Concept:
The Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the geometry of molecules based on the repulsion between electron pairs (bonding and lone pairs) around a central atom.
Step 1: {Determine the valence electrons and steric number.}
Chlorine (Cl) is the central atom with 7 valence electrons. The negative charge adds 1 electron, totaling 8. In ClO$_3^-$, Chlorine forms bonds with three Oxygen atoms.
Step 2: {Identify bonding and lone pairs.}
Chlorine uses 6 electrons to form three double bonds with Oxygen (in its expanded octet state) and retains 2 electrons as one lone pair.
• Number of bond pairs (or sigma bonding sites) = 3
• Number of lone pairs = 1
• Steric Number = 3 + 1 = 4
Step 3: {Predict the shape.}
A steric number of 4 corresponds to a tetrahedral electron geometry. However, with one lone pair, the molecular shape is distorted to minimize repulsion. The resulting arrangement of atoms is pyramidal.