Kapustinskii equation

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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.

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

In this formula, $ν$ 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-).

[edit] See also

[edit] 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