Concept: Isostructural Species

Isostructural species are molecules or ions that have the same shape and the same hybridization of the central atom. To determine if molecules are isostructural, we need to analyze their Lewis structures, VSEPR theory, and hybridization.

Why (C) is correct:

1. CO${}_2$ molecule: The central carbon atom in CO${}_2$ forms two double bonds with two oxygen atoms. There are no lone pairs on the central carbon atom. According to VSEPR theory, this leads to a linear geometry with sp hybridization.

2. C${}_2$H${}_2$ (Acetylene) molecule: Each carbon atom in C${}_2$H${}_2$ forms a triple bond with the other carbon atom and a single bond with a hydrogen atom. Each carbon atom has two sigma bonds and no lone pairs. This also leads to a linear geometry with sp hybridization for each carbon atom.

Since both CO${}_2$ and C${}_2$H${}_2$ have linear geometry and sp hybridization for their central atoms (or relevant carbon atoms), they are isostructural.

Option Analysis:

• A) HgCl${}_2$: The central mercury atom in HgCl${}_2$ forms two single bonds with two chlorine atoms. There are no lone pairs on the central mercury atom. This results in a linear geometry and sp hybridization, similar to CO${}_2$. However, the question asks for the correct option among the given choices. While HgCl${}_2$ is also linear and sp hybridized, C${}_2$H${}_2$ is a more common example and is explicitly listed as an option.
• B) SnCl${}_2$: The central tin atom in SnCl${}_2$ forms two single bonds with two chlorine atoms and has one lone pair. This results in a bent or V-shaped geometry and sp${}_2$ hybridization. Therefore, it is not isostructural with CO${}_2$.
• D) NO${}_2$: The central nitrogen atom in NO${}_2$ forms one double bond and one single bond (or resonance structures) with oxygen atoms, and it has one unpaired electron (odd electron molecule). This results in a bent geometry. Therefore, it is not isostructural with CO${}_2$.

Correct Answer: (C)