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Geochemical Reaction ModelingConcepts and Applications$
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Craig M. Bethke

Print publication date: 1996

Print ISBN-13: 9780195094756

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195094756.001.0001

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The Equilibrium State

The Equilibrium State

3 The Equilibrium State
Geochemical Reaction Modeling

Craig M. Bethke

Oxford University Press

Aqueous geochemists work daily with equations that describe the equilibrium points of chemical reactions among dissolved species, minerals, and gases. To study an individual reaction, a geochemist writes the familiar expression, known as the mass action equation, relating species’ activities to the reaction’s equilibrium constant. In this chapter we carry this type of analysis a step farther by developing expressions that describe the conditions under which not just one but all of the possible reactions in a geochemical system are at equilibrium. We consider a geochemical system comprising at least an aqueous solution in which the species of many elements are dissolved. We generally have some information about the fluid’s bulk composition, perhaps directly because we have analyzed it in the laboratory. The system may include one or more minerals, up to the limit imposed by the phase rule (see Section 3.4), that coexist with and are in equilibrium with the aqueous fluid. The fluid's composition might also be buffered by equilibrium with a gas reservoir (perhaps the atmosphere) that contains one or more gases. The gas buffer is large enough that its composition remains essentially unchanged if gas exsolves from or dissolves into the fluid. How can we express the equilibrium state of such a system? A direct approach would be to write each reaction that could occur among the system’s species, minerals, and gases. To solve for the equilibrium state, we would determine a set of concentrations that simultaneously satisfy the mass action equation corresponding to each possible reaction. The concentrations would also have to add up, together with the mole numbers of any minerals in the system, to give the system’s bulk composition. In other words, the concentrations would also need to satisfy a set of mass balance equations. Such an approach, however, is unnecessarily difficult to carry out. Dissolving even a few elements in water produces many tens of species that need be considered, and complex solutions contain many hundreds of species. Each species represents an independent variable, namely its concentration, in our scheme. For any but the simplest of chemical systems, the problem would contain too many unknown values to be solved conveniently.

Keywords:   Activity coefficient, Basis vector, Charge balance, Eh electrode, Gas buffer, Independent reactions, Mass action equations, Phase rule, Saturation state

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