Problem 173 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following has an optical isomer? [2010] (a) \(\left[\mathrm{Zn}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\right]^{2+}\) (b) \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) (c) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{en})\right]^{3+}\) (d) \(\left[\mathrm{Zn}(\mathrm{en})_{2}\right]^{2+}\) \((\mathrm{en}=\) ethylenediamine \()\)

Step-by-Step Solution

Answer

Option (b) \([\text{Co(en)}_3]^{3+}\) has an optical isomer.

Step 1: Identify Coordination Number and Geometry of Each Complex

For each option, identify the metal center, its coordination number, and geometry:- (a) \([\text{Zn(en)}(\text{NH}_3)_2]^{2+}\): \(\text{Zn}^2+\) with an overall coordination number of 4 (from 1 \(\text{en}\) and 2 \(\text{NH}_3\) ligands) likely forming a tetrahedral complex.- (b) \([\text{Co(en)}_3]^{3+}\): \(\text{Co}^{3+}\) with coordination number 6 (from 3 \(\text{en}\) ligands) forming an octahedral complex.- (c) \([\text{Co}(\text{H}_2\text{O})_4(\text{en})]^{3+}\): \(\text{Co}^{3+}\) with coordination number 6, forming an octahedral complex.- (d) \([\text{Zn(en)}_2]^{2+}\): \(\text{Zn}^2+\) with coordination number 4, forming a tetrahedral complex.

Step 2: Analyze for Chiral Centers and Symmetry

Check for chiral centers and lack of symmetry: - In (a) and (d), \(\text{Zn}\) complexes are tetrahedral and do not typically have optical isomers due to their symmetry and the lack of chiral centers.- In (b), \([\text{Co(en)}_3]^{3+}\), the Co complex contains only the bidentate ligand \(\text{en}\) (ethylenediamine), and can form a chiral complex as the geometry is octahedral but lacks a plane of symmetry.- In (c), \([\text{Co}(\text{H}_2\text{O})_4(\text{en})]^{3+}\), the presence of only one \(\text{en}\) ligand and four identical \(\text{H}_2\text{O}\) ligands generally maintains a center of symmetry.

Step 3: Determine Optical Activity

Determine which complex is optically active:- An octahedral complex can have optical isomers if it lacks symmetry (specifically a plane or center of symmetry). Thus, \([\text{Co(en)}_3]^{3+}\) can exist in two non-superimposable mirror-image forms, or enantiomers, as it is completely surrounded by \(\text{en}\) ligands, which results in its optical activity.

Key Concepts

Coordination Complex

In the world of chemistry, a coordination complex is a compound consisting of a central atom or ion attached to a surrounding array of bound molecules or ions, known as ligands. This formation is crucial in understanding various chemical behaviors and properties. Specifically, transition metals commonly serve as the central atoms in these complexes, which brings their own set of interesting properties, such as variable oxidation states and magnetic characteristics.

Ligands can be neutral molecules or ions and they donate a pair of electrons to the metal center, thus forming coordinate covalent bonds. These ligands help stabilize the metal atom, allowing the complex to exhibit unique chemical properties that can influence reactivity, color, and even biological activity. There are several types of coordination environments, with octahedral, tetrahedral, and square planar being the most prevalent.

The coordination number, which indicates the number of ligand bonds to the central metal atom, plays a critical role in determining the geometry of the complex. For the complexes in this exercise, we can see a variety of coordination environments such as octahedral and tetrahedral, based on the coordination number and types of ligands present.

Chiral Centers

Chiral centers are atoms within a molecule that have non-superimposable mirror images. This concept forms the basis of optical isomerism, which is vital in both chemistry and biology. A molecule with one or more chiral centers can rotate plane-polarized light, leading to optical activity.

For coordination complexes, the presence of chiral centers can dictate the ability to form optical isomers. In this particular exercise, the presence of chiral centers is a critical factor in determining if the complex is optically active. Complexes like \([\text{Co(en)}_3]^{3+}\) have a specific configuration because the arrangement of their ligands prevents a mirror plane or center of symmetry, allowing the formation of enantiomers, which are non-superimposable mirror images.

However, not all coordination complexes can have chiral centers. For example, those forming symmetric configurations such as tetrahedral complexes often lack the asymmetry required to be chiral.

Octahedral Geometry

Octahedral geometry is one of the most common molecular shapes in coordination complexes, especially for metal centers with a coordination number of six. In an octahedral complex, six ligands symmetrically surround the central metal atom, positioned at the corners of an octahedron. This geometry is common because it allows for maximum ligand-metal interaction, resulting in a stable configuration.

One fascinating aspect of octahedral geometry is its potential for optical isomerism. When the ligands are arranged in such a way that the complex does not possess a plane or center of symmetry, it can exhibit optical isomerism. For instance, the complex \([\text{Co(en)}_3]^{3+}\) is a perfect example where the bidentate nature of ethylenediamine ligands creates a chiral environment. This absence of symmetry leads to the formation of two enantiomers, which are mirror images that cannot be superimposed.

In summary, octahedral geometry can greatly influence both the reactivity and the optical properties of coordination complexes, making it a key area of study in inorganic chemistry.