Question

Draw all the geometrical isomers of \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}\right]^{+} .\) Which of these isomers also have an optical isomer? Draw the various isomers.

Short answer

The geometrical isomers of the complex ion \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{BrCl}\right]^{+}\) are: a) Trans isomer: NH_3 ligands are trans to each other, and the en ligand and the two halides (Br and Cl) are in a mer arrangement. b) Cis isomer: NH_3 ligands are cis to each other, and the en ligand and the two halides (Br and Cl) are in a fac arrangement. The cis isomer has an optical isomer (enantiomers), while the trans isomer does not have any optical isomers.

Step-by-step solution

Identify the type of isomerism and the ligands

The given complex ion is \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{BrCl}\right]^{+}\), which consists of one Cr(III) central metal ion bonded to one ethylenediamine (en) ligand, two ammonia (NH_3) ligands, and two different halides (Br and Cl). Since we are asked to find the geometrical isomers of the complex, we will be focusing on cis/trans or fac/mer isomerism, depending on the arrangement of ligands around the central metal ion.

Determine the structure and coordination number of the complex

Since there are six ligand sites, the complex has a coordination number of six and is octahedral in shape. The Cr(III) metal ion is at the center, surrounded by the ligands.

Identify the geometrical isomers

In this octahedral complex, we will examine the possible arrangements of the ligands, keeping in mind the following types of isomerism: 1. Cis/Trans isomerism: Occurs when two ligands of the same type are either on the same plane (cis) or are opposite to each other (trans) on the central metal ion. 2. Fac/Mer isomerism: Refers to the arrangement of three ligands of the same type in either a facial (fac) manner, where they occupy one triangular face of the octahedron, or in a meridional (mer) manner, where they occupy a plane that contains the metal ion. For the given complex ion, the geometrical isomers we need to consider are: 1. Cis or trans to the two NH_3 ligands. 2. Fac or mer for the arrangement of the en ligand and the two halides (Br and Cl). Considering the geometrical isomers, we can draw the following: a) Trans isomer: NH_3 ligands are trans to each other, and the en ligand and the two halides (Br and Cl) are in a mer arrangement. b) Cis isomer: NH_3 ligands are cis to each other, and the en ligand and the two halides (Br and Cl) are in a fac arrangement.

Determine if the geometrical isomers have optical isomers

To decide if the geometrical isomers have optical isomers, we need to check if the complex molecule has any plane of symmetry or center of symmetry. If a geometrical isomer has no plane or center of symmetry, then it will have an optical isomer (the molecule and its mirror image cannot be superimposed). a) Trans isomer: This isomer has a plane of symmetry, and thus, it does not have any optical isomers. b) Cis isomer: This isomer does not have a plane of symmetry or a center of symmetry, and thus, it has optical isomers (enantiomers). In conclusion, the cis isomer of the complex ion \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{BrCl}\right]^{+}\) has an optical isomer, while the trans isomer does not.

Key concepts

Octahedral complexes

Octahedral complexes are a fascinating aspect of coordination chemistry due to their unique geometric arrangement and bonding properties. At the heart of an octahedral complex is a central metal ion surrounded by six ligands. These ligands are arranged at the vertices of an octahedron.
This shape is favored by coordination numbers of six, where the ligands can be either neutral molecules or anions.

• An example of an octahedral complex is \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{BrCl}\right]^{+}\), which you've worked with in your exercise. Here, Cr(III) acts as the central metal ion, with ligands like ethylenediamine, ammonia, and halide ions filling the coordination sphere.

Understanding the structural arrangement is crucial because it directly impacts the properties and reactivity of the complex. The octahedral shape allows for different types of isomerism, such as cis/trans and fac/mer, based on how the ligands are positioned around the central metal.

Optical isomerism

Optical isomerism is a fascinating type of stereoisomerism that arises in coordination compounds, especially those with chiral arrangements. Optical isomers, or enantiomers, are isomers that are non-superimposable mirror images of each other.
These compounds lack planes or centers of symmetry, which allows them to show optical activity.

• In the context of your exercise, the cis isomer of \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{BrCl}\right]^{+}\) exhibits optical isomerism. It is because this arrangement does not possess symmetry planes or centers. As a result, it can form a pair of enantiomers.
• These enantiomers can rotate plane-polarized light in different directions, making them optically active. Optical isomerism is significant in many fields, including pharmaceuticals, as different enantiomers can have very different effects in biological systems.

Coordination compounds

Coordination compounds are intriguing chemical structures consisting of a central metal ion and various ligands forming coordinate covalent bonds.
These compounds are a cornerstone of inorganic chemistry, revealing insights into the behavior of metal ions in various environments.

• The coordination number, or the number of ligand donor atoms bonded to the central metal ion, is crucial in defining the complex's geometry and reactivity. For example, the coordination number of six leads to an octahedral geometry, as seen in the complex \(\left[\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\mathrm{BrCl}\right]^{+}\).
• Coordination compounds can exhibit various isomerism types, including structural and stereo, such as geometrical and optical isomerism.

Coordination chemistry is essential not only in academia but also in industries like catalysis, material science, and medicine, where these compounds play critical roles.