Since the boiling point is the temperature at
which the applied pressure equals the vapor pressure, then we can
view Figure 5 in a different way.
Consider the specific case of water, with vapor pressure given
here. To find
the boiling point temperature at 1 atm pressure, we need to find
the temperature at which the vapor pressure is 1 atm. To do so, we
find the point on the graph where the vapor pressure is 1 atm and
read off the corresponding temperature, which must be the boiling
point. This will work at any given pressure. Viewed this way, for
water Figure 6 gives us
*both* the vapor pressure as a
function of the temperature *and*
the boiling point temperature as a function of the pressure. They
are the same graph.

Recall that, at the boiling point, we observe
that both liquid and gas are at equilibrium with one another. This
is true at every combination of applied pressure and boiling point
temperature. Therefore, for every combination of temperature and
pressure on the graph in Figure 6,
we observe liquid-gas equilibrium.

What happens at temperature/pressure
combinations which are not on the line in Figure 6? To find out, we first start at a
temperature-pressure combination on the graph and elevate the
temperature. The vapor pressure of the liquid rises, and if the
applied pressure does not also increase, then the vapor pressure
will be greater than the applied pressure. We must therefore not be
at equilibrium anymore. All of the liquid vaporizes, and there is
only gas in the container. Conversely, if we start at a point on
the graph and lower the temperature, the vapor pressure is below
the applied pressure, and we observe that all of the gas condenses
into the liquid.

Now, what if we start at a
temperature-pressure combination on the graph and elevate the
applied pressure without raising the temperature? The applied
pressure will be greater than the vapor pressure, and all of the
gas will condense into the liquid. Figure 6 thus actually reveals to us what
phase or phases are present at each combination of temperature and
pressure: along the line, liquid and gas are in equilibrium; above
the line, only liquid is present; below the line, only gas is
present. When we label the graph with the phase or phases present
in each region as in Figure 6, we
refer to the graph as a phase
diagram.

Of course, Figure 6 only includes liquid, gas, and
liquid-gas equilibrium. We know that, if the temperature is low
enough, we expect that the water will freeze into solid. To
complete the phase diagram, we need additional observations.

We go back to our apparatus in Figure 4 and we establish liquid-gas water
phase equilibrium at a temperature of 25°C and 23.8 torr. If
we slowly lower the temperature, the vapor pressure decreases
slowly as well, as shown in Figure 6. If we continue to lower the
temperature, though, we observe an interesting transition, as shown
in the more detailed Figure 7. The
very smooth variation in the vapor pressure shows a slight, almost
unnoticeable break very near to 0°C. Below this temperature,
the pressure continues to vary smoothly, but along a slightly
different curve.

To understand what we have observed, we
examine the contents of the container. We find that, at
temperatures below 0°C, the water in the container is now an
equilibrium mixture of water vapor and solid water (ice), and there
is no liquid present. The direct transition from solid to gas,
without liquid, is called sublimation. For
pressure-temperature combinations along this new curve below
0°C, then, the curve shows the solid-gas equilibrium
conditions. As before, we can interpret this two ways. The
solid-gas curve gives the vapor pressure of the solid water as a
function of temperature, and also gives the sublimation temperature
as a function of applied pressure.

Figure 7 is
still not a complete phase diagram, because we have not included
the combinations of temperature and pressure at which solid and
liquid are at equilibrium. As a starting point for these
observations, we look more carefully at the conditions near
0°C. Very careful measurements reveal that the solid-gas
line and the liquid-gas line intersect in Figure 7 where the temperature is
0.01°C. Under these conditions, we observe inside the
container that solid, liquid, and gas are all three at equilibrium
inside the container. As such, this unique temperature-pressure
combination is called the triple point. At
this point, the liquid and the solid have the same vapor pressure,
so all three phases can be at equilibrium. If we raise the applied
pressure slightly above the triple point, the vapor must disappear.
We can observe that, by very slightly varying the temperature, the
solid and liquid remain in equilibrium. We can further observe that
the temperature at which the solid and liquid are in equilibrium
varies almost imperceptibly as we increase the pressure. If we
include the solid-liquid equilibrium conditions on the previous
phase diagram, we get this, where the
solid-liquid line is very nearly vertical.

Each substance has
its own unique phase diagram, corresponding to the diagram in
Figure 8 for water.

Comments:"Reviewer's Comments: 'I recommend this book. It is suitable as a primary text for first-year community college students. It is a very well-written introductory general chemistry textbook. This […]"