In previous chapters we have introduced many quantities, and we have developed many relations among those many quantities. We use this chapter to summarize the most important of those relations and to show you that we have consistently used a single approach in developing those relations. We start in § 6.1 by reminding you of the subtle distinctions between system states and constraints on interactions that may be in force when we change a state. Constraints are usually imposed in terms of measurables; for example, constant temperature or constant volume or no heat transfer. But such constraints can have profound effects on conceptuals and, in particular, on our choices for the most useful and economical expressions for relating measurables to conceptuals.

At this point we have developed two principal ways for relating conceptuals to measurables: one based on the ideal gas (Chapter 4) and the other based on the ideal solution (Chapter 5). Both routes use the same strategy—determine deviations from a well-defined ideality—with the deviations computed either as differences or as ratios. Since both routes are based on the same underlying strategy, a certain amount of symmetry pertains to the two; for example, the forms for the difference measures—the residual properties and excess properties—are functionally analogous.

We use § 6.2 to emphasize the symmetries that exist among difference measures and among ratio measures. Difference measures are commonly used to compute thermodynamic properties of single homogeneous phases, while ratio measures are most often used in phase and reaction equilibrium calculations.

In this chapter we review elementary concepts that are used to describe Nature. These concepts are so basic that we call them primitives, for everything in later chapters builds on these ideas. You have probably encountered this material before, but our presentation may be new to you. The chapter is divided into primitive things (§ 1.1), primitive quantities (§ 1.2), primitive changes (§ 1.3), and primitive analyses (§ 1.4).

PRIMITIVE THINGS

Every thermodynamic analysis focuses on a system—what you're talking about. The system occupies a definite region in space: it may be composed of one homogeneous phase or many disparate parts. When we start an analysis, we must properly and explicitly identify the system; otherwise, our analysis will be vague and perhaps misleading. In some situations there is only one correct identification of the system; in other situations, several correct choices are possible, but some may simplify an analysis more than others.

A system can be described at either of two levels: a macroscopic description pertains to a system sufficiently large to be perceived by human senses; a microscopic description pertains to individual molecules and how those molecules interact with one another. Thermodynamics applies to macroscopic entities; nevertheless, we will occasionally appeal to microscopic descriptions to interpret macroscopic phenomena. Both levels contain primitive things.

Macroscopic Things

Beyond the system lies the rest of the universe, which we call the surroundings. Actually, the surroundings include only that part of the universe close enough to affect the system in some way.

Much of thermodynamics concerns the causes and consequences of changing the state of a system. For example, you may be confronted with a polymerization process that converts esters to polyesters for the textile industry, or you may need a process that removes heat from a chemical reactor to control the reaction temperature and thereby control the rate of reaction. You may need a process that pressurizes a petroleum feed to a flash distillation unit, or you may need a process that recycles plastic bottles into garbage bags. In these and a multitude of other such situations, a system is to be subjected to a process that converts an initial state into some final state.

Changes of state are achieved by processes that force the system and its surroundings to exchange material or energy or both. Energy may be exchanged directly as heat and work; energy is also carried by any material that enters or leaves a system. A change of state may involve not only changes in measurables, such as T and P, but it may also involve phase changes and chemical reactions. To design and operate such processes we must be able to predict and control material and energy transfers.

Thermodynamics helps us determine energy transfers that accompany a change of state. To compute those energetic effects, we can choose from two basic strategies, as illustrated in Figure 2.1. In the first strategy we directly compute the heat and work that accompany a process.

Multiphase systems and chemical reactions pervade the chemical processing industries. For example, we routinely force the creation of a new phase to exploit the accompanying change in composition; consequently, phase changes are used in many separation processes, including distillation, crystallization, and solvent extraction. In addition, we routinely suppress the creation of a new phase, for example, to maintain inventory of liquids by controlling loss due to evaporation and to meet health and safety standards by controlling evaporation of flammable, hazardous, and toxic substances. Likewise, we often promote chemical reactions to convert inexpensive raw materials into valuable products. But we also try to prevent other reactions that convert valuable materials into costly wastes, and we try to prevent reactions that convert benign substances into hazardous or toxic chemicals. In all such situations, the design and operation of appropriate processes may hinge upon computing proper solutions to phase-equilibrium problems or reaction-equilibrium problems or both.

In previous chapters we developed the thermodynamics of phase and reaction equilibria, and we illustrated certain principles using straight forward computational procedures. We used only simple procedures so as not to detract from thermodynamic issues. In this chapter we consider more complex situations and therefore give more attention to computational techniques. No new thermodynamics is introduced in this chapter; instead, we try to show how the thermodynamics already developed can be used in multicomponent phase and reaction-equilibrium situations.

You are part of a development group assigned to determine the properties and phase behavior of certain mixtures that are to be used in a new process for your company. Your supervisor is relying on the group to provide a quick and thorough assessment of the proposed process: each day of production delay costs the company one million dollars.

You begin by asking how the information will be used: Is it for exploratory research, conceptual design, process development, equipment sizing, troubleshooting? You next ask what processing steps are involved: reactions, separations, heating, cooling, pumping, expansions, recycles? And which steps could affect business decisions for commercialization: Are reaction yields limited by rates or by equilibrium conversions? Are separations hindered by formation of azeotropes or solutropes? If additional solvents are introduced, how will they be removed, so the product is not contaminated? Can any solvents be recycled to avoid disposal and waste? Finally, you ask precisely what properties are being requested. Are they compositions of phases in equilibrium? Densities and enthalpies of single phase liquids, gases, or solids? Reaction rate constants? In short, you must decide what properties are to be quantified and then decide how those values will be used: in appropriate hand calculations or in a process simulator.

At this preliminary stage, you may be tempted to skimp on the quality of property data, but then you remember that inadequate thermodynamic information can lead to improper designs and process failures.

With many million pure substances now known, an essentially infinite number of mixtures can be formed, resulting in a diversity of phase behavior that is overwhelming. Consider just two components: not only can binary mixtures exhibit solid-gas, liquid-solid, and liquid-gas equilibria, but they might also exist in liquid-liquid, solid-solid, gas-gas, gas-liquid-liquid, solid-liquid-gas, solid-solid-gas, solid-liquid-liquid, solid-solid-liquid, and solid-solid-solid equilibria. That's a dozen different kinds of phase equilibrium situations—just for binary mixtures. For multicomponent mixtures the possibilities seem endless.

In this chapter we describe the kinds of phase behavior that are commonly observed in pure fluids, binary mixtures, and some ternary mixtures. The descriptions typically take the form of phase diagrams, and we show how studies of phase behavior can be made systematic by identifying classes of diagrams. Since we are interested in describing what is actually seen, the mixture diagrams presented in this chapter are plotted in terms of measurables: usually temperature, pressure, composition, or a subset of those. Calculations of phase equilibria necessarily involves conceptuals, and such calculations are discussed in Chapter 10. Here we only describe phenomena.

We start in § 9.1 by giving prescriptions for determining the number of properties needed to identify the thermodynamic state in multicomponent mixtures. Those prescriptions include Duhem's theorem and the Gibbs phase rule as special cases. The required number of properties determines the dimensionality of the state diagram needed to represent phase behavior.

In Chapter 4 we used differences and ratios to relate the conceptuals of real substances to those of ideal gases. To compute values for those differences and ratios, we use the equations given in § 4.4 together with a volumetric equation of state. Such equations of state are available for many mixtures, particularly gases; however, few of those equations reliably correlate properties of condensed-phase mixtures. Although some equations of state reproduce the behavior of condensed phases of complex substances, those equations are complicated and applying them can require considerable computational skill and resources. This is particularly true when we attempt to apply equations of state to mixtures of liquids.

Therefore we seek ways for computing conceptuals of condensed phases while avoiding the need for volumetric equations of state. One way to proceed is to choose as a basis, not the ideal gas, but some other ideality that is, in some sense, “closer” to condensed phases. By “closer” we mean that changes in composition more strongly affect properties than changes in pressure or density. The basis exploited in this chapter is the ideal solution. We still use difference measures and ratio measures, but they will now refer to deviations from an ideal solution, rather than deviations from an ideal gas.

We start the development in § 5.1 by defining ideal solutions and giving expressions for computing their conceptual properties.