Activation energy and pre-exponential factor

It is well known that the macroscopic aspects of the kinetics of chemical reactions are expressed in terms of the Arrhenius equation 

In order to obtain a relation between these two experimental parameters and the microscopic cross-section, it is more convenient to use the energy expression (21) for the rate coefficient, rather than the velocity expression (18), viz. 

the experimental activation energy E is defined from eqn. (20) d Infe(T) 

As is seen from eqn. (21), the integrand in the denominator of eqn. (23) is just proportional to the energy distribution of reactive collisions f(E)o(E)u. Thus we can identify the first term on the right-hand side of 

This relationship is visualized clearly by Menzinger and Wolfgang [36] for various types of cross-section function a(E) and the equilibrium Maxwell—Boltzmann distribution function f( ). The effect of nonequilibrium distribution is also discussed. 

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The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

Table 3.6. Experimental activation energies and pre-exponential factors for CO and NO desorbing from a range of clean and well-defined single crystals. All data were obtained in the low coverage regime. [From V.P. Zhdanov, J. Pavlicek and Z. Knor, Catal. Rev.-Sci.

Unraveling catalytic mechanisms in terms of elementary reactions and determining the kinetic parameters of such steps is at the heart of understanding catalytic reactions at the molecular level. As explained in Chapters 1 and 2, catalysis is a cyclic event that consists of elementary reaction steps. Hence, to determine the kinetics of a catalytic reaction mechanism, we need the kinetic parameters of these individual reaction steps. Unfortunately, these are rarely available. Here we discuss how sticking coefficients, activation energies and pre-exponential factors can be determined for elementary steps as adsorption, desorption, dissociation and recombination. 

Figure 7.8. The compensation effect in the desorption ofAg from a ruthenium surface activation energy and pre-exponential factor depend in the same way on coverage. The...

Chen et al. [70] suggested that temperature gradients may have been responsible for the more than 90 % selectivity of the formation of acetylene from methane in a microwave heated activated carbon bed. The authors believed that the highly nonisothermal nature of the packed bed might allow reaction intermediates formed on the surface to desorb into a relatively cool gas stream where they are transformed via a different reaction pathway than in a conventional isothermal reactor. The results indicated that temperature gradients were approximately 20 K. The nonisothermal nature of this packed bed resulted in an apparent rate enhancement and altered the activation energy and pre-exponential factor [94]. Formation of hot spots was modeled by calculation and, in the case of solid materials, studied by several authors [105-108],... 

Since the reactants (R02 ketone) and the transition state have a polar character, they are solvated in a polar solvent. Hence polar solvents influence the rate constants of the chain propagation and termination reactions. This problem was studied for reactions of oxidized butanone-2 by Zaikov [81-86]. It was observed that kp slightly varies from one solvent to another. On the contrary, kt changes more than ten times from one solvent to another. The solvent influences the activation energy and pre-exponential factor of these two reactions (see Table 8.16). 

The published values for the activation energies and pre-exponential factors of transesterification and glycolysis vary significantly. Catalysts and stabilizers influence the overall reaction rate markedly, and investigations using different additives cannot be compared directly. Most investigations are affected by mass transport and without knowledge of the respective mass transport parameters, kinetic results cannot be transferred to other systems. 

Table 13 Arrhenius activation energies and pre-exponential factors for thermal isomerization of tetraphenylethenes [42] and the standard enthalpy differences in benzene solution."...

To calculate the closure temperature using Equation 5-76a, it is necessary to know the diffusion parameters (activation energy and pre-exponential factor A) of the mineral, the grain size and shape, and the cooling rate. Below are some considerations about these parameters. 

The induction time t is of particular interest, since it can be compared to the induction time computed for an adiabatic thermal explosion (See Ref 6, pp 173—74 or Eq 6 of Article on Hot Spots, p H172-R) to provide a check on the correctness of the supposition that the input shock"generates a thermal explosion (at the shock entry face). Unfortunately, an exact quantitative treatment of the induction times of shock-generated thermal explosions suffers from a) uncertainty of the shockgenerated temperature in the LE and b) uncertainty in the Arrhenius kinetic parameters (activation energy and pre-exponential factor) (See Kinetics in this Vol)... 

Fig. 5. The relation between activation energies and pre-exponential factors. X—for hydroxyl —for oxygen atoms.

More explicit knowledge of absolute rate constants, activation energies and pre-exponential factors for elementary reactions involving other active particles, as in the interaction between radicals with a longer carbon chain and various molecules, is necessary for obtaining a better insight into the nature of these regularities. 

Activation energies and pre-exponential factors for the first-order rate coefficients for anthracene oxidation... 

Work on conduction in materials of biological interest such as proteins and oxidized cholesterol suggests that a correlation exists between the activation energies and pre-exponential factors an of the form... 

Fig. 11. Linear correlation between activation energy and pre-exponential factor for different wavelengths (filters UG and BG) and intensities (metal gauze sieves S) of the CO oxidation on ZnO...

The same set-up as used for TPD can be applied to study reactions between adsorbed molecules. In the experiment shown in Figure 2.14, O-atoms have been co-adsorbed with CO [17]. During temperature programming, C02 forms and desorbs instantaneously (see inset of Fig. 2.14). In order to derive the activation energy and pre-exponential factor, we start by assuming that the reaction exhibits first-order kinetics in the surface concentrations of CO and O hence, we can write the rate as ... 

Decomposition rate constants are measured over as wide a temperature range as possible. Only the first one third to one half of the decomposition can be analyzed before it becomes severely autocatalytic. With the rate constants, an Arrhenius plot can be constructed and activation parameters calculated. Activation energies and pre-exponential factors correlate the decomposition rates with temperature. In addition, the magnitude of the activation energy may shed light on the key step in the decomposition process, and Arrhenius parameters are necessary in many explosive code calculations. Our procedure is to input the activation parameters into the Frank-Kamentskii equation [145] and use it to predict critical temperature of a reasonable size (e.g. 1 kilogram) of the energetic material ... 

This paper focuses on the influence of the support on the H/D exchange of CP over supported Pt catalysts. It will be shown that kinetics and selectivities are largely affected by the support material. Particle size effects are separated from support effects. The activity shows a compensation effect, and the apparent activation energy and pre-exponential factor show an isokinetic relationship . This can be explained by different adsorption modes of the CP on the metallic Pt surface. The change in adsorption modes is attributed to a change in the electronic structure of the Pt particles, which in turn is induced by changes in the acid/base properties of the support. 

The Arrhenius expression (Equation 19.1) using the activation energy and pre-exponential factor derived from TGA measurements of a PA6 sample in N2 was incorporated in a standard ID pyrolysis model described in Section 19.6. The thermal properties used in the model are the ones from the ignition tests (Section 19.4.2.2) as described in Section 19.6 in conjunction with the MDSC experiments (Section 19.3.2.2). Figures 19.25a-c show the predicted surface temperature histories for... 

Diffusional Activation Energies and Pre-Exponential Factors of the Eyring Equation for the Diffusion of H-ZSM-11 and H-SSZ-24 Zeolites at Different... 

Note the use of activities, as well as of an equilibrium constant based on activities. The kinetic constants for autocatalyzed and catalyzed reactions, k and k, were determined from initial reaction rates with liquid activity coefficients calculated by UNIQUAC. Near chemical equilibrium the fCT is about 6, while Kx is about 5. Table 8.7 gives activation energies and pre-exponential factors obtained by nonlinear regression. The simulation shows tbat the autocatalysis effect is neghgible below 150 °C, but it might increase to 20% at 180 °C. 

Fig. 5.15. Arrhenius representation. Data are derived from Fig. 5.13. The activation energy and pre-exponential factors are defined in the text...

The two-site reaction kinetics model proposed by Bonn [1] was used to evaluate the kinetic parameters. Activation energies and pre-exponential factors were determined from experiments between 570-630 K at 10 MPa. In order to decrease the strong inter-correlation between pre-exponential factors and activation energies, the reparametrisadon method of Kittrell [4] was used. Values for the pre-exponential factors at a reference temperature and activation energies are presented in Table 2. Experimental and theoretical details on HDM reaction kinetics will be published elsewhere [5]. 

The activation parameters such as activation energy and pre-exponential factor, A calculated by different methods show the decomposition rate is independent of the nature of the rare earth cation. The activation energies are in the range of 60-70 kJ mol-1 with a reaction order in the range 1.4 to 1.6. 

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