Heterogeneous rate expressions

Equation (1.20) is frequently used to correlate data from complex reactions. Complex reactions can give rise to rate expressions that have the form of Equation (1.20), but with fractional or even negative exponents. Complex reactions with observed orders of 1/2 or 3/2 can be explained theoretically based on mechanisms discussed in Chapter 2. Negative orders arise when a compound retards a reaction—say, by competing for active sites in a heterogeneously catalyzed reaction—or when the reaction is reversible. Observed reaction orders above 3 are occasionally reported. An example is the reaction of styrene with nitric acid, where an overall order of 4 has been observed. The likely explanation is that the acid serves both as a catalyst and as a reactant. The reaction is far from elementary. 

For enzymatic and other heterogeneously catalyzed reactions, there may be competition for active sites. This leads to rate expressions with forms such as... 

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas-phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only Steps 1 and 9, and the effects of Steps 2 through 8 are lumped into the pseudohomoge-neous rate expression, a, b,. ..), where a,b,. .. are the bulk, gas-phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

Steps 1 through 9 constitute a model for heterogeneous catalysis in a fixed-bed reactor. There are many variations, particularly for Steps 4 through 6. For example, the Eley-Rideal mechanism described in Problem 10.4 envisions an adsorbed molecule reacting directly with a molecule in the gas phase. Other models contemplate a mixture of surface sites that can have different catalytic activity. For example, the platinum and the alumina used for hydrocarbon reforming may catalyze different reactions. Alternative models lead to rate expressions that differ in the details, but the functional forms for the rate expressions are usually similar. 

The appearance of this heterogeneous form for the rate expression reflects the presence of a mass transfer step in series with the reaction step. If the parameter values are known, this ODE for bi i) can be integrated subject to the initial condition that bi=(bi)o at t = 0. The result can then be used to find a (f). 

Assume A, B, C, and D have similar diffusivities so that local stoichiometry is preserved. Under what circumstances will conversion be maximized by (a) complete segregation (b) by maximum mixedness Heterogeneous reactions are often modeled as if they were homogeneous. A frequently encountered rate expression is... 

In perchloric acid media the reaction is extremely slow and is complicated by the formation of polymeric species of tin, and by heterogeneity. Rabideau has examined the kinetics in mixed perchlorate-chloride solutions, in which media no turbidity is apparent. The rate expression is complex, viz. 

Using the concept of the rate-determining step significantly simplifies the overall rate expression. Therefore, it is widely used in the analysis of kinetie data, especially in the field of heterogeneous catalysis. 

The first of these factors pertains to the complications introduced in the rate equation. Since more than one phase is involved, the movement of material from phase to phase must be considered in the rate equation. Thus the rate expression, in general, will incorporate mass transfer terms in addition to the usual chemical kinetics terms. These mass transfer terms are different in type and number in different kinds of heterogeneous systems. This implies that no single rate expression has a general applicability. 

The Langmuir adsorption isotherm provides a simple mechanistic picture of the adsorption process and gives rise to a relatively simple mathematical expression. It can also be used to obtain a crude estimate of specific surface areas. More important, from the viewpoint of the chemical engineer, it serves as a point of departure for formulating rate expressions for heterogeneous catalytic reactions. 

REACTION RATE EXPRESSIONS FOR HETEROGENEOUS CATALYTIC REACTIONS... 

Reaction Rate Expressions for Heterogeneous Catalytic Reactions... 

In the treatment of rate expressions for heterogeneous catalytic reactions the definition of local reaction rates in terms of interfacial areas (3.0.10) is appropriate. 

If an attempt is made to fit heterogeneous catalytic reaction rate data to a rate expression of the form... 

ILLUSTRATION 6.1 DEVELOPMENT OF A HOUGEN-WATSON RATE EXPRESSION FOR A HETEROGENEOUS CATALYTIC REACTION... 

Equation 8.3.4 may also be used in the analysis of kinetic data taken in laboratory scale stirred tank reactors. One may directly determine the reaction rate from a knowledge of the reactor volume, flow rate through the reactor, and stream compositions. The fact that one may determine the rate directly and without integration makes stirred tank reactors particularly attractive for use in studies of reactions with complex rate expressions (e.g., enzymatic or heterogeneous catalytic reactions) or of systems in which multiple reactions take place. 

Effectiveness Factors for Hougen-Watson Rate Expressions. The discussion thus far and the vast majority of the literature dealing with effectiveness factors for porous catalysts are based on the assumption of an integer-power reaction rate expression (i.e., zero-, first-, or second-order kinetics). In Chapter 6, however, we stressed the fact that heterogeneous catalytic reactions are more often characterized by more complex rate expressions of the Hougen-Watson type. Over a narrow range of... 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (93) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to... 

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