Chapter 4: Applications of Thermodynamics to the Earth 4.1 Introduction 4.2 Activities in Non-ideal Solid Solutions 4.2.1 Mathematical Models of Real Solutions: Margules Equations 4.2.1.1 the Symmetric Solution Model V Bx Cx = + 2 2 2 4.2

n the previous 2 chapters, we developed the fundamental thermodynamic relationships and saw how they are applied to geochemical problems. The tools now in our thermodynamic toolbox are sufficient to deal with most of the phenomena we will encounter in the second half of this book. They are not sufficient, however, to deal with all geochemical problems. In this chapter, will add a final few thermodynamic tools. These allow us to deal with non-ideal behavior and exsolution phenomena in solids and silicate liquids. With that, we can use thermodynamics to determine the pressure and temperature at which rock assemblages formed, certainly one of the most useful applications of thermodynamics to geology. Along the way, we will see how thermodynamics is related to one of the most useful tools in petrology: phase diagrams. Finally, we return to the question of non-ideal behavior in electrolyte solutions and examine in more depth the problems of ion association and solvation and how this affects ion activities. Deviations from ideal behavior tend to be greater in solutions of high ionic strength, which includes such geologically important solutions as hydrothermal and ore-forming fluids, saline lake waters, metamorphic fluids, and formation and oil field brines. We briefly examine methods of computing activity coefficients at ionic strengths relevant to such fluids.