Pseudo-elementary reaction

HOR and the ORR involve two and four electrons, respectively. Since the Butler-Volmer equation is important for expressing the relationship between the current density of an electrochemical reaction and the overpotential, the rate-determining step (RDS) of a multi-electron reaction can be simplified as a pseudo-elementary reaction involving multiple electrons. The Butler-Volmer equation for this reaction is usually written as follows ... 

This is only an approximate representation, in which a is the transfer coefficient and na is the apparent electron number involved in the pseudo-elementary reaction. This na is different from the total electron transfer number of the reaction ( ). 

Elementary reaction. The term elementary reaction has been defined. Sometimes two or more elementary reactions are added, as for example the elementary steps in a Michaelis-Menten enzymatic reaction, and listed as a pseudo-elementary reaction. Catalyst. Acatalyst may be necessary for an elementary reaction to occur at a reasonable rate, as well as positive and negative effectors on the catalyst. We shall be concerned mostly with isothermal reactions. 

In this study, the absorption rates of carbon dioxide into the solution of GMA and Aliquat 336 in such organic solvents as toluene, N-methyl-2-pirrolidinone(NMP), and dimethyl sulfoxide(DMSO) was measured to determine the pseudo-first-order reaction constant, which was used to obtain the elementary reaction rate constants. 

The overall reaction between CO2 and GMA was assumed to consist of two elementary reactions such as a reversible reaction of GMA and catalyst to form an intermediate and an irreversible reaction of this intermediate and carbon dioxide to form five-membered cyclic carbonate. Absorption data for CO2 in the solution at 101.3 N/m were interpreted to obtain pseudo-first-order reaction rate constant, which was used to obtain the elementary reaction rate constants. The effects of the solubility parameter of solvent on lc2/k and IC3 were explained using the solvent polarity. 

Elementary reaction 2H20(aq) H30+(aq)+ OH (aq) (Reaction l-9f) is a zeroth-order reaction (or pseudo-zeroth-order reaction) ... 

It is necessary to repeat our study for nonlinear networks. We discuss this problem and perspective of its solution in the concluding Section 8. Here we again use the experience summarized in the lUPAC Compendium (Ratecontrolling step, 2007) where the notion of controlling step is generalized onto nonlinear elementary reaction by inclusion of some concentration into "pseudo-first-order rate constant". 

In the reactions discussed and exemplified above, reactants, transient species and products are related by linear sequences of elementary reactions. The transient species can be regarded as a kinetic product and, if isolable, subject to the usual tests for stability to the reaction conditions. Multiple products, however, may also occur by a mechanism involving branching. Indeed, the case shown earlier in Fig. 9.5b, where the transient is a cul de sac species, is the one in which the branching to the thermodynamic product P and kinetic product T occurs directly from the reactant. In the absence of reversibility, the scheme becomes as that shown in Scheme 9.8a, where the stable products P and Q are formed as, for example, in the stereoselective reduction of a ketone to give diastereoisomeric alcohols. The reduction of 2-norbornanone to a mixture of exo- and cndo-2-norbornanols by sodium borohydride is a classic case. The product ratio is constant over the course of the reaction and reflects directly the ratio of rate constants for the competing reactions. The pseudo-first-order rate constant for disappearance of R is the sum of the component rate constants. 

Later, it became clear that the concentrations of surface substances must be treated not as an equilibrium but as a pseudo-steady state with respect to the substance concentrations in the gas phase. According to Bodenstein, the pseudo-steady state of intermediates is the equality of their formation and consumption rates (a strict analysis of the conception of "pseudo-steady states , in particular for catalytic reactions, will be given later). The assumption of the pseudo-steady state which serves as a basis for the derivation of kinetic equations for most commercial catalysts led to kinetic equations that are practically identical to eqn. (4). The difference is that the denominator is no longer an equilibrium constant for adsorption-desorption steps but, in general, they are the sums of the products of rate constants for elementary reactions in the detailed mechanism. The parameters of these equations for some typical mechanisms will be analysed below. 

The first-order rate coefficient, k, of this pseudo-elementary process is assumed to vary with temperature according to an Arrhenius law. Model parameters are the stoichiometric coefficients v/ and the Arrhenius parameters of the rate coefficient, k. The estimation of the decomposition rate coefficient, k, requires a knowledge of the feed conversion, which is not directly measurable due to the complexity of analyzing both reactants and reaction products. Thus, a supplementary empirical relationship is needed to relate the feed conversion (conversion of A) to some experimentally accessible variable (Ross and Shu have chosen the yield of C3 and lighter hydrocarbons). It is observed that the rate coefficient, k, is not constant and decreases with increasing conversion. Furthermore, the zero-conversion rate coefficient depends on feed specifications (such as average carbon number, hydrogen content, isoparaffin/normal-paraffin ratio). Stoichiometric coefficients are also correlated with conversion. Of course, it is necessary to write supplementary empirical relationships to account for these effects. 

In molecular reaction schemes, only stable molecular reactants and products appear short-lived intermediates, such as free radicals, are not mentioned. Nearly all the reactions written are considered as pseudo-elementary processes, so that the reaction orders are equal to the mol-ecularities. For some special reactions (such as cocking) first order or an arbitrary order is assumed. Pseudo-rate coefficients are written in Arrhenius form. A systematic use of equilibrium constants, calculated from thermochemical data, is made for relating the rate coefficients of direct and reverse reactions. Generally, the net rate of the reversible reaction... 

The data in Figure 7.13 show reductive-dissolution kinetics of various Mn-oxide minerals as discussed above. These data obey pseudo first-order reaction kinetics and the various manganese-oxides exhibit different stability. Mechanistic interpretation of the pseudo first-order plots is difficult because reductive dissolution is a complex process. It involves many elementary reactions, including formation of a Mn-oxide-H202 complex, a surface electron-transfer process, and a dissolution process. Therefore, the fact that such reactions appear to obey pseudo first-order reaction kinetics reveals little about the mechanisms of the process. In nature, reductive dissolution of manganese is most likely catalyzed by microbes and may need a few minutes to hours to reach completion. The abiotic reductive-dissolution data presented in Figure 7.13 may have relative meaning with respect to nature, but this would need experimental verification. 

The reaction model includes the elementary steps of the initial formation of an energized complex Au2CO (rate constant fca) and its possible unimolecular decomposition back to the reactants (k ) in competition with a stabilizing energy transfer collision with helium buffer gas kg). Assuming all these elementary reaction steps to be again of pseudo-first-order and employing steady state assumption for the intermediate, the overall third-order rate expression is obtained to be [189]... 

Pseudo-First-Order Treatment. A convenient simplification is possible when the concentrations of reactants B and C are much greater than the substrate A. As the reaction progresses, changes in [B] and [C] are small relative to changes in A], and the former can be considered effectively constant. Each elementary reaction can then be considered pseudo-first-order with respect to A. Let... 

Pseudo-Order Reactions As mentioned above, complex reactions can often be expressed by the simple equations of zeroth-, first-, or second-order elementary reactions under certain conditions. For example, the dissolution of many minerals at conditions close to equilibrium is a strong function of the free energy of the reaction (Lasaga, 1998, 7.10), but far from equilibrium the rate becomes nearly independent of the free energy of reaction. In other words, the rate of dissolution will be virtually constant under these conditions, or pseudo-first-order. 

In both cases (Scheme 6.1) the formation of the NPs follows the auto-catalytic mechanism developed by Finke and coworkers [81]. For example, for Ir or Pt(0) NPs, the catalytic hydrogenation (H2 uptake) of 1-decene and cyclohexene, respectively, is used as a reporter reaction via the pseudo-elementary step concept. Scheme 6.3 (where A is the precatalyst [lr(cod)Cl]2 or Pt2(dba)3 and B is the catalyti-cally active lr(0) or Pt(0) nanoclusters. Scheme 6.3). 

If the alkene hydrogenation (step (c). Scheme 6.3) is a fast reaction, on the timescale of steps (a) and (b), it can serve as a reporter reaction for the lr(0) or Pt(0) formation, i.e., the kinetics of the overall reaction are represented only by the steps (a) and (b) in Scheme 6.3. Moreover, the sum of all three steps leads to a kineti-cally equivalent elementary step which relates the overall H2 consumption (cyclohexene) with the formation of lr(0) or Pt(0) NPs, the so-called pseudo-elementary step (d) (Scheme 6.3). 

If neither simplification is appropriate, then the reaction described by equation 6.32 may be studied by carrying out the reaction with a large initial concentration of A or B so that the first elementary reaction is carried out under pseudo-first-order conditions. 

Oscillatory chemical reactions always undergo a complex process and accompany a number of reacting molecules, which are indicated as reactants, products, or intermediates. An elementary reaction is occurred by the decrease in the concentration of reactants and increase in the concentration of products. Initial concentration of the intermediates of such reaction is considered low, which approaches almost pseudo-equilibrium state in middle at this moment speed of production is essentially equal to their rate of consumption. In contrast to this, an oscillatory reaction undergoes with the decrease in the concentrations of reactants and increase in the concentration of the products. But the concentrations of intermediates or catalysts species execute oscillations in far from equilibrium conditions [1]. An oscillatory chemical reaction is accompanied by some essential phenomenology called induction period, excitability, multistability, hysteresis, etc. [1, 4]. These characteristic phenomena could be useful to determine the mechanism and behavior of the oscillating reaction. 

For elementary reactions the kinetics are relatively simple, and there are straightforward mathematical expressions that allow us to solve for rate constants. These simple mechanisms are those we analyze first. They involve first and second order kinetics, along with variations including pseudo-first order and equilibrium kinetics. We also look at a method to measure rate constants known as initial-rate kinetics. We analyze complex reactions only under the simplifying assumption of the steady state approximation (Section 7.5.1), and show how kinetic orders can change with concentration. More advanced methods for analyzing complex reactions are left to texts that specialize in kinetics. 

An elementary reaction involving two or three reactants can, in principle, be treated as a pseudo-first-order reaction using the isolation method. In agreement with this method, if all the reactants except one are in excess, the apparent order of the reaction will be the order relative to the isolated reactant, since the concentrations of the species in excess do not vary appreciably during the reaction. Thus, if a reaction is of order a relative to A, of order b relative to B and of order c relative to C, and if the concentrations of B and C are considerably greater than that of A, experimentally the order of reaction wiU be a and the... 

We already applied this result, directly to replace the set of the steps of diffusion by a single elementary reaction (Chapter 5). We also applied it for some reactions of interfaces (Chapter 4) which made it possible to draw up Table 4.1 by considering the three pseudo-steady state modes of the system of the two elementary steps ... 

Usual elementary reactions are not so simple and Eq. (6.126) is only vahd sufficiently close to equilibrium . Nonetheless the range of applicability may be wider than assumed, since many reactions behave as if they were monomolecular under certain conditions (so-called pseudo-monomolecular reactions). In addition, relevant processes are usually not just single step reactions, in which B only increases at the expense of A and vice versa. The relations between k and k, k are then more involved. Even under those conditions the exchange rate remains the decisive permeability parameter [452] containing k and k of the rate determing step in a symmetrical way. 

When oxygen is removed from a reaction solution of tetrakis-(dimethylamino)ethylene (TMAE), the chemiluminescence decays slowly enough to permit rate studies. The decay rate constant is pseudo-first-order and depends upon TMAE and 1-octanol concentrations. The kinetics of decay fit the mechanism proposed earlier for the steady-state reaction. The elementary rate constant for the dimerization of TMAE with TMAE2+ is obtained. This dimerization catalyzes the decomposition of the autoxidation intermediate. 

---