Kinetic rate equations, deceleratory

Galwey and Hood [160] showed that NajCOj.l.SHjOj decomposed in vacuum (360 to 410 K) to produce Na COj + l.SHjO + O.TSOj. ar-time curves were sigmoidal and the kinetics could be described by the Avrami-Erofeev equation with = 2 or 3. The activation energy was 112 8 kJ mol. The reaction rate between 313 and 343 K was significantly increased by the presence of small amounts of liquid water. This deceleratory reaction was fitted by the first-order equation (E, = 80 10 kJ mol ) and it was concluded that breakdown of hydrogen peroxide proceeded in the liquid water, possibly with trace amounts of impurity transition-metal ions acting as catalysts. 

Isothermal TG studies [33] of the thermal decompositions in Nj of BaOj (763 to 883 K) and SrOj (653 to 803 K) showed overall deceleratory kinetics described by the Ginstling-Brounshtein diffiision model (low a) and the first-order equation at higher nr values, is, values were 185 5 kJ mol for BaOj and 119 2 kJ mol for SrO. Non-isothermal kinetic analyses gave similar is, values for both decompositions (165 5 kJ mol ). It is suggested [33] that the rate of removal of oxygen from the peroxide by diffusion could be drastically altered by the formation of a crystalline layer of oxide on the reactant surface. 

The r-time curves for the decomposition of anhydrous cobalt oxalate (570 to 590 K) were [59] sigmoid, following an initial deceleratory process to a about 0.02. The kinetic behaviour was, however, influenced by the temperature of dehydration. For salt pretreated at 420 K, the exponential acceleratory process extended to flr= 0.5 and was followed by an approximately constant reaction rate to a = 0.92, the slope of which was almost independent of temperature. In contrast, the decomposition of salt previously dehydrated at 470 K was best described by the Prout-Tompkins equation (0.24 < a< 0.97) with 7 = 165 kJ mol . This difference in behaviour was attributed to differences in reactant texture. Decomposition of the highly porous material obtained from low temperature dehydration was believed to proceed outwards from internal pores, and inwards from external surfaces in a region of highly strained lattice. This geometry results in zero-order kinetic behaviour. Dehydration at 470 K, however, yielded non-porous material in which the strain had been relieved and the decomposition behaviour was broadly comparable with that of the nickel salt. Kadlec and Danes [55] also obtained sigmoid ar-time curves which fitted the Avrami-Erofeev equation with n = 2.4 and = 184 kJ mol" . The kinetic behaviour of cobalt oxalate [60] may be influenced by the disposition of the sample in the reaction vessel. 

The isothermal kinetics of decomposition were complex, with at least two overlapping processes taking place. The shapes of the peaks indicated that both processes were initially acceleratory, and then deceleratory. The isothermal rate was assumed to be made up of weighted contributions from individual processes which could be described by the Avrami-Erofeev equation, with various values of n. 

There are no fundamental reasons that could prevent the application of these vaporization equations to cases of thermal decomposition (dissociative vaporization) of a substance, except for the requirement that the rate J must be measured under a steady-state decomposition mode, corresponding to the deceleratory period in the a—t kinetic curve. 

It is possible, however, to extend the ideas already presented to cover these interesting situations better. The form of the rate-law is supposed to obey dX/dt = k f(X), where X is the fractional concentration and k is a rate-coefficient satisfying the Arrhenius equation with k exp(-E/RT). Procedures can be illustrated for deceleratory first-order kinetics for which f(X) = X and m = 1. (Other cases involve only a different intermediate numerical calculation.) The details have been set out by Boddington et al. [12]. Two temperature-excesses need to be... 

---