Lattice Energy and the Madelung Constant

At first glance, calculation of the crystal lattice energy may seem straightforward just take every pair of ions and calculate the sum of the electrostatic energy between each pair, using the following equation. 

Z Zj = ionic charges in electron units To = distance between ion centers e = electronic charge = 1.602 x 10 C 4vso = permittivity of a vacuum = 1.11 X lO C J 

For simple compounds, p = 30 pm works well when is also in pm. Lattice energies are twice as large when charges of 2 and 1 are present, and four times as large when both ions are doubly charged. Madelung constants for some crystal structures are given in Table 7.2. 

Although the preceding equations provide the change in internal energy associated with lattice formation from gas phase ions, the more commonly used lattice entiialpy is = AU + A PV) = AU + An/ r, where A is the change in the number of moles of gas phase ions upon formation of the crystal (e.g., -2 for AB compounds, -3 for AB2 compounds). The value of AnRT generally is relatively small at 298 K (-4.95 kJ/mol for AB, -7.43 kJ/mol for AB2) and AH AU. 

Calculate the lattice energy for NaCl, using the ionic radii from Appendix B-1. TABLE 7.2 Madelung Constants 

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D. Quane, 1970, Textbook Errors, 98 Crystal Lattice Energy and the Madelung Constant , Journal of Chemical Education 47, 396. 

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