Читать книгу Geochemistry - William M. White - Страница 151

Natural systems often contain multiple phases, many of which are solutions of several components; in this chapter, we developed the thermodynamic tools to deal with them.

 We began by defining components, phases, and species. Together, the number of components and phases in a system determine the degrees of freedom of the system:(3.2) which are the number of independent variables we need to specify to completely describe the system. We derived the Clapeyron equation, which described the boundary between two phases, such as graphite and diamond, the P−T space:Figure 3.22 Oxygen buffer curves in the system Fe−Si−O at 1 bar. QIF, IW, WM, FMQ, and MH refer to the quartz–iron–fayalite, iron–wüstite, wüstite–magnetite, fayalite–magnetite–quartz and magnetite–hematite buffers, respectively.(3.3)

 We found the thermodynamic properties of solutions depend on their composition as well as T and P and to deal with this we introduced partial molar quantities, particularly the partial molar Gibbs free energy or chemical potential:(3.13)

 The simplest solutions are ideal ones, where there are no energetic or volumetric effects of solution (ΔH = 0; ΔV= 0), so the enthalpy and volume of an ideal

 solution are simply their sum of the partial molar quantities. There are, however, entropic effects associated with solution, so that(3.31)

 In nonideal solutions, the availability of a species for reaction can differ from its concentration; to deal with this we introduced fugacity and activity; the latter is related to concentration through an activity coefficient:(3.48) The activity coefficient is related to the excess Gibbs free energy associated with nonideal behavior:(3.56a) Much of the problem with dealing with nonideal solutions is reduced to finding values for the activity coefficients.

 Electrolyte solutions, of which seawater is a good example, are common nonideal solutions. We reviewed the nature of these solutions and introduced approaches for calculating activity coefficients in them, such as the Debye–Hückel extended law:(3.74) We then reviewed ways to calculate activities in ideal solid solutions.

 In section 3.9, we introduced the equilibrium constant:(3.85) and found we could directly relate it to the Gibbs free energy of reaction.

 In section 3.11, we introduced the electrochemical potential to deal with changing valance states of elements, that is, oxidation–reduction reactions. This too we could relate to our thermodynamic framework:(3.106) A useful way to represent redox potential in low-temperature systems is the electron activity(3.112) which we could also directly relate to electrochemical potential. Since oxygen is the most common oxidant, in high-temperature systems, the redox state of the system is more commonly represented with oxygen fugacity, ƒO2.