Lattice Energy Estimator (Kapustinskii Equation)

Lattice energy is the energy released when gaseous ions combine to form one mole of an ionic solid. It is a measure of the strength of ionic bonding in a crystal.

Kapustinskii equation (simplified):

U = (K × ν × z⁺ × z⁻) / (r⁺ + r⁻) × (1 - d/(r⁺ + r⁻))

Where:

• U = lattice energy (kJ/mol)
• K = 120,250 kJ·pm/mol (1.2025 × 10⁵), the Kapustinskii constant that pairs with the Born repulsion term below
• ν = number of ions per formula unit (e.g. 2 for NaCl, 3 for MgCl₂)
• z⁺, z⁻ = charges of cation and anion
• r⁺, r⁻ = ionic radii in pm
• d = 34.5 pm (compressibility correction, from Born repulsion)

More commonly used form:

U ≈ (1.2025 × 10⁵ × ν × |z⁺ × z⁻|) / (r⁺ + r⁻) × (1 - 34.5/(r⁺ + r⁻)) kJ/mol, with both radii in picometers

Sign convention: Lattice energy is negative (exothermic) when defined as the energy of formation from ions. It is positive when defined as the energy needed to separate a crystal into ions. This calculator uses the positive convention (energy of dissociation).

Trends in lattice energy:

• Higher charge → higher lattice energy: MgO (|z| = 2) » NaCl (|z| = 1)
• Smaller ions → higher lattice energy: LiF » CsI
• More ions per formula unit → higher energy: Al₂O₃ (ν=5) » NaCl (ν=2)

Common ionic radii (pm):

Born-Haber cycle: Lattice energy cannot be measured directly. It is calculated from a thermodynamic cycle using measurable heats: ΔH_formation = ΔH_atomization + IE + EA + ΔH_lattice

How close is the estimate?

Kapustinskii is an approximation, and the chart shows both it and the Born-Haber values so you can see the size of the gap. Measured against the six reference compounds it lands within about 10% throughout, but not in a single direction:

The singly-charged halides come out a few percent low and the divalent oxides land almost exactly. That is the equation doing what an averaged model does: it uses one repulsion constant and one geometry factor for every structure, so it cannot know that rock salt and periclase pack differently. Use it for comparing compounds and for sanity-checking a Born-Haber result, not as a substitute for one.