potential,. This will be more relevant when we consider phase transitions.
Equations 6.18 and 6.19 can be rewritten as
(
T)
(^)
p
S (6.21)
(
p)
(^)
T
V (6.22)
We can use these equations to predict what direction an equilibrium will
move if conditions ofTor pare changed. Consider the solid-to-liquid phase
transition. Liquids typically have greater entropy than solids, so going from
solid to liquid is an increasein entropy, and the negative sign on the right of
equation 6.21 implies that the slope of the versus Tplot is negative. Thus,
as temperature increases, the chemical potential decreases.Since chemical po-
tential is defined in terms of an energy—here, the Gibbs free energy—and
since spontaneous changes have negative changes in the Gibbs free energies,
as the temperature increases the system will tend toward the phase with the
lowerchemical potential: the liquid. Equation 6.21 explains why substances
melt when the temperature is increased.
The same argument applies for the liquid-to-gas phase transition. In this case,
the slope of the curve is usually higher because the difference in entropy between
liquid and gas phases is much larger in magnitude than the difference in Sbe-
tween solid and liquid phases. However, the reasoning is the same, and equation
6.21 explains why liquids change to gas when the temperature is increased.
The effects of pressure on the equilibrium depend on the molar volumes of
the phases. Again, the magnitude of the effect depends on the relative change
in the molar volume. Between solid and liquid, volume changes are usually
very small. That is why pressure changes do not substantially affect the posi-
tion of solid-liquid equilibria, unless the change in pressure is very large.
However, for liquid-gas (and solid-gas, for sublimation) transitions, the change
in molar volume can be on the order of hundreds or thousands of times.
Pressure changes have substantial effects on the relative positions of phase
equilibria involving the gas phase.
Equation 6.22 is consistent with the behavior of the solid and liquid phases
of water. Water is one of the few substances whose solid molar volume is larger
than its liquid molar volume.* Equation 6.22 implies that an increase in pres-
sure (pis positive) would drive a phase equilibrium toward the phase that has
the lowermolar volume (since for spontaneous changes, the Gibbs free energy
goes down). For most substances, an increase in pressure would drive the equi-
librium towards the solid phase. But water is one of the few chemical sub-
stances (elemental bismuth is another) whose liquid is denser than its solid. Its
Vterm for equation 6.22 is positive when going from liquid to solid, so for
a spontaneous process (that is,negative), an increase in pressure translates
into going from solid to liquid. This is certainly unusual behavior—but it is
consistent with thermodynamics.Example 6.11
In terms of the variables in equations 6.21 and 6.22, state what happens to
the following equilibria when the given changes in conditions are imposed.
Assume all other conditions are kept constant.160 CHAPTER 6 Equilibria in Single-Component Systems
*Another way to say this is that a given amount of liquid is denser than the same amount
of solid.