Phase models for water (H₂O), at left, and carbon dioxide (CO₂), at right.

Depending on the temperature and pressure, a substance can be in any of three phases, solid, liquid or gas. A diagram that shows the pressure-temperature combinations for which these phases exist for a particular substance, and the pressure-temperature curves along which two phases are in equilibrium with each other, is called a phase diagram. Normally, these are two-dimensional plots that have pressure along the vertical axis and temperature along the horizontal axis. The models above add a third axis, pointing from the back of each model to the front, for volume. While all three of these properties are interrelated, the first two, pressure and temperature, are intensive properties. That is, they do not depend on the amount of material in the system; if you divide it into pieces, each piece has the same temperature and pressure as the whole from which you cut it. Volume, however, is an extensive property. If you cut the system into pieces, the total volume equals the sum of the volumes of all the pieces. This is why it is a bit strange to see these diagrams, and it leads to some odd labeling quirks. For any substance, there is a pressure and temperature at which all three phases, solid, liquid and gas, are in equilibrium, which is called the triple point. Because of the addition of the third axis, each of these models has what is labeled as a “triple point line,” which separates two areas in which pairs of phases (solid and vapor, and liquid and vapor) are in equilibrium, instead of two lines along which those pairs of phases are in equilibrium. Still, the third axis does give the advantage of a three-dimensional object that is easy to show to a class. The models are presented in the photograph so that they come reasonably close to showing the 2-dimensional projection that resembles the conventional P vs.T plot.

Both models above share many features in common. We see three main areas in green, labeled “Solid,” “Liquid” and “Vapor.” These are regions where the substance exists in a single phase. Along the lines that separate two regions from each other, those two phases exist in equilibrium with each other, that is, at any given time, equal numbers of molecules of each phase are going into the other phase. Below a line that begins at the lower left and slopes upwards towards the right, the substance is a vapor. Some distance in from the left, there is an almost vertical line, to the left of which the substance is a solid, and to the right of which it is a liquid. As noted above, where these two lines meet – the triple point – all three phases, solid, liquid and vapor, are in equilibrium with each other. For water, the triple point is 273.16 K (0.01 °C) and 4.585 torr. For carbon dioxide, the triple point is -56.6 °C and 5.1 atm. Below this point, either raising the temperature or lowering the pressure causes the solid form to sublime, or go directly into the vapor phase. To observe this with water, we must reduce the pressure to below 4.585 torr. Carbon dioxide at 1 atm is well below the triple point pressure, and a block of frozen dry ice sublimes at -78.5 °C, which is why it is known as “dry ice.”

As noted above, along the roughly vertical line in these models, the solid and liquid phases are in equilibrium. The melting point of a substance at a given pressure, P, is the temperature for which its solid and liquid phases are in equilibrium at that pressure. This roughly vertical line, then, is a plot of the melting point of the substance as a function of pressure. The normal melting point of a substance is its melting point at a pressure of 1 atm. For a pure substance, the freezing point of the liquid equals the melting point of the solid. For pure water, the normal melting point is 0.0024 °C. For air-saturated water, the melting point, also called the ice point, is 0.0000 °C at 1 atm. (Dissolved nitrogen and oxygen lower the freezing point slightly.) For water, which exhibits very unusual behavior, the slope of this line is negative; as you raise the pressure, the melting point decreases. This is because for water, the density, which goes through a maximum at 4 °C for the liquid, is lower for the solid state than it is for the liquid state. Thus, near the equilibrium line, if you raise the pressure, instead of packing more tightly as the solid, the water liquifies. This is due to the extensive hydrogen bonding that occurs among water molecules as a result of their polarity (slight negative charge on the oxygen, with slight positive charges on the hydrogens), which causes them to adopt a particular type of structure in the solid form that is less dense than the liquid state. (See demonstrations 48.15 – Ice bomb, and 88.27 – Crystal models.) The main, green area of the solid phase is labeled “Ice I.” This is the form of ice that we normally see, and it has a hexagonal structure. It can also form a related cubic structure, but this is metastable, and the hexagonal form greatly dominates. At the top left corner, above Ice I, you can see a red area, which is labeled “Ice III.” By examining water over a very large range of pressure and temperature, people have found about sixteen forms of water ice(!). Martin Chaplin, a professor emeritus at London South Bank University, had posted information about the phases of ice. The original link no longer works, but the material is accessible via the web archive here. The statistical physics group at University of Granada has posted a version of that page here. A detailed phase diagram for water, from the same web site, is available through the web archive here. A page with this phase diagram is also now posted here. For carbon dioxide, the slope of the solid-liquid equilibrium line is positive; as you raise the pressure, the melting point increases. Carbon dioxide is more dense as a solid than as a liquid, as are most materials.

As noted above, below the triple point, the solid and liquid phases are in equilibrium with each other. If we follow the equilibrium line from the triple point out towards the right, as also noted above, along this line, the liquid and vapor phases are in equilibrium. You can vary the temperature, T, and once you choose a particular value for T, as long as the two phases are in equilibrium, the vapor pressure of the liquid, P, is fixed by the equilibrium line. The boiling point of a substance at a given pressure, P, is the temperature at which its equilibrium vapor pressure equals P. So this equilibrium line gives the boiling point as a function of pressure. The normal boiling point of a liquid is the temperature at which its equilibrium vapor pressure, P, equals 1 atm. For water, this is 100 °C. For CO₂, the liquid phase does not exist at 1 atm, so instead of boiling, solid carbon dioxide sublimes at a temperature of -78.5 °C.

An interesting feature of the liquid-vapor equilibrium line, which you can see in the models, is that if you follow it out towards high temperature and high pressure, it ends. The point at which it ends is called the critical point, the temperature and pressure at which are called the critical temperature, T_c and critical pressure, P_c. At this point, the liquid and vapor densities become equal, and it is impossible to discern any distinct phases; the system becomes a single phase. (See demonstration 48.37 – Critical point tube.) Above the critical temperature, it is impossible to compress a substance into its liquid state; you must lower the temperature as well. Though it is quite common to use the terms “vapor” and “gas” interchangeably, people often make a distinction between them, and use the term “vapor” to refer to the gaseous state of a substance below the critical point, and the term “gas” to refer to the gaseous state of a substance above the critical temperature. Thus, whereas you can liquify a vapor by only compressing it, you cannot do this with a gas. Anywhere along the liquid-vapor equilibrium line, either raising the pressure or lowering the temperature causes condensation of the vapor into the liquid state. It is possible, though, to start out with the vapor phase, and by varying T and P in such a way as not to cross the equilibrium line – for example by raising the temperature above T_c, then raising the pressure above P_c, then lowering the temperature below T_c – to go around the critical point and transform the vapor into the liquid smoothly. In this way, you can change the density continuously from that of the vapor to that of the liquid, and avoid the sudden change of density associated with condensation. For water, T_c = 647 K (374 °C), and P_c = 218 atm. For carbon dioxide, T_c, = 31 °C, and P_c = 75.27 atm.

References:

1) Weast, Robert C., Editor. Handbook of Chemistry and Physics, 51^st Edition (Cleveland, Ohio: The Chemical Rubber Company, 1970), pp. B-80, D-146.
2) Levine, Ira N. Physical Chemistry (New York: McGraw-Hill, Inc., 1978), pp. 169-173, 177.
3) Zumdahl, Steven S. Chemical Principles, Third Edition (Boston: Houghton-Mifflin, 1998), pp. 774-775, 779-781.