Lattice Energy Calculator

Charge enters as a product, which is why magnesium oxide beats sodium chloride fivefold at a similar size.

Lattice energy745.9 kJ/molby Kapustinskii, which is a fit and not a derivation

Interionic distance283 pm102 + 181 pm

Charge product1this enters linearly, so it dominates

Repulsion correction12.191%the term that stops the ions collapsing together

Without the repulsion term849.5 kJ/mol

Lattice energy is defined here as the energy released when gaseous ions come together, so a larger positive number means a more tightly bound crystal — and a higher melting point, a lower solubility and a harder solid.

The formula

U = 120200 * v * |z+| * |z-| / (r+ + r-) * (1 - 34.5 / (r+ + r-))

Charge dominates, size modulates

The product of the two charges sits in the numerator, so going from a 1:1 salt to a 2:2 salt multiplies the lattice energy by four before any size effect is considered. Magnesium oxide and sodium chloride have similar interionic distances and lattice energies differing by a factor of five, almost entirely for that reason. It is also why MgO melts at 2852 °C and NaCl at 801.

What Kapustinskii is for

A proper lattice energy comes either from a Born-Haber cycle, which needs half a dozen measured quantities, or from a Born-Mayer calculation, which needs the Madelung constant for that particular crystal structure. Kapustinskii's contribution was noticing that the Madelung constant divided by the number of ions is nearly the same for every structure, so a single formula with no structural input gets within a few per cent. It returns 746 kJ/mol for NaCl against a Born-Haber figure near 787.

Models, and where they stop

Slater's rules, the Kapustinskii equation and Pauling's ionic-character expression are all empirical fits, not derivations. They were built to reproduce measured numbers with arithmetic simple enough to do by hand, and they succeed at that within perhaps five or ten per cent. Where a page here quotes one, it says which — a figure from a fitted rule and a figure from a Born-Haber cycle are not the same kind of thing, even when they agree.