Activation energy, apparent factor

Here 17 is the apparent viscosity at temperature T, R is the universal gas constant, and A is an empirical constant, called frequency factor for melt flow. The activation energy values for different systems and at different shear rates are summarized in Table 8. It is evident that activation energy for flow increases with filler loading, but it decreases with an increase in shear rate. 

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

Increases in reaction rate with temperature are often found to obey the Arrhenius equation, from which the apparent values of the reaction frequency factor, A, and the activation energy, E, are calculated. The possibility that the kinetic obedience changes with temperature must also be considered. 

Figure 8.18. Effect of catalyst potential and work function on the apparent activation energy, E, and on the logarithm of the preexponential factor r° rfi is the open-circuit preexponential factor and T0, T are the two isokinetic points of C2H6 oxidation on Pt/YSZ for positive and negative potentials respectively.27 Reprinted with permission from Academic Press.

Figure 8.41 shows the effect of positive overpotential, i.e. increasing work function, on the apparent activation energies E, and preexponential factors kf of the epoxidation (i=l) and deep oxidation (i=2) reactions. After... 

Figure 8.75 shows the dependence of the apparent activation energy Ea and of the apparent preexponential factor r°, here expressed as TOF°, on Uwr. Interestingly, increasing Uwr increases not only the catalytic rate, but also the apparent activation energy Ea from 0.3 eV (UWr=-2 V) to 0.9 eV (UWr-+2V). The linear variation in Ea and log (TOF°) with UWr leads to the appearance of the compensation effect where, in the present case, the isokinetic point (T =300°C) lies outside the temperature range of the investigation. 

Relationships between reaction rate and temperature can thus be used to detect non-classical behaviour in enzymes. Non-classical values of the preexponential factor ratio (H D i 1) and difference in apparent activation energy (>5.4kJmoRi) have been the criteria used to demonstrate hydrogen tunnelling in the enzymes mentioned above. A major prediction from this static barrier (transition state theory-like) plot is that tunnelling becomes more prominent as the apparent activation energy decreases. This holds for the enzymes listed above, but the correlation breaks down for enzymes... 

Results for styrene - yield Ea 21 kcal. Since Ep — Et/2 was found previously to be 6.5 kcal., we conclude that the activation energy Ei for thermal initiation in styrene is 29 kcal., which would be quite acceptable for the process (21), already rejected on other grounds. For methyl methacrylate, Ea—l kcal. and Ep — Et/2 = b kcal. Hence Ei = 22 kcal. These initiation reactions are very much slower than is normal for other reactions with similar activation energies. The extraordinarily low frequency factors Ai apparently are responsible. For methyl methacrylate, Ai is less than unity. Interpreted as a bimo-lecular process, this would imply initiation at only one collision in about 10 of those occurring with the requisite energy ... 

Addition of CO also enhances the N2O conversion, by about a factor of two for Co and tremendously for Fe (figure 6). For Cu a maximum in the N2O conversion appears as a function of the CO/N2O ratio in the feed. This maximum shifts to higher values with increasing temperature (figure 7). The apparent activation energy for Co is hardly altered, for Fe it decreased nearly 1(X) kJ/mol, while for Cu it is increased by 50 kJ/mol. 

The apparent activation energy Sa on each alloy was found to be 41 kJmol which is almost comparable to that on the pure Pt electrode. The values of on the alloys are larger than that on the Pt electrode by factors of 4.0 (Pt54Fe4g), 3.1... 

In a similar fashion, it is easily shown that the apparent activation energy of the reaction may differ appreciably from the intrinsic activation energy of the chemical reaction. The apparent rate constant is equal to the product of the effectiveness factor and the true rate constant and, in the limit of low effectiveness factors, it can be said that... 

This situation is termed pore-mouth poisoning. As poisoning proceeds the inactive shell thickens and, under extreme conditions, the rate of the catalytic reaction may become limited by the rate of diffusion past the poisoned pore mouths. The apparent activation energy of the reaction under these extreme conditions will be typical of the temperature dependence of diffusion coefficients. If the catalyst and reaction conditions in question are characterized by a low effectiveness factor, one may find that poisoning only a small fraction of the surface gives rise to a disproportionate drop in activity. In a sense one observes a form of selective poisoning. 

For situations where the reaction is very slow relative to diffusion, the effectiveness factor for the poisoned catalyst will be unity, and the apparent activation energy of the reaction will be the true activation energy for the intrinsic chemical reaction. As the temperature increases, however, the reaction rate increases much faster than the diffusion rate and one may enter a regime where hT( 1 — a) is larger than 2, so the apparent activation energy will drop to that given by equation 12.3.85 (approximately half the value for the intrinsic reaction). As the temperature increases further, the Thiele modulus [hT( 1 — a)] continues to increase with a concomitant decrease in the effectiveness with which the catalyst surface area is used and in the depth to which the reactants are capable of... 

Gold forms a continuous series of solid solutions with palladium, and there is no evidence for the existence of a miscibility gap. Also, the catalytic properties of the component metals are very different, and for these reasons the Pd-Au alloys have been popular in studies of the electronic factor in catalysis. The well-known paper by Couper and Eley (127) remains the most clearly defined example of a correlation between catalytic activity and the filling of d-band vacancies. The apparent activation energy for the ortho-parahydrogen conversion over Pd-Au wires wras constant on Pd and the Pd-rich alloys, but increased abruptly at 60% Au, at which composition d-band vacancies were considered to be just filled. Subsequently, Eley, with various collaborators, has studied a number of other reactions over the same alloy wires, e.g., formic acid decomposition 128), CO oxidation 129), and N20 decomposition ISO). These results, and the extent to which they support the d-band theory, have been reviewed by Eley (1). We shall confine our attention here to the chemisorption of oxygen and the decomposition of formic acid, winch have been studied on Pd-Au alloy films. 

Film composition Activation energy (kcal/mole) Logio frequency factor, A (Torr CO 2/ min cm2 apparent area) Activity, 150°C (molecules/sec cm2)... 

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],... 

It is apparent that these reactions are close in their enthalpies, but greatly differ in the rate constants. The peroxyl radical reacts with p-cresol by four orders of magnitude more rapidly than with ethylbenzene. Such a great difference in the reactivities of RH and ArOH is due to the different activation energies of these reactions, while their pre-exponential factors are close. This situation was analyzed within the scope of the parabolic model of transition states (see Chapter 6 and Refs. [33-38]). 

Table 7.5 WGS Reaction Kinetics, Apparent Activation Energies, Eaf (Forward), and Modeled Values for the Backward Activation Energy Eab and Pre-Exponential Factors /r0f, kob, Assuming an Elementary Reaction with First-Order Kinetics of the WGS Reaction...

Qualitatively, one can now deduct the apparent activation energy As for the case of a diffusion-limited reaction. If we plot the logarithm of the product of the efficiency factor and the constant for the speed of reaction ln[kij] against 1/T, a typical curve with three regimes can be seen (see Figure 11.15). 

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