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| The '''Kapustinskii equation''' calculates the [[lattice energy]] ''U<sub>L</sub>'' for an [[ionic crystal]], which is experimentally difficult to determine. It is named after [[Anatoli Fedorovich Kapustinskii]] who published the formula in 1956.
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| :<math>U_{L} = {K} \cdot \frac{\nu \cdot |z^+| \cdot |z^-|}{r^+ + r^-} \cdot \biggl( 1 - \frac{d}{r^+ + r^-} \biggr) </math>
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| :{|
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| |where ||''K'' = 1.2025{{e|−4}} J·m·mol<sup>−1</sup>
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| | ||''d'' = 3.45{{e|−11}} m
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| | ||''ν'' is the number of [[ion]]s in the empirical formula,
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| | || ''z<sup>+</sup>'' and ''z<sup>−</sup>'' are the numbers of elementary charge on the cation and anion, respectively, and
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| | || ''r<sup>+</sup>'' and ''r<sup>−</sup>'' are the radii of the cation and anion, respectively.
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| |}
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| The calculated lattice energy gives a good estimation; the real value differs in most cases by less than 5%.
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| Furthermore, one is able to determine the [[ionic radius|ionic radii]] using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like [[sulfate]] (SO{{su|b=4|p=2−}}) or [[phosphate]] (PO{{su|b=4|p=3−}}).
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| ==See also==
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| * [[Born-Landé equation]]
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| * [[Born-Haber cycle]]
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| * [[Madelung constant]]
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| ==Literature==
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| * A. F. Kapustinskii; ''Z. Phys. Chem. Abt. B'' Nr. 22, '''1933''', pp. 257 ff.
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| * A. F. Kapustinskii; ''Zhur. Fiz. Khim.'' Nr. 5, '''1943''', pp. 59 ff.
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| * A. F. Kapustinskii: ''Lattice energy of ionic crystals''. In: ''Quart. Rev. Chem. Soc.'' Nr. 10, '''1956''', pp. 283–294. {{DOI|10.1039/QR9561000283}}
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| [[Category:Chemical bonding]]
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| [[Category:Crystallography]]
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| {{chemistry-stub}}
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