Kinetic Reaction Paths

In kinetic reaction paths (discussed in Chapter 16), the rates at which minerals dissolve into or precipitate from the equilibrium system are set by kinetic rate laws. In this class of models, reaction progress is measured in time instead of by the nondimensional variable . According to the rate law, as would be expected, a mineral dissolves into fluids in which it is undersaturated and precipitates when supersaturated. The rate of dissolution or precipitation in the calculation depends on the variables in the rate law the reaction s rate constant, the mineraTs surface area, the degree to which the mineral is undersaturated or supersaturated in the fluid, and the activities of any catalyzing and inhibiting species. 

In this chapter we consider the problem of the kinetics of the heterogeneous reactions by which minerals dissolve and precipitate. This topic has received a considerable amount of attention in geochemistry, primarily because of the slow rates at which many minerals react and the resulting tendency of waters, especially at low temperature, to be out of equilibrium with the minerals they contact. We first discuss how rate laws for heterogeneous reactions can be integrated into reaction models and then calculate some simple kinetic reaction paths. In Chapter 26, we explore a number of examples in which we apply heterogeneous kinetics to problems of geochemical interest. 

To formulate a kinetic reaction path, we consider one or more minerals A whose rates of dissolution and precipitation are to be controlled by kinetic rate laws. We wish to avoid assuming that the minerals A- are in equilibrium with the... 

The procedure for tracing a kinetic reaction path differs from the procedure for paths with simple reactants (Chapter 13) in two principal ways. First, progress in the simulation is measured in units of time t rather than by the reaction progress variable . Second, the rates of mass transfer, instead of being set explicitly by the modeler (Eqns. 13.5-13.7), are computed over the course of the reaction path by a kinetic rate law (Eqn. 16.2). 

In an example of a kinetic reaction path, we calculate how quartz sand reacts at 100 °C with deionized water. According to Rimstidt and Barnes (1980), quartz reacts according to the rate law,... 

Fig. 16.2. Results of reacting albite at 70 °C with an NaCl solution maintained at pH 1.5, calculated as a kinetic reaction path. Top diagram shows how the saturation index of albite varies with time bottom plot shows change in amount (mmol) of albite.

In this chapter we construct a variety of kinetic reaction paths to explore how this class of model behaves. Our calculations in each case are based on kinetic rate laws determined by laboratory experiment. In considering the calculation results, therefore, it is important to keep in mind the uncertainties entailed in applying laboratory measurements to model reaction processes in nature, as discussed in detail in Section 16.2. 

Fig. 26.6. Variation in mineral volumes over a kinetic reaction path designed to illustrate Ostwald s step sequence. The calculation traces the reaction at 25 °C among the minerals amorphous silica (tine line), cristobalite (medium line), and quartz (bold line). The top diagram shows results plotted against time on a linear scale the time scale on the bottom diagram is logarithmic. The decrease in total volume with time reflects the differing molar volumes of the three minerals.

To incorporate nonlinear rate laws into the solution procedure for tracing kinetic reaction paths (Section 16.3), we need to find the derivative of the reaction rate with respect to the molalities m,- of the basis species A,. The derivatives are given by,... 

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