Phase Diagrams of Pure Substances

CHAPTER 8 PHASE TRANSITIONS AND EQUILIBRIA OF PURE SUBSTANCES 8.2 PHASE DIAGRAMS OF PURE SUBSTANCES... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Thus far we have developed just about all the thermodynamic concepts required by Earth scientists with the exception of those needed to deal with solutions. Since all naturally occurring substances are solutions of one kind or another (although some can usefully be treated as pure substances), this is quite an important limitation, and we will proceed to discuss the treatment of solutions in Chapter 10. However, a great deal can be done with the thermodynamics of pure systems, and in this chapter we discuss a couple of applications of the concepts so far developed which are of particular interest to Earth scientists—the thermal effects associated with adiabatic volume changes, and the T-P phase diagrams of pure minerals. 

Does a critical point exist between the solid and vapor phase in the P/T diagram of pure substances ... 

Freeze drying is mostly done with water as solvent. Fig. 1.1 sows the phase diagram of water and the area in which this transfer from solid to vapor is possible. This step is difficult, even for pure water. If the product contains two or more components in true solutions or suspensions, the situation can become so complicated that simplified model substances have to be used. Such complex systems occur ubiquitously in biological substances. 

Draw a phase diagram of water. What is called a phase, component, and degree of freedom How many phases and degrees of freedom are there at different points of the phase diagram of water What is known as the freezing (boiling) point of pure substances ... 

Fig. 2-4, Typical phase diagram of a pure substance with two lines of isobaric temperature change 123below critical pressure, 45 above critical pressure.

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

Phase rule studies and describes the occurence of modifications and states of aggregation of pure substances or in mixtures in closed systems as well as the changes which occur in those systems when the pressure, temperature and composition of these substances in the system change. The behaviour of many pure substances and mixtures has thus been studied and recorded in diagrams. These diagrams constitute a vital aid for any scientist studying the development of materials, e.g. ceramics. 

A supercritical fluid is a substance above its critical temperature and pressure. Figure 3.4 shows a phase diagram of a pure substance, where curve... 

Figure 3.4. Phase diagram of a pure substance. (Reproduced from Ref. 24, with permission from Kluwer Academic Publishers.)...

QUESTIONS 9-11 REFER TO THE PHASE DIAGRAM OF A PURE SUBSTANCE, SHOWN BELOW ... 

Fig. 3-2. P/V/T phase diagram of a pure substance (pure solvent) showing domains in which it exists as solid, liquid, gas (vapour), and/or sc-fluid (CP = critical point TP = triple point p = mass density). The inserted isotherms T2 (T2 > Tc) and Tj, T3 Tc) illustrate the pressure-dependent density p of sc-fluids, which can be adjusted from that of a gas to that of a Hquid. The influence of pressure on density is greatest near the critical point, as shown by the greater slope of isotherm T2 compared to that of T3, which is further away from Tc- Isotherm Ti demonstrates the discontinuity in the density at subcritical conditions due to the phase change. This figure is taken from reference [220].

A phase diagram of a pure substance is a plot of one system variable against another that shows the conditions at which the substance exists as a solid, a liquid, and a gas. The most common of these diagrams plots pressure on the vertical axis versus temperature on the horizontal axis. The boundaries between the single-phase regions represent the pressures and temperatures at which two phases may coexist. The phase diagrams of water and carbon dioxide are shown in Figure 6.1-1. 

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