Chapter 19: Lattice Energy

Since this process cannot be measured directly, its value must be calculated indirectly using Hess’s law within a specific type of energy cycle known as a Born-Haber cycle. Constructing this cycle requires several fundamental energy values, including the standard enthalpy change of formation and the energy inputs required to transform elements in their standard states into gaseous ions. This transformation involves the enthalpy change of atomisation, which is always a positive, endothermic value representing the formation of one mole of gaseous atoms. For metals, the conversion to cations involves ionization energies. For non-metals, the formation of anions involves electron affinity; the first electron affinity is usually exothermic, while subsequent electron affinities, like the second or third, are always endothermic due to electrostatic repulsion. The overall magnitude of the lattice energy depends on two primary factors: ionic charge and ionic radius. Lattice energy becomes significantly more exothermic (more negative) as the ionic charge increases and as the ionic radius decreases, reflecting higher charge density and stronger electrostatic attraction. The chapter also introduces ion polarization, the distortion of an anion’s electron cloud by a small, highly charged cation, which imparts partial covalent character to the bond. This concept of polarization is key to explaining the decreasing thermal stability observed down Group 2 for carbonates and nitrates, as smaller cations higher up the group (like magnesium) have higher charge densities and are thus better polarizers of the large anions, leading to easier decomposition. Finally, the chapter analyzes energy changes in solution. The standard enthalpy change of solution is the overall enthalpy change when one mole of an ionic solid dissolves, which can be either exothermic or endothermic. This value is the net result of the energy required to break the crystal lattice (related to lattice energy) and the energy released when gaseous ions form ion-dipole bonds with water molecules, defined as the enthalpy change of hydration. The enthalpy change of hydration is always an exothermic process, and its magnitude is greater (more negative) for smaller or more highly charged ions. By applying an energy cycle, it is shown that the total lattice energy plus the enthalpy change of solution equals the total enthalpy change of hydration for the individual ions. This relationship accounts for the decreasing solubility of Group 2 sulfates down the group, where the decreasing hydration enthalpy plays a more significant role than the decreasing lattice energy.