A rigorous method was developed to account for nonuniform temperature distributions in the analysis of kinetic data. The rate constants cannot be determined directly since they are functions of temperature, so equations were derived and solutions developed for the substantially temperature independent kinetic parameters, activation energy, and pre-exponential factor. A digital computer was used to evaluate numerically various integrals involved in the solution of the equations. The method developed here will be useful in all laboratory kinetic studies where limitations of heat transfer do not permit an isothermal experiment and in the analysis of kinetic data obtained from commerical or pilot plant units where the temperature distribution is nearly always nonuniform.

Kinetic studies were made of the thermal decompositions of ethane, ethylene, and acetylene, all of which are high temperature fast reactions. The experimental conditions covered highly nonuniform temperature distributions with peaks from 730° to 1,330°C., a total pressure of 1 atm., varying amounts of nitrogen dilution, and residence times in the millisecond range.