Among the species XeF4, SF4, ICl4^-, BrF3, I3^-, PCl5, SF6, XeF2, XeO3, ClF3, the number of species that possess at least one lone pair on the…

For each species, find the electron geometry and the shape. $\mathrm{XeF_4}$ (two lone pairs, square planar) and $\mathrm{ICl_4^-}$ (two lone pairs, square planar) have symmetrical vectors that cancel. $\mathrm{XeF_2}$ and $\mathrm{I_3^-}$ have three equatorial lone pairs and a linear arrangement, so the dipoles cancel. $\mathrm{SF_4}$ (see-saw), $\mathrm{BrF_3}$ and $\mathrm{ClF_3}$ (T-shaped) and $\mathrm{XeO_3}$ (trigonal pyramidal) have lone pairs but a net dipole moment. $\mathrm{PCl_5}$ (trigonal bipyramidal) and $\mathrm{SF_6}$ (octahedral) are non-polar but have no lone pair on the central atom. Hence four species qualify: $\mathrm{XeF_4,\ ICl_4^-,\ I_3^-,\ XeF_2}$.