## Phase Diagrams

Although the introductory example of H 2O mentioned changes of state caused by varying the temperature, it is known that variation of pressure can also produce such changes. In laboratory experiments, these two environmental factors—temperature and pressure—can each be varied or held constant; they are referred to as independent variables. Figure 1 assigns these variables to axes to form a plot that describes the physical condition at each point in the graph. The vertical axis is the pressure measured in atmospheres (atm).

Figure 1. The phase diagram for water.

A temperature‐pressure graph showing the various states of matter is a phase diagram. Phase refers to a single homogeneous physical state. Different phases have either different compositions or different physical states. In the preceding figure, there are three phases with the same composition in the solid, liquid, and gaseous states of matter.

Begin studying how both temperature and pressure determine the state of H 2O by taking some ice at a temperature of –10°C and pressure of 5 atmospheres, labeled S in Figure 2. If the pressure is held constant but the temperature is increased, the substance heats up along the dashed line marked L, melting to a liquid at point m, about –0.01°C. Alternatively, if you decrease the pressure on the initial solid S, while holding the temperature constant at –10°C, the conditions change downward along path G, and the ice vaporizes abruptly when the pressure has fallen to the point marked n, about 3 × 10 –3 atm. Such a direct change from a solid to a gas is called sublimation; notice that there was no intervening liquid state.

Figure 2. Changing the phase of solid water.

In the graph in Figure 3, study the possible state changes of an initial liquid marked L. The liquid is assumed to begin at 120°C and 30 atmospheres. The high pressure allows this liquid to exist at a temperature exceeding the 100°C boiling point at 1 atmosphere. If the pressure is maintained at a constant 30 atm, cooling the liquid L will produce a change to the left along path S, and the liquid will freeze at point f (about 0.01°C) to solid ice. A second course with constant pressure is heating L toward G 1, and the liquid will abruptly vaporize at boiling point b 1 (about 235°C). Returning to the initial liquid L, you can imagine holding the temperature constant at 120°C while decreasing the pressure toward G 2. When the pressure falls to approximately 2 atm, the liquid will boil at point b 2. Boiling has been induced without heating the liquid.

Figure 3. Changing the phase of liquid water.

In summary, a change of state can be caused by varying only the temperature, varying only the pressure, or varying both temperature and pressure. Most random combinations of temperature and pressure fall within the three areas of a phase diagram in which only a single state is stable. The special temperature‐pressure combinations plotted as lines in the phase diagram of H 2O (see Figure 2) are where two states can coexist. For example, both solid ice and liquid water are stable at precisely 0°C and 1 atm.

Look back at the large phase diagram (Figure 1) and notice the intersection of the three lines at 0.01°C and 6 × 10 –3 atm. Only at this triple point can the solid, liquid, and vapor states of H 2O all coexist. The critical point is the highest temperature and highest pressure at which there is a difference between liquid and gas states. At either a temperature or a pressure over the critical point, only a single fluid state exists, and there is a smooth transition from a dense, liquid‐like fluid to a tenuous, gas‐like fluid. Beyond this point, the substance is often referred to as a super‐critical fluid. Above the critical temperature, it is impossible to apply enough pressure to condense the gas to its liquid phase.

Each substance has its own phase diagram to display how temperature and pressure determine its properties. Figure 4 is the phase diagram for carbon dioxide.

Figure 4. The phase diagram for carbon dioxide.

Use Figure 4 to answer the two practice problems.

• What is the minimum pressure in atmospheres at which CO 2 can occur as a liquid?
• If pressure is held at a uniform 3 atmospheres, at what temperature does solid CO 2 become unstable? What phase begins to appear at this temperature?

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