This expression has the Arrhenius form and E is the maximum value of the potential energy, an activation energy for deposition. This is expected because the potential profile of fig. 2 resembles the plot of the energy against reaction coordinate used in the theory of rate processes. The factor /(//m) accounts for the dependence of the diffusion coefficient on the distance and evaluations show that it can decrease the frequency factor in eqn (16) by two orders of magnitude. [Pg.73]

It is a common—and largely justified—practice to express the temperature dependence of the rate coefficients of bimolecular reactions in the so-called Arrhenius form (Arrhenius, 1889) [Pg.127]

The ThermKin code described in chapter 2 is used to determine the elementary reaction rate coefficients and express the rate coefficients in several Arrhenius forms. It utilizes canonical transition state theory to determine the rate parameters. Thermodynamic properties of reactants and transition states are required and can be obtained from either literature sources or computational calculations. ThermKin requires the thermodynamic property to be in the NASA polynomial format. ThermKin determines the forward rate constants, k(T), based on the canonical transition state theory (CTST). [Pg.120]

The temperature dependence of reactions comes from dependences in properties such as concentration (Cj = PjfRT for ideal gases) but especially because of the temperature dependence of rate coefficients. As noted previously, the rate coefficient usually has the Arrhenius form [Pg.207]

The computer would then look in the rate estimation library for Radical Addition reactions to find the rate parameters that correspond to primary alkyl + ester O . There it would find a set of numerical parameters Ec, a, A, n with estimated uncertainties one could then calculate the forward rate coefficient for the reaction of interest using this Evans-Polanyi modified Arrhenius form [Pg.20]

In using the tables of the present chapter it should be borne in mind that while the results are presented in the form of absolute Arrhenius parameters, the bulk of the data have been derived from measurements of rate coefficient ratios and the absolute values are usually based on estimates of the rate coefficients of the reference reaction. This applies particularly to the radical reactions where the measurements are made relative to the radical combination reaction. Details of the assumptions involved with many of the reference reactions are discussed under the headings of the appropriate radicals. [Pg.41]

In order to solve these equations, we have to be able to evaluate cpj, the species net production rate as a function of conditions and gas composition. If we assume only binary reactions and an Arrhenius temperature dependence for the forward rate coefficients of such reactions, then we can express < j in a reasonably simple form. [Pg.20]

Differences between the models representing homogeneous and heterogeneous reactions will be discussed below, but first the similarities in behaviour will be outlined. In reactions of both types, reaction rates generally increase markedly with temperature. Rate coefficients almost invariably fit one or other form of the Arrhenius equation [Pg.117]

Thermal effects constitute a significant portion of the study devoted to catalysis. This is true of electrochemical reactions as well. In general the reaction rate constants, diffusion coefficients, and conductivities all exhibit Arrhenius-type dependence on temperature, and as a rule of the thumb, for every 10°C rise in temperature, most reaction rates are doubled. Hence, temperature effects must be incorporated into the parameter values. Fourier s law governs the distribution of temperature. For the example with the cylindrical catalyst pellet described in the previous section, the equation corresponding to the energy balance can be written in the dimensionless form as follows [Pg.431]

A more sophisticated approach is given by the so-called molecular reaction schemes. These schemes give a true picture of the stoichiometry and thermochemistry and describe the primary, secondary, etc. kinetic nature of reaction products. Though the rate coefficients of molecular reaction schemes are pseudo rate coefficients, they can generally be expressed in an Arrhenius form and do not depend too much on operating conditions however, they must be determined for each particular type of system and cannot be derived from fundamental kinetic parameters in the literature. [Pg.278]

Of the DSMC chemistry models considered in this article, perhaps the GCE model offers the best blend of convenience, flexibility, and accuracy. This type of model is convenient to use because it employs Arrhenius rate coefficient parameters in its mathematical form. So, provided such data exists for a mechanism of interest, it is relatively easy to perform a DSMC computation. The model also provides flexibility through the parameters a, P, and 7 that allow individual energy modes to be biased in the selection of reacting particles. These parameters can be identified for a particular reaction if experimental or numerical data exists that describe the variation of reaction cross section with collision energy. Finally, the model provides accuracy in that it will reproduce the measured equilibrium rate coefficients under conditions of equilibrium. While these attributes of the GCE model are very positive, and this model appears to be adequate for nonionizing air [Pg.118]

No attempt has been made to provide the intensive detail found in Howard s review of oxyradicals [10], the review of Hendry et al. [43] of H-atom transfer to several radicals or Anbar and Neta s review of HO-radical reactions [44]. Instead, we have attempted to extend the scope of those reviews in two ways (i) rate coefficients are provided for R02-radical addition to many olefins, for ring closures to form cyclic ethers, and for intramolecular abstraction (ii) for each reaction, we have estimated the best value Arrhenius parameters (A-factor and E) and, where such values have been measured they are also listed. We believe the value of absolute rate coefficients is improved substantially by the availability of reliable Arrhenius parameters, with which one can calculate the values of rate coefficients at other temperatures for use in experimental or modelling studies. [Pg.13]

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 [Pg.264]

Surface species in the mechanism are denoted (s) in the species name. In this reaction mechanism, only reaction 7 was written as a reversible reaction all of the rest were specified as irreversible. Formally, reactions 12 and 14 should be third order in the concentration of Pdfs) and O(s), respectively. However, the reaction order has been overridden to make each one first-order with respect to the surface species. In some instances, reactions have been specified with sticking coefficients, such as reactions 1, 3, 11, and 13. The other reactions use the three-parameter modified Arrhenius form to express the temperature-dependent rate constant. [Pg.477]

To apply the results of the chemical activation and the thermal dissociation analysis for comparison to literature or experimental data (when available) it is necessary to construct an elementary chemical reaction mechanism. The mechanism includes all the reactions involved in the chemical activation process, including stabilizations and reactions for thermal dissociation of the stabilized species. The reactions are reversible, so that we implicitly take into account some of the thermal dissociation reactions as the reverse of the forwards (chemically activated) reactions. For example, the dissociation of DBFOO to DBF + O2 is included as being the reverse reaction of DBF + O2 o DBFOO. ThermKin is used to determine the elementary reaction rate coefficients and express the rate coefficients in Arrhenius forms. [Pg.144]

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