Physical Chemistry , 1st ed.

Solving for the boiling point:

TBP632 K

The measured boiling point of mercury is 629 K.

The previous example illustrates how well the Clausius-Clapeyron equation

works, despite the assumptions used in deriving it. It also shows that the va-

por pressure of a substance is related by its logarithmto the absolute temper-

ature. That is,

ln(vapor pressure) T (6.15)

Another way of stating this is by taking the inverse logarithm of both sides

to get

vapor pressure eT (6.16)

As the temperature increases, the vapor pressure increases faster and faster, and

many plots of vapor pressure versus temperature have an exponential look to

them. Equations 6.15 and 6.16 do not conflict with the ideal gas law (in which

pis directly proportional to T) because these two equations apply to phase

equilibria and are not meant to be taken as equations of state for the vapor

phase.

6.6 Phase Diagrams and the Phase Rule

Although phase transitions can seem complicated, there is a simplification: the

phase diagram.Phase diagramsare graphical representations of what phases

are stable under various conditions of temperature, pressure, and volume.

Most simple phase diagrams are two-dimensional, with pressure on one axis

and temperature on the other.

The phase diagram itself is composed of lines that indicate the temperature

and pressure values at which phase equilibrium occur. For example, Figure 6.3

is a partial phase diagram of H 2 O. The diagram shows the stable phase in each

region of the diagram. The lines on the phase diagram represent the phase

transitions. Any point on a line represents a particular pressure and tempera-

ture at which multiple phases can exist in equilibrium. Any point not on a line

indicates a phase that is the predominant stable phase of the compound H 2 O

under those conditions.

Consider the points labeled in Figure 6.3. Point A represents a value for

pressure pAand temperature TAin which the solid form of H 2 O is stable. Point

B represents a set of pressure and temperature conditions pBand TBwhere

melting occurs: solid can exist in equilibrium with liquid. Point C represents

pressure and temperature conditions in which liquid is the stable phase. Point

D represents pressure and temperature conditions in which liquid can exist in

equilibrium with the gas: boiling occurs. Finally, point E represents a set of

pressure and temperature conditions in which the stable phase of H 2 O is

gaseous.

The phase diagram implies that under many conditions solid and liquid can

exist in equilibrium, and under many conditions liquid and gas can exist in

equilibrium. This is certainly the case. But what are these lines giving us? Since

they are a plot of how the pressure changes with change in temperature for the

phase equilibria, the lines represent dp/dT. This quantity can be calculated using

154 CHAPTER 6 Equilibria in Single-Component Systems

Temperature

Pressure

Solid

Liquid

AB C D E

Gas

Figure 6.3 A qualitative, partial phase diagram
(pressure versus temperature) of H 2 O. Specific
points in a phase diagram (like points A, B, C, D,
and E here) indicate conditions of pressure and
temperature and what phase(s) of the component
are stable under those conditions.