Which of the following complex ions will exhibit optical isomerism? (en = 1, 2-diamine ethane).

A coordination compound will be optically active (exist as a pair of non-superimposable mirror images, d- and l-forms) only when its three-dimensional arrangement lacks BOTH a plane of symmetry (σ) and a centre of symmetry (i).
In octahedral complexes this is most commonly obtained when at least one bidentate (chelating) ligand occupies positions so that the arrangement becomes chiral.

Let us examine each ion.

Case A: $$[\text{Cr}(\text{NH}_3)_2\text{Cl}_2]^+$$
The coordination number here is 4. For Cr(III) a four-coordinate complex is normally tetrahedral. In a tetrahedron containing two identical $$\text{NH}_3$$ and two identical $$\text{Cl}^-$$ ligands the molecule possesses a mirror plane passing through the metal and the two unlike ligands. Hence it is achiral and cannot show optical isomerism.

Case B: $$[\text{Co}(\text{en})_2\text{Cl}_2]^+$$
• C.N. = 6 → octahedral.
• Ligand set: two bidentate $$\text{en}$$ ligands (chelates) + two monodentate $$\text{Cl}^-$$ ligands.

Two geometrical forms are possible: cis and trans.
  • Trans: both $$\text{Cl}^-$$ opposite each other → the complex has a C2 axis and a mirror plane, so it is achiral.
  • Cis: the two $$\text{Cl}^-$$ are adjacent. The two $$\text{en}$$ chelate rings now twist in such a way that the molecule lacks σ and i. Its mirror image is non-superimposable, giving d- and l-isomers. Therefore the cis form exhibits optical isomerism.

Case C: $$[\text{Co}(\text{NH}_3)_4\text{Cl}_2]^+$$
This is also octahedral. With four identical $$\text{NH}_3$$ and two identical $$\text{Cl}^-$$ ligands, both the cis and trans isomers possess either a mirror plane or a centre of symmetry, rendering them achiral. Hence no optical isomerism is possible.

Case D: $$[\text{Zn}(\text{en})_2]^{2+}$$
Zn(II) with two bidentate $$\text{en}$$ ligands is four-coordinate and adopts a tetrahedral geometry. The two identical chelate rings are related by a mirror plane, so the ion is achiral and does not exhibit optical activity.

Only the cis isomer of $$[\text{Co}(\text{en})_2\text{Cl}_2]^+$$ is chiral; all other complexes listed possess an internal symmetry element.

Hence, the complex ion that shows optical isomerism is:
Option B which is: $$[\text{Co}(\text{en})_2\text{Cl}_2]^+$$