Final answer:
In PF₃, the central phosphorus atom is surrounded by three fluorine atoms forming single bonds and one lone pair, complying with the octet rule. Each attached fluorine has three lone pairs, resulting in the octet rule being satisfied for each atom in the molecule.
Step-by-step explanation:
To design a Lewis structure for PF₃ that satisfies the octet rule, begin by considering the valence electrons of phosphorus (P) and fluorine (F). Phosphorus has five valence electrons, and each fluorine atom has seven valence electrons. The phosphorus atom will be the central atom, with fluorine atoms surrounding it. To ensure that the octet rule is followed, each fluorine will form a single bond with phosphorus, which accounts for three of phosphorus's valence electrons being shared.
In total, the phosphorus atom will have three single bonds to fluorine, and the remaining two valence electrons will form a lone pair. Therefore, around the phosphorus atom in PF₃, there are three single bonds and one lone pair, not two single bonds and one double bond. Each fluorine atom will have three lone pairs of electrons in addition to the single bond shared with phosphorus.
The Lewis structure of PF₃ shows the central phosphorus atom satisfying the octet rule with an electron arrangement that consists of eight total electrons: six in the bonds with fluorine and two as a lone pair. Each fluorine also complies with the octet rule, having seven valence electrons plus one shared with phosphorus.