Concept: Molecular geometry is determined by the number of bond pairs and lone pairs around the central atom, according to VSEPR theory. The shape depends on the total number of electron domains (bond pairs + lone pairs).

Why (A) is correct:

• ${\mathrm{XeF}}_2$: Xenon (Xe) is the central atom. It has 8 valence electrons. Two electrons are used to form two Xe-F bonds. This leaves 6 electrons, forming 3 lone pairs. Total electron domains = 2 bond pairs + 3 lone pairs = 5. According to VSEPR theory, 5 electron domains lead to a trigonal bipyramidal electron geometry. With 2 bond pairs and 3 lone pairs, the lone pairs occupy the equatorial positions to minimize repulsion, resulting in a linear molecular geometry.
• ${\mathrm{CO}}_2$: Carbon (C) is the central atom. It has 4 valence electrons. It forms two double bonds with two oxygen atoms. Total electron domains = 2 bond pairs (each double bond counts as one domain) + 0 lone pairs = 2. According to VSEPR theory, 2 electron domains lead to a linear molecular geometry.

Since both ${\mathrm{XeF}}_2$ and ${\mathrm{CO}}_2$ have a linear shape, option (A) is correct.

Option Analysis:

• (B) ${\mathrm{BF}}_3$ and ${\mathrm{PCl}}_3$: ${\mathrm{BF}}_3$ has 3 bond pairs and 0 lone pairs (trigonal planar). ${\mathrm{PCl}}_3$ has 3 bond pairs and 1 lone pair (trigonal pyramidal). Shapes are different.
• (C) ${\mathrm{PF}}_5$ and ${\mathrm{IF}}_5$: ${\mathrm{PF}}_5$ has 5 bond pairs and 0 lone pairs (trigonal bipyramidal). ${\mathrm{IF}}_5$ has 5 bond pairs and 1 lone pair (square pyramidal). Shapes are different.
• (D) ${\mathrm{CF}}_4$ and ${\mathrm{SF}}_4$: ${\mathrm{CF}}_4$ has 4 bond pairs and 0 lone pairs (tetrahedral). ${\mathrm{SF}}_4$ has 4 bond pairs and 1 lone pair (see-saw). Shapes are different.

Correct Answer: (A)