Fugacity, definition

The equations for an imperfect vapour analogous to (6-23) and (6 24) may be obtained by a similar procedure. The following method of derivation is rather simpler, and could also have been adopted for the derivation of (6-23) and (6 24). Let / be the fugacity of the volatile substance in the vapour phase, where its chemical potential is Then from the fugacity definition (3 56)... 

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. 

The definition of fugacity is completed by setting the ideal gas state fugacity of pure species / equal to its pressure ... 

The definition of fugacity of a species in solution is parallel to the definition of pure species fugacity. Equation 154 is analogous to the ideal gas expression ... 

According to the definition of Eq. (4-67), G — G/ is the residual Gibbs energy, The dimensionless ratio is another new property called the fugacity coefficient (j). Thus,... 

Hydrogen Electrode an electrode at which the equilibrium (aq.) + jHj, is established. By definition, at unit activity of hydrogen ions and unit fugacity of hydrogen gas the potential of the standard hydrogen electrode h+/y//2 =... 

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 second part of the definition for fugacity requires that k - l, since, in theory, any solid or liquid taken to zero pressure would eventually be a gas for which f=p so that k equals one. 

With this definition, T is the numerical value of the activity for the substance under some pressure p. It is also the ratio of the fugacity of the pure condensed phase under pressure p to that of the phase under 1 bar pressure. 

With our definition of activity as the ratio of the fugacity of the component in the solution to that in the standard state, we find that... 

Equilibrium. Equilibrium between compartments can be expressed either as partition coefficients K.. (i.e. concentration ratio at equilibrium) or in the fugacity models as fugacity capacities and Z. such that K.. is Z./Z., the relationships being depicted in Figur 1. Z is dellned as tfte ratio of concentration C (mol/m3) to fugacity f (Pa), definitions being given in Table I. 

Figure 1. Relationships between fugacity capacities and partition coefficients. See Table 1 for symbol definitions.

Summary. In summary, when modeling with the fugacity concept, all equilibria can be treated by Z values (one for each compartment) and all reaction, advection and transport processes can be treated by D values. The only other quantities requiring definition are compartment volumes and emission rates or initial concentrations. A major advantage is that since all D quantities are in equivalent units they can be compared directly and the dominant processes identified. By converting diverse processes such as volatilization, sediment deposition, fish uptake and stream flow into identical units, their relative importance can be established directly and easily. Further, algebraic manipulation... 

Equation 2.63 is valid for any homogeneous or heterogeneous reaction. The only difference is in the definition of activities. For a species in a perfect gas-phase mixture a = pi/p°, where pi is the partial pressure of species i andp° is the standard pressure (1 bar). For a real gas-phase mixture a =f/p°, where is the fugacity of i. The fugacity concept was developed for the same reason as the activity to extend to real gases the formalism used to describe perfect gas mixtures. In the low total pressure limit (p -> 0), fi = pi. 

For concentrated solutions, the activity coefficient of an electrolyte is conveniently defined as though it were a nonelectrolyte. This is a practical definition for the description of phase equilibria involving electrolytes. This new activity coefficient f. can be related to the mean ionic activity coefficient by equating expressions for the liquid-phase fugacity written in terms of each of the activity coefficients. For any 1-1 electrolyte, the relation is ... 

Equation (10.34) takes cognizance of only one part of the definition of fugacity. The second part of the definition states that although / approaches zero as P approaches zero, the ratio//P approaches one. Hence, this ratio might be integrable to zero pressure. 

As the mixture approaches ideality as the total pressure approaches zero, Equation (10.81) should approach Equation (10.17). The second part of the definition of fugacity for a gaseous component, which is analogous to Equation (10.24), is... 

According to this definition f is equal to the partial pressure P, in the case of an ideal gas. The fugacity coefficient (j>- is defined by... 

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