Lattice Energy Calculator – Born–Haber Cycles and the Ionic Model
Lattice energy is the energy that holds an ionic crystal together: the enthalpy needed to pull one mole of a solid such as NaCl apart into separate gaseous ions. This lattice energy calculator finds it two ways, from a Born–Haber cycle built on measured data and from the electrostatic Born–Landé, Born–Mayer and Kapustinskii equations, and compares the two for 35 built-in salts.
Two sign conventions
Written as lattice dissociation, NaCl(s) → Na⁺(g) + Cl⁻(g), the value is positive: +787.43 kJ/mol. Written as lattice formation, the reverse, it is −787.43 kJ/mol. Both are common in textbooks; the switch at the top flips every lattice value without changing the chemistry.
Walking around a Born–Haber cycle
Lattice energy can't be measured directly, but every other step can. Hess's law says the direct route from the elements to the solid (ΔfH°) equals the long way round, so for NaCl:
ΔH_latt = −ΔfH° + ΔatH(Na) + IE₁(Na) + ΔatH(Cl) + ΔegH(Cl)
= 411.153 + 107.32 + 495.85 + 121.679 − 348.57
= 787.43 kJ/molThe same equation solves for any single unknown, so the cycle can just as well give the electron affinity of chlorine or predict the formation enthalpy of a compound nobody has made. Ionization energies and electron affinities are 0 K energies while ΔfH° is a 298 K enthalpy. Turning each into a 298 K enthalpy adds +5/2 RT per electron removed and −5/2 RT per electron gained, and a neutral salt removes and gains the same number of electrons, so the corrections cancel.
Coulomb's law across a whole crystal
Each ion feels every other ion in the lattice. Summing Coulomb's law over the geometry gives the Madelung constant M (1.747565 for rock salt), and a short-range Born repulsion stops the ions collapsing. The minimum of that energy well is the Born–Landé equation, U = (N_A·e²/4πε₀)·M·z₊z₋/r₀ · (1 − 1/n), where n is the Born exponent set by each ion's noble-gas core (see the Electron Configuration Generator). Kapustinskii's equation replaces M with the number of ions per formula unit, so it needs only the ionic radii and works for salts with awkward structures.
Charge beats size
NaF and MgO have nearly the same ion spacing, 2.317 and 2.106 Å, yet MgO's lattice energy is 4.1 times larger, because its charge product is 4 rather than 1. Size matters second: along NaF → NaCl → NaBr → NaI the anion grows and the lattice energy falls from 927.65 to 702.64 kJ/mol.
When the ionic model fails
For alkali halides the Born–Haber value is only 3–8 % above Born–Landé. For AgCl, AgBr, AgI and CuCl it is 15–21 % above. Soft, polarizing cations distort the anion's electron cloud and add covalent character that point charges can't capture, as Fajans' rules predict.
Lattice energy and solubility
Dissolving a salt breaks the lattice and hydrates the ions, so ΔH_soln = ΔH_hydration − lattice energy. A large lattice energy is one reason MgO is nearly insoluble while NaCl dissolves readily. To take that step, use the Heat of Solution Calculator.
Why MgCl₂ and not MgCl or MgCl₃?
With a Kapustinskii estimate for the lattice, the cycle predicts ΔfH°(MgCl) ≈ −87 kJ/mol: it would form, but 2 MgCl → Mg + MgCl₂ releases about 466 kJ, so it disproportionates. MgCl₃ would need magnesium's third ionization energy, 7733 kJ/mol, which breaks into the neon core and makes ΔfH° about +4140 kJ/mol.