If an equilibrium is established and then the temperature or the pressure is
changed, the equilibrium must shift:that is, the relative amounts of the phases
must change until equation 6.3 is re-established.
What if the chemical potentials of the phases are not equal? Then one (or
more) of the phases is not the stable phase under those conditions. The phase
with the lower chemical potential is the more stable phase. For example, at
10°C, solid H 2 O has a lower chemical potential than liquid H 2 O, whereas at
10°C, liquid H 2 O has a lower chemical potential than solid H 2 O. However,
at 0°C at normal pressure, both solid and liquid H 2 O have the same chemical
potential. They can therefore exist together in the same system, at equilibrium.
Example 6.2
Determine whether the chemical potentials of the two phases listed are the
same or different. If they are different, state which one is lower than the other.
a.Liquid mercury, Hg (), or solid mercury, Hg (s), at its normal melting
point of38.9°C
b.H 2 O () or H 2 O (g) at 99°C and 1 atm
c.H 2 O () or H 2 O (g) at 100°C and 1 atm
d.H 2 O () or H 2 O (g) at 101°C and 1 atm
e.Solid lithium chloride, LiCl, or gaseous LiCl at 2000°C and normal pres-
sure (The boiling point of LiCl is about 1350°C.)
f.Oxygen, O 2 , or ozone, O 3 , at STPSolution
a.At the normal melting point, both solid and liquid phases can exist in equi-
librium. Therefore, the two chemical potentials are equal.
b.At 99°C, the liquid phase of water is the stable phase, so H 2 O,H 2 O,g.
c.100°C is the normal boiling point of water, so at that temperature, the
chemical potentials are equal.
d.At 101°C, the gas phase is the stable phase for H 2 O. Therefore,H 2 O,g
H 2 O,. (See what a difference 2° makes?)
e.Since the stated temperature is above the boiling point of LiCl, the chem-
ical potential of gas-phase LiCl is lower than solid-phase LiCl.
f.Since diatomic oxygen is the stablest allotrope of oxygen, we expect that
O 2 O 3. Note that this example doesn’t involve a phase transition.6.3 Phase Transitions
Having established that different phases of the same component can exist si-
multaneously at equilibrium, we might ask what affects that equilibrium.
Among other things, the movement of heat into or out of the system affects
the equilibrium. Depending on the direction of heat transfer, one phase grows
in amount while the other phase simultaneously decreases in amount. This is
what happens in a phase transition. Most people are probably aware of the fol-
lowing processes that occur with the stated direction of heat flow:
solid liquidliquid gas (6.4)solid gasJJKJJJJQPJKJJJJJheat in (endothermic)
heat out (exothermic)JJKJJJJQPJKJJJJJ
heat in (endothermic)
heat out (exothermic)JJKJJJJQPJKJJJJJ
heat in (endothermic)
heat out (exothermic)6.3 Phase Transitions 145