lattice enthalpy (H
lattice
) is the amount of heat at constant pressure necessary to
separate the solid ionic crystal into its gaseous ions. The good news is that these
two values are just about the same, though opposite in sign; lattice energy de-
scribes a release in energy (E
lattice
= “−”), whereas lattice enthalpy describes
energy that is absorbed (H
lattice
=“+”).
H
lattice
∼
=
−E
lattice
The magnitude of the lattice energies or lattice enthalpies increases as the
charges on the ions increase, as shown in Table 8.3. In the series ScCl
3
,CaCl
2
, and
KCl, the charges decrease on the cation: (+3), (+2), and (+1), respectively,
with a decrease in lattice enthalpies in the order ScCl
3
(4874 kJ/mol), CaCl
2
(2223 kJ/mol), KCl (701 kJ/mol). Coulomb’s law also indicates that as the
distance between the ions decreases, the lattice enthalpies increase. Evidence of
this is found by comparing LiBr (788 kJ/mol), LiCl (834 kJ/mol), and LiF
(1030 kJ/mol). The charges on the ions are the same in this series of compounds,
but the size of the anion decreases from bromide to fluoride. Because the
bromide ion (Br
−
) is larger than Cl
−
or F
−
, LiBr has the smallest lattice enthalpy.
In general, lattice enthalpies are greatest for ionic compounds that are made up of
small, highly charged particles.
Let’s revisit our section-opening question of why fluoride in our toothpaste is
important. As we noted then, the replacement of a hydroxy group in the hydrox-
yapatite, Ca
5
(PO
4
)
3
(OH), mineral that makes up our teeth gives rise to a new
mineral called fluorapatite, Ca
5
(PO
4
)
3
(OH,F). Because F
−
is smaller than OH
−
,
Coulomb’s law dictates that the force of attraction between the Ca
2+
and the F
−
should be greater than that between Ca
2+
and OH
−
in this mineral. This is the
case with, for example, nearly all binary ionic salts of fluoride compared to the
metal hydroxide, so that the lattice enthalpy of, for example, silver fluoride (AgF),
which is 953 kJ/mol, is greater than the lattice enthalpy of silver hydroxide
(AgOH), 918 kJ/mol. It is therefore reasonable to consider that the lattice en-
thalpy of fluorapatite is greater than that of hydroxyapatite. This is one of several
reasons why fluorapatite is more stable than hydroxyapatite when bathed in our
saliva—and more resistant to the formation of cavities. Fluorapatite formation is
even more compelling when fluoride is present in our mouths from municipal
water fluoridation or dental treatments; this is related to a concept called chemi-
cal equilibrium, which we will consider in Chapters 16–18.
EXERCISE 8.4 Predicting Lattice Enthalpies
Use the relationship of ionic sizes to predict whether calcium fluoride (found in
toothpaste) or calcium chloride (sidewalk salt) has the greater lattice enthalpy. Also
predict whether aluminum chloride or sodium chloride has the greater lattice
enthalpy.
First Thoughts
Comparing the lattice enthalpies of two ionic compounds can be accomplished by
realizing that the magnitude of the lattice enthalpy is inversely proportional to the
distance between the individual ions and directly proportional to the size of the nu-
clear charge on the ions. The distance between the ions is directly related to the
individual ionic radii.
Solution
Calcium fluoride (CaF
2
) and calcium chloride (CaCl
2
) differ in the size of the anion
bound to the calcium cation. From the discussion of atomic size, we noted that
fluorine is smaller than chlorine. Moreover, the radius for both anions also follows
this trend; fluoride is a smaller anion than chloride. Coulomb’s law says that CaF
2
8.2 Ionic Bonding 315