{"id":4722,"date":"2024-10-05T20:05:44","date_gmt":"2024-10-05T20:05:44","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4722"},"modified":"2024-10-05T20:05:45","modified_gmt":"2024-10-05T20:05:45","slug":"phase-diagrams-and-the-phase-rule","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/10\/05\/phase-diagrams-and-the-phase-rule\/","title":{"rendered":"\u00a0Phase Diagrams and the Phase Rule"},"content":{"rendered":"\n

You can conveniently display the properties of compounds via phase diagrams. A pure substance can exist in many phases simultaneously of which, as you know, solid, liquid, and gas are the most common. Phase diagrams enable you to view the properties of two or more phases as functions of temperature, pressure, specific volume, concentration, and other variables.<\/p>\n\n\n\n

We discuss phase diagrams in terms of water because presumably you are familiar with the three phases of water, namely, ice, water, and water vapor (steam), but the discussion applies to all other pure substances. The terms\u00a0vapor<\/em>\u00a0and\u00a0gas<\/em>\u00a0are used very loosely in practice. A gas that exists below its critical temperature is usually called a vapor because it can condense. We reserve the word\u00a0vapor<\/strong>\u00a0to describe a gas below its critical point in a process in which the phase change is of primary interest, while we use\u00a0gas<\/strong>\u00a0and\u00a0noncondensable gas<\/strong>\u00a0to describe, respectively, a gas above the critical point and a gas in a process at conditions under which it cannot condense.<\/p>\n\n\n\n

Phase diagrams are based on equilibrium conditions. That is, for phase equilibrium, it is assumed that each phase remains invariant (i.e., constant quantity under constant conditions). On a molecular level, when two or more phases are present, there will always be molecules that move from one phase to another, but under phase equilibrium, the net flux is zero. For example, for a liquid and a vapor in phase equilibrium, the flux of molecules from the liquid into the vapor must be equal to the flux from the vapor to the liquid. In fact, when multiple phases exist, continuous exchange between phases occurs, even at equilibrium.<\/p>\n\n\n\n

Suppose you carry out some experiments with the apparatus shown in\u00a0Figure 7.1. Place a lump of ice in the chamber below the piston, and evacuate the chamber to remove all air (you want to retain only pure water in the chamber). Fix the volume of the chamber by fixing the position of the piston, and start slowly (so that the phases of water that result will be in equilibrium) heating the ice. If you plot the measured pressures as a function of temperature, you will get\u00a0Figure 7.2, a phase diagram in which all of the measurements made have been fitted by a continuous smooth curve for clarity.<\/p>\n\n\n\n

The initial conditions of\u00a0p<\/em>\u00a0and\u00a0T<\/em>\u00a0in the chamber are at point O in\u00a0Figure 7.2\u00a0with the solid in equilibrium with the vapor.<\/p>\n\n\n\n

\"A
Figure 7.1<\/strong> Apparatus used to explore the p<\/em>, V^, and T<\/em> properties of water<\/figcaption><\/figure>\n\n\n\n
\"A
Figure 7.2<\/strong> Results of the experiment of heating at constant volume shown on a phase diagram (p<\/em> versus T<\/em> at constant V^)<\/figcaption><\/figure>\n\n\n\n

As you raise the temperature, the ice would start to melt at point A, the\u00a0triple point<\/strong>, the one\u00a0p-V^-T\u00a0combination at which solid, liquid, and vapor can be in equilibrium. Further increase in the temperature causes the ice to abruptly melt before forming water vapor and the pressure to rise, which is indicated by the curve AB. B is the critical point at which vapor and liquid properties become the same.<\/p>\n\n\n\n

If you had kept the temperature almost constant and raised the pressure on the ice, ice would still exist and be in equilibrium with liquid water along the line AC. The line AC is so vertical that you can use the saturated liquid properties for the properties of the compressed liquid<\/strong>. Ice skating is possible because the high pressure exerted by the thin blade on ice forms a liquid layer with low friction on the blade.<\/p>\n\n\n\n

If the vapor and liquid of a pure component are in\u00a0equilibrium<\/strong>, the\u00a0equilibrium pressure is called the vapor pressure,<\/strong>\u00a0which we will denote by\u00a0p<\/em>*.\u00a0At a given temperature, there is only one pressure at which the liquid and vapor phases of a pure substance may exist in equilibrium.<\/strong>\u00a0Either phase alone may exist, of course, over a wide range of conditions.<\/p>\n\n\n\n

We next take up some terminology associated with processes that are conveniently represented on a\u00a0p*-T<\/em>\u00a0phase chart such as\u00a0Figure 7.3\u00a0(in the definitions of terms that follow, the letters in parentheses refer to the corresponding process denoted in\u00a0Figure 7.3\u00a0by the same sequence of letters):<\/p>\n\n\n\n

\"A
Figure 7.3<\/strong> Various common processes as represented on a p<\/em>*-T<\/em> diagram<\/figcaption><\/figure>\n\n\n\n