Q.$[\text{Co}(\text{en})_3]^{3+}$ shows optical isomerism. Explain why, in terms of molecular symmetry, and describe the relationship between its $d$ and $l$ forms.

[!TLDR] Chiral (no plane of symmetry) → non-superimposable mirror images that rotate plane-polarized light in opposite directions. [!ANSWER] The three chelating en ligands wind around Co in a plane-symmetry-free arr …

$[\text{Co}(\text{en})_3]^{3+}$ is an octahedral complex built from three identical bidentate ethylenediamine ligands, of the general type $\text{M}(\text{AA})_3$. Because the three chelate rings wind around the cobalt centre in a genuinely three-dimensional, propeller-like fashion, the whole ion has no internal plane of symmetry, no centre of symmetry, and no improper rotation axis that could reflect the structure onto itself — it is chiral. A chiral object has a mirror image that cannot be superimposed on the original no matter how it is rotated, exactly like a person's left and right hands. The two non-superimposable mirror-image forms of $[\text{Co}(\text{en})_3]^{3+}$ are labelled $\boldsymbol{d}$ (dextrorotatory) and $\boldsymbol{l}$ (laevorotatory), and they are called enantiomers. Enantiomers are chemically identical in essentially every ordinary respect — same colour, same melting point, same solubility, same reactivity with achiral reagents — but differ in exactly one measurable physical property: each rotates the plane of plane-polarized light passing through a solution of it, and the two forms rotate it by an equal angle but in **opposite di …

Check whether the complex's three-dimensional structure possesses any internal plane, centre, or improper axis of symmetry; if none exists, it is chiral and exists as non-superimposable $d …

Assuming any octahedral complex with three of the 'same' ligand is automatically achiral because it 'looks symmetric' — the $\text{M}(\text{AA})_3$ propeller arrangement of three bidentate chelate rings specifically lacks the needed symmetry element, unlike, for instance, three simp …