Steps, elementary autocatalytic

In the bromate-iron clock reaction, there is an autocatalytic cycle involvmg the species intennediate species HBrO. This cycle is comprised of the following non-elementary steps ... 

Section 3 deals with reactions in which at least one of the reactants is an inorganic compound. Many of the processes considered also involve organic compounds, but autocatalytic oxidations and flames, polymerisation and reactions of metals themselves and of certain unstable ionic species, e.g. the solvated electron, are discussed in later sections. Where appropriate, the effects of low and high energy radiation are considered, as are gas and condensed phase systems but not fully heterogeneous processes or solid reactions. Rate parameters of individual elementary steps, as well as of overall reactions, are given if available. 

In this book we do not wish to limit ourselves to any specific reaction, so we will use a more general representation of a prototype autocatalytic sequence. If we have a reaction, or a sequence of elementary steps which provides a net conversion of a species A to B, we can use the representation... 

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). 

Reliable rate laws have been determined for processes (VI) (A)42, (B)43, and (C)45, and are collected in Table 4. A resolution of this reaction into its component elementary steps is not required for an understanding of how the oscillator is developed. What is important is that we identify the autocatalytic process, which is (VID) = (VIB) + 3 (VIC). 

The phenomenon of self organization occurs at nonstabHities of the sta tionary state and leads to the formation of temporal and spatio temporal dissipative structures. Remember that oscillating instabilities of stationary states of dynamic systems can be observed for the intermediate nonlinear stepwise reactions only, when no fewer than two intermediates are involved (see Section 3.5) and at least one of the elementary steps is kinet icaUy irreversible. The minimal sufficient requirements for the scheme of a process with temporal instabilities are not yet strictly formulated. However, in aU known examples of such reactions, the rate of the kineti caUy irreversible elementary reaction at one of the intermediate steps is at least in a quadratic dependence on the intermediate concentrations. Among these reactions are autocatalytic steps. 

Section 6 deals with the autocatalytic reactions of inorganic and organic compounds with molecular oxygen in the liquid phase, and the highly exothermic processes in the gas phase, collectively known as combustion, which may involve oxygen, other oxidants or decomposition flames and are so important technologically. Catalysis, retardation and inhibition are covered. The kinetic parameters of the elementary steps involved are given, when available, and the reliability of the data discussed. 

Molecular oxygen is the major cause of irreversible deterioration of hydrocarbon substrates, leading to the loss of useful properties and to the ultimate failure of the substrate. The oxidation process of hydrocarbons is autocatalytic oxidation starts slowly, sometimes with a short induction period, followed by a gradual increase in the rate, concomitant with the build up of hydroperoxides, which eventually subside, giving rise to a sigmoidal oxidation curve. When initiators such as peroxides are present, the length of the induction period is absent, or very short, but it can be prolonged by antioxidants, as shown in Fig. 1. The basic autoxidation theory of hydrocarbons involves a complex set of elementary reaction steps in a free radical-initiated chain reaction mechanism the basic tenets of this theory apply equally to polymer oxidation. 

Let us emphasize the following points in closing this description of a very generally useful reaction rate expression. First, the orders of reaction and have no necessary connection with the stoichiometric coefficients but must be determined experimentally. Second, they are, however, con-- jSj = and in the absence of autocatalytic effects by > 0- For an elementary step of a reaction, however, the order... 

Step (R3) determines the rate of the reaction via pathway (A). Step (R2) is crucial for the control of switching from pathway (A) to pathway (B). In reaction (G) HBr02 is autocatalytically produced via route (B). This is not an elementary reaction the rates of reaction (G) and process (B) are limited by step (R5)... 

The hydrogenation kinetics of cydohexene catalyzed by Pt2(dba)3 dispersed in BMI.PFg, BMI.BF4 and BMl,OTf are shown in Fig. 6.3. The kinetics curves were treated using the pseudo-elementary step and fitted (Eq. (6.1) by the following integrated rate equation for metal-salt decomposition (A —> B, hi) and autocatalytic nanoduster surface growth (A + B — 2B, 2). For a more detailed description of the use of the pseudo-elementary step for the treatment of hydrogenation kinetic data and derivation of the kinetic equations see elsewhere [81-83]. 

The autocatalytic elementary reaction step for CO oxidation is the removal reaction of CO from the catalyst surface. The presence of adsorbed CO suppresses the dissociative adsorption of O2, because vacant surface sites are required to accommodate the oxygen atoms that are generated by dissociated molecular oxygen. The CO2 removal reaction, on the other hand, is actually autocatalytic in vacant sites since a molecule of oxygen can ultimately remove two adsorbed CO molecules, thus freeing up two additional sites. 

First elementary reaction steps at an isolated reaction center have been considered and then the increasing complexity of the catalytic stem when several reaction centers operate in parallel and communicate. This situation is common in heterogeneous catalysis. On the isolated reaction center, the key step is the self repair of the weakened or disrupted bonds of the catalyst once the catalytic cycle has been concluded. Catalytic systems which are comprised of autocatalytic elementary reaction steps and communication paths between different reaction centers, mediated through either mass or heat transfer, may show self-organizing features that result in oscillatory kinetics and spatial organization. Theory as well as experiment show that such self-organizing phenomena depend sensitively on the size of the catalytic system. When the system is too small, collective behavior is shut down. 

Autocatalytic reactions in closed, homogeneous systems characteristically start slowly or at imperceptible speeds, accelerate to a maximum rate and then subside until all the material has been transformed. The most deeply studied example is the explosively rapid reaction between oxygen and hydrogen for which the observed rate is the consequence of a network of elementary steps with linear chain-branching. The acceleratory phase is dominated by the sequence HO + H2 -> H2O + H H + 02-> j O+H2 HO + H. The second of these three steps is the slowest, and at low temperatures it controls the rate. The overall stoichiometry corresponds to ... 

Next we analyse chemical reaction systems with autocatalytic steps in which the kinetic reaction terms may be non-linear functions of the concentrations of the intermediate species. We have in mind, once again, a reaction mechanism as shown in (4.11). We require that the number of X molecules changes by 1 or 0 in each elementary reaction step, and similarly for Y. For each set of [Xi, Yi) we can construct at each instance a thermodynamically and kinet-ically equivalent system the mapping from the non-linear to the equivalent linear system is unique. The linear equivalent system is chosen as shown in (5.26), but now the coefficients satisfy the relations given in Table 5.1. 

The cubic rate-law model presented here affords a prototype for many systems of practical interest, including solution-phase kinetics and enzyme reactions. It cannot be stressed too strongly that steps 1(a) and (b) do not have to be regarded as elementary steps. They may be combinations of such steps. Thus the reaction between arsenite and iodate ions, which is autocatalytic [9,10] in the production of r, is well approximated at constant pH by the rate expression... 

Table 6.6 lists some reaction schemes, that can lead to temporal or spatial oscillations all include an autocatalytic elementary step. The catalytic ojq dation of CO on Pt surfaces is a very well investigated process, where periodic patterns, that are characterized by surface reconstruction, can occm over time [147] (see Fig. 6.76). 

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