Physical Chemistry , 1st ed.

The data in Table 21.5 suggest some simple trends. The higher the absolute

charges on the ions, the higher the lattice energy. The larger the ion, the lower

the lattice energy.

There must be some reason for these trends, especially considering the

grand simplicity of the interaction of opposite charges. Coulomb’s law states

that the potential energy of two oppositely charged particles at a distance from

each other is

E

4

q









0

q





r

 (21.12)

where the absolute charges qand qare expressed in units of coulombs (C),

the distance ris expressed in units of meters (m), and  0 is the permittivity of

free space. Note in equation 21.12 that the charge variables qand qinclude

the signs; that is, positive charges have a positive value ofqand negative

charges have a negative value ofq. Therefore, potential energies between op-

posite charges are negative (and therefore contribute to a lowering of energy),

and potential energies between like charges are positive (therefore contribut-

ing to a raising of energy).

Given an understanding of Coulomb’s law, it should be easy to calculate lat-

tice energies given (1) the magnitude of the charge on the ions, and (2) their

separation in the unit cell. It isn’t that easy, though. Coulomb’s law is a model

for the ideal energy of interaction of two and only two charged bodies that

interact at a given distance. An ionic crystal is a conglomerate of many, many

ions that interact over a range of distances. The following example illustrates

the difference between experimental values and the simple coulombic model.

Example 21.11

Sodium chloride, NaCl, has an experimental lattice energy of 769 kJ/mol. If

the distance between Naions and Clions in crystalline NaCl is approxi-

mately 2.78 Å, what would Coulomb’s law predict for the energy of interac-

tion of 1 mole of sodium ions with 1 mole of chloride ions?

Solution

Both sodium and chloride ions have unit charges, but of opposite magni-

tudes. In units of coulombs, a unit charge is 1.602  10 ^19 C. For r

2.78 Å or 2.78  10 ^10 m:

E

E8.297  10 ^19 J

(1.602  10 ^19 C)(1.602  10 ^19 C)



4 [8.854  10 ^12 C^2 /(Jm)](2.78  10 ^10 m)

756 CHAPTER 21 The Solid State: Crystals

Table 21.5 Experimental lattice energies of some ionic crystals

Formula Lattice energy (kJ/mol) Formula Lattice energy (kJ/mol)

LiF 1013 KCl 701

LiCl 834 KBr 671

LiBr 788 CsI 600

NaCl 769 CaF 2 2609

NaBr 732 CaCl 2 2223

Na 2 O 2481 CaSO 4 2489

K 2 O 2238 SrSO 4 2577

TiO 2 12150 BaSO 4 2469

K 2 S 1979 Na 2 SO 4 1827