How to Calculate Lattice Energy

First, what is lattice energy? The energy required to convert one mole of an ionic solid into its constituents gaseous ions is called the lattice energy of the ionic compound. It is measured in kJ/mol. We can also define it as the energy released when the gaseous atoms combine to form a crystal lattice. It depends on the strength of the interactions between cations and anions in the lattice. Lattice Energy of an ionic compound can also be affected by charge of ions, size of ions, polarizability of ions, ionization energy, electron affinity etc.

Lattice energy can't be measured directly, but it can be obtained from the Born–Haber cycle. In this cycle, Hess's law is used to calculate the lattice energy from the measured enthalpy of formation of the ionic compound, along with other thermochemical data. Lattice energy per mole can also be calculated by the Born-Lande equation. Kapustinskii equation also provides the lattice energy.

Lattice energy can also be estimated using Coulomb's law for ionic compounds by this formula-
U = (K x Q₁ x Q₂)/r
Where, U is lattice energy, K is Coulomb's constant (8.9875 × 10⁹Nm²/C², Q₁ and Q₂ are the charges of the ions and r is the distance between the centers of the ions.

Born-Lande Equation

Kapustinskii Equation

Born-Haber Cycle

−∆H_f = ∆H_S + IP + ½∆H_d − EA − U

Each method has its own applications, and the Born-Haber cycle is often used for more accurate and detailed calculations.