Potential-pH diagrams for complex systems

A generalized thermodynamic analysis and a geometric interpretation of potential-pH diagrams for multi-element systems are presented. The presence of reactive gases, e.g. CO₂ and SO₂, and complex-forming species, e.g. NH₃ and Cl^–, are expressly considered. The equilibrium state is described by a set of independent formation reactions of all species containing the active redox element, M. The formation reactions are written in terms of a user-specified set of primitive species, e.g. M, H₂O, H⁺,e, X and Y, where X and Y could be CO₂ and Cl^– for example. Some of these primitive species, e.g. M ande, may be virtual species, that is, they do not have an independent existence as separate entities in the reaction mixture. This procedure permits an explicit algebraic solution for the potential-pH diagram. Examples of Pourbaix and predominance diagrams for complex uranium and chromium systems are given. A defined by Equation 41 - a activity - a _M overall activity of redox element M - D maximum dimensionality of diagram - E electrochemical potential - F Faraday's constant - f degrees of freedom - G _f.n ⁰ standard free energy of formation of speciesn - h _i stoichiometric coefficient for H⁺ in generalized formation reaction - M symbol for redox element - M _i symbol forith species containing redox element M - M _X molal concentration of species M _i - M]_T total dissolved concentration of redox element M - n number of species containing redox element M - P number of phases - P_j symbol for primitive species - p pressure - p _ij stoichiometric coefficient for species P_j in generalized formation reaction - r number of independent reactions - R gas constant - s number of species - t number of primitive species - w _i stoichiometric coefficient for H₂O in generalized formation reaction - X] molal concentration of X - x _i stoichiometric coefficient for species X in generalized formation reaction - y _i stoichiometric coefficient for species Y in generalized formation reaction - z _i stoichiometric coefficient for electrons in generalized formation reaction - _i atoms of redox element in species M _i (_i v_i ^–1) - activity coefficient - chemical potential - v_i stoichiometric coefficient for species M _i in generalized formation reaction (v_{i i} ^–1) - aq aqueous phase - b, c, d dissolved species (M_b, M_c, M_d) containing redox element M - i ith species, M_i (gaseous, solid or dissolved) containing redox element M - j primitive species - M redox element M - s, t, u, v solid phases (M_s, M_t, M_u, M_v) containing redox element M - o standard state - reference electrode