Irreversible reaction step

For a single, elementary, irreversible, reaction step, d> is given by equation (3) and equations (4) and (14) imply that... 

Initially, the algorithm considers each individual reaction step as a partial mechanism. Then, one intermediate after another are examined, and the set of partial mechanisms is modified so that the intermediate does not appear in the net stoichiometry the modification of mechanisms is carried out in a way that preserves the correct direction of irreversible reaction steps. By processing all intermediates in this way, a set of overall mechanisms is constructed. This final set of mechanisms might include duplicate mechanisms and even indirect ones these can be easily discarded. Similar action must be taken in the procedure of H S. Mavrovouniotis (1992) discusses procedures for eliminating such redundant mechanisms in the end, or even preventing their construction. 

Parallel reactions single and consecutive-irreversible reaction steps. 

PARALLEL REACTIONS SINGLE AND CONSECUTIVE IRREVERSIBLE REACTION STEPS... 

The irreversible reaction step was assumed to be the Umiong step. We check this mechanism and rate limiting step by rearrangmg and combining the rate laws for each step. If the mechanism is correct, we will obtam the rate law proposed in part c-... 

Figure 6.15. Ping-pong mechanism with quasi-equilibria binding steps and irreversible reaction steps.

The derivation of rate equations for simultaneous hydrogenation of TMP-aldol and formaldehyde was based on a plausible surface reaction mechanism. According to the mechanism, the aldol, formaldehyde and hydrogen undergo competitive adsorption on the nickel-alumina surface. Adsorbed hydrogen atoms add to the carbonyl bonds of the aldol and formaldehyde. These irreversible reaction steps are presumed to be rate-determining, whereas the product desorption is regarded as rapid. Consequently, the reaction mechanism is written as follows ... 

Distinction can be made between three categories of MCR [7j. Type I MCRs are sequences of reversible reactions whereas type II MCRs are sequences of reversible reactions that are terminated by an irreversible reaction step. Finally, type III MCRs are sequences of irreversible elementary reactions. 

The difference in the timescales of the methane and CO transients implies that CO hydrogenation proceeds with at least one slow irreversible reaction step via a pool of surface intermediates. At... 

It should be noted that some physicochemical assumptions are overlapping and some are complimentary. For example, assuming that some steps are fast automatically means assuming that other steps are slow. In the simplest case—the two-step mechanism—the assumption of a fast first step is identical to the assumption of a rate-limiting second step. Assumptions on the abundance of species and rate-limiting steps can be made both for reversible and irreversible reaction steps. In contrast, the quasiequilibrium assumption cannot be applied to a set of reaction steps that are all reversible. Sometimes many assumptions, not just one or two, are used for the development of a model. An example is the Michaelis-Menten model, which is well known in biocatalysis. In this model, for which the mechanism is shown in Fig. 4.1, the total amount of... 

In theory, aU thermal elementary reactions are reversible, which means that the reaction products may react with each other to reform the reactants. Within the terminology used for reaction kinetics simulations, a reaction step is called irreversible, either if the backward reaction is not taken into account in the simulations or the reversible reaction is represented by a pair of opposing irreversible reaction steps. These irreversible reactions are denoted by a single arrow Reversible reaction steps are denoted by the two-way arrow symbol within the reaction step expression In such cases, a forward rate expression may be given either in the Arrhenius or pressure-dependent forms, and the reverse rate is calculated from the thermodynamic properties of the species through the equilibrium constants. Hence, if the forward rate coefficient kf. is known, the reverse rate coefficient can be calculated fmm... 

Like all other chemical reactions, polymer syntheses may be subdivided into two categories, namely into kinetically controlled (KC) polymerizations and thermodynamically controlled (TC) polymerizations. KC polymerizations are characterized by irreversible reaction steps, equilibration reactions are absent, and the reaction products may be thermodynamically stable or not. TC polymerizations involve rapid equilibration reactions, above all formation of cyclics by back-biting of a reactive chain end (see Formula 5.1), and the reaction products represent the thermodynamic optimum at any stage of the polymerization process. Borderline cases also exist, which means that a rapid KC polymerization is followed by slow equilibration. This combination is typical for many Ring-opening polymerizations (ROPs). 

If a sequence of reaction steps consists only of irreversible steps, then all forward rates must be equal. When this occurs, the intermediates or active centers concentrations will adjust themselves to achieve this. The reaction that consumes the active center or intermediate of the highest concentration is the rate limiting step. Even in this case all rates must be equal. One should be cautious when speaking about the slowest rate perhaps the smallest rate constant would be somewhat better. 

Another multiple-reaction irreversible surface reaction process is the dimer-monomer-monomer (DMM) model as proposed in Ref. 99. This model is suitable for investigating, on the one hand, the influence caused by dimer traces in the MM model, and on the other hand the effect of monomer traces in the ZGB model. In fact, the DMM model assumes the following reaction steps ... 

Strictly speaking, the flow analogy is valid only for consecutive irreversible reactions, and it can be misleading if reverse reactions are significant. Even for irreversible reactions the rds concept has meaning only if one of the reactions is much slower than the others. For reversible reactions the free energy reaction coordinate diagram is a useful aid. In Fig. 5-10, for example, the intermediate 1 is unstable with respect to R and P, and its formation (the kf step) is the rds of the overall reaction. 

Compared with uncatalyzed reactions, catalysts introduce alternative pathways that, in nearly all cases, involve two nr more consecutive reaction steps. Each of these steps has a lower activation energy than does the uncatalyzed reaction. We can nse as an example the gas phase reaction of ozone and oxygen atoms. In the homogeneons uncatalyzed case, the reaction is represented to occur in a single irreversible step that has a high activation energy ... 

It remains a common misconception that radical-radical termination is suppressed in processes such as NMP or ATRP. Another issue, in many people s minds, is whether processes that involve an irreversible termination step, even as a minor side reaction, should be called living. Living radical polymerization appears to be an oxymoron and the heading to this section a contradiction in terms (Section 9.1.1). In any processes that involve propagating radicals, there will be a finite rate of termination commensurate with the concentration of propagating radicals and the reaction conditions. The processes that fall under the heading of living or controlled radical polymerization (e.g. NMP, ATRP, RAFT) provide no exceptions. 

Solution Under the assumption of intrinsic kinetics, all mass transfer steps are eliminated, and the reaction rate is determined by Steps 4-6. The simplest possible version of Steps 4-6 treats them all as elementary, irreversible reactions ... 

Irreversible Unimolecular Reactions. Consider the irreversible catalytic reaction A P of Example 10.1. There are three kinetic steps adsorption of A, the surface reaction, and desorption of P. All three of these steps must occur at exactly the same rate, but the relative magnitudes of the three rate constants, ka, and kd, determine the concentration of surface species. Suppose that ka is much smaller than the other two rate constants. Then the surface sites will be mostly unoccupied so that [S] Sq. Adsorption is the rate-controlling step. As soon as a molecule of A is absorbed it reacts to P, which is then quickly desorbed. If, on the other hand, the reaction step is slow, the entire surface wiU be saturated with A waiting to react, [ASJ Sq, and the surface reaction is rate-controlling. Finally, it may be that k is small. Then the surface will be saturated with P waiting to desorb, [PS] Sq, and desorption is rate-controlling. The corresponding forms for the overall rate are ... 

In the standard ZFK flame model [6], the chemical reaction rate, Q, is governed by a first-order irreversible one-step Arrhenius law... 

Figure 6.7 shows a typical special feature of the polarization curves. In the case of reversible reactions (curve 1), the anodic and cathodic branches of the curve form a single step or wave. In the case of irreversible reactions, independent, anodic and cathodic, waves develop, each having its own inflection or half-wave point. The differences between the half-wave potentials of the anodic and cathodic waves will be larger the lower the ratio fH. ... 

Depending on the mechanism of irreversible reaction, inactivation can appear to proceed through either a single-step or a two-step mechanism (Figure 8.2). In the case of nonspecific affinity labels (see Section 8.2) many amino acid residues on the enzyme molecule, and on other protein molecules in the sample, can be covalently modified by the affinity label. Not every modification event will lead to inactiva-... 

A kinetic model describing the HRP-catalyzed oxidation of PCP by H202 should account for the effects of the concentrations of HRP, PCP, and H202 on the reaction rate. To derive such an equation, a reaction mechanism involving saturation kinetics is proposed. Based on the reaction scheme described in Section 17.3.1, which implies that the catalytic cycle is irreversible, the three distinct reactions steps (Equations 17.2 to 17.4) are modified to include the formation of Michaelis-Menten complexes ... 

This bi-exponential behavior confirms the presence of reversible isomerization steps coupled with irreversible degradation steps and accounts for the role of the di-cis isomers as reaction intermediates, according to the general reaction scheme presented in Figure 12.1. The dependence of the rate constant of each elementary step on temperature allowed the calculation of the respective activation... 

The present chapter will cover detailed studies of kinetic parameters of several reversible, quasi-reversible, and irreversible reactions accompanied by either single-electron charge transfer or multiple-electrons charge transfer. To evaluate the kinetic parameters for each step of electron charge transfer in any multistep reaction, the suitably developed and modified theory of faradaic rectification will be discussed. The results reported relate to the reactions at redox couple/metal, metal ion/metal, and metal ion/mercury interfaces in the audio and higher frequency ranges. The zero-point method has also been applied to some multiple-electron charge transfer reactions and, wheresoever possible, these results have been incorporated. Other related methods and applications will also be treated. 

It is readily apparent that equation 8.3.21 reduces to the basic design equation (equation 8.3.7) when steady-state conditions prevail. Under the presumptions that CA in undergoes a step change at time zero and that the system is isothermal, equation 8.3.21 has been solved for various reaction rate expressions. In the case of first-order reactions, solutions are available for both multiple identical CSTR s in series and individual CSTR s (12). In the case of a first-order irreversible reaction in a single CSTR, equation 8.3.21 becomes... 

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