Which of the following will give four isomers? (a) \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Br}\) (b) \(\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (c) \(\left[\mathrm{Co}\left(\mathrm{PPh}_{3}\right)_{2}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (d) \(\left[\mathrm{Co}(\mathrm{en})_{3}\right] \mathrm{Cl}_{3}\)

Isomers are different forms of a compound that have the same formula but differ in properties. To find which compound will have four isomers, we need to identify if the molecule has chirality centers – atoms with four different groups attached, leading to non-superimposable mirror images, known as enantiomers. In coordination chemistry, this also includes finding whether the complex can exhibit geometrical or optical isomerism.

(a) \[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\] \mathrm{Br} - The compound contains a cobalt ion coordinated by two bidentate ethylenediamine (en) ligands and two chloride ions, possibly leading to cis-trans isomerism, but not four distinct isomers.(b) \[\mathrm{Co}(\mathrm{en})(\mathrm{NH}_{3})_{2}\mathrm{Cl}_{2}\] \mathrm{Cl} - The compound has a cobalt ion coordinated by one bidentate ethylenediamine ligand, two ammonia molecules, and two chloride ions, potentially leading to both geometrical (cis-trans) and optical isomerism because en creates a chiral center at the cobalt ion.(c) \[\mathrm{Co}(\mathrm{PPh}_{3})_{2}(\mathrm{NH}_{3})_{2} \mathrm{Cl}_{2}\] \mathrm{Cl} - This compound has a cobalt ion with a mixture of ligands which could allow for geometrical isomerism but not necessarily four distinct isomers, given that (PPh3) and (NH3) are not bidentate ligands and thus do not create a chirality center.(d) \[\mathrm{Co}(\mathrm{en})_{3}\] \mathrm{Cl}_{3} - Here, the cobalt ion is surrounded by three bidentate ethylenediamine ligands, which could lead to a fac-mer isomerism plus optical isomerism, due to the chiral environment around the cobalt ion, resulting in more than four isomers.

Considering geometrical and optical isomerism for the given complexes, (b) \[\mathrm{Co}(\mathrm{en})(\mathrm{NH}_{3})_{2}\mathrm{Cl}_{2}\] \mathrm{Cl} can form both geometrical and optical isomers due to the presence of ethylenediamine (en) and the arrangement of ligands around the cobalt ion. This compound can exhibit cis-trans isomerism around the cobalt ion due to different possible arrangements of the ammonia and chloride ligands, as well as optical isomerism due to the presence of a chiral center created by the bidentate en ligand.