Physical Chemistry , 1st ed.

Example 21.10

Predict the structure(s) of the following crystals. Consult Table 21.4 for ionic

radii when necessary.

a.Sodium sulfide, Na 2 S

b.Lead, Pb

c.Magnesium, Mg

d.Silver bromide, AgBr

e.Ammonium chloride, NH 4 Cl

Solution

a.From Table 21.4, Nahas a radius of 0.97 Å and S^2 has a radius of

1.84 Å. The ratio rsmaller/rlargeris 0.97/1.84 0.527, so we predict that this

2 1 ionic compound has a rutile structure. (It actually has a fluorite struc-

ture.)

b.Lead is a metallic element that is an atomic solid. We predict that it has

one of the most efficient crystal arrangements, either face-centered cubic or

hexagonal close-packed. (It has an fcc unit cell.)

c.Magnesium is also a metallic, atomic solid. Again, we predict either fcc or

hcp. (Magnesium is hcp.)

d.From Table 21.4, we find that Aghas an ionic radius of 1.26 Å and Br

has a radius of 1.96 Å. The ratio rsmaller/rlargeris 1.26/1.96 0.642, suggest-

ing a sodium chloride structure for this 11 salt. (AgBr does indeed have the

sodium chloride crystal structure.)

e.Ammonium ions have an effective ionic radius of 1.48 Å, and Clions have

a radius of 1.81 Å. The ratio rsmaller/rlargeris 1.48/1.81, which equals 0.818. We

predict a cesium chloride unit cell for ammonium chloride. (NH 4 Cl has the

cesium chloride unit cell.)

The above example shows that the generalities for predicting crystalline unit

cells work but are not infallible. Again, the point should be made that experi-

ment is the only way to know for certain what the unit cell of a crystal is.

21.8 Lattice Energies of Ionic Crystals

When ions of opposite charges come together to make a crystal, there is always

a decrease in the overall energy. It is this decrease in energy that makes the

crystal stable with respect to the individual, separated ions. It is also this de-

crease in energy that leads to the idea of the “energy” of an ionic bond.

The amount of energy given off when one formula unit of moles of ions

come together from the gas phase to make a crystal is called the lattice energy

or lattice enthalpyof the crystal. The second term reinforces the relationship to

the enthalpy of the crystal formation process. For example, by definition, the

lattice energy of sodium chloride, NaCl, is represented by the energy change of

the molar reaction

Na(g) Cl(g) →NaCl (s) lattice energy rxnH (21.11)

Notice that the lattice energy is defined as the negativeofrxnH. This is be-

cause it is understood that energy is always given off when separated ions come

together to make ionic crystals. The lattice energy is therefore simply the ab-

solute magnitude of that exothermic process. Table 21.5 lists some experimen-

tal lattice energies of some simple ionic crystals.

21.8 Lattice Energies of Ionic Crystals 755

O

Ca

O

Ti

CaF 2 (Fluorite)

TiO 2 (Rutile)
Figure 21.29 Typical unit cells for the fluorite
and rutile types of crystals.