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 Fedorovich Kapustinskii who published the formula in 1956.

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

where	K = 1.2025×10^−4 J·m·mol^−1
	d = 3.45×10^−11 m
	ν is the number of ions in the empirical formula,
	z^+ and z^− are the numbers of elementary charge on the cation and anion, respectively, and
	r^+ and r^− are the radii of the cation and anion, respectively, in picometers.

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 ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like sulfate (SO2−
4) or phosphate (PO3−
4).

See also

• Born-Landé equation
• 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