Concept: The bond angle in molecules with a central atom and three identical surrounding atoms (like PX\u2083, where X is a halogen) is primarily influenced by the electronegativity of the surrounding atoms and the size of the surrounding atoms. These factors affect the electron density distribution and the repulsion between bond pairs.

Why (A) is correct:

All the given molecules (${\mathrm{PF}}_3,{\mathrm{PCl}}_3,{\mathrm{PBr}}_3,{\mathrm{PI}}_3$) have a central phosphorus atom bonded to three halogen atoms and one lone pair of electrons. According to VSEPR theory, they all have a trigonal pyramidal geometry. The bond angle in such molecules is influenced by the electronegativity and size of the halogen atoms.

1. Electronegativity of Halogen: As the electronegativity of the surrounding atom (X) decreases, the bond pair electrons are pulled less towards the halogen and more towards the central phosphorus atom. This increases the electron density around the central atom, leading to greater repulsion between the bond pairs, and thus an increase in the bond angle.

The electronegativity order of halogens is $\mathrm{F}>\mathrm{Cl}>\mathrm{Br}>\mathrm{I}$.

2. Size of Halogen: As the size of the surrounding atom (X) increases, the steric repulsion between the larger halogen atoms increases, which tends to open up the bond angle.

The size order of halogens is $\mathrm{F}<\mathrm{Cl}<\mathrm{Br}<\mathrm{I}$.

Both effects (decreasing electronegativity and increasing size of halogen) work in the same direction to increase the bond angle from ${\mathrm{PF}}_3$ to ${\mathrm{PI}}_3$.

Therefore, the order of bond angles is ${\mathrm{PF}}_3<{\mathrm{PCl}}_3<{\mathrm{PBr}}_3<{\mathrm{PI}}_3$.

Option Analysis:

• A) ${\mathrm{PF}}_3<{\mathrm{PCl}}_3<{\mathrm{PBr}}_3<{\mathrm{PI}}_3$: This order correctly reflects the increase in bond angle as the electronegativity of the halogen decreases and its size increases.
• B) ${\mathrm{PF}}_3<{\mathrm{PBr}}_3<{\mathrm{PCl}}_3<{\mathrm{PI}}_3$: This order incorrectly places ${\mathrm{PBr}}_3$ before ${\mathrm{PCl}}_3$.
• C) ${\mathrm{PI}}_3<{\mathrm{PBr}}_3<{\mathrm{PCl}}_3<{\mathrm{PF}}_3$: This order is the reverse of the correct trend.
• D) ${\mathrm{PF}}_3>{\mathrm{PCl}}_3<{\mathrm{PBr}}_3<{\mathrm{PI}}_3$: This order is inconsistent and contains an incorrect comparison (${\mathrm{PF}}_3>{\mathrm{PCl}}_3$).

Correct Answer: (A)