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CHAPTER
7

One-Component

Phase Equilibrium

and Surfaces CHAPTER OUTLINE
7.1
The Phase Rule
7.2 One-Component Phase
Equilibrium

7.3 The Clapeyron Equation
The two kinds of material equilibrium are reaction equilibrium and phase equilibrium 7.4 Solid–Solid Phase
(Sec. 4.1). We studied reaction equilibrium in ideal gases in Chapter 6. We now begin Transitions
the study of phase equilibrium. The phase-equilibrium condition (4.88) and (4.91) is
that for each species, the chemical potential of that species must be the same in every 7.5 Higher-Order Phase
phase in which the species is present. Transitions
The main topics of Chapter 7 are the phase rule, one-component phase equilibrium,
and surfaces. Section 7.1 derives the phase rule, which tells us how many intensive vari- 7.6 Surfaces and Nanoparticles
ables are needed to specify the thermodynamic state of a system apart from specifica- 7.7 The Interphase Region
tion of the sizes of the phases. Sections 7.2 to 7.5 are restricted to systems with one
component and discuss phase diagrams for such systems. A one-component phase di- 7.8 Curved Interfaces
agram shows the region of temperature and pressure in which each of the various
phases of a substance is stable. Since the equilibrium condition at fixed T and P is the 7.9 Colloids
minimization of the Gibb’s energy G, the most stable phase of a pure substance at a
given T and P is the phase with the lowest value of G m. (Recall that for a pure sub- 7.10 Summary
m
stance, G m.) Section 7.2 discusses the typical features of one-component phase di-
m
agrams and Sec. 7.3 derives the Clapeyron equation, which gives the slopes of the
phase-equilibrium lines on a P-versus-T one-component phase diagram. Sections 7.4
and 7.5 discuss special kinds of phase transitions (solid–solid and higher-order).
Phase equilibrium and phase transitions occur widely in the world around us, from
the boiling of water in a teakettle to the melting of Arctic glaciers. The water cycle of
evaporation, condensation to form clouds, and rainfall plays a key role in the ecology
of the planet. Laboratory and industrial applications of phase transitions abound, and
include such processes as distillation, precipitation, crystallization, and adsorption of
gases on the surfaces of solid catalysts. The universe is believed to have undergone
phase transitions in its early history as it expanded and cooled after the Big Bang
(M. J. Rees, Before the Beginning, Perseus, 1998, p. 205), and some physicists have
speculated that the Big Bang that gave birth to the universe was a phase transition pro-
duced by random fluctuations in a preexisting quantum vacuum (A. H. Guth, The
Inflationary Universe, Perseus, 1997, pp. 12–14 and chap. 17).

7.1 THE PHASE RULE
Recall from Sec. 1.2 that a phase is a homogeneous portion of a system. A system
may have several solid phases and several liquid phases but usually has at most one
gas phase. (For systems with more than one gas phase, see Sec. 12.7.) In Secs. 7.2 to
7.5 we shall consider phase equilibrium in systems that have only one component.