Born–Haber cycle

A cycle of reactions used for calculating the lattice energies of ionic crystalline solids. For a compound MX, the lattice energy is the enthalpy of the reaction
M⁺(g) + X⁻(g) → M⁺X⁻(s) ΔHL

The standard enthalpy of formation of the ionic solid is the enthalpy of the reaction

M(s) + ½X₂(g) → M⁺X⁻(s) ΔHf

The cycle involves equating this enthalpy (which can be measured) to the sum of the enthalpies of a number of steps proceeding from the elements to the ionic solid. The steps are:

(1) Atomization of the metal:
M(s) → M(g) ΔH₁

(2) Atomization of the nonmetal:

½X2(g) → X(g) ΔH₂

(3) Ionization of the metal:

M(g) → M+(g) + e ΔH₃

This is obtained from the ionization potential.

(4) Ionization of the nonmetal:

X(g) + e → X⁻(g) ΔH₄

This is the electron affinity.

(5) Formation of the ionic solids:

M⁺(g) + X⁻(g) → M⁺X⁻(s) ΔHL

Equating the enthalpies gives:

ΔHf = ΔH₁ + ΔH₂ + ΔH₃ + ΔH₂ + ΔHL

from which ΔHL can be found. It is named after the German physicist Max Born (1882–1970) and Fritz Haber.