Kapustinskii equation

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

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In this formula, $u$ 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 sulfate (SO₄^2-) or phosphate (PO₄^3-).

ee also

* Born-Haber cycle
* Madelung constant

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. DOI|10.1039/QR9561000283