By definition of the reaction rates, rh and the stoichiometric coefficients, vih the term [Pg.261]

By using the natural logarithm of the reaction rate coefficient definition [10.42], we have [Pg.241]

As the reaction rate may not be assessed directly, the definition invokes an auxiliary parameter pk (e.g., an enzyme concentration) that is assumed to act only on the rate v. Note that X may stand for an arbitrary steady-state property with the coefficients for concentrations Cs and flux CJ as the most important examples. [Pg.177]

The reaction rate coefficients in the above equations may be related to reaction rates per pair of particles 2/, in nuclear physics (e.g., Fowler et al., 1975 Harris et al., 1983) by k = Xj/(1 + 5/ ), where 8 = 0 except for i= , for which 5/ = 1. That is, for Reactions 2-145 and 2-147 in which two identical particles collide to react, the definition of k is half of defined by nuclear physicists and for reactions in which different particles collide, the definition of k is the same as Xij. The reaction rate coefficients depend on temperature in a complicated way (Table 2-3) and may be calculated as the average value of the product of relative velocity times cross section. The concentrations of the intermediate species can be derived as follows. From Equation 2-155, 145 [ H] = ki4e[ H]pH]. That is. [Pg.152]

It is noteworthy that the form of the rate (r = / (state of the system) does not actually depend on our choice of reaction rate definition. Only the rate coefficients and their dimensions change with each rate definition (Levenspiel, 1972). [Pg.59]

Note. The unit of k is based on time (s) and concentration (mol/cmi). The reaction rate coefficients as a function of temperature are from Fowler et al. (1975) and Harris et al. (1983). Note that for Reactions 2-145 and 2-147, the definition of k is consistent with chemists definition used in this book and is half of Xij defined by nuclear physicists. That is, k = Xij/(l + 8j,), where Xi, is the reaction rates per pair of particles, and 5 , = 0 except for i=j for which 5 , = 1. The concentration unit is not converted to mol/L. [Pg.154]

The reaction rate is properly defined in terms of the time derivative of the extent of reaction. It is necessary to define k in a similar fashion in order to ensure uniqueness. Definitions in terms of the various rt would lead to rate constants that would differ by ratios of their stoichiometric coefficients. [Pg.27]

According to the above definitions, diffusion-controlled reactions are generally characterized by kdiff kchem- It should be noted though, that for reactions between highly mobile radical species, this condition is not always satisfied [19, 20]. In such cases, both the dififiision and chemical reaction rate coefficient contribute to the value of the observed rate coefficient. Noyes [19] and Rise [20] have reviewed several theoretical aspects of the calculation of diffusion-controlled reaction rates in solution. [Pg.11]

This is the situation exploited by the so-called isolation method to detennine the order of the reaction with respect to each species (see chapter B2.1). It should be stressed that the rate coefficient k in (A3,4,10) depends upon the definition of the in the stoichiometric equation. It is a conventionally defined quantity to within multiplication of the stoichiometric equation by an arbitrary factor (similar to reaction enthalpy). [Pg.763]

The constant K issned from the partition function wonld be the constant of an equilibrium between the activated complex and reactants. Considering the definitions of equilibrium constants, the free energy related to the reaction can be introduced and the reaction rate coefficient becomes [Pg.240]

Thus the presence of steps for the interaction between various intermediates in the detailed mechanisms is only a necessary condition for the multiplicity of steady states in catalytic reactions. A qualitative analysis of the dynamic system (5) for mechanism (4) showed that the existence of several stable steady states with a non-zero reaction rate needs the following additional conditions (a) the stoichiometric coefficients of intermediates must fit definite relationships ensuring the kinetic competition of these substances [violation of conditions (6)] (b) the system parameters must satisfy definite inequalities. [Pg.274]

Kinetic theory indicates that equation (32) should apply to this mechanism. Since the extent of protonation as well as the rate constant will vary with the acidity, the sum of protonated and unprotonated substrate concentrations, (Cs + Csh+), must be used. The observed reaction rate will be pseudo-first-order, rate constant k, since the acid medium is in vast excess compared to the substrate. The medium-independent rate constant is k(), and the activity coefficient of the transition state, /, has to be included to allow equation of concentrations and activities.145 We can use the antilogarithmic definition of h0 in equation (33) and the definition of Ksh+ in equation (34) [Pg.27]

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. [Pg.172]

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