Kapustinskii equation

The Kapustinskii equation calculates the Lattice Energy UL for an ionic crystal, which is experimentally difficult to determine. It is named after Anatoli Kapustinskii who published the formula in 1956.


 * $$U_{L} = - 1202.5 \cdot \frac{\nu \cdot |z^+| \cdot |z^-|}{r^+ + r^-} \cdot \biggl( 1 - \frac{0.345}{r^+ + r^-} \biggr) $$

In this formula, $$ \nu $$ is the number of ions in the empirical formula, $$ z $$ is the anionic and cationic charge, respectively, and $$ r $$ is the radius of the anion / cation. It is important to remember that the units of the radii in this equation are Ångström, and the lattice energy is given in kJ/mol. The calculated lattice energy gives a good estimation; the real value differs in most cases by less than 5 %.

Furthermore, one is able to determine the atomic radii using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like sulphate (SO42-) or phosphate (PO43-).

Literature

 * A. F. Kapustinskii; Z. Phys. Chem. Abt. B Nr. 22, 1933, pp. 257 ff.
 * A. F. Kapustinskii; Zhur. Fiz. Khim. Nr. 5, 1943, pp. 59 ff.
 * A. F. Kapustinskii: Lattice energy of ionic crystals. In: Quart. Rev. Chem. Soc. Nr. 10, 1956, pp. 283–294.

Kapustinskii-Gleichung