Animated Solution for Chemistry - Coordination Compounds: Consider the complex ions, trans-[Co(en)2Cl2]+ (A) and cis-[Co(en)2Cl2]+ (B). The correct statement regarding them is

The Dance of Symmetry: Optical Activity in Coordination Complexes

Have you ever wondered why some molecules interact with light differently than others? The secret lies in their geometry, specifically their symmetry. In this problem, we explore the fascinating world of coordination chemistry by examining the optical activity of the $trans$ and $cis$ isomers of the $[Co(en{)}_{2}C{l}_2{]}^{+}$ complex.

Optical activity is the ability of a chiral molecule to rotate the plane of plane-polarized light. But what makes a molecule chiral? A molecule is chiral if it cannot be superimposed on its mirror image. The simplest way to check for chirality is to look for a Plane of Symmetry (POS).

If a molecule has a plane of symmetry—a plane that cuts it into two identical mirror-image halves—it is achiral and optically inactive. If it lacks a plane of symmetry, it is chiral and optically active.

Let's look at the $trans\text{-}[Co(en{)}_{2}C{l}_2{]}^{+}$ complex. In the $trans$ configuration, the two identical ligands (in this case, the chloride ions, $C{l}^{-}$) are positioned exactly opposite to each other, at an angle of $180^{\circ }$. The two bidentate ethylenediamine ($en$) ligands occupy the equatorial plane.

Because the chloride ions are perfectly opposed, we can easily pass a plane through the equatorial region (containing the cobalt atom and the two $en$ ligands). This plane perfectly reflects the top chloride ion onto the bottom chloride ion. Since this plane of symmetry exists, the $trans$ isomer is superimposable on its mirror image. Therefore, it is optically inactive.

Now, let's shift our focus to the $cis\text{-}[Co(en{)}_{2}C{l}_2{]}^{+}$ complex. In the $cis$ configuration, the two chloride ions are adjacent to each other, at an angle of $90^{\circ }$. The two $en$ ligands occupy the remaining positions.

If you try to find a plane that cuts this molecule into two identical halves, you will fail. The adjacent placement of the chloride ions and the bulky, bridging nature of the $en$ ligands destroy any potential plane of symmetry. Because it lacks a plane of symmetry, the $cis$ isomer is non-superimposable on its mirror image. It is a chiral molecule and is therefore optically active.

By simply analyzing the spatial arrangement of the ligands, we can confidently conclude that the $trans$-form (A) cannot be optically active due to its high symmetry, while the $cis$-form (B) can be optically active because it lacks symmetry. This elegant relationship between 3D geometry and physical properties is what makes coordination chemistry so beautiful!