Final answer:
PCl5 is nonpolar due to its symmetrical trigonal bipyramidal shape which causes its bond dipoles to cancel out. PCl3 is polar because its trigonal pyramidal shape results in an uneven distribution of charge due to its lone pair of electrons.
Step-by-step explanation:
The polarity of a molecule depends on both its bond polarities and its molecular shape. In the case of PCl5, the molecule has a trigonal bipyramidal shape with symmetry that causes the dipole moments to cancel out, resulting in a nonpolar molecule. In contrast, PCl3 has a trigonal pyramidal shape due to the presence of a lone pair on the phosphorus atom, which creates an asymmetric shape and a net dipole moment, making PCl3 a polar molecule.
It's important to note that each P-Cl bond is polar due to the difference in electronegativity between phosphorus and chlorine. However, the overall polarity of a molecule is determined by the vector sum of all individual bond dipoles in the context of the molecule's geometry. PCl5's symmetry allows for the dipoles to cancel out, whereas PCl3's asymmetry does not.