Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

18 EXPERIMENTAL METHODS FOR SLOW REACTIONS(c) Explosion limitsFor a given temperature, at high enough pressures, the exothermicity of thereaction leads to explosion. The critical concentration for the explosion limit ina spherical RV is given by7'f(C,) = ShRT;/VHk,Ee(TIwhere f(C,) is a function of the critical concentration equal to C: for an nth orderreaction, S/V is the surface to volume ratio, h is the heat transfer coefficient, R isthe gas constant (per mole), H is the exothermicity of the reaction, k, is the ratecoefficient for the reaction at the temperature To and E is the activation energy.For laminar convection h is given bywhere h is the coefficient of thermal conductivity of the gas mixture and t is theradius of the spherical RV. Substituting for h, S and V, we havef(C,) = 6hRT;/r2k,EH(V)This differs from the equation of Rice7' and Frank-Kamenet~kii~, by a factor of1.81. Their equation considers pure heat conduction only, and is as followsf(Cc) = 3.32hRT~/r2koEH(W)These equations predict the explosion limit for dtBP as 590 or 330 torr at 150" Cin a spherical RV with a radius of 5 cm7,.The phenomenon of explosion limits is best illustrated by reference to the H2 + 0,~ystern~'.~~. The rate of reaction of a stoichiometric mixture of H, and 0, isshown as a function of pressure in Fig. 10. At a pressure of - 2 torr, a slow steadyreaction occurs. At a certain critical pressure, a few torr, explosion occurs, thisbeing the first or lower limit PI or P,. Explosion is favoured by an increase in thediameter of the RV and by added inert gases, since the surface plays an importantrole in chain termination processes and these gases hinder diffusion to the walls.The nature of the surface will also be important (see p. 11). Starting at 200 torrand reducing the initial pressure, normal reaction proceeds until at N 100 torrexplosion again occurs. This is the second or upper limit P, or Pu. At very muchhigher pressures another limit is reached which is known simply as the third limitP,. Here explosion is probably both a chain-branching and thermal process, andoccurs at several hundred torr. The limits are shown as a function of temperatureand pressure in Fig. 11.There are three main techniques for mzasuring explosion limits in static systems.