Which of the following is a linear molecule?

The correct option is CO₂.

To determine which molecule is linear, we can use the Valence Shell Electron Pair Repulsion (VSEPR) theory to analyze the steric number (the number of bonded atoms plus the number of lone pairs on the central atom) and the resulting molecular geometry.

1. Carbon Dioxide (${\mathrm{CO}}_2$):
The central atom is carbon (C), which has 4 valence electrons. Each of the two oxygen (O) atoms requires 2 electrons to complete its octet. Therefore, carbon forms two double bonds, one with each oxygen atom, sharing all 4 of its valence electrons:
$O=C=O$
Since there are no lone pairs on the central carbon atom, it has only 2 bonding regions. To minimize repulsion between these electron density regions, the bonds arrange themselves as far apart as possible, resulting in a linear geometry with a bond angle of 180°.

2. Why the other options are not linear:
• Sulfur Dioxide (${\mathrm{SO}}_2$): The central sulfur atom has 6 valence electrons. It forms two double bonds with the oxygen atoms, leaving one lone pair on the sulfur atom. The presence of this lone pair exerts repulsion on the bonding pairs, bending the molecule into a bent (angular) shape with a bond angle of approximately 120°.
• Nitrogen Dioxide (${\mathrm{NO}}_2$): The central nitrogen atom has 5 valence electrons. It forms bonds with two oxygen atoms, leaving one unpaired electron on the nitrogen. This single electron acts similarly to a lone pair, causing the molecule to have a bent geometry (bond angle of approximately 134°).
• Chlorine Dioxide (${\mathrm{ClO}}_2$): The central chlorine atom has 7 valence electrons. It has two bonding regions and three non-bonding valence electrons (a lone pair and an unpaired electron), resulting in a bent molecular structure.