Question

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

Short answer

There are two geometrical isomers for the complex \(\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}^{+}\): cis-isomer and trans-isomer. Among these isomers, only the trans-isomer exhibits optical isomerism, with two enantiomers: \( [\text{en}^{S}] \) and \( [\text{en}^{R}] \).

Step-by-step solution

Identify the coordination sphere and the geometrical arrangement of the ligands

The given complex, \(\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}^{+}\), has a central chromium atom (Cr) which is bonded to an ethylenediamine (en) ligand, two ammonia (NH3) ligands, a bromine (Br) atom, and a chlorine (Cl) atom. The coordination sphere of the metal atom (Cr) contains six coordination sites, making it an octahedral complex.

Draw the geometrical isomers

Considering the octahedral arrangement, there are two possible geometrical isomers for this complex: 1. Cis-isomer: In this case, the two NH3 ligands and the Br and Cl ligands occupy adjacent coordination sites (90° apart) on the octahedral sphere. \[ \begin{matrix} \text{Cl} & - & \text{Cr} & - & \text{Br} \\ & \diagup & | & \diagdown& \\ \text{NH}_3 & & \text{en}& & \text{NH}_3 \end{matrix} \] 2. Trans-isomer: In this case, the two NH3 ligands are on opposite sides of the octahedral sphere (180° apart), and the Br and Cl ligands are also on opposite sides. \[ \begin{matrix} \text{NH}_3 & - & \text{Cr} & - & \text{Br} \\ & \diagup & | & \diagdown& \\ \text{NH}_3 & & \text{en}& & \text{Cl} \end{matrix} \]

Determine optical isomers

Now, we need to determine whether the geometrical isomers also exhibit optical isomerism. Optical isomers are non-superimposable mirror images of each other, known as enantiomers. In order for a complex to have optical isomers, it must lack a center of symmetry or a plane of symmetry. For the cis-isomer, we can identify a plane of symmetry. The presence of a plane of symmetry indicates that this geometrical isomer does not exhibit optical isomerism. However, the trans-isomer does not have a center of symmetry or a plane of symmetry, which means that it exhibits optical isomerism. Below are the two enantiomers of the trans-isomer: Enantiomer 1: \[ \begin{matrix} \text{NH}_3 & - & \text{Cr} & - & \text{Br} \\ & \diagup & | & \diagdown& \\ \text{NH}_3 & & \text{en}^{S}& & \text{Cl} \end{matrix} \] Enantiomer 2: \[ \begin{matrix} \text{NH}_3 & - & \text{Cr} & - & \text{Br} \\ & \diagup & | & \diagdown& \\ \text{NH}_3 & & \text{en}^{R}& & \text{Cl} \end{matrix} \] In conclusion, the given complex, \(\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}^{+}\), has two geometrical isomers, cis and trans. Only the trans-isomer exhibits optical isomerism, with two enantiomers: \( [\text{en}^{S}] \) and \( [\text{en}^{R}] \).

Key concepts

Coordination Chemistry

Coordination chemistry is a fascinating branch of chemistry focused on coordinating compounds, which consist of a central atom or ion, usually a metal, surrounded by molecules or ions called ligands. This study is significant because it helps explain the behavior of complex ions in solutions, their structural variations, and their chemical reactivity.
In a coordination compound, the central metal atom has coordination sites where ligands attach, forming a stable complex. The number of these sites defines the coordination number, which is crucial in determining the shape and properties of the complex.
Coordination chemistry not only provides insights into a compound's geometrical arrangement but also into different isomeric possibilities, such as geometrical and optical isomerism. These isomers have important implications in fields like medicinal chemistry and materials science, as they can exhibit different biological activities or material properties.

Optical Isomerism

Optical isomerism is an intriguing phenomenon found in coordination chemistry where complexes form non-superimposable mirror images known as enantiomers. These are like left and right hands, which are mirror images but cannot be perfectly aligned one on top of the other. Optical isomers occur in octahedral complexes when the arrangement around the central metal lacks symmetry.
The presence of optical isomers can significantly influence the properties of a compound, especially in biological systems where they may interact differently. For instance, one enantiomer might be biologically active while the other is inactive or even harmful. Therefore, understanding optical isomerism is crucial in the synthesis of pharmaceuticals and in the design of new materials.
Optical activity is detected using polarimetry, which measures the direction and angle by which an enantiomer rotates plane-polarized light. This property is a direct consequence of the chiral nature of the compound.

Octahedral Complex

An octahedral complex is a common type of coordination compound featuring six ligands symmetrically bound to a central metal atom, forming an octahedron. This geometric arrangement is prevalent due to the stability it provides to the metal complex.
The shape arises from the sp³d² hybridization of orbitals of the metal atom, allowing the ligands to attach at vertices of an octahedron, equidistant from each other. The symmetry of the octahedral geometry allows for diverse isomeric forms, especially in the presence of different types of ligands.
In the context of geometrical isomerism, an octahedral complex can have different spatial arrangements of ligands. For example, the mentioned complex features cis and trans configurations, depending on whether like ligands are adjacent or opposite each other, which influences the complex's optical qualities.

Ligands

Ligands are essential entities in coordination chemistry, acting as the molecules or ions that donate a pair of electrons to a central metal atom or ion, forming a coordinate covalent bond. They can range from simple ions like chloride to complex molecules like ethylenediamine (en).
Ligands determine the stability, reactivity, and overall properties of the coordination complex. They can be neutral, negatively charged, and can even vary in size and geometric shape. Additionally, ligands are classified based on the number of bonding sites available for attachment to the metal atom.

• Monodentate ligands: These donate a single pair of electrons and attach to a metal at one bonding site, e.g., ammonia (NH₃).
• Bidentate ligands: These can attach through two sites, forming a more robust complex, e.g., ethylenediamine (en).
• Polydentate ligands: These have multiple binding sites and create what we call chelate complexes, enhancing stability even more.

Understanding the role of ligands is vital in optimizing the design and functionality of coordination complexes, especially for applications in catalysis, energy storage, and molecular recognition.