Tanaka's formula

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 = 1.2025Template:E J·m·mol−1
	d = 3.45Template:E 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.

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 using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like sulfate (SOTemplate:Su) or phosphate (POTemplate:Su).

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. Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting .

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