Temperature Gradients in Reacting Systems

Abstract

A study of the heat conduction equation for reactions going on in a spherical flask leads to a calculation of three parameters, 1" the mean lifetime for the establishment of stationary states, AT m the maximum temperature difference between the walls of the vessel and the reacting gas, and the average temperature difference (AT m)Av. These are given by pCvr02 RHr02in which p is the density, Cv the specific heat at constant volume, ro the radius of the vessel, K the coefficient of thermal conductivity, R the specific rate of reaction, and H the heat of reaction.In liquid systems under usual conditions 1" is of the order of r02 minutes (ro in cm) while (AT m)Av is about ±O.2°C (for H = ±1O kcal, half-life = 1 hour, ro= 5 cm) so that such effects are usually negligible. In gases on the other hand (AT m)Av can be of the order of magnitude of 2°C or higher depending on the various conditions, resulting in significant errors in observed rate constants and activation energies. The effects of added inert gases, pressure, vessel packing, and other parameters are discussed. A very crude treatment of convection shows that it is not expected to alter appreciably the magnitude of (AT m)Av.