Determination of Reaction Rates by the Use of Cubic Spline Interpolation

TLDR: In this paper, the cubic spline interpolation method is used for kinetic data analysis, and its application to experimental data is demonstrated and its performance is quantitatively compared with better known but less accurate methods.

Abstract: The differential method of van't Hoff is a powerful method for kinetic data analysis if accurate rates of reaction can be found. Differentiation methods reported in the literature are inadequate, particularly when applied to data which is unequally spaced or which is subject to random error. A need is therefore expressed for a general numerical method of differentiation which can be readily applied in kinetic analysis. This paper suggests the use of the cubic spline, an interpolation method which overcomes the difficulties of other methods and gives exceptionally accurate derivatives. The theory of the cubic spline, its properties, and uses are discussed. Its application to experimental data is demonstrated and its performance is quantitatively compared with better known but less accurate methods.