Deceleratory reaction

Magnitudes of n have been empirically established for those kinetic expressions which have found most extensive application e.g. values of n for diffusion-limited equations are usually between 0.53 and 0.58, for the contracting area and volume relations are 1.08 and 1.04, respectively and for the Avrami—Erofe ev equation [eqn. (6)] are 2.00, 3.00 etc. The most significant problem in the use of this approach is in making an accurate allowance for any error in the measured induction period since variations in t [i.e. (f + f0)] can introduce large influences upon the initial shape of the plot. Care is needed in estimating the time required for the sample to reach reaction temperature, particularly in deceleratory reactions, and in considering the influences of an induction period and/or an initial preliminary reaction. 

This deceleratory reaction obeyed the parabolic law [eqn. (10)] attributed to diffusion control in one dimension, normal to the main crystal face. E and A values (92—145 kJ mole-1 and 109—10,s s-1, respectively) for reaction at 490—520 K varied significantly with prevailing water vapour pressure and a plot of rate coefficient against PH2o (most unusually) showed a double minimum. These workers [1269] also studied the decomposition of Pb2Cl2C03 at 565—615 K, which also obeyed the parabolic law at 565 K in nitrogen but at higher temperatures obeyed the Jander equation [eqn. (14)]. Values of E and A systematically increased... 

Singh and Palkar [726] identified an initial deceleratory reaction in the decomposition of silver fulminate. This obeyed first-order kinetics (E = 27 kJ mole-1) and overlapped with the acceleratory period of the main reaction, which obeyed the power law [eqn. (2), n = 2] with E = 119 kj mole-1. The mechanism proposed included the suggestion that two-dimensional growth of nuclei involved electron transfer from anion to metal. 

As well as deceleratory reactions, kineticists often find that some chemical systems show a rate which increases as the extent of reaction increases (at least over some ranges of composition). Such acceleratory, or autocatalytic, behaviour may arise from a complex coupling of more than one elementary kinetic step, and may be manifest as an empirically determined rate law. Typical dependences of R on y for such systems are shown in Figs 6.6(a) and (b). In the former, the curve has a basic parabolic character which can be approximated at its simplest by a quadratic autocatalysis, rate oc y(l - y). 

The curves in Fig. 5.1(b) with n + I art non-linear but do share the feature that the rate is highest at the beginning of the reaction ( = 0) and the rate decreases monotonically in each case as the extent of reaction increases. This feature is characteristic of deceleratory reactions. As the number of elementary steps and intermediate species (particularly if these involve reactive species such as radicals) increases, so the possibility of more interesting shapes for the reaction rate curve increases. Two such interesting shapes are illustrated in Fig. 5.1(c). These are characteristic of reactions that display an acceleratory phase at low extents of reaction before attaining a maximum prior to a final deceleratory phase at high extents at the end of the reaction as the state of chemical equilibrium is... 

Fig. 5.1. Variation of reaction rate R with extent of reaction (a) linear relationship for first-order reaction (b) non-linear deceleratory reactions of overall order n (c) reactions showing chemical feedback in the form of autocatalysis (d) comparison of chemical and...

Isothermal and non-isothermal kinetic experiments on the dehydration of (NH4)2C204.H20 were compared [142] using multiple sets of data. Isothermal experiments identified the contracting area expression as giving the best fit for the predominantly deceleratory reaction and , = 73 kJ mol". Different expressions were identified (A1.5, A3 or D3) using rising temperature methods. 

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. 

Singh and Palkar [71] studied the decomposition of silver fulminate across the interval 463 to 483 K. The initial deceleratory reaction (E, = 27 kJ mol" ) was much more significant than the corresponding process in the mercury salt and overlapped with the onset of the subsequent acceleratory process, which fitted the power law, with n = 2 and = 119 kJ mol. The suggested mechanism is an initial electron-transfer step from the anion to the product metal during the two-dimensional advance of the interface. 

The decomposition of copper(II) squarate, as with the copper(II) carboxylates, proceeded to completion in two distinct rate processes with stepwise cation reduction [113]. The first step (nr < 0.5) fitted zero-order kinetics withii = 150 15 kJ mof between 530 and 590 K. The second step was approximately first-order with an increase in to 210 20 kJ mol and reaction temperature, 590 to 670 K. No reaction interface could be identified in scanning electron microscopic studies. Silver squarate decomposed [114] between 473 and 510 K without melting, by a predominantly deceleratory reaction with E = 190 8 kJ mol. ... 

Nickel maleate decomposed [121] in a sli tly lower temperature range (543 to 583 K, , = 188 12 kJ mol ) by a deceleratory reaction. It was concluded that the reaction rate was controlled by maintained nucleation involving the continual formation of nickel particles, the growth of which was inhibited by the deposition of carbonaceous residues. 

Isothermal ur-time curves (340 to 393 K) showed an induction period followed by a deceleratory reaction which could be described by the contracting volume equation with a discontinuity at or = 0.35. The value of (71 kJ moT ) for this step was close to the enthalpy of dissociation and the apparent energy barrier to the difihision-controlled reammination reaction was small (about 8 kJ mol ). The energy barrier to deammination was identified [41] as rupture of the cation-ligand bond. The subsequent irreversible breakdown of the diammine (above 513 K) yielded residual NiO and the kinetics were comparable in some respects with the decomposition of NH4CIO4. 

Let us assume a simple first-order deceleratory reaction in the CSTR with kinetic rate constant k = The overall rate of reaction at the steady state... 

We may generalize the treatment to any deceleratory reaction of order m, and when the exothermicity is large it is the quotient (B/m) that is important in describing the increase in from its zero-order value e. Rather roughly. 

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