# 11.6 Phase Diagrams

The equilibrium between a liquid and its vapor is not the only dynamic equilibrium that can exist between states of matter. Under appropriate conditions of temperature and pressure a solid can be in equilibrium with its liquid state or even with its vapor state. A phase diagram is a graphical way to summarize the conditions under which equilibria exist between the different states of matter. It also allows us to predict the phase of a substance that is stable at any given temperature and pressure.

The general form of a phase diagram for a substance that exhibits three phases is shown in Figure 11.24. The diagram contains three important curves, each of which represents the conditions of temperature and pressure at which the various phases can coexist at equilibrium.

Figure 11.24 General shape for a phase diagram of a system exhibiting three phases: gas, liquid, and solid.

1. The line from A to B is the vapor-pressure curve of the liquid. It represents the equilibrium between the liquid and gas phases. The point on this curve where the vapor pressure is 1 atm is the normal boiling point of the substance. The vapor-pressure curve ends at the critical point (B), which is at the critical temperature and critical pressure of the substance. Beyond the critical point the liquid and gas phases become indistinguishable.
2. The line AC represents the variation in the vapor pressure of the solid as it sublimes at different temperatures.
3. The line from A through D represents the change in melting point of the solid with increasing pressure. This line usually slopes slightly to the right as pressure increases. For most substances the solid is denser than the liquid; therefore, an increase in pressure usually favors the more compact solid phase. Thus, higher temperatures are required to melt the solid at higher pressures. The melting point of a substance is identical to its freezing point. The two differ only in the temperature direction from which the phase change is approached. The melting point at 1 atm is the normal melting point.

Point A, where the three curves intersect, is known as the triple point. All three phases are at equilibrium at this temperature and pressure. Any other point on the three curves represents an equilibrium between two phases. Any point on the diagram that does not fall on a line corresponds to conditions under which only one phase is present. Notice that the gas phase is the stable phase at low pressures and high temperatures. The conditions under which the solid phase is stable extend to low temperatures and high pressures. The stability range for liquids lies between the other two regions.

## The Phase Diagrams of H2O and CO2

Figure 11.25 shows the phase diagrams of H2O and CO2. Notice that the solid-liquid equilibrium (melting point) line of CO2 follows the typical behavior; its melting point increases with increasing pressure. In contrast, the melting point of H2O decreases with increasing pressure. Water is among the very few substances whose liquid form is more compact than its solid form (see Figure 11.11).

Figure 11.25 Phase diagram of (a) H2O and (b) CO2. The axes are not drawn to scale in either case. In (a), for water, note the triple point A (0.0098°C, 4.58 torr), the normal melting (or freezing) point B (0°C, 1 atm), the normal boiling point C (100°C, 1 atm), and the critical point D (374.4°C, 217.7 atm). In (b), for carbon dioxide, note the triple point X (-56.4°C, 5.11 atm), the normal sublimation point Y (-78.5°C, 1 atm), and the critical point Z (31.1°C, 73.0 atm).

The triple point of H2O (0.0098°C and 4.58 torr) is at much lower pressure than that of CO2 (-56.4°C and 5.11 atm). For CO2 to exist as a liquid, the pressure must exceed 5.11 atm. Consequently, solid CO2 does not melt, but sublimes when heated at 1 atm. Thus, CO2 does not have a normal melting point; instead, it has a normal sublimation point, -78.5°C. Because CO2 sublimes rather than melts as it absorbs energy at ordinary pressures, solid CO2 (Dry Ice™) is a convenient coolant. For water (ice) to sublime, however, its vapor pressure must be below 4.58 torr. Freeze-drying of food is accomplished by placing frozen food in a low-pressure chamber (below 4.58 torr) so that the ice in it sublimes.

#### SAMPLE EXERCISE 11.6

Referring to Figure 11.26, describe any changes in the phases present when H2O is (a) kept at 0°C while the pressure is increased from that at point 1 to that at point 5 (vertical line); (b) kept at 1.00 atm while the temperature is increased from that at point 6 to that at point 9 (horizontal line).

Figure 11.26 Phase diagram of H2O.

SOLUTION (a) At point 1, H2O exists totally as a vapor. At point 2, a solid-vapor equilibrium exists. Above that pressure, at point 3, all the H2O is converted to a solid. At point 4, some of the solid melts and an equilibrium between solid and liquid is achieved. At still higher pressures all the H2O melts, so that only the liquid phase is present at point 5.

(b) At point 6, the H2O exists entirely as a solid. When the temperature reaches point 4, the solid begins to melt and an equilibrium condition occurs between the solid and the liquid phases. At an even higher temperature, point 7, the solid has been converted entirely to a liquid. When point 8 is encountered, vapor forms and a liquid-vapor equilibrium is achieved. Upon further heating to point 9, the H2O is converted entirely to the vapor phase.

#### PRACTICE EXERCISE

Using Figure 11.25(b), describe what happens when the following changes are made in a CO2 sample initially at 1 atm and -60°C. (a) Pressure increases at constant temperature to 60 atm. (b) Temperature increases from -60°C to -20°C at constant 60 atm pressure. Answers: (a) CO2(g) CO2(s); (b) CO2(s) CO2(l)