with no plane of symmetry.

Step 2: Analyze Compound (a)

The compound \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\right]^{+} \) has a square planar geometry if one equatorial position is occupied by \(\mathrm{Cl}\), leading to no chirality due to symmetry. This suggests it does not show optical activity.

Step 3: Analyze Compound (b)

The compound \( \left[\mathrm{Pt}(\mathrm{Br})(\mathrm{Cl})(\mathrm{I})\left(\mathrm{NO}_{2}\right)\left(\mathrm{C}_{6}\mathrm{H}_{5} \mathrm{N}\right)\left(\mathrm{NH}_{3}\right)\right]^{-} \) has all different ligands around the metal center. This breaks symmetry, making it possible to exhibit chirality and optical activity.

Step 4: Analyze Compound (c)

The compound \( \operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{Cl}_{2}\right]^{+} \) with \( \mathrm{en} \) as bidentate ligands can form a chiral center with a cis configuration, meaning it has a tendency to exhibit optical activity due to the lack of a plane of symmetry.

Step 5: Analyze Compound (d)

The compound \( \operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})_{2}\mathrm{Cl}_{2}\right]^{+} \) similarly forms a chiral center as there is no plane of symmetry in this cis configuration with bidentate \( \mathrm{en} \) ligands, therefore likely exhibits optical activity.

Step 6: Determine the Non-Optically Active Compound

Based on the analysis, compound (a) \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\right]^{+} \) does not exhibit optical activity due to its symmetric square planar structure.

Key Concepts

Optical Activity

Optical activity is a fascinating property of certain chemical compounds. It involves the ability of a compound to rotate plane-polarized light. This occurs due to the asymmetry present in the molecule, which is why only chiral compounds, or those lacking a plane of symmetry, can show optical activity.
In simpler terms, if you imagine shining a flashlight through sunglasses, where the light can be "twisted" just by the structure of a molecule, that is optical activity.

• Compounds that exhibit optical activity are typically those with chiral centers.
• A chiral center often arises from an atom bonded to four different groups.

In coordination chemistry, the presence or absence of a plane of symmetry greatly influences whether a complex will display optical activity. This aspect is crucial when working with coordination compounds such as \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\right]^{+}\)
which lacks optical activity due to its symmetrical structure.

Stereochemistry

Stereochemistry involves the study of spatial arrangements of atoms in molecules. It's the science of how we visualize complex structures of molecules three-dimensionally—a crucial aspect in understanding how molecules behave and interact.
In the realm of coordination chemistry, stereochemistry becomes especially important. Various compounds may have the same formula but differ in how their atoms are arranged in space. These differences can lead to significant variations in properties.

• Many coordination compounds exhibit both structural and stereoisomerism.
• It's important to identify whether a compound's arrangement allows for optical isomerism— a form of stereoisomerism.

For example, the interaction of ligands in a coordination compound greatly influences its optical properties—as we saw with\(\operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{Cl}_{2}\right]^{+}\).
Stereochemistry helps decipher compound behaviors and is invaluable in applications like drug design.

Crystal Field Theory

Crystal Field Theory (CFT) is a powerful model used to explain the electronic properties of transition metal complexes. This theory suggests that the interaction of metal ions with surrounding ligands can cause a split in the d-orbitals' energy levels.
Such splitting is integral to understanding the color and magnetic properties of complexes.

• The extent of the d-orbitals' energy splitting depends on the nature and arrangement of the ligands.
• Different arrangements can lead to varied absorption of light's wavelengths, often resulting in the vibrant colors seen in many metal complexes.

For instance, CFT helps explain why compounds like \(\left[\mathrm{Pt}(\mathrm{Br})(\mathrm{Cl})(\mathrm{I})\left(\mathrm{NO}_{2}\right)\left(\mathrm{C}_{6}\mathrm{H}_{5} \mathrm{~N}\right)\left(\mathrm{NH}_{3}\right)\right]^{-}\)
can be colorful due to ligand variation that influences energy level differences. It's fascinating how such small changes on a molecular level can lead to feeling different colors to the human eye!

Hybridisation Theory

Hybridisation Theory is essential for comprehending the geometry of coordination compounds. Hybridisation involves the mixing of atomic orbitals to form new hybrid orbitals, which can influence geometry and bonding.
In coordination chemistry, knowing the hybridisation of the central metal atom helps predict the shape of the complex:

• By understanding which orbitals combine, we can anticipate the geometry of the molecule.
• This influences not only the shape but also the stability and reactivity of the coordination compound.

For example, a coordination compound such as \([\mathrm{Cr}(\mathrm{NH}_{3})_{4}\mathrm{Cl}_{2}]^{+}\),
with potential square planar geometry, can often be explained by hybridisation of the metal's orbitals.
This concept opens the door to predict various structural possibilities in coordination chemistry efficiently.