Fugacity changes

Second is the calculationof the fugacity change resulting from the pressure increase, P to P, that changes the state from saturated hquid to compressed hquid. 

Figure 1. Schematic diagram for finding the fugacity change from solid to liquid state of a pure substance.

Only the fugacity change with respect to pressure and temperature variation has been considered for the pure gases. For a mixed gas system, interactions between the different gas molecules and atoms must also be taken into account. The second virial coefficient, Bm(T), for a binary mixture between molecules 1 and 2 can be expressed as... 

These electrode constructions also reduce the rate of the fugacity change at the lower part of the electrode caused by the short-circuit, but does not decrease the final magnitude of this effect. Complete elimination, however, is achieved by the relative motion of the melt and electrode, eg, by stirring the melt or in streaming melts as in continuously working industrial melting tanks. 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

These initial estimates are used in the iteration function. Equation (37), to obtain values of the 2 s that do not change significantly from one iteration to the next. These true mole fractions, with Equation (3-13), yield the desired fugacity... 

In 1972, Soave published a method of calculating fugacities based on a modification of the Redlich and Kwong equation of state which completely changed the customary habits and became the industry standard. In spite of numerous attempts to improve it, the original method is the most widespread. For hydrocarbon mixtures, its accuracy is remarkable. For a mixture, the equation of state is ... 

The second step is the evaluation of the change in fugacity of the liquid with a change in pressure to a value above or below For this isothermal change of state from saturated liquid at to liquid at pressure P, Eq. (4-105) is integrated to give... 

If Gf is arbitrarily set equal to zero for all elements in their standard states, then for compounds Gf = AG°, the standard Gibbs-energy change of formation for species i. In addition, the fugacity is eliminated in favor of the fugacity coefficient by Eq. (4-79),/ = yi jP. With these substitutions, the equation for becomes... 

The fugacity coefficient for C02(g) at this temperature and total pressure is 1.188 and the heat capacity change for the reaction is given by... 

By now we should be convinced that thermodynamics is a science of immense power. But it also has serious limitations. Our fifty million equations predict what — but they tell us nothing about why or how. For example, we can predict for water, the change in melting temperature with pressure, and the change of vapor fugacity with temperature or determine the point of equilibrium in a chemical reaction but we cannot use thermodynamic arguments to understand why we end up at a particular equilibrium condition. 

Now consider the effect of pressure. For reversible reactions, pressure can have a significant effect on the equilibrium conversion. Even though the equilibrium constant is only a function of temperature and not a function of pressure, equilibrium conversion can still be influenced through changing the activities (fugacities) of the reactants and products. 

We illustrate these concepts by applying various fugacity models to PCB behavior in evaluative and real lake environments. The evaluative models are similar to those presented earlier (3, 4). The real model has been developed recently to provide a relatively simple fugacity model for real situations such as an already contaminated lake or river, or in assessing the likely impact of new or changed industrial emissions into aquatic environments. This model is called the Quantitative Water Air Sediment Interactive (or QWASI) fugacity model. Mathematical details are given elsewhere (15). 

---