Problem 2 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The complex that can show optical activity is: (a) trans-[Cr(Cl_{2} ) ( o x ) _ { 2 } ] ^ { 3 - } (b) trans- \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{CN})_{4}\right]^{-}\) (c) cis- \(\left[\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{CN})_{4}\right]^{-}\) (d) cis- \(\left[\mathrm{CrCl}_{2}(\mathrm{ox})_{2}\right]^{3-} \quad\) (ox \(=\) oxalate)

Step-by-Step Solution

Answer

The option (d) cis-[CrCl_{2}(ox)_{2}]^{3-} is optically active.

Step 1: Understand Optical Activity

Optical activity refers to the ability of a compound to rotate the plane of polarized light. For a complex to be optically active, it must not possess a plane of symmetry or a center of symmetry.

Step 2: Analyze trans-Isomers

Trans-isomers generally have a plane of symmetry due to their geometric arrangement. This symmetry prevents them from being optically active. Therefore, both the options (a) trans-[Cr(Cl_{2})(ox)_{2}]^{3-} and (b) trans-[Fe(NH_{3})_{2}(CN)_{4}]^- are likely not optically active.

Step 3: Analyze cis-Isomers

Cis-isomers, unlike trans-isomers, may lack a plane of symmetry, which allows them to potentially be optically active. We will consider options (c) cis-[Fe(NH_{3})_{2}(CN)_{4}]^- and (d) cis-[CrCl_{2}(ox)_{2}]^{3-} as candidates for optical activity.

Step 4: Consider Ligand Types

In cis-[Fe(NH_{3})_{2}(CN)_{4}]^-, the ammonia and cyanide ligands create a structure that often still has symmetry, preventing optical activity. However, in cis-[CrCl_{2}(ox)_{2}]^{3-}, the oxalate ligands can form chelate rings that can break symmetry.

Step 5: Identify Chiral Complex

Cis-[CrCl_{2}(ox)_{2}]^{3-} with bidentate oxalate ligands often forms a chiral configuration, as these ligands can occupy adjacent coordination sites in a way that lacks an internal plane of symmetry, making it optically active.

Key Concepts

Understanding Chiral Complexes

Chiral complexes are fascinating due to their ability to rotate plane-polarized light, a property known as optical activity. This is akin to how our left and right hands are mirror images but cannot be perfectly overlapped. In chemistry, for a complex to be chiral, it must lack an internal plane of symmetry or a center of symmetry. Chiral complexes often include metal centers surrounded by various ligands arranged in a non-superimposable manner.

A complex like cis-\([\mathrm{CrCl}_{2}(\mathrm{ox})_{2}]^{3-}\) can exhibit chirality. The oxalate ligands form chelate rings that lead to a non-symmetric arrangement of the ligands around the metal center, leading to optical activity. This absence of symmetry is crucial for chirality, as it leads to the distinct property of rotating polarized light in specific ways.

Exploring Cis-Trans Isomerism

Cis-trans isomerism is a type of stereoisomerism important in coordination chemistry. Here, the arrangement of specified ligands around a central atom or ion affects the geometrical properties of the complex.

In a cis isomer, like cis-\([\mathrm{Fe(NH}_{3})_{2}(\mathrm{CN})_{4}]^{-}\), the two identical ligands are adjacent to each other. This close juxtaposition can sometimes break the symmetry, occasionally allowing for potential optical activity if other symmetry elements are absent. However, the trans isomer has the ligands on opposite sides, introducing a plane of symmetry that prevents optical activity. This is key in understanding why cis complexes might be more apt to exhibit optical activity compared to their trans counterparts, which are typically symmetric and thus optically inactive.

Basics of Coordination Chemistry

Coordination chemistry revolves around complexes formed by the coordination of molecules or ions around a central metal atom. These complexes consist of a coordination sphere where ligands directly coordinate to the metal center.

Ligands can be uni- or multidentate, referring to the number of donor sites they have to attach to the metal. In cis-\([\mathrm{CrCl}_{2}(\mathrm{ox})_{2}]^{3-}\), the oxalate is a bidentate ligand, meaning it forms two bonds with the central chromium ion. This ability to bind in multiple spots brings about unique geometries and potential isomeric forms such as cis and trans. These geometrical arrangements deeply impact the complex's overall properties, including whether it is chiral and whether it can exhibit optical activity. Understanding these basic ideas helps explain why certain complexes are optically active, while others are not, underscoring the importance of symmetry and ligand arrangement.