Lattice energy measures how strongly the ions in an ionic solid are held together β a number chemists use to explain melting points, solubility, and hardness. This calculator estimates lattice energy with the Kapustinskii equation, a simplified model that needs only ion charges, the number of ions per formula unit, and ionic radii, rather than the full crystal structure a more rigorous calculation would require.
How the Kapustinskii equation estimates lattice energy
The Kapustinskii equation treats an ionic solid as a collection of hard, oppositely charged spheres held together by simple Coulombic attraction, then adds a short-range repulsion correction (the 1 β 34.5/rβ term) to account for the fact that ions can't overlap indefinitely. Because it doesn't need the compound's actual crystal geometry β the Madelung constant that a full Born-LandΓ© calculation requires β it works for compounds whose structure is unknown or hypothetical, at the cost of typically running a few percent away from the experimental (Born-Haber cycle) value. For sodium chloride, the equation gives about 746 kJ/mol against an experimental value near 787 kJ/mol β a good estimate, not an exact one.
Why ion charge dominates lattice energy
Lattice energy scales directly with the product of the two ion charges, z+ times zβ. Magnesium oxide (MgΒ²βΊ, OΒ²β») has a charge product of 4, four times sodium chloride's charge product of 1 β and its calculated lattice energy, about 3798 kJ/mol, is roughly five times NaCl's 746 kJ/mol, even though magnesium oxide's ions are smaller and pack closer together. This is why compounds built from 2+/2β or 3+/2β ion pairs (oxides, many minerals) tend to have dramatically higher melting points and hardness than simple 1+/1β salts.
Why smaller ions bind more strongly
Holding charges constant, lattice energy rises as the ions get smaller, because the Coulombic attraction between two point charges grows as they move closer together. Lithium fluoride and sodium chloride share the same +1/β1 charge pair, but LiF's ions sum to a radius of 209 pm versus NaCl's 283 pm β and LiF's estimated lattice energy, about 960 kJ/mol, is nearly 30% higher. This radius effect is the reason lattice energy generally decreases moving down a group of the periodic table (larger ions) and increases moving up it.