Activation energy diffusional effect

Under normal circumstances the true activation energy term in equation 12.3.85 will far exceed the diffusional activation term calculated from either equation 12.3.86 or equation 12.3.87 and, to a good approximation, it may be said that in the limit of low effectiveness factors... 

Diffusional mass transfer processes can be essential in complex catalytic reactions. The role of diffusion inside a porous catalyst pellet, its effect on the observed reaction rate, activation energy, etc. (see, for example, ref. 123 and the fundamental work of Aris [124]) have been studied in detail, but so far several studies report only on models accounting for the diffusion of material on the catalyst surface and the surface-to-bulk material exchange. We will describe only some macroscopic models accounting for diffusion (without claiming a thorough analysis of every such model described in the available literature). 

Because the electronic distribution and nuclear configuration of the donor and the acceptor in the (Class II) successor complexes are similar to those of the free donor/acceptor product (i.e. radical pair), it is reasonable to suggest that products can originate directly from the successor complex (pathway Pi). Such a reaction, which includes an electron-transfer step, does not necessarily proceed via a pair of free ion radicals, and the effective activation energy can be even lower than that required by pathway P2. When the follow-up reaction involves the coupling of radicals, the reaction directly proceeding from the (ET) successor complex state can be kinetically favorable (since it excludes diffusional processes). 

The only allowed motion is the exchange of the vacancy with one of its neighboring atoms. The exchange rate depends on the local environment, i.e. on the relative position of the vacancy and the impurity atom. This takes into account the effect of the lattice stress induced by the tracer atom on the energy landscape observed by the vacancy. Each rate is simply proportional to the Boltzmann factor e-AE/kBT wjjere is the activation energy for the considered diffusional move and kBTis the thermal... 

By using such a model, it was found that the pilot plant data for the three commercial shift catalysts yielded intrinsic kinetic rate constants and activation energies in good agreement with experimental values for small catalyst particles with no diffusional limitation. Ruthven also derived expressions to account for the effect of pressure on catalytic activity. 

The authors did not report any diffusional limitation in agreement with the results of Bodrov et ai (1967a). The activation energy for temperatures between 700-900°C was found to be 35 5 kcal/mol, which, as can be seen from Table 3.1 suggests the absence of diffusion effects. 

Kinetics are readily determined in the laboratory under carefully controlled conditions such that the effects of diffusional resistances are entirely eliminated. The intrinsic kinetics so determined yield the rate constant, the orders of the reaction with respect to the reactants, catalyst, and the activation energy. These are unique to a given gas-liquid or gas-liquid-solid catalyst system and do not vary with the type or size of the multiphase reactor. This matter is briefly discussed later in Section 2.5. 

A very simple method of ascertaining the importance of diffusional processes (k a and is to study the effect of temperature on the overall rate of consumption of the gas-phase solute. An Arrhenius plot (In vs. 1/T) gives the activation energy, AE (slope=AE/R), of the process consuming the gas-phase reactant. When AE is less than 20kJ/mol, it is inferred that one or both of the two diffusional steps (k a... 

The contribution of surface diffusion to the overall effective diffusivity, however, depends on the product KD rather than on the surface diffusivity alone (Eq. (5.20)]. Since the diffusional activation energy ( ) is generally smaller than the heat of sorption, this product, and therefore the relative contribution of surface diffusion, normally decreases with increasing temperature. Such a trend is illustrated by the data given in Table 5.1. 

Diffusional constants may depend strongly on micropore filling. This, in essence, is due to site blocking effects. It explains the often observed relationship between overall experimentally measured diffusional rate constant activation energies and heats of adsorption. 

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