Apparent activation energy diffusion

Figure 2.12 shows the rate, the coverages, the reaction orders, and the normalized apparent activation energy, all as a function of temperature. Note the strong variations of all these parameters with temperature, in particular that of the rate, which initially increases, then maximizes and decreases again at high temperatures. This characteristic behavior is expected for all catalytic reactions, but is in practice difficult to observe with supported catalysts because diffusion phenomena come into play. 

The presence of diffusion limitations has a strong effect on the apparent activation energy one measures. We can express both the rate constant, k, and the diffusion constant, Defr, in the Arrhenius form ... 

Hence, the apparent activation energy is half the value we would obtain if there were no transport limitations. Obviously it is important to be aware of these pitfalls when testing a catalyst. Indeed, apparent activation energies generally depend on the conditions employed (as discussed in Chapter 2), and diffusion limitation may further cause them to change with temperature. 

When solving for the apparent activation energy in the diffusion limited region we obtain... 

Normally the activation energy for diffusion in the gas phase is much smaller than the activation energy for a catalyzed reaction, and hence, according to Eqs. (38) and (46), the overall or apparent activation energy for the diffusion-limited process is half of what it would be without transportation limitation. If we plot the rate as a function of reciprocal temperature one observes a change in slope when transport limitations starts to set in. 

Figure 5.37. Arrhenius plot illustrating the effect on the apparent activation energy of pore diffusion and transport limitations through the stagnation layer surrounding a catalyst...

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... 

Here, we consider the consequences of being in the region of strong pore-diffusion resistance (77 - 11(f)" as apparent activation energy (f)" is given by equation 8.5-20b. 

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). 

Regime of transport limitation, here

diffusion through the hydrodynamic boundary layer. The apparent activation energy under these conditions gets close to zero. Every educt molecule reacts instantaneously on the outer catalyst surface, no educt diffusion inside the catalyst particle takes place. 

Relation between True Activation Energy and Apparent Activation Energy Found in Zone II. It has been shown 101, 103) that the rate of reaction in the diffusion controlled zone is given by... 

Robert B. Anderson. Some information on mass transfer processes may be obtained from activation energies. If a reaction were moderately rapid and diffusion in the liquid phase were rate controlling, the apparent activation energy should be 1-2 kcal./mole. If reaction occurs in pores and were diffusion plus reaction controlled, the activation energy should be one-half that of the surface process, which should still be a large value. What apparent activation energy was found in your oxidation reactions ... 

The data were found to give a reasonably good fit to Eq. (4-21). The apparent rate constants K, and K2 gave linear Arrhenius plots with apparent activation energies of 85 and 43 kJ/mole, respectively. A more detailed study of the inter-relationships between the chemical kinetics, the viscosity and the conversion could provide a useful insight into the nature of these diffusion-controlled reactions. 

Some data on the effect of temperature are given in figures 2a and b. Below 313 K an activation energy of 90 KJ/mol is estimated for both kj and k y. Above 313 K diffusion limitation occurs, resulting in a decreasing apparent activation energy and also in a lower selectivity at higher temperature. 

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