Kinetics introductory example

The machinery how to obtain the generating function from a kinetic scheme is shown in a simple introductory example. 

The last chapter in this introductory part covers the basic physical chemistry that is required for using the rest of the book. The main ideas of this chapter relate to basic thermodynamics and kinetics. The thermodynamic conditions determine whether a reaction will occur spontaneously, and if so whether the reaction releases energy and how much of the products are produced compared to the amount of reactants once the system reaches thermodynamic equilibrium. Kinetics, on the other hand, determine how fast a reaction occurs if it is thermodynamically favorable. In the natural environment, we have systems for which reactions would be thermodynamically favorable, but the kinetics are so slow that the system remains in a state of perpetual disequilibrium. A good example of one such system is our atmosphere, as is also covered later in Chapter 7. As part of the presentation of thermodynamics, a section on oxidation-reduction (redox) is included in this chapter. This is meant primarily as preparation for Chapter 16, but it is important to keep this material in mind for the rest of the book as well, since redox reactions are responsible for many of the elemental transitions in biogeochemical cycles. 

In addition to the general steric requirements reported in the introductory section for macromolecular isomorphism, if chains differ in chemical structure, they must also show some degree of compatibility to intimate mixing and not too much different crystallization kinetics. The first condition is strictly similar to the one that applies to liquid mixtures. As a well known example, liquids without reciprocal affinity in general cannot form a unique phase. Attempts to obtain mixed crystals from polyethylene and polyvinyl or polyvinylidene fluoride has been unsuccessful hitherto, in spite of the similarity in shape and size of their chains. In view of the above somewhat strict requirements, it is not surprising that relatively few examples of this type of isomorphism have been reported. 

Let us begin the discussion of the last example of solid state kinetics in this introductory chapter with the assumption of local equilibrium at the A/AB and AB/B interfaces of the A/AB/B reaction couple (Fig. 1-5). Let us further assume that the reaction geometry is linear and the interfaces between the reactants and the product AB are planar. Later it will be shown that under these assumptions, the (moving) interfaces are morphologically stable during reaction. 

There are many books on chemical engineering kinetics, and the reader may wish to browse through several of them to see how they introduce the subject. Most of them are intended for the introductory, undergraduate course. Here are two examples primarily aimed at the U.S. market ... 

We have found that Stella is an effective tool to teach introductory kinetics and equilibrium concepts. Although it is true that all of this could be done in a spreadsheet or an equation solver, we believe that the presence of the Diagram window provides a strong visual connection between the model that is built and the mathematics behind the model. This example illustrates a realistic simulation of a real chemical phenomenon, of the sort recommended by Atkins. ... 

Because this is an introductory text, we have chosen our examples so that they will fit one of these three simple models. In some cases, however, reaction kinetics can be quite complicated and the appropriate model might be none of the three we tried here. If none of these three plots were linear, we would have to conclude that the reaction was not zero, first, or second order. Similar integrated rate law models can be derived for other cases, but this is beyond the scope of an introductory class. 

As stated in the introductory section, the main source of performance losses is the cathodic overpotential caused by the oxygen reduction reaction (ORR), which has therefore been the subject of several studies. As stated in the beginning of this section, the largest contribution to the performance loss is caused by the slow kinetics of the ORR. In order to reconsider the given example, at a current density ig = 1500 mA/cm the ohmic loss amounts just to 80 mV, whereas the performance loss due to the ORR is 400 mV. The reduction reaction by itself depends on factors such as the catalyst composition, particle sizes, pH-value and potential. 

The purpose of this section is to apply the introductory statistics materials to each of the traditional three reactors. The emphasis is on batch reactors since most of the experimental work conducted for the purpose of generating kinetic models, employs batch reactors. As such, most of the illustrative examples to follow are concerned with this class of reactor. Examples on CSTRs and tubular reactors are also presented in two later subsections. 

This book is based on my class notes at the Hebrew University of Jerusalem and at the University of California, Los Angeles. The level is that of senior undergraduate or graduate students. The prerequisite is a class in chemical kinetics. Some familiarity with spectroscopy and with statistical mechanics is beneficial but not essential, and introductory material is provided where necessary. The scope of the book is more than can be covered in a lecture course of one semester. The first six chapters develop the tools and iUustrate their applications. The examples are usually simple ones that can be used to make tiie point. The development in these chapters is linear, there are sections tiiat can be skipped, but the order of topics is sequential. There are people who will want to get as quickly as possible to Chapter 5. This is understandable, but 1 recommend first to go at least through Sections 2.1, 2.2, and 2.3. In the following six chapters tiie text is arranged... 

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