Final answer:
The 5 Cl 3s-orbitals of PCl5 span the symmetry species consistent with sp³d hybridization as part of forming a trigonal bipyramidal structure with no lone pairs.
Step-by-step explanation:
The symmetry species that the 5 Cl 3s-orbitals of PCl5 span can be understood by considering the hybridization of the central phosphorus atom and the overall molecular geometry. PCl5 is a trigonal bipyramidal molecule, meaning it has a central phosphorus atom surrounded by five chlorine atoms with no lone pairs. The phosphorus atom uses its 3s orbital, three 3p orbitals, and one 3d orbital to form sp³d hybrid orbitals. Each of these orbitals is used to form a bond with a chlorine atom. Therefore, these hybrid orbitals are consistent with the trigonal bipyramidal symmetry of the molecule.