The Nature of Equilibrium

The most commonly encountered coexisting phases in industrial practice are vapor and liquid, although liquid/liquid, vaporlsolid, and liquid/solid systems are also found. In this chapter we first discuss the nature of equilibrium, and then consider two rules that give the lumiber of independent variables required to detemiine equilibrium states. There follows in Sec. 10.3 a qualitative discussion of vapor/liquid phase behavior. In Sec. 10.4 we introduce tlie two simplest fomiulations that allow calculation of temperatures, pressures, and phase compositions for systems in vaporlliquid equilibrium. The first, known as Raoult s law, is valid only for systems at low to moderate pressures and in general only for systems comprised of chemically similar species. The second, known as Henry s law, is valid for any species present at low concentration, but as presented here is also limited to systems at low to moderate pressures. A modification of Raoult s law that removes the restriction to chemically similar species is treated in Sec. 10.5. Finally in Sec. 10.6 calculations based on equilibrium ratios or K-values are considered. The treatment of vapor/liquid equilibrium is developed further in Chaps. 12 and 14. 

Equilibrium is a static condition in which no changes occur in the macroscopic properties of a system with time. This implies a balance of all potentials that may cause change. In engineering practice, the assumption of equilibrium is justified when it leads to results of satisfactory accuracy. For example, in the reboiler for a distillation column, equilibrium between vapor and 

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First, consider the nature of equilibrium from the kinetic viewpoint. If the reaction... 

The nature of equilibrium in such cases is characterized by the nature of the roots of the following characteristic equation... 

In other words, in normal cases the nature of equilibrium is determined only by the linear terms. This is also intuitively obvious since, as the trajectory approaches the singular point (at the origin), both x and y decrease indefinitely so that ultimately only the linear terms of the first order of magnitude remain. 

Conceptualizing a geochemical model is a matter of defining (1) the nature of equilibrium to be maintained, (2) the initial composition and temperature of the equilibrium system, and (3) the mass transfer or temperature variation to occur over the course of the reaction process envisioned. 

As noticed in a review of P [2]t, an important early reference had been overlooked, namely the two notes of Jouguet [3], Observations sur les principes et les theoremes generaux de la statique chimique (pp. 61-180) and Sur les lois de la dynamique chimique relatives aux sens des reactions irreversibles (pp. 181-194). In these papers (of which I was culpably unaware when writing P) Jouguet carefully establishes the notion of independence of reactions and the invariants of a system of reactions and considers the ramifications of the phase rule. In particular he is quite clear as to the way in which stoicheiometry lays a foundation for thermodynamics and in going on to discuss the nature of equilibrium he shows that its uniqueness is a consequence of its stability. Thus much of the content of 2-4 of P is to be found in Jouguet. His second note, however, is concerned with the direction... 

The Langmuir equation may be derived as follows. Imagine a particular experiment in which a quantity of carbon adsorbent is added to a beaker of sample containing pollutant. Immediately, the solute will be sorbed onto the adsorbent until equilibrium is reached. One factor determining the amount of the sorbed materials has to be the number of adsorption sites in the carbon. The number of these sites may be quantified by the ratio XIM. By the nature of equilibrium processes, some of the solutes adsorbed will be desorbed back into solution. While these solutes are desorbing, some solutes will also be, again, adsorbed. This process continues on, like a seesaw this seesaw behavior is a characteristic of systems in equilibrium. 

On the surface, the combination of cation exchanger and anion exchanger would mean that pure water is produced. As shown in Equations (16.1) and (16.2), however, the unit process of ion exchange is governed by equilibrium constants. The values of these constants depend upon how tightly the removed ions from solution are bound to the bed exchanger sites. In general, however, by the nature of equilibrium constants, the concentrations of the affected solutes in solution are extremely small. Practically, then, we may say that pure water has been produced. 

The three principal ingredients of the reaction rate expression are shown in the top boxes of Fig. 1.1. Stoichiometry deals with the changes of composition that may take place by reaction. From thermostatics we can learn much about the heat effects of reactions and the nature of equilibrium, and from chemical kinetics we shall take any result that is available and useful. These three factors form the anatomy of our subject, whose physiology emerges when we ask just what they mean in terms of the behavior of the reaction rate expression. In Chap. 4 we will examine the reaction rate expression and in Chap. 5 we will see what this implies for the course of the reaction in time. But we must also look at the interaction of physical and... 

We begin by discussing the nature of equilibrium and the difference between chemical and physical equihbrium. We define the equilibrium constant in terms of the law of mass action. (14.1)... 

Most introductory accounts use the combination (la), (26) and (3a), which is one of the easiest to grasp. However, the disadvantage of averaging over the quantum states of molectdes as in (la), is that the statistical formulae which are obtained are applicable only to qrstems in which the particles are independent, as in perfect gases. In many elementary accounts of this method it is also necessary to adopt a subterfuge in order to introduce an important term, n , into the formulae. The method (26) may also lead to an erroneous impression of the nature of equilibrium, for it might be taken to imply that the system stays always in the particular distribution known as the most probable distribution. Tliis would be to preclude fluctuation phenomena. 

We have considered in Section 5.2.2 the nature of equilibrium relationships in solvent extraction of a species in the presence of a chemical reaction in either phase or at the interface. 

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