Answer :

To determine which molecule has a bent geometry, let's analyze the molecular geometries of the given options.

1. HCN (Hydrogen Cyanide):
- In HCN, the carbon atom forms a triple bond with the nitrogen atom and a single bond with the hydrogen atom. There are no lone pairs on the central carbon atom. This results in a linear configuration with a bond angle of 180°.

2. [tex]$H_2O$[/tex] (Water):
- Water has two hydrogen atoms each bonded to an oxygen atom. Oxygen has two lone pairs of electrons. The electron geometry is tetrahedral, but because lone pairs occupy more space than bonding pairs, the actual shape of the molecule is bent with a bond angle of approximately 104.5°.

3. [tex]$CO_2$[/tex] (Carbon Dioxide):
- In carbon dioxide, the carbon atom forms two double bonds with two oxygen atoms. There are no lone pairs on the central carbon atom. The molecule is linear with a bond angle of 180°.

4. HF (Hydrogen Fluoride):
- HF consists of one hydrogen atom bonded to one fluorine atom. This is a diatomic molecule with no bending because there are no bonding pairs around a central atom other than the two atoms involved.

Therefore, among these options, the molecule with a bent geometry is:

B. [tex]$H_2O$[/tex] (Water)