Animated Solution for Chemistry - Coordination Compounds: Which one of the following has an optical isomer? (en = ethylenediamine)

Optical isomerism is one of the most fascinating phenomena in coordination chemistry. It occurs when a molecule is chiral, meaning it cannot be superimposed on its mirror image. Just like your left and right hands are mirror images but cannot perfectly overlap, chiral molecules exist as two distinct forms called enantiomers.

For a coordination complex to exhibit optical isomerism, it must satisfy a strict geometric condition: it must lack both a Plane of Symmetry (POS) and a Center of Symmetry (COS). Let's apply this principle to analyze the given options and find our chiral champion.

Let's begin by looking at options (a) $[Zn(en)(N{H}_3{)}_2{]}^{2+}$ and (d) $[Zn(en{)}_2{]}^{2+}$. Zinc in the $+2$ oxidation state has a $3d^{10}$ electronic configuration. With a coordination number of 4, it forms tetrahedral complexes.

In a tetrahedral geometry, the presence of symmetrical bidentate ligands like ethylenediamine ('en') often leads to a highly symmetric structure. For instance, in $[Zn(en{)}_2{]}^{2+}$, the two 'en' rings are arranged such that the molecule possesses a $S_4$ improper axis of rotation, which renders it optically inactive. Similarly, $[Zn(en)(N{H}_3{)}_2{]}^{2+}$ has a plane of symmetry passing through the zinc atom and the two ammonia ligands, perfectly bisecting the 'en' ring. Thus, both of these tetrahedral complexes are achiral.

Moving on to option (c), $[Co(H_{2}O{)}_4(en){]}^{3+}$, we encounter an octahedral complex of the type $M{A}_4(BB)$. Here, the central cobalt ion is surrounded by four water molecules and one bidentate 'en' ligand.

Imagine slicing this molecule with a plane that passes through the cobalt ion and the entire 'en' ligand. This plane will perfectly reflect the two water molecules on one side onto the two water molecules on the other side. Because this Plane of Symmetry exists, the molecule is identical to its mirror image and is therefore optically inactive.

Finally, we arrive at option (b), $[Co(en{)}_3{]}^{3+}$. This is an octahedral complex of the type $M(AA{)}_3$, where the central metal is coordinated to three symmetrical bidentate ligands.

When you construct this molecule in 3D space, the three 'en' rings wrap around the cobalt ion like the blades of a propeller. Try as you might, you cannot find a single plane that cuts this molecule into two identical mirror halves. It completely lacks a plane of symmetry and a center of symmetry.

Because of this inherent asymmetry, $[Co(en{)}_3{]}^{3+}$ is chiral. It exists as two non-superimposable mirror images, commonly referred to as the dextrorotatory ($d$) and levorotatory ($l$) forms. This makes it the only complex among the choices that exhibits optical isomerism!