Lattice Energy Estimator (Kapustinskii Equation)
Estimate ionic lattice energy using the Kapustinskii equation.
Enter ion charges, ionic radii, and coordination number to calculate lattice energy in kJ/mol.
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 = 107,900 kJ·pm/mol (Kapustinskii constant for 1:1 salts)
- 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 ≈ (1202.5 × ν × |z⁺ × z⁻|) / (r⁺ + r⁻) × (1 - 34.5/(r⁺ + r⁻)) kJ/mol
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):
| Ion | Radius | Ion | Radius |
|---|---|---|---|
| Li⁺ | 76 | F⁻ | 133 |
| Na⁺ | 102 | Cl⁻ | 181 |
| K⁺ | 138 | Br⁻ | 196 |
| Mg²⁺ | 72 | O²⁻ | 140 |
| Ca²⁺ | 100 | S²⁻ | 184 |
| Al³⁺ | 54 | N³⁻ | 146 |
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