Physical Chemistry , 1st ed.

compound H 2 O. One of the noteworthy points is that there are actually several

types of solid H 2 O, that is, ice. Note the pressure and temperature scales, how-

ever. We are not likely to experience these forms of ice outside the laboratory.

Figure 6.7 shows a phase diagram of helium. Because helium is a gas at

temperatures down to 4.2 K, the temperature axis on this diagram does not

have a large temperature range. At the other extreme, Figure 6.8 shows a phase

diagram of carbon. Notice the regions where diamond is the stable phase.

Although pressure and temperature are the common variables for phase

diagrams in chemistry, volume can also be plotted on an axis in a phase dia-

gram, as shown in Figure 6.9. There are also three-dimensional phase dia-

grams that plot pressure, volume, and temperature; Figure 6.10 shows an ex-

ample of that.

Phase diagrams are very useful in helping to understand how single-

component systems act under a change in condition: simply plot the change on

6.6 Phase Diagrams and the Phase Rule 157

40

0

0.0001

Temperature (K)

100

Pressure (bar)

Superfluid

B phase

0.001 0.01 0.1 1 10

30

20

10

Solid

Gas

Superfluid

A phase

Normal liquid

Figure 6.7 The phase diagram of helium, He, does not need a large temperature
range. Notice that solid He does not exist unless pressures are large.

103

10 –^2

0

Temperature ( 103 K)

6

Pressure (kbar)

54321

102

10

1

10 –^1

Gas

Diamond

Graphite

Liquid

T

Volume

V 1

Temperature

V 2

Gas

P

Liquid

Volume

Pressure

1-phase

2-phase region

region

Temperature

Figure 6.10 A three-dimensional phase diagram

can plot the phases present in a system for given sets

of pressures, temperatures, and volumes.

Figure 6.8 A phase diagram of carbon, showing where

the graphite allotrope is stable and where the diamond

allotrope is stable.

Figure 6.9 An example of a temperature-volume phase diagram. At a certain pres-
sure P, the phase diagram specifies what phase must be present except between V 1 and
V 2 (for the given pressure). Under these conditions, a varying amount of liquid phase
(shaded area) may be present and still satisfy the given conditions ofTand P. In part
because of this ambiguity, temperature-volume phase diagrams aren’t as common as
pressure-temperature phase diagrams.