Lattice Energy Calculator (Kapustinskii)

How it works

U ≈ 1.2025 × 10⁵ · ν·|z₊z₋| ÷ r₀ · (1 − 34.5/r₀) kJ/mol, r₀ in pm (Kapustinskii); U = N_A·A·|z₊z₋|e² ÷ (4πε₀r₀) · (1 − 1/n) (Born–Landé)

Lattice energy is the energy released when gaseous ions assemble into a crystal — the main reason ionic solids are hard, high-melting and often poorly soluble. It scales with the product of the charges and inversely with the ion separation, so MgO (2+/2−, small ions) at ~3,800 kJ/mol dwarfs NaCl at ~780. Kapustinskii’s formula needs no knowledge of the crystal structure, replacing the Madelung constant with an average that works to within a few percent; Born–Landé uses the real structure’s Madelung constant and a compressibility exponent.

Worked example

NaCl: r₀ = 102 + 181 = 283 pm, ν = 2, z = 1: U = 1.2025 × 10⁵ × 2 ÷ 283 × (1 − 0.122) = 746 kJ/mol; Born–Landé gives 755 and the Born–Haber experimental value is 787.

Frequently asked questions