Prout-Tompkins equation

This is known as the Prout—Tompkins equation and has found application to many systems, in addition to the thermal decomposition of potassium permanganate [465] with which it is often associated. The kinetic behaviour of silver permanganate was somewhat different and in a variation of... 

The kinetics and mechanism of vacuum decomposition of AgMn04 at 378—393 K [466] are believed to differ from the behaviour of KMn04 in that the effective chain branching coefficient diminishes with time and this leads (Chap 3, Sect. 3.2) to the modified form of the Prout—Tompkins equation... 

Bircumshaw and Edwards [1029] showed that the rate of nickel formate decomposition was sensitive to reactant disposition, being relatively greater for the spread reactant, a—Time curves were sigmoid and obeyed the Prout—Tompkins equation [eqn. (9)] with values of E for spread and aggregated powder samples of 95 and 110 kJ mole-1, respectively. These values are somewhat smaller than those subsequently found [375]. The decreased rate observed for packed reactant was ascribed to an inhibiting effect of water vapour which was most pronounced during the early stages. 

References to a number of other kinetic studies of the decomposition of Ni(HC02)2 have been given [375]. Erofe evet al. [1026] observed that doping altered the rate of reaction of this solid and, from conductivity data, concluded that the initial step involves electron transfer (HCOO- - HCOO +e-). Fox et al. [118], using particles of homogeneous size, showed that both the reaction rate and the shape of a time curves were sensitive to the mean particle diameter. However, since the reported measurements refer to reactions at different temperatures, it is at least possible that some part of the effects described could be temperature effects. Decomposition of nickel formate in oxygen [60] yielded NiO and C02 only the shapes of the a—time curves were comparable in some respects with those for reaction in vacuum and E = 160 15 kJ mole-1. Criado et al. [1031] used the Prout—Tompkins equation [eqn. (9)] in a non-isothermal kinetic analysis of nickel formate decomposition and obtained E = 100 4 kJ mole-1. 

The Prout—Tompkins equation [eqn. (9)] was obeyed (E = 169 kJ mole-1). The first step in the reaction was identified as... 

The rate equation [eqn. (26)], given above for the reaction of magnesium oxalate, is also obeyed [1012] by the decomposition of zinc oxalate (620—646 K), although here the catalytic (second) term is dominant, so that behaviour approximated to the Prout—Tompkins equation [eqn. (9)]. The value of E (201 8 kJ mole 1) was the same as that found... 

The a—time curves for the vacuum decomposition at 593—693 K of lanthanum oxalate [1098] are sigmoid. Following a short induction period (E = 164 kJ mole-1), the inflexion point occurred at a 0.15 and the Prout—Tompkins equation [eqn. (9)] was applied (E = 133 kJ mole-1). Young [29] has suggested, however, that a more appropriate analysis is that exponential behaviour [eqn. (8)] is followed by obedience to the contracting volume equation [eqn. (7), n = 3]. Similar kinetic characteristics were found [1098] for several other lanthanide oxalates and the sequence of relative stabilities established was Gd > Sm > Nd > La > Pr > Ce. The behaviour of europium(III) oxalate [1100] is exceptional in that Eu3+ is readily reduced... 

In an inert atmosphere, the decomposition at 573—623 K of uranyl(VI) oxalate [1101] obeys the Prout—Tompkins equation [eqn. (9)] with E = 261 4 kJ mole-1. The residual product is U02 and, under low pressure accumulatory conditions, the final CO2/CO ratio is 9. In air, the reaction proceeds in two stages. The initial process obeys the Prout—Tompkins equation and is identified as a surface reaction. Thereafter, decomposition fits the Avrami—Erofe ev equation [eqn. (6), n = 2], involving isolated disc-like grains of reactant, to yield amorphous U03 as the final product. Values of E for both stages of reaction are close to that found for reaction in the inert atmosphere ( 260 kJ mole-1) and comparable with theoretical predictions [88],... 

The predominant gaseous products of the decomposition [1108] of copper maleate at 443—613 K and copper fumarate at 443—653 K were C02 and ethylene. The very rapid temperature rise resulting from laser heating [1108] is thought to result in simultaneous decarboxylation to form acetylene via the intermediate —CH=CH—. Preliminary isothermal measurements [487] for both these solid reactants (and including also copper malonate) found the occurrence of an initial acceleratory process, ascribed to a nucleation and growth reaction. Thereafter, there was a discontinuous diminution in rate (a 0.4), ascribed to the deposition of carbon at the active surfaces of growing copper nuclei. Bassi and Kalsi [1282] report that the isothermal decomposition of copper(II) adipate at 483—503 K obeyed the Prout—Tompkins equation [eqn. (9)] with E = 191 kJ mole-1. Studies of the isothermal decompositions of the copper(II) salts of benzoic, salicylic and malonic acids are also cited in this article. 

Silver oxide An early (1905) study by Lewis [34] of the kinetics of decomposition of Ag20 was a notable contribution. The dissociation in oxygen (760 Torr, 593 to 623 K) showed a long induction period followed by a sigmoid nr-time curve which fitted the Prout-Tompkins equation with = 133 kJ mol. Benton and Drake [35] studied the kinetics of the reversible dissociation using a sample of finely-divided active metal. The rate of reaction at 433 K fitted the expression ... 

The decomposition of LiACH4 involves an initial rate process which may arise from impurities [23] (either >A -OH + H-AC< - >Af-0-A < + or an organometallic compound). The possibility of melting was mentioned. When the contribution from the initial process had been subtracted, the subsequent isothermal reaction between 400 and 432 K gave sigmoid or-time curves that were fitted by the modified Prout-Tompkins equation and E, was about 100 kJ mol. The third stage in the... 

Decompositions of the compounds [M(SCH3)2] (n(CH3)2S + nMS where M is Zn or Cd) fitted the first-order or Prout-Tompkins equations with = 143 to 191 kJ mol [53,54], Kinetic behaviour depended upon the surface area of the reactant. 

Rienaecker and Werner [36] suggested that Baj(Mn04)2 is the initial decomposition product, by analogy with results for KMn04- Isothermal ar-time curves for vacuum decomposition at 413 to 463 K were sigmoid [37] following an initial (or= 0.04) burst of gas. The acceleratory process was fitted by the Prout-Tompkins equation ( , = 151 kJ mol ) and the power law with = 2. Fragmentation into thin platelets was observed. The deceleratory period could be described by the first-order equation with , = 124 kJ mol. ... 

The kinetics of decomposition of AgMn04 in vacuum between 378 and 393 K [38] differ fi om the behaviour of KMn04 in that the acceleratory periods of the ar-time curves are described by the modified form of the Prout-Tompkins equation ... 

The first two reactions give sigmoid ur-time curves that are well expressed by the Prout-Tompkins equation. These are believed to involve a branching-chain mechanism. The third process is fitted by the contracting volume equation, possibly due to decomposition through ion-pair evaporation. The thermal stabihty of N02CJ04 is decreased [42] by the incorporation of impurities which increase the mnnber of cation vacancies, whereas the creation of anion vacancies has the opposite effect. 

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