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) \(\left[\mathrm{Pt}(\mathrm{Br})(\mathrm{Cl})(\mathrm{I})\left(\mathrm{NO}_{2}\right)\left(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{~N}\right)\left(\mathrm{NH}_{3}\right)\right]^{-}\) (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

(a) \([\mathrm{Cr}(\mathrm{NH}_{3})_{4}\mathrm{Cl}_{2}]^{+}\) does not show optical activity.

Step 1: Understand Optical Activity

Optical activity refers to the ability of a compound to rotate the plane of polarized light. Only compounds that are chiral exhibit optical activity. In coordination complexes, chirality is typically due to the lack of an internal plane of symmetry.

Step 2: Analyze Compound (a)

The complex \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\right]^{+}\) has a coordination number of 6, often resulting in an octahedral shape. As it contains symmetrical ligands and two identical chloride ions, it may have a plane of symmetry and does not necessarily show chirality.

Step 3: Analyze Compound (b)

The complex \(\left[\mathrm{Pt}(\mathrm{Br})(\mathrm{Cl})(\mathrm{I})\left(\mathrm{NO}_{2}\right)\left(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{~N}\right)\left(\mathrm{NH}_{3}\right)\right]^{-}\) is square planar due to the coordination of 4 different ligands around Pt, making it unsymmetrical with no plane of symmetry, suggesting it can be optically active.

Step 4: Analyze Compound (c)

The complex \(\operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}\) features ethylenediamine (en) as a bidentate ligand, which could create chirality. However, due to the "cis" configuration and presence of symmetrical ligands, internal symmetry can be disrupted, creating potential optical activity in this configuration.

Step 5: Analyze Compound (d)

The complex \(\operatorname{Cis}\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\) has two ethylenediamine (en) ligands in cis position, which can cause chirality by creating an asymmetric coordination sphere due to the spatial arrangement of en ligands and chlorides. This often results in optical activity.

Step 6: Determine the Non-optically Active Compound

Based on the analyses, \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\) is least likely to exhibit optical activity due to potential symmetry caused by identical ligands. Typically, these configurations do not disrupt symmetry enough to cause chirality.

Key Concepts

Optical Activity

Optical activity is a fascinating property of certain compounds, particularly those that can rotate the plane of polarized light. This phenomenon is closely connected to chirality, a concept we will explore shortly. When light passes through an optically active compound, the light waves are twisted depending on the nature of the compound. This occurs because the molecules in these compounds have structures that differ in spatial arrangement, making them non-superimposable on their mirror images. In simpler terms, think of it like a screw. As you twist the screw, it can either go left or right, and likewise, optically active compounds can rotate light in different directions. This property is primarily found in chiral molecules, those without internal symmetry, meaning every chiral molecule is inherently unique.

Chirality in Complexes

Chirality in coordination compounds arises when the central metal atom is surrounded by ligands arranged in a non-superimposable manner. This lack of an internal plane of symmetry makes the molecule chiral. Consider a left and right hand; they are mirror images but cannot be perfectly aligned atop each other. This is similar to how chiral complexes behave.
In coordination chemistry, chirality often results from geometric arrangements of ligands around the central ion, such as tetrahedral or octahedral configurations. For example, in cis-configurations where different ligands occupy adjacent positions, the molecule gains a specific three-dimensional shape that mirrors cannot match. Thus, these arrangements often lead to chiral behavior and, consequently, optical activity.
Recognizing chirality in coordination compounds helps chemists predict the optical properties of the molecules.

Hybridisation in Coordination Chemistry

Hybridisation is a key concept in explaining the geometry of coordination complexes. It involves the mixing of atomic orbitals to form new hybrid orbitals suitable for bonding with ligands. For instance, a coordination number of 6, typical of octahedral complexes, often involves the hybridisation of the central metal's orbitals like \(d^2sp^3\).
This hybridisation indicates how electrons are spatially distributed around the central metal, which directly influences the geometry of the molecule. For example, in square planar complexes, \(d^sp^2\) hybridisation may be observed, which involves different sets of orbitals leading to diverse geometries such as square planar or even tetrahedral. Understanding hybridisation is therefore critical in predicting not only the structure but also the reactivity and other chemical behaviors of the coordination compound.

Crystal Field Theory

The Crystal Field Theory (CFT) provides a fundamental framework to understand the colors and magnetic properties of coordination complexes. It focuses on the distribution of d-electrons in the presence of ligands. When ligands approach a central metal ion, they affect its d-orbitals, splitting them into different energy levels due to electrostatic interactions. This splitting determines whether a complex absorbs light in specific wavelengths, contributing to its distinctive color.
Furthermore, CFT can predict magnetic behavior by elucidating whether or not electrons in these split d-orbitals will pair up. For example, a larger energy gap often results in low-spin configurations where electrons pair up, leading to diamagnetism. Conversely, smaller gaps yield high-spin configurations and paramagnetism. This theory is essential for explaining why some complexes are colorful and why others are not. It forms a basis for understanding many physical properties related to electronic structure in complex ions.

Structural Isomerism

Structural Isomerism in coordination compounds is a concept explaining compounds having the same chemical composition but differing in the arrangement of atoms or groups. Imagine two houses built with identical bricks, but arranged differently to form distinct structures.
There are several types of structural isomerism, including linkage isomerism where ligands can attach to the central atom in different ways; and coordination isomerism, involving the exchange of ligands between cation and anion parts of different coordination spheres. Another type is ionization isomerism, happening if an ion inside the coordination sphere can replace one outside.
Recognizing structural isomerism is crucial because it affects not just the physical form of the compound but also its reactivity, interactions in biological systems, and sometimes even its color or magnetic properties. Understanding these isomers enriches one's comprehension of the vast diversity and functionality of coordination compounds.