Trends in Lattice Energy: Ion Size and Charge

Lattice energy is associated with the formation or separation of an ionic lattice. Yet, when sodium chloride or magnesium oxide form, their lattice energy differs significantly. Why does each ionic compound have a different lattice energy, and which factors does it depend on?

An ionic compound consists of an orderly arrangement of a large number of charged ions attracted to each other by electrostatic interactions.

According to Coulomb’s law, the potential energy of two ions is inversely proportional to the distance between the ions, which in turn depends on the ionic radius.

In the periodic table, the ionic radius of the alkali and alkaline earth metals increases down the column. As the size of the metal ion increases, the distance between ions, or the bond length, becomes larger as well. For example, the bond length of lithium bromide and potassium bromide differs between 217 pm and 282 pm, respectively.

Due to the increased internuclear distance, the attraction between the ions decreases and it becomes much easier to separate the ions. Thus the lattice energy to separate solid lithium bromide is larger than for potassium bromide being +807 kJ/mol versus +682 kJ/mol, respectively.

In addition to the ionic radius, the magnitude of lattice energy also depends on the ion charges. According to Coulomb’s law, the potential energy of ions is directly proportional to the product of their charges.

Consider two ionic compounds sodium fluoride and calcium oxide. The ionic distance in both compounds is similar, but the lattice energy of calcium oxide is almost four times greater than sodium fluoride.

Both sodium and fluoride are monovalent ions; the product of their charge is 1. However, calcium and oxide ions are divalent and the product of their charge is 4, which is four times greater than sodium fluoride.

This is why it takes nearly four times as much energy to separate the calcium oxide into gaseous ions as compared to sodium fluoride.

Thus, the magnitude of lattice energy is directly proportional to the product of the ion charges and is inversely proportional to the distance between the ions.