A Nonlinear Ordinary Differential Equation for Generating Graphical Rate Equations from Concentration Versus Time Data

When reaction progress kinetic analysis is implemented on data obtained using a spectroscopic or chromatographic technique such as ATR–FTIR, NMR, absorbance spectroscopy, HPLC or GC, an initial step involves fitting a mathematical function to the experimental concentration versus time data. This function is then differentiated to give graphs of rate versus substrate concentration (graphical rate equations). It is important that the function be able to accurately describe the experimental data without introducing bias or artifacts. Here, we put forward a nonlinear ordinary differential equation that can be fitted to experimental concentration versus time data for applications in reaction progress kinetic analysis. We show that it can be applied to data from catalytic transformations showing diverse types of kinetic behavior.