Compositions of coexisting fluids at elevated pressure-temperature conditions can be calculated by applying thermodynamics as in any other chemical equilibrium. This calculation requires the evaluation of the thermodynamic properties of the phase components i at the respective pressure P , temperature T , and the individual abundances x i, i.e., composition. In comparison with solids, fluids normally have distinct PVT -behaviors. Furthermore, because of their disordered state and the relatively weak bonding between molecules, fluid species mix much more easily than solid-phase components. The evaluation of the thermodynamic properties of fluids requires, therefore, special treatment and procedures that differ significantly from those used for solids. For fluids, this treatment includes a distinct and different standard state than for solids and a special description of the volume V as a function of P , T (or P as a function of V and T ) and x i, i.e., an equation of state (EOS). For geological systems, which are usually defined by the variables P and T , the Gibbs free energy G is the function of choice to describe equilibria. At constant P and T the chemical equilibrium condition is defined by (the Table 1⇓ lists the symbols used): View this table: Table 1. Notation and symbols \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathit{dG} = 0\] \end{document}(1) The partial derivative of G with respect to P is the volume V \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\left(\frac{{\partial}\mathit{G}}{{\partial}\mathit{P}}\right)\mathit{\_{T,n\_{i}}} = \mathit{V}\] \end{document}(2) Therefore, the pressure-dependence of G is obtained by integration of Equation (2) with boundaries from the reference pressure P r, i.e., ambient pressure of 0.1 MPa, to the required P \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathit{G\_{(P,T)}} = \mathit{G\_{(P\_{r},T)}} + {{\int}\_{\mathit{P_{r}}}^{\mathit{P}}}\mathit{VdP}\] \end{document}(3) For the practical treatment of mixed phases, G has to be replaced by its partial derivative with respect to composition, the chemical potential μi of the phase component i 1 \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[{\mu}\mathit{\_{i}} = \left(\frac{{\partial}\mathit{G}}{{\partial}\mathit{n\_{i}}}\right)\mathit{\_{P,T,n\_{j{\neq}i}}}\] \end{document}(4) For solids using the standard state of a pure phase component at reference conditions P r and …