Draw diagrams for any cis, trans, and optical isomers that could exist for the following (en is ethylenediamine): (a) \(\left[\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{NO}_{2}\right) \mathrm{Cl}\right]^{+}\) (b) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}\) (c) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{4}\right]\) (d) \(\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+}\) (e) \(\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]\)

Cis and trans isomerism is a type of geometric isomerism that arises in coordination compounds when two identical ligands can occupy two different positions around a central atom. In cis isomers, the identical ligands are situated next to each other, whereas in trans isomers, they are opposite each other.

For instance, the compound \(\left[\mathrm{Co}(\mathrm{en})_{2}(\mathrm{NO}_{2})\mathrm{Cl}\right]^{+}\) exhibits cis and trans isomerism; the \(\mathrm{NO}_{2}\) and \(\mathrm{Cl}\) ligands can either be adjacent (cis) or across from each other (trans) on the octahedral metal center. Similarly, \(\left[\mathrm{Pt}(\mathrm{NH}_{3})_{2}\mathrm{Cl}_{2}\right]\) can also form both isomers, influencing the compound's reactivity and physical properties.

Optical isomerism occurs when two molecules are mirror images of each other but cannot be superimposed, similar to a person's left and right hands. These two forms, called enantiomers, have identical physical and chemical properties except for their interaction with plane-polarized light and reactions in biological systems.

The \(\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+}\) complex is capable of exhibiting optical isomerism. As it contains three bidentate ligands, it presents multiple binding sites that can form 'right-handed' or 'left-handed' arrangements that are mirror images of each other, leading to enantiomers.

Geometric isomerism encompasses the cis and trans forms as mentioned before but can also involve variations in the position of the ligands which are not necessarily identical. This type of isomerism is prevalent in coordination complexes where ligands can adopt different spatial arrangements.

For example, in the complex \(\left[\mathrm{Co}(\mathrm{en})_{2}\mathrm{Cl}_{2}\right]^{+}\), regardless of whether the chloride ligands are next to each other (cis) or across from each other (trans), different geometric isomers are formed. These isomers might exhibit different chemical reactivity and physical properties, such as solubility and melting points.

Ethylenediamine (en) is a classic example of a bidentate ligand, meaning it has two donor atoms that can simultaneously bind to a single metal ion, forming a five-membered chelate ring in the process. This chelation effect often stabilizes the coordination complex and can significantly influence its isomeric properties.

As demonstrated in the complexes \(\left[\mathrm{Co}(\mathrm{en})_{2}(\mathrm{NO}_{2})\mathrm{Cl}\right]^{+}\) and \(\left[\mathrm{Cr}(\mathrm{en})_{3}\right]^{3+}\), the ethylenediamine ligand forms rings with the cobalt and chromium metal centers respectively. The presence of bidentate ligands like ethylenediamine can increase the complexity of isomerism in coordination compounds by adding another layer of potential structural variation.