Fugacity thermodynamic definition

Set out the relevant form of the thermodynamic definition of K value. At this low system pressure, the vapor-phase nonideahty is negligible. Since neither component has a very high vapor pressure at the system temperature, and since the differences between the vapor pressures and the system pressure are relatively small, the pure-liquid fugacities can be taken to be essentially the same as the vapor pressures. 

The linear form (5.1.2) is the simplest expression that can be devised for the composition dependence of a fugacity, and in fact (5.1.2) can be considered to be a thermodynamic definition of ideal solution. Even the ideal-gas mixture, for which (ffj = 1, is a special kind of ideal solution that is, the ideal-gas fugacity takes the form (5.1.2) with... 

Standard potential values are usually those of ideal unimolal solutions at a pressure of 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively). A pressure of 1 bar = 10 Pa was recommended as the standard value to be used in place of 1 atm = 101 325 Pa (the difference corresponds to a 0.34-mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as the standard value if not, the standard pressure should be that of the inert gas over the solution or melt. In a certain case, a standard potential can be established in a system with nonunity activities, if the combination of the latter substituted in the Nemst equation equals unity. For any sohd component of redox systems, the chemical potential does not change in the course of the reaction, and it remains in its standard state. In contrast to the common thermodynamic definition of the standard state, the temperature is ignored, because the potential of the standard hydrogen (protium) electrode is taken to be zero at any temperature in aqueous and protic media. The zero temperature coefficient of the SHE corresponds to the conventional assumption of... 

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

At constant temperature, the activity coefficient depends on both pressure and composition. One of the important goals of thermodynamic analysis is to consider separately the effect of each independent variable on the liquid-phase fugacity it is therefore desirable to define and use constant-pressure activity coefficients which at constant temperature are independent of pressure and depend only on composition. The definition of such activity coefficients follows directly from either of the exact thermodynamic relations... 

The chemical potential provides the fundamental criteria for determining phase equilibria. Like many thermodynamic functions, there is no absolute value for chemical potential. The Gibbs free energy function is related to both the enthalpy and entropy for which there is no absolute value. Moreover, there are some other undesirable properties of the chemical potential that make it less than suitable for practical calculations of phase equilibria. Thus, G.N. Lewis introduced the concept of fugacity, which can be related to the chemical potential and has a relationship closer to real world intensive properties. With Lewis s definition, there still remains the problem of absolute value for the function. Thus,... 

Polymorphism can be detected by the differences in physical properties due to individual characteristics. Based on the fugacity, which relates to the thermodynamic term, entropy of the solid molecule, polymorphism may be defined as monotropic or enantiotropic. Furthermore, combination of these two systems, monotropic and enantiotropic, may yield a third system. The definition of these categories may best be illustrated by the solubility-temperature plots, based on the van t Hoff equation. In a monotropic category as shown in Figure 9, the solubility of form I (the stable form) and that of form II (the metastable form) will not intersect each other at the transition temperature calculated only from the extrapolation of the two curves. In the enantiotropic category (Fig. 10), the solubility of form I (the stable form) and that of form II (the metastable form) will intersect each other at the transition temperature. In the combined category (Fig. 11), for which there are two transition temperatures, the solubility of form III will not intersect any other curves. 

The equation (5.77) suggests similar relation for a real fluid, but where the pressure would be substituted by a more general property. Thus, by definition we may link the variation of Gibbs free energy with a thermodynamic property of a real fluid, called fugacity f, by the following differential equation ... 

To preserve thermodynamic consistency, we require that the general expression (4.3.8) revert to the special form (4.3.7) if om- substance is indeed an ideal gas. Therefore as the second part of the definition, we require that the ideal-gas fugacity obey... 

The brief survey presented here must necessarily begin with a discussion of thermodynamics as a language most of Section 1.2 is concerned with the definition of thermodynamic terms such as chemical potential, fugacity, and activity. At the end of Section 1.2, the phase-equilibrium problem is clearly staled in several thermodymunic forms each of these forms is particularly suited for a particular situation, as indicated in Sections 1.S, 1.6, and 1.7. 

The formulation of engineering problems in phase equilibria begins with a set of abstract equations relating the component fugacities ft of each component i in a multiphase syslon. Tianslation of these equations into useM working relatiotiships is done by definition (throu tiie fiigacity coefficieiit and/or the activiqr coefficient y,) and by thermodynamic manipulation. Different problems require diffincnt translations we have illustrated many of the standard procedures by examples in Sections 1.3, 1.6, and 1.7. 

Equilibrium phenomena of liquid and vapour phases of binary and ternary mixtures, as well as the analytical and graphic representation of the equilibrium of the two phases have been discussed in the introduction written b) Hausen. The introduction also contains discussion of the thermodynamic basis of phase equilibria, definitions of the characteristic concepts of the activity coefficient and the fugacity as well as equations that represent phase equilibria. More references can be found in the papers quoted in the next section entitled "References on the Thcrmodjmamics of the Liquid-Vapour Equilibrium . 

The definition oifugacity can be attributed to the thermodynamics giant G. N. Lewis. Unlike the other concepts we have seen so far in this text, it developed inductively rather than deductively. In fact, fugacity is undoubtedly but one of many ways to get around the mathematical anomalies of the chemical potential however, it is the way that is used in practice, and we will learn about it next. 

We can also get thermodynamic property data to solve for the left-hand side of Equation (7.7) through an equation of state. At constant temperature (as mandated by the definition of fugacity), we can write the fundamental property relation of the Gibbs energy of pure species i as ... 

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