Activity fugacity and

The comprehension of the laws which govern any material system is greatly facilitated by considering the energy and entropy of the system in the various states of which it is capable. Gibbs (1875). From the Dover edition (1961), p. 55. 

In the thermodynamic treatment of phase equilibria, auxiliary thermodynamic functions such as the fugacity coefficient and the activity coefficient are often used. These functions are closely related to the Gibbs energy. The fugacity of component i in a mixture, J, is defined by Eq. (4a) together with (4b). 

According to this definition, fi is equal to the partial pressure Pi in the case of an ideal gas. The fugacity coefficient i is defined by Eq. (5) and is a measure of the deviation from ideal gas behavior. 

The fugacity coefficient can be calculated from an equation of state by Eq. (6) or (7) 

The activity coefficient of component i, y [Eq. (11)], is a measure of the deviation from ideal solution behavior, so the fugacity of a nonideal liquid solution can be written as Eq. (12). 

The activity coefficient y can be calculated from a model for the molar excess Gibbs energy g, Eq. (13). 

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Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

The heart of the question of non-ideality deals with the determination of the distribution of the respective system components between the liquid and gaseous phases. The concepts of fugacity and activity are fundamental to the interpretation of the non-ideal systems. For a pure ideal gas the fugacity is equal to the pressure, and for a component, i, in a mixture of ideal gases it is equal to its partial pressure yjP, where P is the system pressure. As the system pressure approaches zero, the fugacity approaches ideal. For many systems the deviations from unity are minor at system pressures less than 25 psig. 

Fugacities and activities can be determined using this concept. 

Other important equations of state which can be related to fugacity and activity have been developed by Redlich-Kwong [56] with Chueh [10], which is an improvement over the original Redlich-Kwong, and Palmer s summary of activity coefficient methods [51]. 

In Section HI, we discussed the relation between fugacities and activity coefficients in liquid mixtures, and we emphasized that we have a fundamental choice regarding the way we wish to relate the fugacity of a component to the pressure and composition. This choice follows from the freedom we have in choosing a convention for the normalization of activity coefficients. 

Fugacity, like other thermodynamics properties, is a defined quantity that does not need to have physical significance, but it is nice that it does relate to physical quantities. Under some conditions, it becomes (within experimental error) the equilibrium gas pressure (vapor pressure) above a condensed phase. It is this property that makes fugacity especially useful. We will now define fugacity, see how to calculate it, and see how it is related to vapor pressure. We will then define a related quantity known as the activity and describe the properties of fugacity and activity, especially in solution. 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

In Chapter 6, fugacity and activity are defined and described and related to the chemical potential. The concept of the standard state is introduced and thoroughly explored. In our view, a more aesthetically satisfying concept does not occur in all of science than that of the standard state. Unfortunately, the concept is often poorly understood by non-thermodynamicists and treated by them with suspicion and mistrust. One of the firm goals in writing this book has been to lay a foundation and describe the application of the standard state in such a way that all can understand it and appreciate its significance and usefulness. 

The concepts of fugacity and activity have no strict physical significance but are introduced to transform... 

Holloway J. R. (1977). Fugacity and activity of molecular species in supercritical fluids. In Thermodynamics in Geology, D. G. Fraser, ed. Reidel, Dordrecht. 

One of your friends has difficulty understanding what the chemical potential of a given compound in a given system expresses. Try to explain it in words to him or her. What do the quantities fugacity and activity describe How are they related to the activity coefficient ... 

Since the fugacity and activity coefficients are mathematically complex functions of the compositions, finding corresponding compositions of the two phases at equilibrium when the equations are known requires solutions by trial. Suitable procedures for making flash calculations are presented in the next section, and in greater detail in some books on thermodynamics, for instance, the one by Walas (1985). In making such calculations, it is usual to start by assuming ideal behavior, that is,... 

After the ideal equilibrium compositions have been found, they are used to find improved values of the fugacity and activity coefficients. The process is continued to convergence. 

Since the equations for fugacity and activity coefficients are complex, solution of this kind of problem is feasible only by computer. Reference is made in Example 13.3 to such programs. There also are given the results of such a calculation which reveals the magnitude of deviations from ideality of a common organic system at moderate pressure. 

It has been said chemists have solutions 3 Solutions are involved in so many chemical processes1 that we must have the mathematical tools to comfortably work with them, and thermodynamics provides many of these tools. Thermodynamic properties such as the chemical potential, partial molar properties, fugacities, and activities, provide the keys to unlock the description of mixtures. 

The Lee-Erbar-Edmister method is of the same type, but uses different expressions for the fugacity and activity coefficients. The vapor phase equation of state is a three-parameter expression, and binary interaction corrections are included. The liquid phase activity and fugacity coefficient expressions were derived to extend the method to lower temperatures and to improve accuracy. Binary interaction terms were included in the liquid activity coefficient equation. 

Standard (electrode) potential — (E ) represents the equilibrium potential of an electrode under standard-state conditions, i.e., in solutions with the relative activities of all components being unity and a pressure being 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively) at temperature T. A pressure of 1 bar = 105 Pa was recommended as the standard value to be used in place of 1 atm = 101,325 Pa (the difference corresponds to 0.34 mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as... 

Unfortunately, K values are generally composition-dependent through the fugacity and activity coefficients. Only in ideal systems is the composition dependency removed ... 

It is interesting to note that the vapor and liquid compositions are usually different for ideal mixtures. We can see this from Eq. (6.6), since different pure component vapor pressures are rarely equal at the same temperature. This picture changes when nonideal mixtures are considered. As we see from Eq. (6.55, the vapor and liquid mole fractions can become equal when the fugacity and activity coefficients alter the pressure ratio enough to cause the K value to become unity. We then have an azeotrope. 

As the fugacities are not in themselves quantities which are easily established experimentally, it is necessary to relate them to easily determinable quantities—e.g., temperature, pressure, and composition. This is done by introducing the fugacity and activity coefficients and yi which are defined as follows,... 

Although the composition of an ideal solution can be predicted theoretically, few solutions are ideal, and fugacities and activity coefficients are seldom available for real systems. Hence, in general, too little is known of the direct relationships between solubilities and the specific properties of the solute and the solvent to permit prediction of solubility curves. The characteristics of each system must be determined experimentally. In many cases, it is not even possible to predict the effect of temperature on the solubility values of a given solute-solvent system. 

Since the equations for fugacity and activity coefficients are complex, solution of this kind of problem is feasible only by com-... 

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