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 nonsuperimposable mirror image. Draw the structures of the three isomers. Which one is chiral?

Short answer

The \(\mathrm{fac}\) isomer is chiral.

Step-by-step solution

Understanding Geometric Isomerism

Geometric isomerism occurs in coordination complexes when ligands can attach in different spatial arrangements around the central metal ion. For this complex, we have ethylenediamine (\((\mathrm{en})\)) as a bidentate ligand, and ammonia (\((\mathrm{NH}_3)\)) and water (\((\mathrm{H}_2O)\)) as monodentate ligands.

Identifying Possible Isomers

The complex [\(\mathrm{Co} (\mathrm{en}) (\mathrm{NH}_3)_2 (\mathrm{H}_2O)_2\)]^{3+} can display different isomeric arrangements. Since the \((\mathrm{en})\) ligand always occupies two adjacent positions (chelate), varying positions of \((\mathrm{NH}_3)\) and \((\mathrm{H}_2O)\) provide different isomers: (1) \(\mathrm{fac}\) isomer and (2) \(\mathrm{mer}\) isomers.

Drawing the cis and trans Isomers

1. Draw the \(\mathrm{fac}\) isomer: All three pairs of identical ligands (\((\mathrm{NH}_3)_2\) and \((\mathrm{H}_2O)_2\)) are adjacent, forming a face on the octahedron.2. Draw the \(\mathrm{mer}\) isomer: The identical \((\mathrm{NH}_3)_2\) and \((\mathrm{H}_2O)_2\) ligands are across from each other, forming a meridian line.

Determining Chirality

To find which isomer is chiral, we need to look for non-superimposable mirror images. In this case, none of the isomers fit the criteria of a chiral center as typically defined for octahedral complexes. However, if you rearrange \((\mathrm{NH}_3)\) to be across in \(\mathrm{mer}\) orientation with \((\mathrm{H}_2O)\), it can result in optical isomerism.

Drawing the Chiral Isomer

To achieve chirality, configure one NH3 such that it is adjacent but not mirrored by any opposing ligands. This configuration yields a unique orientation that doesn't mirror symmetry when rotated: specifically, the isomer where two \((\mathrm{NH}_3)\) adjacent and one opposite \(\mathrm{H}_2O\) yields an octahedron with non-superimposable images.

Key concepts

Coordination Complexes

Coordination complexes are fascinating structures formed when ligands bond with a central metal ion. In these complexes, ligands can be atoms, ions, or molecules that donate a pair of electrons to the metal. The properties of coordination complexes depend on the type of ligands and their arrangement around the metal ion.

Key features of coordination complexes include:

• Central Metal Ion: Often a transition metal, which can accommodate different numbers of ligands.
• Ligands: Compounds like ammonia (\(\text{NH}_3\)) and water (\(\text{H}_2\text{O}\)), which donate electron pairs to the metal.
• Coordination Number: The total number of ligand attachments to the metal ion.
• Geometric Arrangement: Ligands can form spatial shapes like octahedrons or tetrahedrons around the metal.

Understanding the geometric arrangements is crucial because different configurations can lead to interesting properties and behaviors, such as catalytic activity in industrial processes or colors in gemstones.

Chirality

Chirality is a concept from chemistry where a structure is not superimposable on its mirror image, much like a pair of hands. This property makes a molecule chiral. In coordination complexes, chirality arises from a specific spatial arrangement of ligands around the central metal ion.

To identify chirality:

• Look for a non-superimposable mirror image: A chiral complex will appear different when viewed in a mirror, akin to how left and right hands are different.
• Check the spatial arrangement: The ligands should be arranged in such a way that swapping them results in a different, unique complex.

For example, in the given cobalt complex, arranging the ammonia ligands in a specific pattern can lead to a chiral structure, which cannot be matched by rotating or flipping the molecule. This property can drastically alter the complex's interactions with other molecules, making chirality a key player in many chemical reactions, including those in biological systems.

Optical Isomerism

Optical isomerism is a type of chirality seen in coordination complexes. When a complex can exist in two non-superimposable, mirror-image forms, it's undergoing optical isomerism. These different forms are known as enantiomers, and they have the ability to rotate plane-polarized light, but in opposite directions.

Important points to consider:

• Enantiomers: Each optical isomer is an enantiomer with distinct properties, especially in biological contexts where they can interact differently with enzymes.
• Light Rotation: One enantiomer will rotate light to the right (dextrorotatory), and the other to the left (levorotatory). This unique property helps in identifying these isomers.[/li]
• Importance: Optical isomerism plays a significant role in pharmaceuticals, as one enantiomer can be beneficial while the other might be less effective or even harmful.

In the context of the cobalt coordination complex, achieving optical isomerism involves carefully arranging the ligands to disturb the symmetry, leading to the creation of these chiral isomers. Understanding and manipulating optical isomerism is crucial in the fields of synthetic chemistry and drug development.