The basic theory for the element-potential method of determining equilibrium is based on the minimization of Gibb’s free energy. The Gibb’s function of a system is:

(6–1)

where is the partial molal Gibb’s function and is the number of moles of each species in the system. is the total number of species.

For ideal-gas mixtures or ideal solutions, the partial molal Gibb’s functions are given by:

(6–2)

where is the Gibb’s function for the pure species , evaluated at the system temperature and pressure; is the universal gas constant; and is the mole fraction of the k th species.

The equilibrium solution at a given temperature and pressure is the distribution of that minimizes the system Gibb’s function, , subject to atomic population constraints (and non-negative ). The atomic population constraints are:

(6–3)

where is the number of the j th atoms that appear in the k th molecule, is the total population in moles of the j th atom in the system, and is the total number of different elements that are present in the system.

Details regarding the relationship between the partial molar Gibb’s functions and the elemental potentials for the atoms, as well as the explicit form of the equations solved in the STANJAN library, are described in the STANJAN report.[51]