Question

Three geometric isomers are possible for \(\left[\mathrm{Co (\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]^{3+} .\) One of the three is chiral; that is, it has a non-superimposable mirror image. Draw the structures of the three isomers. Which one is chiral?

Short answer

The chiral isomer is the **cis isomer**, specifically where \( \text{NH}_3 \) and \( \text{H}_2\text{O} \) are adjacent.

Step-by-step solution

Understand the Coordination Complex

The given complex is \( \left[\text{Co}\,(\text{en})(\text{NH}_3)_2(\text{H}_2\text{O})_2\right]^{3+}\), where \(\text{Co}\) is the central metal ion, \text{en} is ethylenediamine which is a bidentate ligand, \(\text{NH}_3\) and \(\text{H}_2\text{O}\) are monodentate ligands. This complex has a coordination number of 6, leading to an octahedral geometry.

Determine Geometric Isomers

Given the ligands, three geometric isomers are possible due to different arrangements of the ligands around the \(\text{Co}\) center in an octahedral geometry. In these isomers, ethylenediamine occupies one face due to its bidentate nature, and \(\text{NH}_3\) and \(\text{H}_2\text{O}\) can occupy different positions either adjacent to each other (cis) or opposite each other (trans).

Draw the Geometric Isomers

1. **Cis isomer (cis-\(\text{NH}_3\)**): In this arrangement, the \(\text{NH}_3\) molecules are adjacent, and \(\text{H}_2\text{O}\) molecules are also adjacent. The ethylenediamine ligand is fixed.2. **Cis isomer (cis-\(\text{H}_2\text{O}\)**): The \(\text{H}_2\text{O}\) molecules are adjacent, and \(\text{NH}_3\) molecules are also adjacent similar to cis-\(\text{NH}_3\).3. **Trans isomer**: The \(\text{NH}_3\) molecules are opposite each other, and \(\text{H}_2\text{O}\) molecules are opposite each other.

Identify the Chiral Isomer

In an octahedral complex, chirality arises when there is no plane of symmetry and a non-superimposable mirror image exists. This typically occurs in cis isomers. The chiral isomer in this complex is the cis-isomer where both non-identical ligands (\(\text{NH}_3\) and \(\text{H}_2\text{O}\)) are adjacent in one plane.

Conclusion

Thus, the three isomers are: cis-\(\text{NH}_3\), cis-\(\text{H}_2\text{O}\), and trans. The chiral one is a cis isomer, specifically the ones where \( \text{NH}_3 \) and \( \text{H}_2\text{O} \) are adjacent.

Key concepts

Chiral Isomers

Chiral isomers are special types of molecules that have non-superimposable mirror images. This property is much like how your left and right hands are mirror images but cannot be perfectly overlaid onto one another. Chiral molecules lack symmetry, which means they do not have a plane, center, or axis of symmetry. This unique feature is critical in chemistry, particularly in pharmaceuticals, where different isomers can have very different effects in biological systems.

• Chirality occurs often in coordination complexes when there are specific arrangements of ligands around the central metal atom.
• In the discussed coordination complex, the chirality arises in the cis-isomer configuration where two different kinds of ligands are next to each other, disrupting any symmetry.

Octahedral Geometry

Octahedral geometry is a common shape for coordination complexes, especially when they have a coordination number of six. Imagine a central atom at the center of an octahedron with ligands at each of the vertices.
This geometry allows for multiple isomeric forms, including both geometric and optical (chiral) isomers.

• In an octahedral complex, the positions where ligands attach are referred to as axial and equatorial, depending on their orientation.
• These positions can lead to variations in isomer forms, such as cis and trans isomers, based on how ligands group together.

The complex discussed exhibits octahedral geometry around the cobalt ion, with specific arrangements of its ligands leading to the formation of both chiral and achiral isomers.

Coordination Complex

A coordination complex consists of a central metal ion bonded to surrounding molecules or ions called ligands. The nature and arrangement of these ligands influence the properties and reactivity of the complex. In our example, the cobalt ion serves as the central atom.

• The complex is denoted by \( \left[\text{Co}(\text{en})(\text{NH}_3)_2(\text{H}_2\text{O})_2\right]^{3+} \), where "en" refers to ethylenediamine, a bidentate ligand.
• The coordination complex's geometry is defined by the number of coordinate bonds the metal ion forms, which in this case is six, leading to an octahedral structure.

Such complexes are significant in chemical applications and industrial processes.

Ligands

Ligands are ions or molecules that bind to a central metal atom to form a coordination complex. They are crucial in defining the structure and function of the complex.

• Bidentate ligands, like ethylenediamine (en), can form two bonds with the metal, influencing the stability and shape of the complex due to their ability to occupy two adjacent positions.
• Monodentate ligands, such as \(\text{NH}_3\) and \(\text{H}_2\text{O}\), can only occupy one coordination site but play a crucial role in the geometric and chemical properties of the complex.

The way ligands coordinate and occupy space around the central metal affects isomerism, potential chirality, and the overall chemical behavior of the complex.