Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

4 THE SOLID-SOLID INTERFACE 259and the other symbols have their usual meaning. By various transformations, anexpression is obtained which suggests that the reaction order, n, is related to thequantity of material not reacted at T,. From the variation in the quantity reactedwith T,,, , Kissinger proposed the shape index shown in Fig. 43 to estimate the orderof reaction. Changes in the activation energy and frequency factor only have asmall effect on the shape of the curve. From the ratio of the slopes at the inflectionpoints'(see Fig. 43b) where the reaction rate is constant, the reaction order can becalculated from the expressionn = 1.26S*where the shape index (S) = a/b.A basic assumption in Kissinger's analysis is that reaction occurs equally in allparts of the specimen. Disagreement between the results of various authors showsthat this assumption is not generally true and the results are particularly influencedby particle size and sample geometry. Borchardt and Daniels351 have derived anexpression forre]'-'*the rate coefficient (k) derived from a DTA curvek = C,dATldt -k KAT[K(A-a)-CPATlXwhere x is the order of reaction, K is the heat transfer coefficient of the samplecell, A is the total area under the curve, ct is the area swept out in time t, Vis thevolume of reactant and No the number of moles initially present. Cp is the specificheat of the sample at constant pressure and ATis the temperature difference betweenthe sample and reference material. The quantities a, AT and dAT/dt are measuredfrom the DTA curve as shown in Fig. 44.Fig. 4 4.Determination of rate coefficients from the DTA curve. At time t, a is the area swept out,AT is the temperature difference and dATjdr is the slope of the curve. From ref. 351.References pp. 270-278