Selectivity kinetic problem

Equation (10) defines the selectivity kinetic problem since K is the only parameter to be determined. Equation (10) can be integrated directly to give... 

Exploitation of analytical selectivity. We have seen, in our discussion of the A —> B C series reaction (Scheme IX), that access to the concentration of A as a function of time is valuable because it permits to be easily evaluated. Modern analytical methods, particularly chromatography, constitute a powerful adjunct to kinetic investigations, and they render nearly obsolete some very difficult kinetic problems. For example, the freedom to make use of the pseudoorder technique is largely dependent upon the high sensitivity of analytical methods, which allows us to set one reactant concentration much lower than another. An interesting example of analytical control in the study of the Scheme IX system is the spectrophotometric observation of the reaction solution at an isosbestic point of species B and C, thus permitting the A to B step to be observed. 

Solution to the activity kinetic problem requires integration of the selectivity transformation Eq. (11) ... 

To effectively determine the start-of-cycle reforming kinetics, a set of experimental isothermal data which covers a wide range of feed compositions and process conditions is needed. From these data, selectivity kinetics can be determined from Eq. (12). With the selectivity kinetics known, Eqs. (17) and (18a)-(18c) are used to determine the activity parameters. It is important to emphasize that the original definition of pseudomonomolecular kinetics allowed the transformation of a highly nonlinear problem [Eq. (5)] into two linear problems [Eqs. (12) and (15)]. Not only are the linear problems easier to solve, the results are more accurate since confounding between kinetic parameters is reduced. 

The successful numerical solution of differential equations requires attention to two issues associated with error control through time step selection. One is accuracy and the other is stability. Accuracy requires a time step that is sufficiently small so that the numerical solution is close to the true solution. Numerical methods usually measure the accuracy in terms of the local truncation error, which depends on the details of the method and the time step. Stability requires a time step that is sufficiently small that numerical errors are damped, and not amplified. A problem is called stiff when the time step required to maintain stability is much smaller than that that would be required to deliver accuracy, if stability were not an issue. Generally speaking, implicit methods have very much better stability properties than explicit methods, and thus are much better suited to solving stiff problems. Since most chemical kinetic problems are stiff, implicit methods are usually the method of choice. 

J. Comer, PrRoySoc 197A, 90 106(1949) 6)Corner, Ballistics(1950), 42ff 7)Symposium on Kinetics of Propellants, JPhysChem 54, 847-954(1950) 8)R.D. Geckler, "The Mechanism of Combustion of Solid Propellants , in "Selected Combustion Problems-Fundamentals and Aeronautical Applications ,... 

A reverse kinetic problem consists in identifying the type of kinetic models and their parameters according to experimental (steady-state and unsteady-state) data. So far no universal method to solve reverse problems has been suggested. The solutions are most often obtained by selecting a series of direct problems. Mathematical treatment is preceded by a qualitative analysis of experimental data whose purpose is to reduce drastically the number of hypotheses under consideration [31]. 

The second approach is a fractional-step method we call asymptotic timestep-splitting. It is developed by consideration of the specific physics of the problem being solved. Stiffness in the governing equations can be handled "asymptotically" as well as implicitly. The individual terms, including those which lead to the stiff behavior, are solved as independently and accurately as possible. Examples of such methods include the Selected Asymptotic Integration Method (4,5) for kinetics problems and the asymptotic slow flow algorithm for hydrodynamic problems where the sound speed is so fast that the pressure is essentially constant (6, 2). ... 

In nature and industry it happens most frequently that a reaction is not carried out with a pure feed but with a mixture of two or more related compounds that react in parallel or in series with a common reactant or on the same catalyst. More than one single reaction must then be considered, and we have to deal with a reaction network. In order to Ulustrate the physical ideas, a network of only two reactions will be treated, but generalization is only a matter of patience. Let us examine in turn the case of catalytic reactions 2md that of chain reactions. There are two problems. The Hrst one is a problem where time does not enter explicitly — it is a problem of selectivity. The second problem is the kinetic problem itself What is the total rate when both reactions go side by side ... 

Thus we see how the first and foremost problem of reactions in series — that of selectivity — can be controlled by the coupling between the reaction. For catalytic sequences in parallel, it is worth while to consider also briefly the second problem, i.e., the kinetic problem itself. It consists in finding out... 

Samsonova et al. showed that both the ethoxylation of the hydroxy groups into hydroxyethylterephthalate and bis(hydroxyethyl)terephthalate, and the oligomerization of ethylene oxide, are sufficiently slow to consider that the reaction of terephthalic acid with gthylene oxide is highly selective. The problem of the relative contribution of the second carboxylic group of terephthalic acid to the kinetics will be discussed later. 

Kinetic problems with reaction systems in the pharmaceutical industry are more concerned with selectivity in complex systems than with conversion rate. 

Mixing-Kinetic Problem. The reaction scheme that has received the most attention in both theoretical and experimental investigations of the effects of mixing on selectivity is the competitive-consecutive reaction. In addition, the parallel reaction system is receiving attention for its importance in reactions and pH adjustments. These systems are discussed in Chapter 13 and highlighted here because of their fundamental importance in the fine chemicals and pharmaceutical industries. The reaction scheme is as follows ... 

Selectivity The analysis of closely related compounds, as we have seen in earlier chapters, is often complicated by their tendency to interfere with one another. To overcome this problem, the analyte and interferent must first be separated. An advantage of chemical kinetic methods is that conditions can often be adjusted so that the analyte and interferent have different reaction rates. If the difference in rates is large enough, one species may react completely before the other species has a chance to react. For example, many enzymes selectively cat-... 

Selectivity in FIA is often better than that for conventional methods of analysis. In many cases this is due to the kinetic nature of the measurement process, in which potential interferents may react more slowly than the analyte. Contamination from external sources also is less of a problem since reagents are stored in closed reservoirs and are pumped through a system of transport tubing that, except for waste lines, is closed to the environment. 

Whereas Hquid separation method selection is clearly biased toward simple distillation, no such dominant method exists for gas separation. Several methods can often compete favorably. Moreover, the appropriateness of a given method depends to a large extent on specific process requirements, such as the quantity and extent of the desired separation. The situation contrasts markedly with Hquid mixtures in which the appHcabiHty of the predominant distiHation-based separation methods is relatively insensitive to scale or purity requirements. The lack of convenient problem representation techniques is another complication. Many of the gas—vapor separation methods ate kinetically controUed and do not lend themselves to graphical-phase equiHbrium representations. In addition, many of these methods require the use of some type of mass separation agent and performance varies widely depending on the particular MSA chosen. 

In summary, the problem this book addresses is how to select a catalyst in laboratory experiments that will be the best for commercial processes and how to develop kinetic expressions both valid in production units and useful in maximizing profits in safe operations. 

Sections 3.1 and 3.2 considered this problem Given a complex kinetic scheme, write the differential rate equations find the integrated rate equations or the concentration-time dependence of reactants, intermediates, and products and obtain estimates of the rate constants from experimental data. Little was said, however, about how the kinetic scheme is to be selected. This subject might be dismissed by stating that one makes use of experimental observations combined with chemical intuition to postulate a reasonable kinetic scheme but this is not veiy helpful, so some amplification is provided here. 

The standard state chosen for the calculation of controls its magnitude and even its sign. The standard state is established when the concentration scale is selected. For most solution kinetic work the molar concentration scale is used, so A values reported by different workers are usually comparable. Nevertheless, an important chemical question is implied Because the sign of AS may depend upon the concentration scale used for the evaluation of the rate constant, which concentration scale should be used when A is to serve as a mechanistic criterion The same question appears in studies of equilibria. The answer (if there is a single answer) is not known, though some analyses of the problem have been made. Further discussion of this issue is given in Section 6.1. 

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