Apparent activation energy of diffusion

Figure 5. The FR spectra of the isobutane/H-ZSM-5 diameter. The apparent activation energy of diffusion (E.) of systems at 373 K and 133 isobutane obtained from the Arrhenius plot was 21 kJ mol Pa (A) Z57, (B) Z34 and (Figure 6, open symbols). This value is about three times higher (C) Z15. The sample than that obtained for the diffusion n-butane [12]. At 373 K and amount was 50 mg.

Tables Apparent activation energy of diffusion for n-hexane in MFI-type zeolites and a comparison with literature...

Topic 4.5.2 Apparent activation energy of diffusion processes... 

However, the behavior of the catalysts measured in this work is different. At temperatures above 400 K the catalytic activity becomes limited, in agreem t with the Thiele theory. However, the apparent activation energy gradually decreases from 94 to 6 kJ/mol, rather than to 50 kJ/mol, which implies that the apparent activation energy of diffusion is exhibited. Nevertheless, the size of the wider pores in the pellet does appear to affect strongly the activity. Therefore, it is impossible that merely external diffusion limitation, that is, diffusion from the bulk of the gas flow to tiie external surface of the catalyst body, is rate-determining. Since the catalyst spheres had the same diameter, the activity of all catalysts should be equal if external transport is determining the activity. As the concentration of reactants inside the particle is nearly zero, the pore size should be of no importance. However, this is in contradiction with the measurements. 

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... 

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. 

Pore diffusion leads to a reduction by half of the apparent activation energy of enzyme reactions, as in the case of chemical reactions (Levenspiel, 1999). In the literature it has been reported that pore diffusion leads to enhanced apparent temperature and pH stability owing to broadening of the optimal activity regions as a function of temperature and pH activity (Karanth, 1978). Hindered pore diffusion... 

It has been pointed out (Anbar and Hart, 1967 Logan, 1967) that reactions near the diffusion-controlled limit are expected to have a constant apparent activation energy of 3-4 kcal mole-1, which is equal to the activation energy of diffusion of solutes in water (AE f), irrespective of their actual energy of activation (AEaet). For reactions proceeding at rates slower than 108 m-1 sec-1, the measured activation energy represents the actual enthalpy barrier of the reaction. 

If Bd may bo treated as independent of T, this equation gives AHd + RT = BdAHv. Here A Hd and A Hv are apparent activation energies for diffusion (at zero diluent concentration) and viscosity (of pure polymer), respectively. This affords Bd with another physical interpretation, i.e., Bd = AHdjAHv, since RT is quite small in general. 

An apparent activation energy of about 90kJ/mol corroborated the assumption of the oxygen diffusion limitation in the catalyst bulk. 

A detailed investigation of the nuclear spin-lattice relation time, T l. in liquid [Ni(CO)J and [Fe(CO)s] as a function of temperature and resonance frequency has been carried out 212). It was concluded that relaxation occurs only by two mechanisms, i.e., spin-rotation interaction and anisotropic chemical shift. It was possible to obtain the anisotropic chemical shift difference of 440 ppm for [Ni(CO)4] and 408 ppm for [Fe(CO)s] and the spin-rotation constants. Apparent activation energies for diffusion of 1.0 kcal/mole for [Ni(CO)4] and 2.9 kcal/mole for [Fe(CO)5] were derived. 

Figure 11, the effect of temperature on color degradation, also reveals that the color degradation is strongly controlled by the diffusivity of the reactants. The apparent activation energy of used catalyst was 3/4 of that of fresh catalyst. 

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