Average stoichiometric number

Here, Ais the free energy change of Reaction 17.3 (kJ mol 1), R is the gas constant (8.3143 J K-1 mol-1), and 7k is absolute temperature (K). Factor co is the reciprocal of the average stoichiometric number, which can be taken as the number of times the rate determining step in Reaction 17.3 occurs per turnover of the reaction (Jin and Bethke, 2005). 

It is worth noting that the values of both k+ and co in Equation 17.9 depend on how the kinetic reaction (Reaction 17.3) is written. If we were to arbitrarily double each of the reaction s coefficients, the value of the rate constant k+ would be cut in half, because twice as many of the reactant species would be consumed, and twice as many product species produced, per reaction turnover. The rate determining step, furthermore, would occur twice as often per reaction turnover, doubling the average stoichiometric number and requiring co to be halved as well. 

Taking the rate limiting step in the electron transport chain to be trans-membrane proton translocation, which occurs about five times per sulfate consumed (Rabus et al., 2006), the average stoichiometric number x (entered into REACT as to = 1/x) for Reaction 18.7 is five. Sulfate reducers conserve about 45 kJ mol-1 of sulfate consumed (Qusheng Jin, unpublished data), so we set AGp to this value and m to one. From equations 18.12 and 18.14, then, we can write... 

Experimental studies of Methanosarcina and current understanding of the organism s metabolic pathway allow us to estimate the parameters in the thermodynamic term (Qusheng Jin, personal communication). The methanogens conserve about 24 kJ (mol acetate)-1, so we set AGp to 48 kJ mol-1 and m to one half. A double proton translocation occurs within the central metabolic pathway, furthermore, so, if we take these as the rate limiting steps, the average stoichiometric number / is two. 

Equation (83) may also be considered as applicable for a reaction on a nonuniform surface with different stoichiometric numbers of nonequilibrium stages in this case, however, the average stoichiometric number in (83) is determined not by (80), but in a more complicated manner the definition must involve averaging with respect not only to stages, but also to the kinds of the surface sites. 

In compliance with the treatment given in Section VIII, this is explained by the stoichiometric numbers of both slow stages being equal to 1 so that the average stoichiometric number v = 1. 

Like the kinetic concepts of Christiansen and Horiuti, those of Temkin were far ahead of their common acceptance by the catalytic community. Even today, more than 50 years after the Temkin-Pyzhev paper, the idea of virtual fiigacity is not well understood by the majority of workers in catalytic kinetics. It is safe to predict that many of the other ideas of Temkin, like that of average stoichiometric number or reaction routes, will influence younger catalytic ki-neticists who now have access to powerful computers. 

The integral may be calculated from the stoiehiometry dependence of the chemical diffusion coefficient, y is the average stoichiometric number of the compound AyB. " Equation (9.36) allows the determination of the tarnishing rate constant as a function of all combinations of activities of the components at both sides of the sample. 

Table II provides a summary of the results on the characteristics of aminopropyl terminated poly(dimethyl-diphenyl)-siloxane oligomers synthesized. These reactions were conducted in bulk at 160°C with K0H as the initiator. As can be seen from Table II the stoichiometric number average molecular weights sought and obtained are in very good agreement. The level of diphenylsiloxane incorporation was determined by UV spectroscopy. There is no absorption of dimethylsiloxane backbone in the spectral range of 240 to 280 nm. On the other hand, phenyl groups absorb very strongly over these wavelengths (Figure 3). For quantitative analysis we have used the absorption peak at 270 nm as the reference.

Ihis number v is the mean stoichiometric number of the rate-determining multiple steps. The mean stoichiometric number is thus represented by the energy average (afiiniiy average) of the stoichiometric niunbers v weighed with the step affinity 4gi in the respective rate-determining steps. 

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. 

A general relationship between Zintl-Klemm concept and defect formation has been formulated [15, 16] recently. For a compoimd AaB, nstoichiometric numbers) the total number of valence electrons E per formula unit relates to the average number of bonds per atom N and to the number of defects d. 

Thus, p evaluated in this way has the physical meaning of an average of stoichiometric numbers of the constituent steps, each weighted in the affinity values associated with them. 

Since A can be obtained from thermodynamic data, and a a can be determined if V and V are known, a a plays a very important role in verifying reaction mechanism. If there is no rate determining step in a catalytic reaction, the concept of average chemical stoichiometric number can be introduced. The kinetics of reverse reaction can be determined from that of forward-reaction kinetics by crj or... 

Geometric average (mean) of stoichiometric numbers of an electrolyte [dimensionless]... 

There are two methods that are considered fundamental in the use of potentiometric titrations to determine the properties of a solution. The first was developed by Bodlander and Fittig (1902). The main feature of this method was to obtain a description of the stoichiometric constant in a reaction between a metal (M) and a ligand (L). However, it is usually desirable to also obtain a value for the stability constant itself since only how the expression looks for the reaction is not sufficient. A method for doing this using potentiometric titrations was introduced by Bjerrum (1941). In this method, Bjerrum usedthe average ligand number defined by... 

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