Heterogeneously catalyzed surface reactions rate equations

Rate Equations for Heterogeneously Catalyzed Surface Reactions... 

Most important, heterogeneous surface-catalyzed chemical reaction rates are written in pseudo-homogeneous (i.e., volumetric) form and they are included in the mass transfer equation instead of the boundary conditions. Details of the porosity and tortuosity of a catalytic pellet are included in the effective diffusion coefficient used to calculate the intrapellet Damkohler number. The parameters (i.e., internal surface area per unit mass of catalyst) and Papp (i.e., apparent pellet density, which includes the internal void volume), whose product has units of inverse length, allow one to express the kinetic rate laws in pseudo-volumetric form, as required by the mass transfer equation. Hence, the mass balance for homogeneous diffusion and multiple pseudo-volumetric chemical reactions in one catalytic pellet is... 

Two important ways in which heterogeneously catalyzed reactions differ from homogeneous counterparts are the definition of the rate constant k and the form of its dependence on temperature T. The heterogeneous rate equation relates the rate of decline of the concentration (or partial pressure) c of a reactant to the fraction / of the catalytic surface area that it covers when adsorbed. Thus, for a first-order reaction,... 

Heterogeneously catalyzed reactions are usually studied under steady-state conditions. There are some disadvantages to this method. Kinetic equations found in steady-state experiments may be inappropriate for a quantitative description of the dynamic reactor behavior with a characteristic time of the order of or lower than the chemical response time (l/kA for a first-order reaction). For rapid transient processes the relationship between the concentrations in the fluid and solid phases is different from those in the steady-state, due to the finite rate of the adsorption-desorption processes. A second disadvantage is that these experiments do not provide information on adsorption-desorption processes and on the formation of intermediates on the surface, which is needed for the validation of kinetic models. For complex reaction systems, where a large number of rival reaction models and potential model candidates exist, this give rise to difficulties in model discrimination. 

The effect that a solvent exerts on the rate of a heterogeneously catalyzed reaction depends on the reaction substrate, the catalytically active species and the nature of the catalyst support. 2 Because of this complexity, attempts to derive a general equation relating reaction rate with some property or properties of the solvent have been imsuccessful. 2.l4 The primary reason for this failure is that the solvents are not present merely as diluents in which the reactants are dissolved, they are also capable of interacting with the catalyst surface so they can also modify the extent to which different types of substrates are adsorbed. 

The reactivity of the compound in a heterogeneously catalyzed reaction depends on the rate constant of the surface reaction and on the adsorption coefficient. If the kinetic equation (3) is reduced to a zero-order equation with respect to the concentration of the initial compound, the rate constant... 

A higher form of interpretation of the effect of solvents on the rate of heterogeneously catalyzed reactions was represented by the Langmuir-Hinshelwood kinetics (7), in the form published by Hougen and Watson (2), where the effect of the solvent on the reaction course was characterized by the adsorption term in the kinetic equation. In catalytic hydrogenations in the liquid state kinetic equations of the Hougen-Watson type very frequently degrade to equations of pseudo-zero order with respect to the concentration of the substrate (the catalyst surface is saturated with the substrate), so that such an interpretation is not possible. At the same time, of course, also in these cases the solvent may considerably affect the reaction. As is shown below, this influence is very adequately described by relations of the LFER type. 

Rate expressions of the form of Equation 5.153 are known as Hougen Watson or Langmuir-Hinshelwood kinetics [17, This form of kinetic expression is often used to describe the species production rates for heterogeneously catalyzed reactions. We complete the section on the kinetics of elementary surface reactions by returning to the methane synthesis reaction listed in Section 5.2. The development proceeds exactly as outlined in Section 5.2. But now it is necessary to add a site-balance expression (Equation 5,129) in Step 3. 

Total pressure analysis of the initial reactant product conversion rate can distinguish between these two mechanisms, provided that rates of conversion can be measured at sufficiently high pressure. The rate expressions given by equations (14-188) and (14-191) have units of mol/area-time for surface-catalyzed chemical reactions. However, rate data obtained from heterogeneous catalytic reactors are typically reported in units of mol/time per mass of catalyst. One obtains these units simply by multiplying the kinetic rate law (i.e., mol/area-time) by the internal surface area per mass of catalyst (i.e., S ), which is usually on the order of 100 m /g. If the feed stream to a packed catalytic reactor contains pure ethanol, then the initial reactant product conversion rate for the four-step mechanism is... 

The kinetic rate constant kj corresponds to the kinetics of heterogeneous surface-catalyzed chemical reactions in the boundary conditions, whereas the rate law is written on a pseudo-volumetric basis when chemical reaction terms are included in the mass transfer equation. 

Homogeneous reactions occur in the fluid phase, and the volume available for reaction is sV. Solid-catalyzed reactions occur on the catalyst surface, and area available for the reaction is Vpca where V is the total reactor volume (i.e., gas plus catalyst), is the average density of catalyst in the reactor (i.e., mass of catalyst per total reactor volume), and is the surface area per mass of catalyst. The pseudohomogeneous reaction rate calculated using Equation (10.37) is multiplied by eF to get the rate of formation of component A in moles per time. The equivalent heterogeneous rate is based on the catalyst surface area and is multiplied by Vpc flc to obtain the rate of formation of component A in moles per time. Setting the two rates equal gives... 

The reaction of aqueous sodium cyanide with 1-bromooctane, shown in equation (27), is catalyzed by tri-n-butylphosphonium ions (61 n= 1, DF 0.17, 2% DVB) as shown in Scheme 24. Reaction rates in heterogeneous mixtures can be limited by mass transport steps as well as intrinsic reactivity. Mass transfer of the cyanide ion from water to the particle surface, mass transfer of the 1-bromooctane from organic liquid to the particle surface and intraparticle diffusion of both reactants from the particle surface to the active sites within the gel polymer are required. Reaction... 

Step 11. Write all the boundary conditions that are required to solve this boundary layer problem. It is important to remember that the rate of reactant transport by concentration difhision toward the catalytic surface is balanced by the rate of disappearance of A via first-order irreversible chemical kinetics (i.e., ksCpJ, where is the reaction velocity constant for the heterogeneous surface-catalyzed reaction. At very small distances from the inlet, the concentration of A is not very different from Cao at z = 0. If the mass transfer equation were written in terms of Ca, then the solution is trivial if the boundary conditions state that the molar density of reactant A is Cao at the inlet, the wall, and far from the wall if z is not too large. However, when the mass transfer equation is written in terms of Jas, the boundary condition at the catalytic surface can be characterized by constant flux at = 0 instead of, simply, constant composition. Furthermore, the constant flux boundary condition at the catalytic surface for small z is different from the values of Jas at the reactor inlet, and far from the wall. Hence, it is advantageous to rewrite the mass transfer equation in terms of diffusional flux away from the catalytic surface, Jas. 

The principles of homogeneous reaction kinetics and the equations derived there remain valid for the kinetics of heterogeneous catalytic reactions, provided that the concentrations and temperatures substituted in the equations are really those prevailing at the point of reaction. The formation of a surface complex is an essential feature of reactions catalyzed by solids and the kinetic equation must account for this. In addition, transport processes may influence the overall rate heat and mass transfer between the fluid and the solid or inside the porous solid, > that the conditions over the local reation site do not correspond to those in the bulk fluid around the catalyst particle. Figure 2.1-1 shows the seven steps involved when a molecule moves into the catalyst, reacts, and the product moves back to the bulk fluid stream. To simplify the notation the index s, referring to concentrations inside the solid, will be dropped in this chapter. 

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