Page 119 - Modern physical chemistry

110 Relationships between Phases

In the laboratory, a person may detennine the extreme conditions under which each
phase of a given mixture is stable. A total of c + 1 coordinates would be involved. The
boundaries between the phases may then be plotted. The result is called a phase diagram.
For a given system, there is only one gaseous phase. But the number of condensed phases
is detennined by how many mutual immiscibilities can be maintained. For liquids, this would
equal the number of sufficiently different components present. With solids, the number of
phases may exceed the number of components. A solid with a given composition may be
able to assume several structures, depending on the pressure and temperature.

Example 6. 1.
What does the Gibbs phase rule tell us about a one-component system?
When c = 1, equation (6.1) becomes
1=3-p.
When only one phase is present, this reduces to
1=2.

On a pressure-temperature diagram, the region for such a phase appears as an area. When
two phases are present, we have
1=l.

On a pressure-temperature diagram, the points where the two phases coexist in equilib-
rium form a curved line. When three phases are present, we have
1=0.

There is now no freedom; three phases coexist in equilibrium at a point.

6.3 Equilibrium States for Water
The conditions under which the different possible phases of a system are stable can
be presented in a table and with a graph. Data which have been obtained for one of the
most important chemical substances, water, will be summarized here in both ways.
In the laboratory, numerous samples of water have been studied at various pressures
and temperatures. Notable particularly is the pioneering work of Percy W. Bridgman at
high pressures.
The ranges over which the various phases are stable are presented by figure 6.1. In
the area marked G, only the gas is stable. In the area marked L, only the liquid is stable.
In the area marked I, only ice I is stable, and so on. The different areas are separated by
curves, along which two phases may coexist. Where three curves meet, the correspond-
ing three phases may coexist. These points of intersection are called triple points. Exper-
imental triple points for water are listed in table 6.l.
The triple point vapor-liquid-ice I is at 0.0098° C rather than at 0.0000° C since zero
on the Celsius scale is defined as the freezing point of water saturated with air at 1 atm.
Under these conditions, the freezing point has been lowered 0.0024 by dissolved air and
0.0074 by the pressure.
At triple point B, pure water has no degree of freedom; no intensive variable can
change without causing one of the phases to disappear. Liquid water in equilibrium with
water vapor, on curve BA, has one degree of freedom. If the temperature is varied, the
pressure also varies along the curve. Liquid water by itself has two degrees of freedom.