Answer :

To determine the molecular geometry and molecular polarity for the chlorite ion ([tex]\( \text{ClO}_2^-\)[/tex]), we can follow a step-by-step approach:

### 1. Determine the total number of valence electrons
First, we need to calculate the total number of valence electrons in the [tex]\(\text{ClO}_2^-\)[/tex] ion:

- Chlorine (Cl) has 7 valence electrons.
- Each Oxygen (O) atom has 6 valence electrons.
- There are two Oxygen atoms, so [tex]\(2 \times 6 = 12\)[/tex] valence electrons.
- The [tex]\(\text{ClO}_2^-\)[/tex] ion has an extra electron due to the negative charge.

Adding these together, we get:
[tex]\[ 7 (\text{Cl}) + 12 (2 \times \text{O}) + 1 (\text{extra electron for the charge}) = 20 \text{ valence electrons} \][/tex]

### 2. Draw the Lewis structure
To draw the Lewis structure, we follow these steps:
- Place the central atom, which is Chlorine (Cl).
- Arrange the two Oxygen atoms around the Chlorine atom.
- Distribute the 20 valence electrons around the atoms, to satisfy the octet rule as much as possible.

A plausible Lewis structure is:
[tex]\[ \begin{array}{c} O \\ \\ | \\ Cl - O \end{array} \][/tex]
Each oxygen will have lone pairs and there will also be lone pairs on Chlorine to complete the octet, considering resonance structures and formal charges.

### 3. Determine the electron domain geometry
Using Valence Shell Electron Pair Repulsion (VSEPR) theory, the molecular shape considers the regions of electron density around the central atom. For [tex]\(\text{ClO}_2^-\)[/tex], we count:
- Two bonding pairs (from Cl to each O).
- One lone pair on the Chlorine atom.

This gives three regions of high electron density around the Chlorine atom:
- Two bonding pairs
- One lone pair

The electron domain geometry with three regions of electron density is trigonal planar.

### 4. Determine the molecular geometry
The actual shape of the molecule (molecular geometry) considers only the positions of the atoms (not the lone pairs). With one lone pair among the electron regions, the shape is bent or V-shaped.

### 5. Assess molecular polarity
Polarity in a molecule arises from an uneven distribution of electron density.
- The [tex]\(\text{ClO}_2^-\)[/tex] ion has a bent shape, which causes asymmetry in the distribution of electron density.

Since the molecule is not symmetrical and the difference in electronegativity between Cl and O atoms causes dipoles, the net dipole moment will not cancel out, making the molecule polar.

### Conclusion
- Molecular Geometry: Bent
- Molecular Polarity: Polar

Thus, the molecular geometry of [tex]\(\text{ClO}_2^-\)[/tex] is bent, and the molecule is polar.