General Analysis—Single Reaction

4 EXTERNAL TRANSPORT 9.4.1 General Analysis—Single Reaction 

Concentration gradients between the bulk fluid in the reactor and the external surface of a catalyst particle can also influence the rate of reaction, i.e., the apparrat catalyst activity and the product distribution, i.e.,theapparentcatalystsdectivity.First,let sdeal with therate of reactitHi. 

The magnitude of the resistances to heat and mass transfer through the boundary layer, i.e., the thickness of the boundary layer, depends on the velocity of the fluid relative to the catalyst particle. As this velocity increases, the heat-transfer coefficient between the bulk fluid and the surface of the catalyst particle increases and the mass-transfer coefficient between the bulk fluid and the catalyst surface increases. Therefore, the magnitude of the concentration and temperature differences between the bulk fluid and the particle surface will depend on the relative velocity, as well as on the properties of the fluid. 

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The two requirements, small reactor size and maximization of desired product, may run counter to each other. In such a situation an economic analysis will yield the best compromise. In general, however, product distribution controls consequently, this chapter concerns primarily optimization with respect to product distribution, a factor which plays no role in single reactions. 

We continue the analysis of ideal, isothermal, constant-volume batch reactors with single reactions and consider now chemical reactions involving more than one reactant. Consider the general reaction form... 

The results of the above analysis of reactions involving two proton transfers may be compared with those for reactions in which only a single transfer is kinetically relevant (Sec. III.3.a). For a single transfer the existence of an equilibrium between catalyst and substrate always produces the appearance of specific catalysis by hydrogen or hydroxyl ions, and the detection of general acid-base catalysis therefore excludes... 

For the single-reaction cases, we performed dimensional analysis and found a dimensionless number, the Thiele modulus, which measures the rate of production divided by the rate of diffusion of some component. A complete analysis of the first-order reaction in a sphere suggested a general approach to calculate the production rate in a pellet in terms of the rate evaluated at the pellet exterior surface conditions. This motivated the definition of the pellet effectiveness factor, which is a function of the Thiele modulus. 

The second prerequisite is that enzyme reaction should be irreversible. In theory, the estimation of prarameters by kinetic analysis of reaction curve is still feasible when reaction reversibility is considered, but the estimated prarameters possess too low rehabihty to have practical roles (data impnbhshed). Generally, a prepraration of a substance with contaminants less than 1% in mass content can be taken as a pure substance. Namely, a reagent leftover in a reaction accoimting for less than 1% of that before reaction can be negligible. For convenience, therefore, an enzyme reaction is considered irreversible when the leftover level of a substrate of interest in equilibrium is much less than l%of its initial one. To promote the consumption of the substrate of interest, the concentrations of other substrates should be preset at levels much over 10 times the initial level of the substrate of interest. In this case, the enzyme reaction is ap>p)arently irreversible and follows kinetics on single substrate. Or else, the use of scavenging reactions to remove products can drive the reaction forward. The concurrent uses of both approaches are usually better. 

Each reaction of the network is stoichiometrically simple in the sense that its advancement is described by a single parameter the extent of reaction (see next section). A stoichiometrically simple reaction will be called a single reaction or a reaction for short. The expression simple reaction is best avoided since, in general, a stoichiometrically simple reaction is far from simple. Indeed, in the vast majority of cases, a single reaction docs not lake place as written. It proceeds through a sequence oJ steps involving reactive intermediates that do not appear in the equation for reaction. In what follows, a sequence of steps will be called a sequence. The identification of these intermediates and the definition of the proper sequence arc the central problems of the kinetic analysis. This is logically the second task of the kineticist but it is not the last one. 

The effect of substrate concentration on enzymatic reaction was first put forward in 1903 (Henri, 1903), where the conversion into the product involved a reaction between the enzyme and the substrate to form a substrate-enzyme complex that is then converted to the product. However, the reversibility of the substrate-enzyme complex and its final breakdown into the substrate and free enzyme regeneration was generally ignored. In 1913, Michaelis and Menten took this into consideration and proposed the scheme shown in Equation 4.1 for a one-substrate enzymatic reaction. Experimental data, that is, the initial reaction rates, were collected to support their analysis. The reaction mechanism, which is one of the most common mechanisms in enzymatic reactions, was based on the assumption that only a single substrate and product are involved in the reaction. 

The approach to be followed in the determination of rates or detailed kinetics of the reaction in a liquid phase between a component of dissolved gas and a component of the liquid is, in principle, the same as that outlined in Chapter 2 for gas-phase reactions on a solid catalyst. In general, the experiments are carried out in flow reactors of the integral type. The data may be analyzed by the integral or the differential method of kinetic analysis. However, for a single reaction, two continuity equations, in general, are required one for the absorbing component A in the gas phase and one for A in the liquid phase. In addition, a material balance is required, linking the consumption of B, the reactant of the liquid phase, to that of A. The continuity equations for A, which contain the rate equations derived in... 

This discussion is meant to provide you some context for this chapter, where we cover a thermodynamic analysis of reacting systems the calculations we perform in this chapter do not account for rates of product formation. They are valid only at equilibrium, when the reactions are thermodynamically controlled. The fundamental question we wish to address is, What effect do temperature, pressure, and composition have on the equilibrium conversion in a chemically reacting system This analysis tells us nothing about the rates at which a chemical reaction will proceed. It does, however, tell us to what extent a reaction is possible. As in phase equilibria, we will use the Gibbs energy of the system to study chemical reaction equilibria. To illustrate the use of G, we will first consider a specific reaction (Section 9.2). We will then describe the general formalism for a single reaction (Sections 9.3-9.5) and multiple reactions (Sections 9.7-9.8). 

As on previous occasions, the reader is reminded that no very extensive coverage of the literature is possible in a textbook such as this one and that the emphasis is primarily on principles and their illustration. Several monographs are available for more detailed information (see General References). Useful reviews are on future directions and anunonia synthesis [2], surface analysis [3], surface mechanisms [4], dynamics of surface reactions [5], single-crystal versus actual catalysts [6], oscillatory kinetics [7], fractals [8], surface electrochemistry [9], particle size effects [10], and supported metals [11, 12]. 

Before the actual sample preparation procedure is described some general observations should first be made. However excellent the sample preparation and however sophisticated the equipment, the accuracy of the analysis will only be as good as the quality of the sample that is taken. If the sample is that of a reaction mixture from an organic synthesis laboratory, it is likely to be taken from a single bottle or container, by a professional chemist, and is likely to be truly representative of the bulk of the material. 

Evidence is provided by this analysis that (a) structural considerations discriminate among at least four practical classes of pi delocalization behavior, each of which has limited generality (b) the blend of polar and pi delocalization effect contributions to the observed effect of a substituent is widely variable among different reaction or data sets (the contributions may be opposite as well as alike in direction), depending upon structural considerations and the nature of the measurement (c) solvent may play an important role in determination of the observed blend of effects (d) it is the first three conditions which lead to the deterioration of the single substituent parameter treatment as a means of general and relatively precise description of observed electronic substituent effects in the benzene series. 

Progress in molecular biology has provided a new perspective. Techniques such as the polymerase chain reaction and single-strand conformation polymorphism analysis have greatly facilitated the molecular analysis of erythroenzymopathies. These studies have clarified the correlation between the functional and structural abnormalities of the variant enzymes. In general, the mutations that induce an alteration of substrate binding site and/or enzyme instability might result in markedly altered enzyme properties and severe clinical symptoms. 

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