Question

Draw all the geometrical isomers of \(\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}^{+1}\) . Which of these isomers also have an optical isomer? Draw the various isomers.

Short answer

There are two geometrical isomers for the complex \(\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}^{+1}\): cis and trans. In the cis configuration, the monodentate ligands are adjacent to each other, while in the trans configuration, they are opposite to each other. However, neither of these geometrical isomers have optical isomers, as the cis isomer has a plane of symmetry and the trans isomer does not have any chiral carbon centers.

Step-by-step solution

Draw the geometrical isomers

To draw the geometrical isomers of the complex, we will consider different arrangements of the monodentate ligands (\(\mathrm{NH_3, Br, Cl}\)) around the metal ion Cr. Isomer 1 (cis): In the cis isomer, the monodentate ligands are adjacent to each other: \( \begin{array}{r} \mathrm{Cr} (\mathrm{en})\left(\mathrm{NH}_{3}\right)\left(\mathrm{Br}\right)\\ \hspace{1.3cm} |\\ \hspace{1.3cm}\mathrm{Cl} \end{array} \) Isomer 2 (trans): In the trans isomer, the monodentate ligands are opposite to each other: \( \begin{array}{r} \mathrm{Cr} (\mathrm{en})\left(\mathrm{NH}_{3}\right)\left(\mathrm{Br}\right)\\ \hspace{1.7cm} | \\ \hspace{1.7cm} \mathrm{NH_3} \\ \hspace{1.7cm} | \\ \mathrm{Cl} \end{array} \)

Identify optical isomers

Now, we need to determine which of these geometrical isomers also have optical isomers. Optical isomers are non-superimposable mirror images of each other, which means they have a chiral carbon atom and a plane of symmetry that cannot be overlapped when rotated or flipped. Isomer 1 (cis): For the cis isomer, there is a plane of symmetry that divides the complex into two symmetrical halves. Since this isomer has a plane of symmetry, it does not have optical isomers. Isomer 2 (trans): For the trans isomer, there is no plane of symmetry which means it could possibly have an optical isomer. However, since there are no chiral carbon centers in the ethylenediamine ligand or elsewhere, this complex does not have optical isomers either. In conclusion, there are two geometrical isomers of the complex \(\mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}^{+1}\), namely cis and trans, but neither of them have optical isomers.

Key concepts

Coordination Compounds

Coordination compounds are fascinating structures formed by a central metal atom or ion surrounded by molecules or ions, called ligands. The metal atom and its attached ligands together constitute what is known as a coordination complex. These compounds exhibit unique and intriguing properties such as color, magnetic behavior, and catalytic activity, which make them extremely important in fields like chemistry and biology.

One key aspect of coordination compounds is their ability to form different geometrical shapes, depending on the ligands' spatial arrangement around the central metal. The number of ligands attached to the metal, known as the coordination number, often influences these shapes. Common shapes include octahedral, square planar, and tetrahedral.

• Coordination complexes can show interesting variations in structure and geometry.
• The ligands generally dictate the preference for particular shapes, leading to multiple possible arrangements (isomerism).
• The variety of colors displayed by coordination compounds is typically due to the absorption of light by the metal-ligand complexes.

Understanding coordination compounds also involves studying the bonding between the ligands and the metal atom, often explained by theories such as Crystal Field Theory (CFT) or Ligand Field Theory (LFT). These interactions affect the properties and stability of the compound.

Cis-Trans Isomers

Cis-trans isomerism is a type of geometrical isomerism where two or more ligands can occupy different positions around a central metal ion. In coordination chemistry, this kind of isomerism is most commonly found in square planar and octahedral complexes.

The concept of cis and trans isomers refers to the relative positioning of identical ligands:

• Cis isomer: Here, two identical ligands are positioned adjacent to each other. This proximity can affect the physical properties, like melting and boiling points, and sometimes the reactivity.
• Trans isomer: In this arrangement, the identical ligands are on opposite sides of the central metal atom, creating a more symmetric compound.

In some cases, cis and trans isomers can have significantly different chemical properties. For example, the cis form may be more reactive due to steric hindrance, while the trans form may be more stable. Identifying the possible geometrical isomers is a crucial step in understanding the behavior of coordination compounds and their application in real-world scenarios.

Cis-trans isomerism also plays an essential role in tailoring the function and efficiency of compounds, particularly in pharmaceuticals and electronic materials.

Optical Isomerism

Optical isomerism is a fascinating aspect of stereochemistry, where isomers, known as enantiomers, exist as non-superimposable mirror images of each other. This happens due to the presence of chirality in a molecule, where no internal plane of symmetry exists.

In the context of coordination compounds:

• Chirality often arises due to specific ligand arrangements, especially in complexes with octahedral or tetrahedral geometries.
• Optical isomers are crucial in biochemistry and medicinal chemistry, where each isomer can have distinct biological activities.

The non-superimposable nature of optical isomers means they will polarize light differently. This property is conventionally tested using polarimeters, which distinguish between the left-handed (levorotatory) and right-handed (dextrorotatory) enantiomers.

It's important to remember that not all coordination complexes are capable of exhibiting optical isomerism. The presence of symmetry elements usually negates this possibility, just as with the example of our initial exercise, where neither of the geometrical isomers of \( \mathrm{Cr}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{BrCl}^{+1}\) displayed optical isomerism due to either having a plane of symmetry or lack of sufficient chiral centers.