Question 7.EP.2: In each of the following pairs of ionic solids, the ions are...
In each of the following pairs of ionic solids, the ions are arranged into similar lattices. Which one has the largest lattice energy: (a) CaO or KF? (b) NaF or CsI?
Strategy
Questions like this require us to find some basis for comparison. In this particular case, the factors associated with lattice energy have to do with the ions that make up the compound. We have two factors to consider. Smaller ions tend to have stronger coulombic interactions because the distance between the nuclei is smaller, and ions with larger charges have stronger interactions. An examination of these two factors may allow us to predict which substance has the larger lattice energy.
(a) In CaO, calcium exists as Ca^{2+} and oxygen as the oxide ion, O^{2-}. In KF, the constituent ions are K^{+} and F^{-}. Because both are from elements in the same row of the periodic table, the sizes of the two cations should not be too different. The same is true for the anions, so to a first approximation, we might discount the size factor. CaO should have the larger lattice energy because the charges on its ions are larger than the charges on the ions in KF. (Note that if we wanted to look more closely at the sizes, we would expect that K^{+} would be slightly larger than Ca^{2+} and O^{2-} would be slightly larger than F^{-}. Because the larger cation is in KF and the larger anion is in CaO, our assumption that size would not be very important seems good.)
(b) All of the ions in this problem are singly charged, so the size difference must be the key issue. Na^{+} and F^{-} are smaller than Cs^{+} and I^{-}, so the lattice spacing in NaF must be smaller. Therefore, NaF should have the larger lattice energy.
Discussion
To get started here, we needed to determine the identities of the ions involved. (One way to do this is to consider the jump in ionization energy we explored in Example Problem 7.1. However, with just a little practice, it is easy to determine the likely charges for most main group elements based on their location in the periodic table.) Ionic charge and radius were taken into consideration, based on the positions of the ions in the periodic table. The use of this “periodic reasoning” points out the importance of learning the trends in the periodic table. Note, however, that to be able to make the comparisons in this problem, the lattice structures of the compounds in question must be similar.