Diffusional-influenced reaction rates

The combined effect of diffusional and reaction rate resistances can have a considerable influence on the relative global rate of the two reactions. 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

A zero-order reaction thus becomes a half-order reaction, a first-order reaction remains first order, whereas a second-order reaction has an apparent order of 3/2 when strongly influenced by diffusional effects. Because k and n are modified in the diffusion controlled region then, if the rate of the overall process is estimated by multiplying the chemical reaction rate by the effectiveness factor (as in equation 3.8), it is imperative to know the true rate of chemical reaction uninfluenced by diffusion effects. 

There are many factors that influence the outcome of enzymatic reactions in carbon dioxide. These include enzyme activity, enzyme stability, temperature, pH, pressure, diffusional limitations of a two-phase heterogeneous mixture, solubility of enzyme and/or substrates, water content of the reaction system, and flow rate of carbon dioxide (continuous and semibatch reactions). It is important to understand the aspects that control and limit biocatalysis in carbon dioxide if one wants to improve upon the process. This chapter serves as a brief introduction to enzyme chemistry in carbon dioxide. The advantages and disadvantages of running reactions in this medium, as well as the factors that influence reactions, are all presented. Many of the reactions studied in this area are summarized in a manner that is easy to read and referenced in Table 6.1. 

For rate laws that are noninteger or complex functions of the concentration, Cas is found by trial and error solution of the flux expression equated to the reaction rate. The influence of diffusional resistance on the observed reaction rate is especially apparent for a very fast surface reaction. For that case, the surface concentration of reactant is very small compared to its concentration in the bulk fluid. The observed rate is then written according to Equation (6.2.15), but ignoring Cas-... 

The influence of diffusional limitations in gas phase reactions has been extensively treated by Wheeler and from a chemical engineering viewpoint by Hougen and Watson More recently a monograph by Satterfield and Sherwood has appeared. The problem of diffusion can be separated into two parts, the first is diffusion or mass transfer to the external surface of the catalyst and second, for those catalysts which are porous, diffusion within the catalyst pores. When diffusion is the rate limiting process, reaction rate, selectivity and activation energy are affected. 

After drying and reduction, the Pd-Ag/C catalysts are composed of bimetallic Eilloy nanoparticles ( 3 nm). CO chemisorption coupled to TEM and XRD analysis showed that that, for catalysts 1.5% wt. in each metal, the bulk composition of the alloy is close to 50% in each metal, whereas the surface is 90% in Ag and 10% in Pd [9]. Mass transfer limitations can be detected by testing the same catalyst with various pellet sizes [18]. Indeed, if the reactants diffusion is slow due to small pore sizes, the longer the distance between the pellet surface and the metal particle, the larger the influence of the difiusion rate on the apparent reaction rate. Pd-Ag catalysts with various pellet sizes were thus tested in hydrodechlorination of 1,2-dichloroethane. Results were compared to those obtained with a Pd-Ag/activated charcoal catalyst. Fig. 4 shows the evolution of the effectiveness factor of the catalysts, i.e. the ratio between the apparent reaction rate and the intrinsic reaction rate, as a function of the pellet size. The intrinsic reaction rate was considered equal to the reaction rate obtained with the smallest pellet size. When rf = 1, no diffusional limitations occur, and the catalyst works in chemical regime. When j < 1, the observed reaction rate is lower than the intrinsic reaction rate due to a slow diffusion of the reactants and products and the catalyst works in diffusional regime [18]. 

In the absence of a boundary layer and internal and external diffusional influences, the cyclohexanone oxime conversion follows the requirements of Bassett-Habgood kinetic treatment [20] for first order reaction processes in which the rate determining step is the suiiface reaction ... 

Transfer reactions do not change the total number of radicals in the mixture and therefore usually (ideally) do not influence the rate of polymerization (nor copolymer composition). However, there might be indirect effects on the rate (especially in systems with strong diffusional limitations, where a lowering of the rate may be observed with increased concentrations of CTA or solvent). If the transfer radicals have low activity, then retardation may be observed. 

The rate of this and many other such phase boundary reactions depends upon the instantaneous state of the surface. For tarnishing processes, this generally means that the rate depends upon the instantaneous activities of the components at the phase boundary as well as upon the temperature. As long as diffusional equilibrium is maintained, and the outer phase boundary reaction alone is rate-controlling, the activity of the metal at the phase boundary between oxidation product and gas is constant and equal to one. There are indications [50] that the electronic defects can particularly influence the rate of dissociation of the gases at the phase boundary between oxidation product and gas. Use is made of this property of solid surfaces in the field of heterogeneous catalysis [4]. Since the defect concentration is determined by the activities of the components in the reaction product, it is understandable that the rate of the phase boundary reaction should, in general, depend upon the component activities in the reaction product at the phase boundary. 

Immobilized Derivatives of Enzymes.— Numerous reviews have appeared surveying the field of enzyme immobilization. - Diffusional influences on the parametric sensitivity of immobilized enzyme catalysts have been mathematically analysed. Particular account was taken of external mass transfer and intraparticle diffusion effects which can significantly influence the dependence of the observed reaction rate on operating parameters such as temperature and pH. 

These latter results illustrate the controversy on the influence of extra-framework species in zeolites for catalytic reactions. Note that on the one hand the extra-framework aluminum includes synergistic effects and, hence, increases the activity. On the other hand, the introduction of diffusional constraints resulting from a partial blockage of the pores or acid sites leads to a decrease of the reaction rates. Therefore, the evaluation of acid-base properties using the rates of test reactions over various catalysts might be restricted to a certain degree, and without a detailed analysis of the acid site and strength distribution only zeolites of one structural type, or even with the same preparation history, can be reliably compared. 

Water is critical for enzymes because it influences enzyme structure via nonco-valent bonding. A too-low water content generally reduces enzymic activity, whereas a too-high content can also reduce the reaction rates by causing the aggregation of enzyme particles and hence diffusional limitations. The optimum water content is often within a narrow range. 

Steps 1 and 7 are highly dependent on the fluid flow characteristics of the system. The mass velocity of the fluid stream, the particle size, and the diffusional characteristics of the various molecular species are the pertinent parameters on which the rates of these steps depend. These steps limit the observed rate only when the catalytic reaction is very rapid and the mass transfer is slow. Anything that tends to increase mass transfer coefficients will enhance the rates of these processes. Since the rates of these steps are only slightly influenced by temperature, the influence of these processes... 

In this case, the electrogenerated R will encounter Z as it diffuses away from the electrode and will react to form P. This diffusional mixing of two reactants (R and Z in this example) is the basis for chronoabsorptometry (and other electrochemical techniques) as a kinetic method. The homogeneous chemical reaction of R will perturb its accumulation by a magnitude that is proportional both to k and to the concentration of Z. The influence of this perturbation is apparent from the concentration-distance profiles for R, which are illustrated for a rate constant of 107 L/(mol s) in Figure 3.9. 

The modeling of RD processes is illustrated with the heterogenously catalyzed synthesis of methyl acetate and MTBE. The complex character of reactive distillation processes requires a detailed mathematical description of the interaction of mass transfer and chemical reaction and the dynamic column behavior. The most detailed model is based on a rigorous dynamic rate-based approach that takes into account diffusional interactions via the Maxwell-Stefan equations and overall reaction kinetics for the determination of the total conversion. All major influences of the column internals and the periphery can be considered by this approach. 

Zeolite Beta has also been studied for isobutane/butene alkylation (65, 66), but it was less selective to the desired TMP than USY, suggesting some diffusional limitations for these highly branched products at the relatively low reaction temperatures used. In fact, an increase of activity was observed when decreasing the crystal size of the Beta zeolite (66). As for USY zeolites, the activity, selectivity and deactivation rate of Beta zeolite were influenced by the presence of EFAL species (67). Medium pore zeolites, such as ZSM-5 and ZSM-11 were also found active for alkylation, but at temperatures above 100°C (68, 69). Moreover, the product obtained on ZSM-5 and ZSM-11 contained more light compounds (C5-C7), and the Os fraction was almost free of trimethylpentanes, indicating serious pore restrictions for the formation of the desired alkylation products. 

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