Errors in Determining the Rate Constant of a First-order Gaseous Reaction by the Flow Method

Abstract

The rate constant of a gaseous reaction calculated from data obtained by the conventional flow method is subject to errors arising from departures from piston flow and thermal equilibrium in the reaction tube. An approximate theoretical analysis of the errors is given for the first-order pyrolysis or isomerization of an organic vapour. In the case of a reaction occurring near 1000°K in a tube 2 cm in diameter, it is shown that for the measured value of the rate constant to be accurate within about 10% the experimental conditions should be such that z > t_c/p > 0.5, where p cmHg is the total pressure and t_c sec the average contact time. The upper limit (z) of t_c/p increases from 3 under conditions of 50% conversion to 10 at 25% and ∞ at 0%. The analysis is applied to measurements of the rate of pyrolysis of toluene. Lack of thermal equilibrium could be at least partly responsible for the observed effect of contact time on the rate constant but does not account for the effect of pressure. The error incurred by assuming piston flow in an isothermal reactor when in fact viscous flow is occurring is discussed in the Appendix.