Page 229 - Physical Chemistry

lev38627_ch07.qxd 3/14/08 12:51 PM Page 210

210
Chapter 7 components, the solute and the solvent, and evaluate dn of the solute and the solvent
One-Component Phase Equilibrium ignoring solvation, association, or dissociation.
and Surfaces
Note the following restrictions on the applicability of the phase rule (7.9). There must be
no walls between phases. We equated the temperatures of the phases, the pressures of the
phases, and the chemical potentials of a given component in the phases. These equalities
need not hold if adiabatic, rigid, or impermeable walls separate phases. The system must
be capable of P-V work only. If, for example, we can do electrical work on the system by
applying an electric field, then the electric field strength is an additional intensive variable
that must be specified to define the system’s state.

7.2 ONE-COMPONENT PHASE EQUILIBRIUM

In Secs. 7.2 to 7.5, we specialize to phase equilibrium in systems with one indepen-
dent component. (Chapter 12 deals with multicomponent phase equilibrium.) We shall
be concerned in these sections with pure substances.
An example is a one-phase system of pure liquid water. If we ignore the dissoci-
ation of H O, we would say that only one species is present (c 1), and there are no
2
reactions or additional restrictions (r 0, a 0); hence c ind 1 and f 2. If we take

account of the dissociation H O ∆ H OH , the system has three chemical
2

species (c 3), one reaction-equilibrium condition [m(H O) m(H ) m(OH )],
2

and one electroneutrality or stoichiometry condition [x(H ) x(OH )]. Therefore
c ind 3 1 1 1, and f 2. Thus, whether or not we take dissociation into ac-
count, the system has one independent component and 2 degrees of freedom (the tem-
perature and pressure).
With c ind 1, the phase rule (7.11) becomes
f 3 p for c ind 1
If p 1, then f 2; if p 2, then f 1; if p 3, then f 0. The maximum f is 2.
For a one-component system, specification of at most two intensive variables de-
scribes the intensive state. We can represent any intensive state of a one-component
system by a point on a two-dimensional P-versus-T diagram, where each point corre-
sponds to a definite T and P. Such a diagram is a phase diagram.
A P-T phase diagram for pure water is shown in Fig. 7.1. The one-phase regions
are the open areas. Here p 1 and there are 2 degrees of freedom, in that both P and
T must be specified to describe the intensive state.
Along the lines (except at point A), two phases are present in equilibrium. Hence
f 1 along a line. Thus, with liquid and vapor in equilibrium, we can vary T anywhere
along the line AC, but once T is fixed, then P, the (equilibrium) vapor pressure of
liquid water at temperature T, is fixed. The boiling point of a liquid at a given pres-
sure P is the temperature at which its equilibrium vapor pressure equals P. The nor-
mal boiling point is the temperature at which the liquid’s vapor pressure is 1 atm.
Line AC gives the boiling point of water as a function of pressure. The H O normal
2
boiling point is not precisely 100°C; see Sec. 1.5. If T is considered to be the indepen-
dent variable, line AC gives the vapor pressure of liquid water as a function of tem-
perature. Figure 7.1 shows that the boiling point at a given pressure is the maximum
temperature at which a stable liquid can exist at that pressure.
The change in 1982 of the thermodynamic standard-state pressure from 1 atm to
1 bar did not affect the definition of the normal-boiling-point pressure, which remains
at 1 atm.
Point A is the triple point. Here solid, liquid, and vapor are in mutual equilib-
rium, and f 0. Since there are no degrees of freedom, the triple point occurs at a