Eliminating Measurement Dynamics From Kinetic Data

When analyzing data to evaluate a rate model, the dynamics of the measuring device must be distinguished from the effects of the rate process. This is of special concern to chemical engineers because the time constants and time delays of instruments used to measure chemical composition can be as large or larger than the time constants of the chemical reactions being studied. Researchers may use sophisticated instruments to mitigate this problem but the cost of such instruments often prohibits their use in the undergraduate laboratory. This paper presents an alternative approach. By developing a transfer function to describe the dynamics of the instrument, the effect of the instrument can be removed from the data mathematically. The specific application presented in this paper is the collection and analysis of kinetic data for the alkaline hydrolysis of methyl acetate. For this reaction, the rate can be monitored with an inexpensive pH meter. The transfer function for the meter was determined by fitting the constants in a second-order, lead-lag model to data from a series of step-change experiments. It was assumed that the pH in the batch reactor for each kinetic experiment could be described by a generic, four-parameter function x(t); the expected form of the kinetic rate expression was not used in selecting this function. The choice of the function was based on the observed shape of the pH versus time curve and the need to have a function with a simple Laplace transform. The transform of x(t) was multiplied by the transfer function for the meter and this product represents the transform of the observed pH. After taking the inverse of the product, the parameters in x(t) were determined for each experiment by fitting the model to the pH data. The correlation coefficients for all of the experiments were quite good so it was concluded that x(t) gave an accurate representation of pH in the reactor. The method was successful in eliminating the dynamics of the pH meter from the observed pH. Since the approach taken was not tailored to this specific application, the general methodology could be applied to other situations.