Data Fitting Techniques with Applications to Mineral Dissolution Kinetics
Data Fitting Techniques with Applications to Mineral Dissolution Kinetics
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DOI：
10.1007/978-0-387-73563-4_6
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
J. Bandstra;S. Brantley
中科院分区：
文献类型：
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作者：
J. Bandstra;S. Brantley
化学动力学中的一个常见问题是速率定律的发展，该定律描述了反应速率对周围条件的依赖性，例如反应物质的浓度或反应介质的温度（见第11章）。1）。解决这个问题的最直接的方法是在系统变化的条件下测量反应速率，然后对这些数据进行数学分析，以确定速率定律的形式，并生成构成拟议速率定律的任何未知常数或参数的估计值。本书的其他章节提供了设计动力学实验和为各种地球化学反应选择适当速率定律的信息。在本章中，我们描述了数学分析-统称为曲线拟合或回归分析-可用于选择与给定数据集匹配的速率方程，以生成速率方程中任何未知参数的估计值（例如，速率常数或反应级数），并量化与参数估计值相关的不确定性。当我们遍历这个完全定量的过程时，我们将试图描述观察动力学数据的基本定性过程：绘制曲线，检查这些曲线的特征，绘制概念草图。
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.