Concept: Molecular geometry is determined by the number of electron domains (bonding pairs and lone pairs) around the central atom, as predicted by VSEPR theory. A linear structure implies a bond angle of 180° and typically occurs when the central atom has two electron domains and no lone pairs.

Why (B) is correct:

The central atom in ${\mathrm{CO}}_2$ is carbon. Carbon forms two double bonds with two oxygen atoms. There are no lone pairs on the central carbon atom. Thus, there are two electron domains around the central carbon atom. According to VSEPR theory, two electron domains with no lone pairs result in a linear geometry with a bond angle of 180°.

Option Analysis:

• A) ${\mathrm{SO}}_2$: The central atom is sulfur. Sulfur forms two double bonds with two oxygen atoms and has one lone pair. This gives three electron domains (two bonding pairs, one lone pair), resulting in a bent or V-shaped geometry.
• B) ${\mathrm{CO}}_2$: The central atom is carbon. Carbon forms two double bonds with two oxygen atoms and has no lone pairs. This gives two electron domains, resulting in a linear geometry.
• C) ${\mathrm{CO}}_3^{2-}$: The central atom is carbon. Carbon forms one double bond and two single bonds with three oxygen atoms, and has no lone pairs. This gives three electron domains, resulting in a trigonal planar geometry.
• D) ${\mathrm{SO}}_4^{2-}$: The central atom is sulfur. Sulfur forms four single bonds (or two double and two single bonds in resonance structures) with four oxygen atoms and has no lone pairs. This gives four electron domains, resulting in a tetrahedral geometry.

Correct Answer: (B)