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
½X2(g) → X(g) ΔH₂
M(g) → M+(g) + e ΔH₃
(4) Ionization of the nonmetal:
X(g) + e → X⁻(g) ΔH₄
(5) Formation of the ionic solids:
M⁺(g) + X⁻(g) → M⁺X⁻(s) ΔHL
ΔHf = ΔH₁ + ΔH₂ + ΔH₃ + ΔH₂ + ΔHL