Methods Based on Free Energies

The second major class of equilibrium-solving routines uses the Gibbs free energies of all species (at the temperature and pressure of interest) rather than equilibrium constants for reactions among the species. Frequently the only other input data required is the total amount, or concentration, of each chemical element in the system (i.e., total moles of Ca, Na, S, Cl, etc.), and perhaps Eh, pH, and temperature. 

There is an important fundamental distinction between the free energy based programs and those using equilibrium constants, and this often determines which method to use in specific applications. The free energy programs actually require much more fundamental thermodynamic information, and this can restrict their usefulness. 

To illustrate this problem, consider a simple reaction involving minerals and dissolved aqueous species such as 

The equilibrium constant for such reactions can be measured experimentally, and that gives the standard state free energy of the reaction from 

There are four species in reaction (19.43) and for the sake of argument we will assume that the standard state free energies of formation AfG° are well known for Au(c) and H2(9) but have not been measured for 1128(09) and HAu(HS)2. This is very often a problem with high temperature aqueous species for which free energy data are scarce. If the free energies of all four species were available, then they could be used to calculate the free energy of the reaction  

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Methods Based on Free Energy Perturbation Methods... 

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