Solids Kapustinskii equation

The method outlined above is capable of extension to a number of groups though no very wide use has been made of it. Sherman (114) calculated the proton affinity of water by assuming that the lattice energy of hydroxonium perchlorate (Hs0+C104 ) was the same as that of NH4+C104 since the unit cells of the two solids are isomorphous and very nearly the same size. He obtained a value of 182 kcal/mole. The proton affinities of the methylamines could be obtained by this method if their lattice energies were known. Certainly, approximate values could be obtained by the use of the Kapustinskii equation. 

The vaporization of an ionic solid results in ion pairs and other more complicated aggregates. If a direct measurement of lattice energy is not possible, how can we confirm or disprove the results of the Born-Lande (or the Kapustinskii) equation The answer lies in thermodynamic cycles. 

If the lattice type and Madelung constant for an ionic solid are not yet known, the lattice energy can still be approximated using an empirical equation developed by Kapustinskii, shown in Equation (12.7). Only the charges on each ion, the stoichiometric total number of ions (v), and the interionic separation need to be known in order to make the calculation. If Tq is entered into Equation (12.7) in units of pm, the calculated lattice energy will be in units of kj/mol. Using the values in Example 12-1 for NaCI and v = 2,Uq = -746 kj/mol, a difference of only 5% from the experimental value is obtained. 

FIGURE 28 Crystalline radii for the ions O), calculated using the Born-Haber cycle and Kapustinskii s equation from the enthalpies of formation found with the use of Kim and Oishi s scheme (Kim and Oishi, 1979) A, Shannon s data (Shannon, 1976). The solid curve connects the values calculated from the fit of polynomial (28). Reproduced from Chervonnyi and Chervonnaya (2005c) with permission from Pleiades Publishing, Ltd. 

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