Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

12 EXPERIMENTAL METHODS FOR SLOW REACTIONSwhere h is the coefficient of thermal conductivity, p is the density, cv is the heatcapacity of the gas at constant volume, Q is the specific rate of the reaction andH is the molar heat of reaction. If concentration and density gradients are small,this equation reduces toaT/at = hV2T/pc,.+QH/pcv(J)Here it is assumed that h and c, do not change appreciably with time or positionin the vessel and that convection is negligible. For a spherical vessel of radius r,the maximum temperature difference AT,,, is given by5*AT,,, = QHr2/6h(K)Averaged over the vessel, this becomesATav = O.4ATm,, = QHr2/15h(L)If r is 5 cm and we consider the decomposition of di-tert.-butyl peroxide at160" C' (H = 40 kcal.mo1e-', at 5 x M (100 mm Hg), Q = 2.5 x mole.~m-~. sec-l and h = loF4 cal. cm.-'. sec-I), we find a significant temperaturedifference given byATav = r2/15 = 1.67"(MIThe time taken for the thermal gradient to be set up is given byt = r2pCv/n2RTh(N)where p is the pressure at a temperature T, Cv is now the molar heat capacity atconstant volume, and R is the gas constant in cal.mole-'.deg-'. With C, = 6 cal.mole-'.deg-', a thermal gradient is established in one second. However, if r isreduced to 0.5 cm, ATav turns out to be two powers of ten lower, which is negligible.This effect was studied by Batt and Benson', when it was shown that asignificant difference occurs between the two sets of Arrhenius parameters obtainedusing spherical and octopus-shaped RV's respectively.(b) Pressure measurementDirect pressure measurements may be made with conventional manometers usingmercury, silicone oils, hydrocarbon oils, butyl phthalate and other fluids.Apart from the danger of their affecting the reaction studied directly, by chemicalreaction, vapour adsorption or modifying the surface of the RV, they produce avarying "dead space". It is important to keep the "dead space" between 1 and 4 %