# 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-}}$