10.6 Phase Diagram

Phase Diagram is a graph of pressure vs. temperature for a substance. It shows melting, boiling, and sublimation points at different pressures, the triple point and critical point. The temperatures and pressures at which a given phase of a substance is stable (that is, from which the molecules have the lowest escaping tendency) is an important property of any substance. Because both the temperature and pressure are factors, it is customary to plot the regions of stability of the various phases in P – T coordinates, as in this generic phase diagram (or phase map) for a hypothetical substance.

Figure 10.22

Source: https://www.chem1.com/acad/webtext/virtualtextbook.html

The best way to remember which area corresponds to each of these states is to remember the conditions of temperature and pressure that are most likely to be associated with a solid, a liquid, and a gas. Low temperatures and high pressures favor the formation of a solid. Gases, on the other hand, are most likely to be found at high temperatures and low pressures. Liquids lie between these extremes.

You can therefore test whether you have correctly labeled a phase diagram by drawing a line from left to right across the top of the diagram, which corresponds to an increase in the temperature of the system at constant pressure. When a solid is heated at constant pressure, it melts to form a liquid, which eventually boils to form a gas.

Phase diagrams can be used in several ways. We can focus on the regions separated by the lines in these diagrams, and get some idea of the conditions of temperature and pressure that are most likely to produce a gas, a liquid, or a solid. We can also focus on the lines that divide the diagram into states, which represent the combinations of temperature and pressure at which two states are in equilibrium.

The points along the line connecting points in the phase diagram in the figure above represent all combinations of temperature and pressure at which the solid is in equilibrium with the gas or gas condenses to form a solid.

At every point along this line, the solid goes to gaseous state at the same rate at which the gas condenses to solid.

At every point along this line, the liquid vaporises at the same rate at which the vapor condenses.

At every point along this line, the solid melts at the same rate at which the liquid freezes.

The line is almost vertical because the melting point of a solid is not very sensitive to changes in pressure. For most compounds, this line has a small positive slope, as shown in the figure above. The slope of this line is slightly negative for water, however. As a result, water can melt at temperatures near its freezing point when subjected to pressure. The ease with which ice skaters glide across a frozen pond can be explained by the fact that the pressure exerted by their skates melts a small portion of the ice that lies beneath the blades.

Point B in this phase diagram represents the only combination of temperature and pressure at which a pure substance can exist simultaneously as a solid, a liquid, and a gas. It is therefore called the triple point of the substance, and it represents the only point in the phase diagram in which all three states are in equilibrium. Point C is the critical point of the substance, which is the highest temperature and pressure at which a gas and a liquid can coexist at equilibrium.

The figure below shows what happens when we draw a horizontal line across a phase diagram at a pressure of exactly 1 atm. This line crosses the line between points B and D at the melting point of the substance because solids normally melt at the temperature at which the solid and liquid are in equilibrium at 1 atm pressure. The line crosses the line between points B and C at the boiling point of the substance because the normal boiling point of a liquid is the temperature at which the liquid and gas are in equilibrium at 1 atm pressure and the vapor pressure of the liquid is therefore equal to 1 atm.

The phase diagram below shows the boundary between three states on an expanded scale.   “A Typical Phase Diagram for a Substance That Exhibits Three Phases—Solid, Liquid, and Gas—and a Supercritical Region”;

In order to depict the important features of a phase diagram over the very wide range of pressures and temperatures they encompass, the axes are not usually drawn to scale, and are usually highly distorted. This is the reason that the “melting curve” looks like a straight line in most of these diagrams.

Figure 10.22

Source: www.openstax.org/

The Phase Diagram of Water

Figure 10.23

Source: www.openstax.org/

Above diagram shows the phase diagram of water and illustrates that the triple point of water occurs at 0.01°C and 0.00604 atm (4.59 mmHg). Far more reproducible than the melting point of ice, which depends on the amount of dissolved air and the atmospheric pressure, the triple point (273.16 K) is used to define the absolute (Kelvin) temperature scale. The triple point also represents the lowest pressure at which a liquid phase can exist in equilibrium with the solid or vapor. At pressures less than 0.00604 atm, therefore, ice does not melt to a liquid as the temperature increases; the solid sublimes directly to water vapor. Sublimation of water at low temperature and pressure can be used to “freeze-dry” foods and beverages is first cooled to subzero temperatures and placed in a container in which the pressure is maintained below 0.00604 atm. Then, as the temperature is increased, the water sublimes, leaving the dehydrated food (such as that used by backpackers or astronauts) or the powdered beverage (as with freeze-dried coffee).

Note the high critical temperature and critical pressure. These are due to the strong van der Waals forces between water molecules. that is, the melting point of ice decreases with increasing pressure; at 100 MPa (987 atm), ice melts at −9°C. Water behaves this way because it is one of the few known substances for which the crystalline solid is less dense than the liquid (others include antimony and bismuth). Increasing the pressure of ice that is in equilibrium with water at 0°C and 1 atm tends to push some of the molecules closer together, thus decreasing the volume of the sample. The decrease in volume (and corresponding increase in density) is smaller for a solid or a liquid than for a gas, but it is sufficient to melt some of the ice.

Unusual features for carbon dioxide: cannot exist in the liquid state at pressures below
5.11 atm (triple point). CO₂ sublimes at normal pressures.

Solid carbon dioxide, commonly known as Dry Ice, is widely used as a refrigerant. The phase diagram shows why it is “dry”. The triple point pressure is at 5.11 atm, so below this pressure, liquid CO₂ cannot exist; the solid can only sublime directly to vapor. Gaseous carbon dioxide at a partial pressure of 1 atm is in equilibrium with the solid at 195K (−79 °C, 1); this is the normal sublimation temperature of carbon dioxide. The surface temperature of dry ice will be slightly less than this, since the partial pressure of CO₂ in contact with the solid will usually be less than 1 atm. Notice also that the critical temperature of CO₂ is only 31°C. This means that on a very warm day, the CO₂ in a fire extinguisher will be entirely vaporized; the vessel must therefore be strong enough to withstand a pressure of 73 atm.

Figure 10.24

Source: Source: https://www.chem1.com/acad/webtext/virtualtextbook.html

There are other solids whose vapor pressure overtakes that of the liquid before melting can occur. Such substances sublime without melting; a common example is solid carbon dioxide (“Dry Ice”) at 1 atm (see the CO₂ phase diagram below).https://en.wikipedia.org/wiki/Supercritical_carbon_dioxide

This view of the carbon dioxide phase map employs a logarithmic pressure scale and thus encompasses a much wider range of pressures, revealing the upper boundary of the fluid phase (liquid and supercritical). Supercritical carbon dioxide (CO₂ above its critical temperature) possesses the solvent properties of a liquid and the penetrating properties of a gas; one major use is to remove caffeine from coffee beans.

Because pressures and temperatures can vary over very wide ranges, it is common practice to draw phase diagrams with non-linear or distorted coordinates. This enables us to express a lot of information in a compact way and to visualize changes that could not be represented on a linearly-scaled plot.

It is important that you be able to interpret a phase map, or alternatively, construct a rough one when given the appropriate data. Take special note of the following points:

The three colored regions on the diagram are the ranges of pressure and temperature at which the corresponding phase is the only stable one.

The three lines that bound these regions define all values of (P,T) at which two phases can coexist (i.e., be in equilibrium). Notice that one of these lines is the vapor pressure curve of the liquid as described above. The “sublimation curve” is just a vapor pressure curve of the solid. The slope of the line depends on the difference in density of the two phases.