Kinetic autocatalysis

The first difference in a detonation wave which is favorable for stability is the fact that due to the decrease in the speed of sound (added to the mass velocity) to less than the propagation velocity, independence is achieved from the conditions behind the wave. On the other hand, application of small perturbations also leads to variation in the rate of the chemical reaction. It is impossible now to foresee the result of a calculation of stability with respect to small perturbations which might prove dependent on peculiarities of the chemical kinetics (autocatalysis, activation heat). 

Let us introduce a finite chemical reaction rate. One might think that the type of the chemical kinetics (autocatalysis or a classical reaction of some order) is in a certain sense not in itself essential autocatalysis changes the absolute value of the induction period and places it in dependence on small admixtures in the original mixture, but the form of the kinetic curve itself hardly changes since, in a classical reaction as well, with any significant activation heat one observes significant self-acceleration related to the increase in temperature. 

Miloserdov EM, McKay D, Munoz BK, Samouei H, Macgregor SA, Grushin VV (2015) Exceedingly facile Ph-X activation (X = E, Cl, Br, I) with Ru(II) arresting kinetics, autocatalysis, and mechanisms. Angew Chem Int Ed 6 8466-8470... 

Much of the early work was inconclusive confusion sprang from the production by the reaction of water, which generally reduced the rate, and in some cases by production of nitrous acid which led to autocatalysis in the reactions of activated compounds. The most extensive kinetic studies have used nitromethane,acetic acid, sulpholan,i and carbon tetrachloride as solvents. 

The kinetics of the reactions were complicated, but three broad categories were distinguished in some cases the rate of reaction followed an exponential course corresponding to a first-order form in others the rate of reaction seemed to be constant until it terminated abruptly when the aromatic had been consumed yet others were susceptible to autocatalysis of varying intensities. It was realised that the second category of reactions, which apparently accorded to a zeroth-order rate, arose from the superimposition of the two limiting kinetic forms, for all degrees of transition between these forms could be observed. 

The observation of two limiting kinetic forms was considered to be symptomatic of the occurrence of two reactions, designated non-catalytic and catalytic respectively. The non-catalytic reaction was favoured at higher temperatures and with lower concentrations of dinitrogen pentoxide, whereas the use of lower temperatures or higher concentrations of dinitrogen pentoxide, or the introduction of nitric acid or sulphuric acid, brought about autocatalysis. 

The kinetics of nitration of anisole in solutions of nitric acid in acetic acid were complicated, for both autocatalysis and autoretardation could be observed under suitable conditions. However, it was concluded from these results that two mechanisms of nitration were operating, namely the general mechanism involving the nitronium ion and the reaction catalysed by nitrous acid. It was not possible to isolate these mechanisms completely, although by varying the conditions either could be made dominant. 

Chloroanisole and p-nitrophenol, the nitrations of which are susceptible to positive catalysis by nitrous acid, but from which the products are not prone to the oxidation which leads to autocatalysis, were the subjects of a more detailed investigation. With high concentrations of nitric acid and low concentrations of nitrous acid in acetic acid, jp-chloroanisole underwent nitration according to a zeroth-order rate law. The rate was repressed by the addition of a small concentration of nitrous acid according to the usual law rate = AQ(n-a[HN02]atoioh) -The nitration of p-nitrophenol under comparable conditions did not accord to a simple kinetic law, but nitrous acid was shown to anticatalyse the reaction. 

The dependence of reaction rates on pH and on the relative and absolute concentrations of reacting species, coupled with the possibility of autocatalysis and induction periods, has led to the discovery of some spectacular kinetic effects such as H. Landolt s chemical clock (1885) an acidified solution of Na2S03 is reacted with an excess of iodic acid solution in the presence of starch indicator — the induction period before the appearance of the deep-blue starch-iodine colour can be increased systematically from seconds to minutes by appropriate dilution of the solutions before mixing. With an excess of sulfite, free iodine may appear and then disappear as a single pulse due to the following sequence of reactions ... 

Kinetic studies on the bulk polyesterification of a,o-dicarboxy poly(hexamethylene adipate) with a,polymeric medium. Solomon s mechanism1 can be considered as reasonable. 

Zollinger, 1981). In the presence of less than 5 ppb of 02 it obeys first-order kinetics in glass vessels, but zero-order kinetics in Teflon vessels. With between 60 and 100 ppb of 02, a fast initial reaction slackens off after about 15% conversion autocatalysis is observed on exposure to air, but in 100% 02 there is again a first-order reaction. 

Dean, A., Detailed kinetic modeling of autocatalysis in methane pyrolysis, J. Phys. Chem., 94, 1432, 1990. 

Autocatalysis is a special type of molecular catalysis in which one of the products of reaction acts as a catalyst for the reaction. As a consequence, the concentration of this product appears in the observed rate law with a positive exponent if a catalyst in the usual sense, or with a negative exponent if an inhibitor. A characteristic of an autocat-alytic reaction is that the rate increases initially as the concentration of catalytic product increases, but eventually goes through a maximum and decreases as reactant is used up. The initial behavior may be described as abnormal kinetics, and has important consequences for reactor selection for such reactions. 

To illustrate quantitatively the kinetics characteristics of autocatalysis in more detail, we use the model reaction... 

Several calculation methods for establishing reaction kinetics from the scanning DSC results are discussed in the literature [91-97]. Kinetic constants can be obtained from scanning DSC tests under favorable circumstances that include (1) the availability of a sample that even in milligram quantities is truly representative of the process material, and (2) kinetics that are uncomplicated by multiple reactions or by the presence of autocatalysis or inhibitor effects. 

Formaldehyde, in aqueous acidic solution, undergoes cyclotrimerization to trioxane (1,3,5-trioxacyclohexane), and also disproportionation to methanol and formic acid, with some resultant formation of methyl formate. The kinetic behaviour observed suggests a significant autocatalysis by formic acid. 

Useful reviews of the kinetics of autocatalytic reactions have recently been published by Mata-Perez and Perez-Benito (22) and by Schwartz Q2) For an autocatalytic reaction a plot of r/c, where r is the rate of reaction and c the concentration of reactant, as a function of c should be linear with a negative slope (22). When this analysis is applied to the possibility of autocatalysis of liquids production by LOG, no dependence of r/c on c was found. In fact, least uares "correlation coefficients were in the range 0.01 - 0.03. Although the initid hypothesis of autocatalysis by thiols is shown to be untenable, an alternative is the possibility of autocatalysis by H2S. 

Asymmetric autocatalysis has the following intrinsic merits (1) the efficiency is high because the process is automultiplication (2) in an ideal asymmetric autocatalysis, no decrease in the amount of catalyst and no deterioration of the catalytic activity should be observed because the amount of catalyst increases during the reaction and (3) there is no need to separate the catalyst from the product because their structures are identical. Frank proposed a kinetic model of asymmetric autocatalysis without mentioning a specific compound or reaction." ... 

ENCOUNTER-CONTROLLED RATE SECOND-ORDER REACTiON CHEMICAL KINETICS ORDER OF REACTION NOYES EQUATION MOLECULARITY AUTOCATALYSIS FIRST-ORDER REACTION... 

The approach of this work is to measure product compositions and mass balances in much detail in a time resolved manner and to relate this to the controlling kinetic principles and elemental reactions of product formation and catalyst deactivation. Additionally the organic matter, which is entrapped in the zeolite or deposited on it, is determined. The investigation covers a wide temperature range (250 - 500 °C). Four kinetic regimes are discriminated autocatalysis, retardation, reanimation and deactivation. A comprehensive picture of methanol conversion on HZSM5 as a time on stream and temperature function is developed. This also explains consistently individual findings reported in literature [1 4]. 

The mechanism of the asymmetric autocatalysis with amplification of has been examined experimentally by us171 and other groups172. It is basically understood that the aggregation of the isopropylzinc alkoxide of 5-pyrimidyl alkanol is involved in the reaction. Kinetic analysis of the reaction shows that the reaction is second order in the isopropylzinc alkoxide of 5-pyrimidyl alkanol171. 

Figure 21 shows a reaction scheme for the above reactions. The scheme also includes the distinct behavior under excess thiolate conditions, which reveals a faster adduct decomposition. The kinetics are complicated, showing induction periods that are indicative of autocatalysis through a chain reaction initiated by the RS(n-1)-radicals, Eq. (28) ... 

To quantify this idea in mathematical terms, we can recognize that we are really talking about the partial derivative quantities d(da/dt)/da and d(db/dt)/db. Stability has been associated in some sense with these two quantities being negative (i.e. da/dt decreases as a increases, so d(da/dt)/da < 0), instability with these being positive. In most normal chemical systems, e.g. those with deceleratory kinetics, the two partial derivatives will be negative. It is a characteristic of autocatalysis, however, that at least one of these may become positive — at least over some ranges of composition and experimental conditions. 

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). 

In the previous sections, the autocatalytic species B is only removed from the reactor by means of outflow or by conversion back to the original reactant A. We now consider the case where B can undergo an additional decay process, B - C, similar to that considered in the model of chapter 2. Returning to irreversible steps, the kinetic scheme becomes, for autocatalysis,... 

This situation stems from the peculiarities of the simplest representations of autocatalytic reactions, as discussed previously. In chapter 2, we considered a kinetic scheme in which the autocatalysis proceeded in parallel with an uncatalysed step A - B. We can expect that the inclusion of such a step here will have a strong influence on the behaviour at long residence times, as there will then always be a route from A to B. We consider this in the next section. 

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