Problem 94 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following will have three stereo-isomeric forms? (1) \(\left[\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]\) (2) \(\mathrm{K}_{3}\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) (3) \(\mathrm{K}_{3}\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2} \mathrm{Cl}_{2}\right]\) (4) \(\left[\mathrm{Co}\left(\mathrm{en}_{2}\right) \mathrm{ClBr}\right]\) (Here, en = ethylene diamine) (a) 1 and 2 (b) 1 and 3 (c) 1 and 4 (d) 3 and 4

Step-by-Step Solution

Answer

(b) 1 and 3, (d) 3 and 4

Step 1: Understanding the Concept of Stereo-Isomers

Stereo-isomers occur when compounds have the same structural formula but differ in the arrangement of atoms in space. In coordination compounds, this often occurs due to the different three-dimensional orientations of ligands around the central metal atom.

Step 2: Analyze Compound 1

For compound \( \left[\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right] \), there are two types of ligands present: three \( \mathrm{NO}_{3} \) and three \( \mathrm{NH}_{3} \). These can be arranged such that there are two geometric isomers (facial and meridional) and an optical isomer, making a total of 3 stereoisomers.

Step 3: Analyze Compound 2

For \( \mathrm{K}_{3}\left[\mathrm{Co}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right] \), the ligand \( \mathrm{C}_{2}\mathrm{O}_{4}^{2-} \) (oxalate) is a bidentate ligand, and the complex is octahedral. All ligands are identical (symmetrical bidentate), leading only to optical isomers and thus two forms: the chiral pair of optical isomers.

Step 4: Analyze Compound 3

In \( \mathrm{K}_{3}\left[\mathrm{Co}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{2} \mathrm{Cl}_{2}\right] \), there are two \( \mathrm{C}_{2}\mathrm{O}_{4} \) and two \( \mathrm{Cl} \) ligands. It forms two geometric isomers (cis and trans). The \( \mathrm{cis} \) isomer can further exhibit optical activity, hence, forming three stereo-isomers (2 optical + 1 geometric).

Step 5: Analyze Compound 4

For \( \left[\mathrm{Co}\left(\mathrm{en}_{2}\right) \mathrm{ClBr}\right] \), we have one pair of bidentate ethylenediamine and two monodentate (Cl, Br) ligands. This can lead to both geometric (cis/trans) isomers and the \( \mathrm{cis} \) isomer can also show optical isomerism if the bidentate ligand's orientation leads to non-superimposable mirror images, resulting in three stereo-isomers in total.

Step 6: Determine the Valid Options

Based on the analysis, compound 1 has 3 stereoisomers, compound 3 has 3 stereoisomers, and compound 4 has 3 stereoisomers. However, compound 2 does not have 3 stereoisomers, as it only has optical isomer pairs. Thus, options containing compounds 1 and 3 (b) and 3 and 4 (d) are correct.

Key Concepts

Coordination Compounds

Coordination compounds, also known as complex compounds, are molecules composed of a central metal atom or ion bonded to a surrounding array of molecules or anions, known as ligands. These ligands form coordinate covalent bonds with the metal center, contributing electron pairs. Coordination compounds are crucial in various applications, such as catalysis and biological systems.
Key points about coordination compounds include:

• They typically involve a metal center bound to ligands.
• Coordination numbers, often ranging from 2 to 12, indicate the count of ligand bonds to the metal.
• The spatial arrangement of ligands is described by the geometry of the compound, such as octahedral, square planar, or tetrahedral.
• The metal-ligand interaction can drastically change the properties of the compound, affecting color, reactivity, and magnetic behavior.

Optical Isomers

Optical isomers are a type of stereoisomer that are non-superimposable mirror images of each other, similar to how left and right hands appear. These isomers are chiral, meaning they have asymmetry that prevents them from being identical upon superimposition. In coordination chemistry, optical isomers arise when a complex with chiral geometry forms.
Important aspects of optical isomers include:

• Chirality in coordination compounds typically occurs in tetrahedral and octahedral geometries.
• Compounds exhibiting optical isomerism do not possess a plane of symmetry or center of symmetry.
• Optical isomers rotate plane-polarized light in different directions, identified as either 'dextro' (right) or 'levo' (left).
• This property is significant in fields like pharmaceuticals, where the activity of a drug might differ for each isomer.

Geometric Isomers

Geometric isomers occur when ligands can assume different spatial arrangements around a central metal atom, despite having the same connectivity. They are common in square planar and octahedral complexes, where ligands can adopt distinct positions relative to each other, like cis and trans forms.
Key insights into geometric isomers include:

• Geometric isomers differ in the arrangement of identical ligands, and they can affect the physical and chemical properties of the compound.
• Cis isomers have similar ligands positioned adjacent to each other, while trans isomers have them opposite.
• In cases like octahedral complexes, geometric isomers can further be classified into facial (fac) and meridional (mer) configurations, indicating different ligand grouping.
• These isomers can play a role in the color, reactivity, and stability of coordination compounds.

Bidentate Ligands

Bidentate ligands are types of ligands that can form two bonds with a central metal atom or ion. The term "bidentate" comes from "bi-" meaning two and "-dentate" meaning teeth, suggesting these ligands "bite" the metal in two places. This creates a more stable coordination compound due to ring formation.
Key points about bidentate ligands include:

• Bidentate ligands are typically organic molecules such as ethylenediamine ("en") and oxalate, which have two donor atoms.
• The chelate effect describes the increased stability of metal complexes with bidentate ligands compared to similar complexes with monodentate ligands.
• They are often responsible for specific geometric arrangements and can influence optical and geometric isomerism.
• The presence of bidentate ligands can lead to the formation of chelate rings, adding to the compound’s durability and affecting its reactivity.

Octahedral Complexes

Octahedral complexes are a common geometric arrangement in coordination chemistry where six ligands symmetrically surround a central metal ion. This arrangement results in a shape resembling an octahedron, with each ligand placed at a vertex.
Significant features of octahedral complexes include:

• The octahedral geometry is depicted by the union of eight equilateral triangles, constructing a polyhedron with six vertices.
• Octahedral complexes are often seen in transition metals due to their electron configuration and spatial preference.
• This geometry facilitates diverse isomeric forms, including both optical and geometric isomers, due to varied ligand orientations.
• Octahedral complexes find broad applications in fields like organometallic chemistry and catalysis due to their structural and chemical features.