23.1.3—Born–Haber cycles for ionic solids

A Born–Haber cycle applies Hess’s law to an ionic solid. Typical steps are atomisation, ionisation energies, electron affinities, bond dissociation for a non-metal, and lattice formation, linked to the standard enthalpy of formation.

Write every species and state on the energy path. For +2 cations include two successive ionisation energies; for −2 anions include the second electron affinity with its correct sign.

For MgO(s), the cycle includes Mg atomisation, IE₁ + IE₂, oxygen atomisation, EA₁ + EA₂ and lattice formation, summing to ΔHf°.

A cycle is not a list of numbers: omitting a gaseous atom or using the wrong electron-affinity direction invalidates the result.