Data Fitting Techniques with Applications to Mineral Dissolution Kinetics

A common problem in chemical kinetics is the development of a rate law that describes the dependence of the reaction rate on the surrounding conditions such as concentrations of reacting species or temperature of the reacting media (see Chap. 1). The most direct approach to solving this problem is to measure reaction rates under systematically varied conditions and then to perform mathematical analyses on these data to determine the form of the rate law and to generate estimates of any unknown constants, or parameters, that make up the proposed rate law. Other chapters in this book provide information both for designing kinetics experiments and for selecting appropriate rate laws for a variety of geochemical reactions. In this chapter we describe the mathematical analyses – known collectively as curve fitting or regression analysis – that can be used to select a rate equation that matches a given data set, to generate estimates for any unknown parameters in the rate equation (e.g., rate constants or reaction orders), and to quantify the uncertainty associated with the estimated values for the parameters. As we traverse this entirely quantitative process we will attempt to describe the underlying, qualitative process of looking at kinetic data: plots to make, features of these plots to examine, and conceptual sketches to draw. In order to fit a curve to data one must first obtain the data. Over the past few decades, researchers have produced numerous high quality studies on the kinetics of mineral dissolution and the effects of experimental conditions such as pH, temperature, concentration of dissolved metal ions, mineral composition, etc. We have compiled this dissolution rate data for a number of rocks and minerals including apatite, basalt, biotite, hornblende, kaolinite, olivine, plagioclase, potassium feldspar, pyroxene, and quartz. We will use these data, which are available in Appendix I of