Application of Moderation Theorems to Metasomatic Processes

Abstract

Moderation theorems can be used to predict the consequences of perturbing a system from a stable equilibrium state to an adjacent nonequilibrium state. Although in the absence of external constraints, the moderation theorem known as the Le Chatelier-Braun principle affords accurate prediction of the consequences of such perturbations in closed systems, it is not applicable to many reactions of geologic interest in open systems. As demonstrated by De Donder (1933), De Donder and Van Rysselberghe (1936), and Prigogine and Defay (1954), constraints imposed by the second law of thermodynamics commonly lead to contradictions of the Le Chatelier-Braun principle in the latter systems. Derivation of moderation criteria for simultaneous independent hydrolysis reactions for minerals indicates that the criteria can be applied directly to overall dehydration/decarbonation reactions in metasomatic processes. Although moderation with respect to the mole fraction of a perturbed component always occurs in fluids in which ideal mixing takes place, whether or not moderation of metasomatic reactions takes place with respect to addition to, or removal from the fluid of a small amount of a given component such as CO2 or H2O depends on the stoichiometry of the reaction. De Donder’s fundamental inequality (De Donder, 1922) can be used to calculate limiting fluid compositions for moderation with respect to addition or removal of such components. Isothermal-isobaric perturbation of equilibrium in the vicinity of these limiting compositions may lead to dramatic changes in the relative masses of reactants and products. Some CO2-H2O metasomatic reactions will not moderate in response to changes in the mass of either CO2 or H2O in the intermediate range of \({X_{{\rm{C}}{{\rm{O}}_{\rm{2}}}}}\). Explicit recognition of moderation constraints in open systems and application of moderation theorems to both experimental and field observations facilitates considerably interpretation of phase relations and correlation of trends in the relative masses of metasomatic minerals to changes in temperature, pressure, and fluid composition.