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 find their Lewis structures, determine the hybridization of the central atom, and predict their molecular geometry using VSEPR theory.

Why (A) is correct:

Let's analyze the structure of ${\mathrm{CO}}_2$ and the given options:

• ${\mathrm{CO}}_2$: The central atom is Carbon. Carbon forms two double bonds with two oxygen atoms. There are no lone pairs on the central carbon atom. The steric number is 2 (2 bond pairs + 0 lone pairs). This corresponds to sp hybridization and a linear geometry.

  $\mathrm{O}=\mathrm{C}=\mathrm{O}$

• A) ${\mathrm{HgCl}}_2$: The central atom is Mercury. Mercury forms two single bonds with two chlorine atoms. There are no lone pairs on the central mercury atom. The steric number is 2 (2 bond pairs + 0 lone pairs). This corresponds to sp hybridization and a linear geometry.

  $\mathrm{Cl}-\mathrm{Hg}-\mathrm{Cl}$

  Since both ${\mathrm{CO}}_2$ and ${\mathrm{HgCl}}_2$ have sp hybridization and a linear geometry, they are isostructural.

Option Analysis:

• B) ${\mathrm{SnCl}}_2$: The central atom is Tin. Tin forms two single bonds with two chlorine atoms and has one lone pair. The steric number is 3 (2 bond pairs + 1 lone pair). This corresponds to sp² hybridization and a bent (V-shaped) geometry. Thus, it is not isostructural with ${\mathrm{CO}}_2$.

• C) ${\mathrm{C}}_2{\mathrm{H}}_2$ (Ethyne): This molecule has two carbon atoms. Each carbon atom is sp hybridized and forms a triple bond with the other carbon and a single bond with a hydrogen atom. The overall molecule is linear, but it's a polyatomic molecule with multiple central atoms, and its bonding is different from ${\mathrm{CO}}_2$ in terms of the number of central atoms and types of bonds. While both are linear, the question usually implies a single central atom for isostructural comparison unless specified. More importantly, ${\mathrm{CO}}_2$ has a single central atom, while ${\mathrm{C}}_2{\mathrm{H}}_2$ has two central atoms.

• D) ${\mathrm{NO}}_2$: The central atom is Nitrogen. Nitrogen forms one double bond and one single bond with oxygen atoms, and it has one unpaired electron (odd electron molecule). The steric number is approximately 2.5 (2 bond pairs + 0.5 lone pair for the odd electron). It has sp² hybridization and a bent geometry. Thus, it is not isostructural with ${\mathrm{CO}}_2$.

Correct Answer: (A)