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Having derived a set of equations describing the equilibrium state of a multicomponent system and devised a scheme for solving them, we can begin to model the chemistries of natural waters. In this chapter we construct four models, each posing special challenges, and look in detail at the meaning of the calculation results. In each case, we use program REACT and employ an extended form of the Debye-Hückel equation for calculating species' activity coefficients, as discussed in Chapter 7. In running REACT, you work interactively following the general procedure: • Swap into the basis any needed species, minerals, or gases. Table 6.1 shows the basis in its original configuration (as it exists when you start the program). You might want to change the basis by replacing SiO2(aq) with quartz so that equilibrium with this mineral can be used to constrain the model. Or to set a fugacity buffer you might swap CO2(g) for either H+ or HCO-3. • Set a constraint for each basis member that you want to include in the calculation. For instance, the constraint might be the total concentration of sodium in the fluid, the free mass of a mineral, or the fugacity of a gas. You may also set temperature (25°C, by default) or special program options. • Run the program by typing go. • Revise the basis or constraints and reexecute the program as often as you wish. In this book, input scripts for running the various programs are set in a "typewriter" typeface. Unless a script is marked as a continuation of the previous script, you should start the program anew or type reset to clear your previous configuration. For a first chemical model, we calculate the distribution of species in surface seawater, a problem first undertaken by Garrels and Thompson (1962; see also Thompson, 1992). We base our calculation on the major element composition of seawater (Table 6.2), as determined by chemical analysis. To set pH, we assume equilibrium with CO2 in the atmosphere (Table 6.3).

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.