Question

Draw structures of all the geometric and optical isomers of each of the following cobalt complexes: (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) (b) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right]^{2+}\) (c) \(\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\)

Short answer

(a) No isomers; (b) Two geometric (cis, trans); (c) Two optical isomers.

Step-by-step solution

Analyze the Cobalt Complex in Part (a)

The complex \([\mathrm{Co}(\mathrm{NH}_3)_6]^{3+}\) is an octahedral coordination complex with six ammonia ligands symmetrically arranged around the cobalt center. Since all the ligands are identical (\(\mathrm{NH}_3\)), there are no geometric or optical isomers in this case.

Analyze the Cobalt Complex in Part (b)

The compound \([\mathrm{Co}(\mathrm{NH}_3)_5\mathrm{Cl}]^{2+}\) is also expected to be an octahedral complex. The presence of a single \(\mathrm{Cl}^-\) ligand changes the symmetry. There are two possible geometric isomers: a "trans-isomer," where the \(\mathrm{Cl}^-\) is opposite to an \(\mathrm{NH}_3\) ligand, and a "cis-isomer," where the \(\mathrm{Cl}^-\) is adjacent to its neighboring \(\mathrm{NH}_3\) ligands. The complex does not have any optical isomers since it doesn't exhibit chirality either in the trans or cis form.

Analyze the Cobalt Complex in Part (c)

The complex \([\mathrm{Co}(\mathrm{C}_2\mathrm{O}_4)_3]^{3-}\) involves three bidentate \(\mathrm{C}_2\mathrm{O}_4^{2-}\) (oxalate) ligands, leading to a highly symmetrical octahedral shape. Here, optical isomers do exist because of the arrangement of bidentate ligands, leading to non-superimposable mirror images (known as enantiomers). However, geometric isomers are not possible in this all-bidentate setting.

Key concepts

Geometric Isomers

Geometric isomers are molecules that have the same chemical formula but a different spatial arrangement of atoms. In the case of coordination complexes, particularly octahedral ones, these isomers occur when ligands are arranged differently around the central metal ion. For example, in the complex

• \([\text{Co}(\text{NH}_3)_5\text{Cl}]^{2+}\),
• the chlorine (Cl) and ammonia (\(\text{NH}_3\)) ligands can be arranged in either a 'cis' or 'trans' formation.
  • In the 'cis' isomer, the Cl and some of the \(\text{NH}_3\) ligands are next to each other.
  • In the 'trans' isomer, they appear opposite to one another.

This difference in spatial arrangement can result in distinct properties and reactivities for cis and trans isomers. However, not all complexes can form geometric isomers. For instance, in complexes with identical ligands, like

• \([\text{Co}(\text{NH}_3)_6]^{3+}\),

no geometric isomers exist because the ligands are symmetrically arranged around the central metal ion.

Optical Isomers

Optical isomers, or enantiomers, are types of isomers that are mirror images of each other but are not superimposable. This is similar to how your left and right hands are mirror images but cannot be perfectly aligned on top of each other. These isomers arise when a molecule is chiral, meaning it lacks an internal plane of symmetry. In coordination chemistry, certain complexes become chiral due to their ligand arrangement. The complex

• \([\text{Co}(\text{C}_2\text{O}_4)_3]^{3-}\)

possesses three bidentate ligands, forming an octahedral structure that can adopt such chiral configurations. Though they do not differ in the connectivity of the atoms, these isomers interact differently with polarized light and may have unique biological activities. Optical isomers are key because they play significant roles in fields like pharmacology, where the orientation can affect how a substance interacts with biological systems.

Octahedral Coordination Complexes

Octahedral coordination complexes are a common and vital class of structures in inorganic chemistry. These complexes involve a central metal atom surrounded by six ligand atoms or groups. The ligands are arranged at the vertices of an octahedron, a geometric shape with eight triangular faces.

• An example of this is the complex
  • \([\text{Co}(\text{NH}_3)_5\text{Cl}]^{2+}\),
  • where a cobalt ion is surrounded by five ammonia molecules and one chloride ion.
• These complexes can display both geometric and optical isomerism, depending on the ligand arrangement and symmetry.

One fascinating aspect of octahedral complexes is the variety of properties they exhibit due to their isomeric forms. Properties such as color, magnetism, and reactivity can vary drastically among different isomers, making the study of these complexes crucial to understanding coordination chemistry. They also illustrate the importance of spatial arrangements in molecular chemistry, influencing how molecules interact and respond to different environments.