Formation and consumption of

Because of the small rate coefficient of H2 H- HO2 H2O2 + H (see below) and the low HO2 concentrations in high-temperature combustion, hydrogen peroxide is mainly formed by OH recombination (Fig. 19), especially at elevated pressure (see Warnatz, 1982). Relative collision efficiencies for third bodies in this reaction are given in Section 1.2. 

This reaction may be important in low-temperature oxidation because of its chain-branching character. The slow H2O2 formation rate and the large activation energy of this decomposition reaction mean that it has only minor importance in high-temperature combustion. 

Peelers and Mahnen (1973a) deMore and Tschuikow-Roux 5.0 X 10  

these reactions are relatively unimportant for high-temperature combustion because of the slow H2O2 formation rate. Data for H 4 H2O2 and OH + H2O2 are presented in Figs. 20 and 21, since the rate coefficients of the Leeds report cannot be recommended any longer. 

No direct measurements are available for this reaction. The rate coefficient recommended in the Leeds report is taken here it was determined from the rate coefficient of the reverse reaction and the equilibrium constant. 

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As for the quasi (pseudo)-steady-state case, the basic assumption in deriving kinetic equations is the well-known Bodenshtein hypothesis according to which the rates of formation and consumption of intermediates are equal. In fact. Chapman was first who proposed this hypothesis (see in more detail in the book by Yablonskii et al., 1991). The approach based on this idea, the Quasi-Steady-State Approximation (QSSA), is a common method for eliminating intermediates from the kinetic models of complex catalytic reactions and corresponding transformation of these models. As well known, in the literature on chemical problems, another name of this approach, the Pseudo-Steady-State Approximation (PSSA) is used. However, the term "Quasi-Steady-State Approximation" is more popular. According to the Internet, the number of references on the QSSA is more than 70,000 in comparison with about 22,000, number of references on PSSA. 

In the delayed emission spectrum of eosin in glycerol or ethanol two bands are present, the relative intensities of which are strongly temperature-dependent (see Fig. 12). The visible band at 1.8 has a contour identical with that of the fluorescence band. It no doubt corresponds to the visible phosphorescence observed by Boudin.26 To interpret the results it was assumed that this band of delayed fluorescence was produced by thermal activation of the eosin triplet to the upper singlet level followed by radiative transition from there to the ground state. The far red band was assumed to correspond to the direct transition from the triplet level to the ground state and was therefore called phosphorescence. To determine the relationship between the intensities of the two bands we write the equations for the formation and consumption of triplet molecules as follows ... 

The skeletal or short mechanism is a minimum subset of the full mechanism. All species and reactions that do not contribute significantly to the modeling predictions are identified and removed from the reaction mechanism. The screening for redundant species and reactions can be done through a combination of reaction path analysis and sensitivity analysis. The reaction path analysis identifies the species and reactions that contribute significantly to the formation and consumption of reactants, intermediates, and products. The sensitivity analysis identifies the bottlenecks in the process, namely reactions that are rate limiting for the chemical conversion. The skeletal mechanism is the result of a trade-off between model complexity and model accuracy and range of applicability. 

The nitrogen atoms are then oxidized to NO by reaction with OH (R116), or they can be converted to N2 by reaction with NO (R114b). At lower temperatures the oxidation mechanism for HCN is more complicated, involving formation and consumption of a number of pollutant species including oxicyanides, amines (NH,), and nitrous oxide (N20). 

In this reaction scheme, the quantity and the duration of XI would depend on the velocity of the formation and consumption of VII, and also on the velocity of forward and reverse reactions between the structures VII and XI, thus accounting for the observation that they are significantly affected by the reaction conditions. 

For a steady-state reaction the formation of a molecule of an intermediate in an act of an elementary reaction must be compensated by consumption of this molecule in some other elementary reaction. If a new molecule of the same or another intermediate is formed in this reaction, it must also be consumed. Sooner or later a moment comes when a complete compensation of the formation and consumption of the intermediate molecules occurs in... 

In general, the sensitivity of the overall rate to the forward rate constant for step i is always proportional to the reversibility of the preceding step that produces the reaction intermediate in step i however, the proportionality constant depends on the stoichiometric coefficients for the formation and consumption of the reactive intermediates. For example, if the reactive intermediate is consumed once in step i and produced twice in the preceding step j, then [Pg.184]

Equipped with this principle, let us now continue the derivation of the rate law for SN reactions. The approximation [carbenium ion] = 0 must be replaced by Equation 2.6. Let us now set the left-hand side of Equation 2.6, the change of the carbenium ion concentration with time, equal to the difference between the rate of formation of the carbenium ion and its consumption. Because the formation and consumption of the carbenium ion are elementary reactions, Equation 2.7 can be set up straightforwardly. Now we set the right-hand sides of Equations 2.6 and 2.7 equal and solve for the concentration of the carbenium ion to get Equation 2.8. With this equation, it is possible to rewrite the previously unusable Equation 2.5 as Equation 2.9. The only concentration term that appears in Equation 2.9 is the concentration of the alkylating agent. In contrast to the carbenium ion concentration, it can be readily measured. 

Coherence of Steady State and Dynamic Results. A steady state rate expression based on steps 1 to 3 can be derived by assuming step 3 to be in equilibrium and the rates of formation and consumption of 0qo to be equal ... 

The methodology was applied to fed-batch baker s yeast production on a 200-m3 scale [33]. The typical phases in a baker s yeast cultivation were visualized including lag phase, formation and consumption of ethanol and increase and decrease of cell mass. Fusion of signals from external sensors for volume, aeration flow rate and dissolved ethanol resulted in different character of the trajectory in the PCA but with the same principal information. 

The reaction mechanism of this system involved the transfer of phases across the solid liquid interface. Hence, quantification using Equation (22) produced values that were overestimated. To determine the absolute phase abundances, powdered diamond was selected as an inert internal standard and was weighed into the starting solids. Acid was then added to this mixture and the standard concentration taken as its weight fraction of the sample in its entirety, i.e., solids and liquids in total. For each dataset the results of the quantitative phase analysis were adjusted according to the known amount of standard present in the system [Equation (16)]. This allowed the determination of variation in the amorphous content of the system to be assessed via Equation (17)] as well as the formation and consumption of crystalline phases. The amorphous content... 

This point of view is shared by Postnikov and his research workers [12, 26], who consider that keto-imide compounds may be formed even at the early stage of PA production. They were the first to construct the simplest scheme of reaction capable to describe mechanism of PA photooxidation taking into account formation and consumption of ketoimide compound ... 

The second way of treating kinetics is by means of the steady-state condition, that is, the rates of all steps prior to and including the rds are proceeding at the same rate at a given potential and constant current density. Then a differential expression for the rates of formation and consumption of an intermediate (in a multistep process) can be written for a given potential and the net derivative equated to 0 for the supposed steady state. 

The reaction occurs at the solid-liquid interface. Thus, the kinetic rates must depend on the surface state of the solid and include an absorption term which can vary from one substrate to another one. With this hypothesis, the formation and consumption of 2C14FNB and 4C12FNB can vary independently with the surface state. 

According to the QSS approximation, the rates of formation and consumption of the surface intermediates are approximately equal, so that the time derivatives of the coverages of the intermediates may be set equal to zero... 

The growing radicals are very reactive intermediate species that conform to what in chemical kinetics is called a quasi-steady state (QSS) or stationary state hypothesis [11, 12]. This means that the rate of formation and consumption of that species become nearly equal in a very short timescale as a consequence, the absolute value of the derivative becomes very small and negligible compared with the derivatives of other species in the system (e.g., d[M]/df) and for practical purposes can be approximated as zero. Note, however, that this does not imply constancy of the value of [P], as sometimes interpreted by some authors, but this will be more clear later. By making the QSS approximation in Equation 4.5... 

Examination of the possibility of a Z mechanism typically requires the steady-state approximation. This approximation assumes that a vanishingly small (and constant) concentration of the intermediate, ML5, is present during the reaction by assuming that the rates of formation and consumption of the intermediate are equal. If these rates are the same, the change in the [ML5] must equal zero (and this species cannot accumulate) during the reaction. Expressed as a rate equation,... 

The integral area of protons of residual monomer is shown in Figure 7. The monomer concentration decreases with each incremental addition of H2O2. However, unlike phenol and p-sulfonated phenol, in this case, the dimer concentration increases and gradually decreases. There is no equilibrium stage in which both the formation and consumption of dimer takes place. This suggests that the reactivity of monomer may be higher compared to dimers and the rate of consumption of dimers accelerates only when the monomer concentration is depleted to a very low level. 

One of the main tasks of a formal kinetics is a description of the dynamics of chemical system composition via its transition from the initial indignant state into the final equilibrium one. Two factors have an influence on the dynamics of chemical system composition. Firstly, stoichiometric bonds caused by the conservation laws at chentical transformations, that is, the proportions of formation and consumption of component and intermediate substances that are assigned to equations of the final and an elementary reaction. Stoichiometric bonds have a constant influence and do not depend on the current state of a system. The second factor is correlative bonds (so-called interaction bonds) they are continuously formed in the process and represent a function of the system state and a function of its evolution step, respectively. 

The first step, a strong collision between a bath gas molecule (M) and a reactant AB, transfers enough energy to AB to reach a state above the reaction barrier (excitation step). This energized state AB then either rearranges to the products A + B (reaction) or it loses energy in a subsequent collision to re-form AB (deactivation). After a short time, formation and consumption of AB will be in balance, or in other words the concentration of AB (symbolized as [AB ]) reaches a constant value, called the steady-state concentration. At this time the condition d[AB ]ss/dt — 0 holds. If we assume that the time required to achieve the steady-state condition is negligible compared to the total reaction time, then the apparent unimolecular rate constant, for the reaction AB A + B can be derived as follows ... 

FIGURE 8 Kinetics of product formation and consumption of DBE during ozonolysis at... 

Figure 8.5 depicts an example from the Pt WGS model of the output fiom RPA regarding the formation and consumption of a select surface species, for example, H O, at a select set of operating conditions and location of a reactor, often at the reactor exit (RPA depends on spatial location since concentrations, coverages, and reaction rates... 

The findings have practical Implications for nutrition and food safety. They may be useful to food processors and consumers who wish to minimize the formation and consumption of unnatural, deleterious compounds during commercial and home food processing. 

One specific case should be considered in more detail For ki k2, the concentration and thus also the change of the concentration of the intermediate B with time is very low compared to the other two components, as depicted in Figure 4.3.5 for ki=0.05k2- Then the rate of consumption of reactant A approximately equals the rate of formation of C, and the rate of formation and consumption of the... 

When C is being formed at the rate of 0.086 M/s, A is being consumed at a rate of 0.172 M/s and B is being consumed at a rate of 0.258 M/s. Balance the equation based on the relative rates of formation and consumption of produas and reactants. 

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