TJiermo~imica Acts, 25 (1978) 201-297 ~) ~ ~b:nti~ Publishing Compaany, Atr~tc=xlam - Printed in The Netherlands INTEGRATION OF THE RATE CONSTANT AND LINEARIZATION OF THE KINETIC EQUATIONS IN NON-ISOTHERMAL REACTION KINETICS GABOR VAR.H EGYI Hungarian Aetut,,my of Sciences. Re.~earch rnhoratory for Inorganic Chem£ttry, 1112 Budape_xt, B,,dn6r~i tit 45 (Huffy) (R__~_'ved 23 September 1977) ABSTRACT The theory of reaction rates gives approximations of the type A T b e -E/at for rate constants. In thermal analysis the case where b = 0 is used in kinetic calculations. However, if b is regarded as a variable, treatment of the non-isothermal kinetic equations is not more complicated than in the special case orb = 0. In this paper Pad~ approximations, described in the literature of the special functions, and Legendre's continued fractions are proposed for evaluation of the AJ'T b e -rmr d T inte~o~a!s. The Coats-Redfern type methods for the determination of the kinetic parameters are disc~ analysing the errors of approximation involved in their deduction. On this basis a modified parameter estimation scheme is proposed. INTRODUCTION In thermal analysis the widely used expression for the rate constant (k) is k = A c -EI~T (1) Application of eqn. (1) seems to be the most suitable way of describing the overall kinetics of reactions having a complex mechanism. The theory of unimolecular reactions, however, leads to the approximation k = A To -~lRr (2) while in the case of a solid + g~a~ - - .... type bimolecular reaction the expres_sion k = A T °-s e -Elxr (3) seems to b¢ more correct than ¢qn. (1). (Here the factor T °-5 is connected with the number of ga~ molecules colliding with the reaction surface in unit time). In thermoanalytical calculations the simplified eqn. (1) is used when uni- mol~'nlar dccmmposition or a solid + gas --* ... type reaction is claimed to be rate dctormining. Since eqns. (2) and 0) can be well approximated by eqn. (1) in a not too wide range and values ofEand A corresponding to eqns. (2) and (3) can be calculated