Question

How many geometric isomers are in the following species: (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{4}\right]^{-}\) (b) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right] ?\)

Short answer

(a) 2 isomers (cis and trans); (b) 2 isomers (fac and mer).

Step-by-step solution

Identify the Coordination Number

The coordination number of a complex is the number of ligand donor atoms bonded to the central metal ion. For both complexes (a) and (b), cobalt (Co) is the central metal ion. Since cobalt usually forms six-coordinate octahedral complexes, the coordination number is 6 for both species.

Analyze Possible Geometries

Given that the coordination number is 6, both complexes have octahedral geometry. This is typical for complexes with a coordination number of 6 and allows for various geometric arrangements of the ligands around the metal center.

Evaluate Isomerism in [Co(NH3)2Cl4]^-

For (a) \([\text{Co(NH}_3)_2\text{Cl}_4]^−\), the ligands include two \(\text{NH}_3\) and four \(\text{Cl}^-\). These can arrange in two ways: with both \(\text{NH}_3\) ligands adjacent (cis) or opposite (trans) to each other. Therefore, there are 2 geometric isomers: cis and trans.

Evaluate Isomerism in [Co(NH3)3Cl3]

For (b) \([\text{Co(NH}_3)_3\text{Cl}_3]\), the ligands include three \(\text{NH}_3\) and three \(\text{Cl}^-\). These can also arrange in two geometric ways: all the same type of ligands adjacent forming a meridional (mer) arrangement, or with one ligand between two others forming a facial (fac) arrangement. Hence, there are 2 geometric isomers: fac and mer.

Key concepts

Coordination Complex

A coordination complex consists of a central metal atom or ion surrounded by molecules or ions known as ligands. These ligands donate electrons to the metal, forming coordinate or dative bonds. Coordination complexes are central concepts in chemistry, especially when discussing transition metals, because they help explain how metals interact with other chemical species.

• The metal ion acts as the coordination center.
• Ligands can be neutral or charged.
• Each ligand has at least one donor atom, ideally donating a pair of electrons to the metal.

This concept is fundamental in understanding geometric isomerism, which emerges from different arrangements of these ligands around the central metal.

Octahedral Geometry

Octahedral geometry is one of the most common shapes found in coordination complexes, particularly for coordination numbers of six. In this arrangement, six ligands are symmetrically distributed around the central metal atom, occupying the corners of an octahedron.

• The angles between any two ligands are 90 degrees (for adjacent ligands).
• This geometry allows for greater stability and various arrangements for ligands, leading to different possible isomers.
• It is frequently observed in complexes with transition metals like cobalt.

Understanding octahedral geometry is crucial for identifying the potential types of geometric isomerism in a complex.

Ligand Arrangement

The arrangement of ligands within a coordination complex significantly affects its chemical properties. Two main types of arrangements in such complexes are crucial: cis and trans, as well as fac and mer. Ligand arrangement dictates the spatial relationship among the ligands and can entirely alter the chemical behavior of a complex.

• Cis Arrangement: Similar ligands are adjacent to each other.
• Trans Arrangement: Similar ligands are opposite each other across the central metal.
• Different arrangements lead to different chemical reactivities and physical properties.

By understanding these arrangements, chemists can predict how the complex will react with other substances.

Cis-Trans Isomerism

Cis-trans isomerism is a form of geometric isomerism where the position of identical ligands relative to each other around the central metal ion varies. It is most common in complexes exhibiting octahedral or square planar geometries. This isomerism is particularly important for molecules' reactivity, optical activity, and color.

• Cis Isomer: Two identical ligands are adjacent.
• Trans Isomer: Two identical ligands are on opposite sides.

In the context of the exercise, [Co(NH₃)₂Cl₄]^- can exhibit both cis and trans isomers due to different possible spatial positioning of the ligands around cobalt.

Fac-Mer Isomerism

Fac-mer isomerism is observed in octahedral complexes with the general formula M(A)₃(B)₃. It depends on how the ligands are arranged around the central metal ion and affects the chemical properties of the complex.

• Facial (fac) Isomer: Three identical ligands form one face of the octahedron, meaning they are adjacent to each other.
• Meridional (mer) Isomer: Three identical ligands span across the metal center, with one ligand between the other two.

In the case of [Co(NH₃)₃Cl₃], understanding fac-mer isomerism helps predict the structural and reactivity differences between its isomers.