Quasi-equilibrium reaction rate

Equation (44) means that reaction (39) is at quasi-equilibrium. The rate of reaction can be written ... 

The adsorption (7.8) is assumed to be fast and in a quasi-equilibrium. Reaction (7.9) is the rate-determining step, and (7.10) is a fast following reaction step in solution leading to the stable fluoro-aquo complex. These assumptions lead to a first-order process for HF... 

Enzyme reaction kinetics were modelled on the basis of rapid equilibrium assumption. Rapid equilibrium condition (also known as quasi-equilibrium) assumes that only the early components of the reaction are at equilibrium.8-10 In rapid equilibrium conditions, the enzyme (E), substrate (S) and enzyme-substrate (ES), the central complex equilibrate rapidly compared with the dissociation rate of ES into E and product (P ). The combined inhibition effects by 2-ethoxyethanol as a non-competitive inhibitor and (S)-ibuprofen ester as an uncompetitive inhibition resulted in an overall mechanism, shown in Figure 5.20. 

Reaction rates for the acid catalyzed elementary steps in hydrocracking can be expressed as follows when the metal catalyzed (de)-hydrogenation reactions are in quasi equilibrium ... 

In this approximation we assume that one elementary step determines the rate while all other steps are sufficiently fast that they can be considered as being in quasi-equilibrium. If we take the surface reaction to AB (step 3, Eq. 134) as the rate-determining step (RDS), we may write the rate equations for steps (1), (2) and (4) as ... 

It is important to realize that the assumption of a rate-determining step limits the scope of our description. As with the steady state approximation, it is not possible to describe transients in the quasi-equilibrium model. In addition, the rate-determining step in the mechanism might shift to a different step if the reaction conditions change, e.g. if the partial pressure of a gas changes markedly. For a surface science study of the reaction A -i- B in an ultrahigh vacuum chamber with a single crystal as the catalyst, the partial pressures of A and B may be so small that the rates of adsorption become smaller than the rate of the surface reaction. 

The orders of reaction, U , ivith respect to A, B and AB are obtained from the rate expression by differentiation as in Eq. (11). In the rare case that we have a complete numerical solution of the kinetics, as explained in Section 2.10.3, we can find the reaction orders numerically. Here we assume that the quasi-equilibrium approximation is valid, ivhich enables us to derive an analytical expression for the rate as in Eq. (161) and to calculate the reaction orders as ... 

In the following we shall examine a model system for the car catalyst where CO and NO react to yield the more environmentally friendly products CO2 and N2. The reaction shall be split up into the following elementary steps, which all are assumed to be in quasi-equilibrium, except step 2, which is assumed to be the rate-limiting step ... 

Gomez-Sainero et al. (11) reported X-ray photoelectron spectroscopy results on their Pd/C catalysts prepared by an incipient wetness method. XPS showed that Pd° (metallic) and Pdn+ (electron-deficient) species are present on the catalyst surface and the properties depend on the reduction temperature and nature of the palladium precursor. With this understanding of the dual sites nature of Pd, it is believed that organic species S and A are chemisorbed on to Pdn+ (SI) and H2 is chemisorbed dissociatively on to Pd°(S2) in a noncompetitive manner. In the catalytic cycle, quasi-equilibrium ( ) was assumed for adsorption of reactants, SM and hydrogen in liquid phase and the product A (12). Applying Horiuti s concept of rate determining step (13,14), the surface reaction between the adsorbed SM on site SI and adsorbed hydrogen on S2 is the key step in the rate equation. 

However, if reaction 3 is rate limiting we can deduce something useful and we will illustrate the quasi-equilibrium method by using it to derive the kinetic equation under these conditions. This method assumes that all reactions prior to the rate limiting step are in equilibrium. Thus, for reaction 1 ... 

If reaction 2 is rate limiting, then from the quasi-equilibrium hypothesis... 

Surface Coverage and Reaction Rate. If precursor complex formation is fast relative to electron transfer and product release, it can be treated as a quasi-equilibrium step ... 

For first-order reactions then, there is no compressibility term in the expression for In k, no matter what concentration scale is used. For higher order reactions involving molar concentrations, Eq. (22) could be applied when accurate rate data are available. Whether Eq. (27) should be applied depends on the method used for obtaining the data. If a spectrophotometric determination of the relative decrease in [A] is used, a relative measure of (d In k/dp)T is obtained from Eq. (27). If an absolute determination of [A] can be made at various times, Eq. (24) can be used directly, and k and (d In k/dp)T can be immediately obtained. The situation is easily generalized to higher order kinetics. In some cases, where AVf < 0 and the method of measurement detects [A] but not [X ], there may be a slight displacement of the quasi-equilibrium with pressure which leads to different initial concentrations of A. When AVf can be determined from Eq. (22), it may appear pressure-dependent, i.e.,... 

As will be discussed in the following chapter, most combustion systems entail oxidation mechanisms with numerous individual reaction steps. Under certain circumstances a group of reactions will proceed rapidly and reach a quasi-equilibrium state. Concurrently, one or more reactions may proceed slowly. If the rate or rate constant of this slow reaction is to be determined and if the reaction contains a species difficult to measure, it is possible through a partial equilibrium assumption to express the unknown concentrations in terms of other measurable quantities. Thus, the partial equilibrium assumption is very much like the steady-state approximation discussed earlier. The difference is that in the steady-state approximation one is concerned with a particular species and in the partial equilibrium assumption one is concerned with particular reactions. Essentially then, partial equilibrium comes about when forward and backward rates are very large and the contribution that a particular species makes to a given slow reaction of concern can be compensated for by very small differences in the forward and backward rates of those reactions in partial equilibrium. 

When the overall rate of a multistep reaction is determined solely by a single elementary step whose rate is extremely small compared with the rates of the other elementary steps, the multistep reaction is called the reaction of a single rate-determining step. In such a multistep reaction, as shown in Fig. 7-11 (a), all the elementary steps except for the rate-determining step are cmisidered to be in quasi-equilibrium. Note that the multistep reaction of a sin le rate-determining step is rather uncommon in practice. 

We consider a transfer reaction of redox electrons in which the interfacial transfer of electrons is in quasi-equilibrium ( Hh =0) and the diffusion of redox particles determines the overall reaction rate. The anodic diffusion current, and the anodic limiting current of diffusion, inm, in the stationary state of the electrode reaction are given, respectively, in Eqns. 8-33 and 8-34 ... 

The point at which the straight line of (tph) versus Eintersects the coordinate of electrode potential represents the flat band potential. Equation 10-15 holds when the reaction rate at the electrode interface is much greater than the rate of the formation of photoexcited electron-liole pairs here, the interfadal reaction is in the state of quasi-equilibrium and the interfadal overvoltage t)j, is dose to zero. 

The potential, E, for the onset of the photoexdted reaction relative to the equilibrium electrode potential E of the same reaction can also be derived in a kinetics-based approach [Memming, 1987]. Here, we consider the transfer of anodic holes (minority charge carriers) at an n-type semiconductor electrode at which the hole transfer is in quasi-equilibrium then, the anodic reaction rate is controlled by the photogeneration and transport of holes in the n-type semiconductor electrode. The current of hole transport, has been given by Eqn. 8-71 as a function of polarization ( - ,) as shown in Eqn. 10-20 ... 

The derivation of initial velocity equations invariably entails certain assumptions. In fact, these assumptions are often conditions that must be fulfilled for the equations to be valid. Initial velocity is defined as the reaction rate at the early phase of enzymic catalysis during which the formation of product is linear with respect to time. This linear phase is achieved when the enzyme and substrate intermediates reach a steady state or quasi-equilibrium. Other assumptions basic to the derivation of initial rate equations are as follows ... 

THE RAPID-EQUILIBRIUM TREATMENT. The first rate equation for an enzyme-catalyzed reaction was derived by Henri and by Michaelis and Menten, based on the rapid-equilibrium concept. With this treatment it is assumed that there is a slow catalytic conversion step and the combination and dissociation of enzyme and substrate are relatively fast, such that they reach a state of quasi-equilibrium or rapid equilibrium. 

Readers might have noticed that the two chain reactions, (i) Reactions 2-121 and 2-122 and (ii) Reactions 2-116 and 2-117, are similar, but were treated differently. Reactions 2-116 and 2-117 were treated using the quasi-equilibrium assumption, but may also be treated using the steady-state concept. The result is a more complicated expression, which would reduce to the experimental reaction rate law if < ii6b- Readers can work this problem out as an exercise. Therefore, the... 

This approximation will in most cases provide a very significant simplification in particular for large reaction mechanisms. In the quasi-equilibrium approximation the transient behavior is eliminated. Further, the description of changes in rate-limiting step has been lost. 

One of the reaction steps is assumed rate limiting, this step has a forward rate constant. This model maps onto the quasi equilibrium approximation. 

Rate determining step (cont.) electrocatalysis and, 1276 methanol oxidation, 1270 in multistep reactions, 1180 overpotential and, 1175 places where it can occur, 1260 pseudo-equilibrium, 1260 quasi equilibrium and, 1176 reaction mechanism and, 1260 steady state and, 1176 surface chemical reactions and, 1261 Real impedance, 1128, 1135 Reciprocal relation, the, 1250 Recombination reaction, 1168 Receiver states, 1494 Reddy, 1163... 

In its turn, the non-monotonous behaviour of Y(r, t) results in a similar behaviour of the reaction rate K(t) in time (Fig. 6.48). The local maximum of K (f) observed at t = 101 (for a given L) for different initial concentrations likely arises due to the initial conditions used, which do not take into account peculiarities of the spatial distribution of charged particles a more adequate one would be a quasi-equilibrium pair distribution with incorporated potential screening. 

Enzymes are biocatalysts, as such they facilitate rates of biochemical reactions. Some of the important characteristics of enzymes are summarized. Enzyme kinetics is a detailed stepwise study of enzyme catalysis as affected by enzyme concentration, substrate concentrations, and environmental factors such as temperature, pH, and so on. Two general approaches to treat initial rate enzyme kinetics, quasi-equilibrium and steady-state, are discussed. Cleland s nomenclature is presented. Computer search for enzyme data via the Internet and analysis of kinetic data with Leonora are described. 

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