Catalysts, general reactant concentration

The last part of the polarization curve is dominated by mass-transfer limitations (i.e., concentration overpotential). These limitations arise from conditions wherein the necessary reactants (products) cannot reach (leave) the electrocatalytic site. Thus, for fuel cells, these limitations arise either from diffusive resistances that do not allow hydrogen and oxygen to reach the sites or from conductive resistances that do not allow protons or electrons to reach or leave the sites. For general models, a limiting current density can be used to describe the mass-transport limitations. For this review, the limiting current density is defined as the current density at which a reactant concentration becomes zero at the diffusion medium/catalyst layer interface. 

The catalytic principle of micelles as depicted in Fig. 6.2, is based on the ability to solubilize hydrophobic compounds in the miceUar interior so the micelles can act as reaction vessels on a nanometer scale, as so-called nanoreactors [14, 15]. The catalytic complex is also solubihzed in the hydrophobic part of the micellar core or even bound to it Thus, the substrate (S) and the catalyst (C) are enclosed in an appropriate environment In contrast to biphasic catalysis no transport of the organic starting material to the active catalyst species is necessary and therefore no transport limitation of the reaction wiU be observed. As a consequence, the conversion of very hydrophobic substrates in pure water is feasible and aU the advantages mentioned above, which are associated with the use of water as medium, are given. Often there is an even higher reaction rate observed in miceUar catalysis than in conventional monophasic catalytic systems because of the smaller reaction volume of the miceUar reactor and the higher reactant concentration, respectively. This enhanced reactivity of encapsulated substrates is generally described as micellar catalysis [16, 17]. Due to the similarity to enzyme catalysis, micelle and enzyme catalysis have sometimes been correlated in literature [18]. 

As mentioned earlier, if the rate of a catalytic reaction is proportional to the surface area, then a catalyst with the highest possible area is most desirable and that is generally achieved by its porous structure. However, the reactants have to diffuse into the pores within the catalyst particle, and as a result a concentration gradient appears between the pore mouth and the interior of the catalyst. Consequently, the concentration at the exterior surface of the catalyst particle does not apply to die whole surface area and the pore diffusion limits the overall rate of reaction. The effectiveness factor tjs is used to account for diffusion and reaction in porous catalysts and is defined as... 

To keep the mathematics as simple as possible, we treat the catalyst pellet as an infinitely flat plate (b = 0 in eq 139). The solution of eq 139 depends on whether the reactant concentration will drop to zero at some point Xo inside the pellet, in the case that the reaction rate is strongly influenced by diffusion, or will be finite everywhere in the pellet interior, if there is only a moderate effect of diffusion. This is a general feature of zero-order reactions which arises from the assumption that the reaction will proceed at a constant rate until the reactant is completely exhausted. 

For historical interest and to illustrate a general facet of systems with arbitrary distribution of catalyst material over free catalyst and reaction intermediates, the classical models of enzyme catalysis are briefly reviewed. They show "saturation kinetics " An increase in reactant concentration causes a shift of catalyst material from free catalyst to an intermediate, so that the rate has an asymptotic limit that can at most be approached even at the highest reactant concentrations. 

Industrial catalytic oxidation reactions are carried out at high reactant concentrations over a variety of supported metal catalysts. Because most industrial processes operate with well-characterized inlet streams (usually one reactant plus an oxidant), there has been little need to understand the complex processes that may occur in mixtures. As shown in Table 2, these reactions are typically carried out at temperatures greater than 400 °C, with the exception of ethene and CO oxidation. Such temperatures are generally required to achieve economical reaction rates (high ac-... 

One way to estimate the influence of transport processes is to use directly experimental results observed under given experimental conditions. In general, the experimentalist has information concerning observed reaction rates, bulk reactant concentrations, and temperature, as well as the catalyst pellet form and dimensions. With these details at hand, the Weisz module can be estimated. For example, for spherical catalytic particles, see Equation 2.180. 

Fig. 3.8 presents a schematic of catalysis in a porous solid. The reactant concentration at the outer boundary of the stagnant film is the concentration of reactant in the feed, that is, it is Cbf in moles/m. Reactant molecules move across the stagnant film by molecular diffusion, which we generally model as a linear concentration difference. That difference is Cbf Csf, where Csf is the concentration of reactant at the surface of the catalyst in moles/m. Reactant then diffuses from the surface of the catalyst along pores to the catalytic sites inside the solid. Reactant movement within the pore is also by molecular diffusion, which we model as a linear concentration difference. Catalytic sites occur along the length of the pore, thus reactant concentration... 

The general theoretical approach is to develop the mathematical equations for simultaneous mass transfer and chemical reaction, as the reactants and products difHise into and out of the porous catalyst. When reaction occurs simultaneously with mass transfer within a porous structure, a concentration gradient is established. Since interior surfaces are thus exposed to lower reactant concentrations than surfaces near the exterior, the overall reaction rate throughout the catalyst particle under isothermal conditions is less than it would be if there were no mass transfer limitations. As will be shown, the apparent activation energy, the catalyst selectivity, and other important observed characteristics of a reaction are also dependent upon the structure of the catalyst and the effective diffusivity of reactants and products (Charles and Thomas, 1963). 

The term order is related to the exponents in the rate law and is used in two ways (1) If m = 1, we say that the reaction is first order in A. If n = 2, the reaction is second order in B, and so on. (2) The overall order of reaction is the sum of all the exponents m + n + -. The proportionality constant k relates the rate of reaction to reactant concentrations and is called the rate constant of the reaction. Its value depends on the specific reaction, the presence of a catalyst (if any), and the temperature. The larger the value ofk, the faster a reaction goes. The order of the reaction establishes the general form of the rate law and the appropriate units of k (that is, depending on the values of the exponents). With the rate law for a reaction, we can... 

The sulfonated resin is a close analogue of -toluenesulfonic acid in terms of stmcture and catalyst performance. In the presence of excess water, the SO H groups are dissociated, and specific acid catalysis takes place in the swelled resin just as it takes place in an aqueous solution. When the catalyst is used with weakly polar reactants or with concentrations of polar reactants that are too low to cause dissociation of the acid groups, general acid catalysis prevails and water is a strong reaction inhibitor (63). 

The role that acid and base catalysts play can be quantitatively studied by kinetic techniques. It is possible to recognize several distinct types of catalysis by acids and bases. The term specie acid catalysis is used when the reaction rate is dependent on the equilibrium for protonation of the reactant. This type of catalysis is independent of the concentration and specific structure of the various proton donors present in solution. Specific acid catalysis is governed by the hydrogen-ion concentration (pH) of the solution. For example, for a series of reactions in an aqueous buffer system, flie rate of flie reaction would be a fimetion of the pH, but not of the concentration or identity of the acidic and basic components of the buffer. The kinetic expression for any such reaction will include a term for hydrogen-ion concentration, [H+]. The term general acid catalysis is used when the nature and concentration of proton donors present in solution affect the reaction rate. The kinetic expression for such a reaction will include a term for each of the potential proton donors that acts as a catalyst. The terms specific base catalysis and general base catalysis apply in the same way to base-catalyzed reactions. 

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