Fixed activity and fugacity paths

In a fixed activity path, the activity of an aqueous species (or those of several species) maintains a constant value over the course of the reaction path. A fixed fugacity path is similar, except that the model holds constant a gas fugacity instead of a species activity. Fixed activity paths are useful in modeling laboratory experiments in which an aspect of a fluid s chemistry is maintained mechanically. In studying reaction kinetics, for example, it is common practice to hold constant the pH of 

To calculate a fixed activity path, the model maintains within the basis each species At whose activity at is to be held constant. For each such species, the corresponding mass balance equation (Eqn. 4.4) is reserved from the reduced basis, as described in Chapter 4, and the known value of a, is used in evaluating the mass action equation (Eqn. 4.7). Similarly, the model retains within the basis each gas Am whose fugacity is to be fixed. We reserve the corresponding mass balance equation (Eqn. 4.6) from the reduced basis and use the corresponding fugacity fm in evaluating the mass action equation. 

A complication to the calculation procedure for holding an aqueous species at fixed activity is the necessity of maintaining ionic charge balance over the reaction path. If the species is charged, the model must enforce charge balance at each step in the calculation by adjusting the concentration of a specified component, as discussed in Section 4.3. For example, if the pH is fixed over a path and the charge balance component is Cl-, then the model will behave as if HC1 were added to or removed from the system in the quantities needed to maintain a constant H+ activity. 

In an example of a fixed fugacity path we model the dissolution of pyrite (FeS2) at 25 °C. We start in REACT with a hypothetical water in equilibrium with hematite (Fe203) and oxygen in the atmosphere 

We can write the overall reaction by which hematite forms, using the slopes-of-the-lines method discussed in Chapter 13. Initially, the reaction proceeds as, 

2 Mineralogical results (top) of reacting pyrite at 25°C into a dilute water held closed to O2, and variation in pH (bottom) over the reaction. 

---