How this instrument works
Lattice energy is the energy released when gas-phase ions come together to form one mole of an ionic solid (equivalently, the energy needed to tear that solid apart back into gaseous ions). It is the single number that best explains why some ionic compounds — like magnesium oxide — are hard, high-melting, and barely soluble, while others — like sodium chloride — dissolve in water without much trouble: the stronger the electrostatic pull holding the lattice together, the more energy it takes to break it apart.
The rigorous way to get lattice energy is the Born-Haber cycle, which combines several experimentally measured energies (sublimation, ionization, electron affinity, bond dissociation, formation enthalpy) through Hess's law. That works, but it needs a stack of separate measurements for every compound. The Kapustinskii equation sidesteps all of that: it treats the crystal as a simple electrostatic (Coulombic) sum between point-like ions and only needs the ion charges, how many ions are in the formula unit, and each ion's radius — figures you can look up in a table of Shannon effective ionic radii in a few seconds.
The trade-off is precision. Because Kapustinskii's equation ignores details like crystal geometry (the specific way ions pack together) and covalent character in the bonding, it typically lands within about 5% of the true, Born-Haber-derived value rather than matching it exactly. For quick comparisons — is this compound's lattice held together more tightly than that one, and by roughly how much — that's more than good enough, which is exactly why the equation remains a standard first-pass tool in inorganic chemistry.
- Enter the number of ions in one formula unit into Ions per formula unit, v — 2 for NaCl (one Na+, one Cl-), 3 for CaCl2 (one Ca2+, two Cl-).
- Enter the cation's charge magnitude into Cation charge magnitude, |z+| and the anion's into Anion charge magnitude, |z-| — use the number only, ignore the sign.
- Enter the cation's ionic radius in picometers into Cation ionic radius (pm), and the anion's into Anion ionic radius (pm) — Shannon effective ionic radii tables are the standard source.
- Read Lattice energy, U (kJ/mol) below the inputs — it recalculates instantly as any field changes.
- Treat the result as an estimate, typically within about 5% of a full Born-Haber-cycle value, not an exact match to it.
Worked example — ordinary table salt, NaCl
Enter 2 into Ions per formula unit, v (one Na+ and one Cl- per formula unit), 1 into both charge fields (both ions carry a single charge), 102 into Cation ionic radius (pm) for six-coordinate Na+, and 181 into Anion ionic radius (pm) for Cl- — both are standard Shannon effective ionic radii. Lattice energy, U reads about 745.9 kJ/mol.
The real, Born-Haber-cycle-derived lattice energy of NaCl is close to 787 kJ/mol, so this Kapustinskii estimate sits within roughly 5% of the accepted value — exactly the accuracy the equation is known for. That gap is the price of skipping the detailed structural and bonding data the Born-Haber cycle folds in, in exchange for needing only four simple numbers to get a same-ballpark answer instantly.
Questions
What does lattice energy actually measure?
The energy released when free-floating gas-phase cations and anions come together to form one mole of the solid ionic crystal (or, run in reverse, the energy you'd have to supply to break that crystal back apart into separated gaseous ions). Larger lattice energy means the ions are held together more strongly, which shows up as a higher melting point, greater hardness, and often lower solubility in water.
How accurate is the Kapustinskii equation compared to the Born-Haber cycle?
It's an approximation, typically within about 5% of the value a full Born-Haber cycle (built from separately measured sublimation, ionization, electron affinity, and formation energies) would give. Kapustinskii's equation treats the ions as simple charged points and doesn't account for the crystal's actual packing geometry or any covalent character in the bonding, so for compounds with significant covalent contribution — like many transition-metal compounds — the gap from the true value can be larger than 5%.
Where do I find ionic radii to enter here?
Shannon effective ionic radii tables (R.D. Shannon, Acta Crystallographica A32, 1976) are the standard source used by essentially every general chemistry textbook and inorganic chemistry reference. Values depend slightly on the ion's coordination number (how many neighboring ions surround it), so use the radius listed for the coordination environment closest to your compound's actual structure — six-coordinate values are the most commonly tabulated default.
Why does MgO have such a dramatically larger lattice energy than NaCl?
Because charge enters the Kapustinskii formula as the product |z+| x |z-|, and that product grows fast. NaCl has singly charged ions on both sides (1 x 1 = 1), while MgO has doubly charged ions on both sides (2 x 2 = 4) — a fourfold larger charge factor before ionic radius is even considered. Combined with MgO's smaller ion sizes (which shrink the denominator and further boost U), this is why MgO's lattice energy comes out close to 3,800 kJ/mol versus NaCl's roughly 746 kJ/mol here.
Is ions per formula unit always just 2?
No — it equals the total count of ions written in the compound's simplest formula. NaCl has 2 (one cation, one anion); CaCl2 or MgF2 have 3 (one cation, two anions); Ca3(PO4)2 has 5 (three Ca2+ plus two PO4^3-). Get this number from the compound's chemical formula before entering the charges and radii for the individual ion types.
Can this be used for compounds with significant covalent bonding?
It will still produce a number, but the result will be less reliable the more covalent the bonding actually is. The Kapustinskii equation's core assumption is that the ions behave as simple charged spheres interacting electrostatically — an assumption that holds well for classically ionic compounds like alkali halides and alkaline-earth oxides, but breaks down for compounds where electron density is meaningfully shared between the ions rather than fully transferred.