Kapustinski equation

The Kapustinski equation is used to determine the lattice energy of salts , which is difficult or impossible to determine experimentally. According to Anatoli Kapustinski , who published the equation in 1956 , the following applies to the lattice energy : ${\displaystyle U_{\mathrm {g} }}$

${\displaystyle U_{\mathrm {g} }=1202{,}5\cdot {\biggl (}{\frac {\nu \cdot z_{\mathrm {k} }\cdot z_{\mathrm {a} }}{r_{\mathrm {k} }+r_{\mathrm {a} }}}{\biggr )}\cdot {\biggl (}1-{\frac {0{,}345}{r_{\mathrm {k} }+r_{\mathrm {a} }}}{\biggr )}\;{\biggl [}{\frac {\text{kJ}}{\text{mol}}}{\biggr ]}}$

Here and are the radii of the anion or the cation in Ångström , and the charge of the anion (<0) or cation (> 0) and the number of particles per formula unit. The Kapustinskii equation can, however, also be used to determine ion radii , provided that the lattice energy is known, which is extremely useful for complex ions such as or . Even if the lattice energy cannot be calculated exactly with this formula, it still gives a good approximation, since the deviation is usually less than 5%. ${\displaystyle r_{\mathrm {a} }}$ ${\displaystyle r_{\mathrm {k} }}$ ${\displaystyle z_{\mathrm {a} }}$ ${\displaystyle z_{\mathrm {k} }}$ ${\displaystyle \nu }$ ${\displaystyle {\text{SO}}_{4}^{2-}}$ ${\displaystyle {\text{PO}}_{4}^{3-}}$

See also

• Madelung constant
• Born-Landé equation

literature

• Anatoli Fjodorowitsch Kapustinski: In: Journal for physical chemistry. Department B: Chemistry of Elementary Processes, Structure of Matter . Volume 22, 1933, pp. 257 ff.
• Anatoli Fjodorowitsch Kapustinski: In: Žurnal fizičeskoj chimii No. 5, 1943, p. 59 ff.
• Anatoli Fjodorowitsch Kapustinski: Lattice energy of ionic crystals. In: Quarterly Reviews of the Chemical Society . Volume 10, No. 3, 1956, doi : 10.1039 / QR9561000283 , pp. 283-294.