Stoichiometric parallel

Figure 3-2. Two reaction equations showing two completely different uses for the (+) symbol a) giving a fully balanced single reaction, b) combining two parallel reactions into a single equation that is not stoichiometrically balanced.

In this chapter we will discuss the results of the studies of the kinetics of some systems of consecutive, parallel or parallel-consecutive heterogeneous catalytic reactions performed in our laboratory. As the catalytic transformations of such types (and, in general, all the stoichiometrically not simple reactions) are frequently encountered in chemical practice, they were the subject of investigation from a variety of aspects. Many studies have not been aimed, however, at investigating the kinetics of these transformations at all, while a number of others present only the more or less accurately measured concentration-time or concentration-concentration curves, without any detailed analysis or quantitative kinetic interpretation. The major effort in the quantitative description of the kinetics of coupled catalytic reactions is associated with the pioneer work of Jungers and his school, based on their extensive experimental material 17-20, 87, 48, 59-61). At present, there are so many studies in the field of stoichiometrically not simple reactions that it is not possible, or even reasonable, to present their full account in this article. We will therefore mention only a limited number in order for the reader to obtain at least some brief information on the relevant literature. Some of these studies were already discussed in Section II from the point of view of the approach to kinetic analysis. Here we would like to present instead the types of reaction systems the kinetics of which were studied experimentally. 

We considered micro-pA), values in Section 3.6. A parallel concept applies to partition coefficients (of multiprotic molecules) namely, if an ionizable substance of a particular stoichiometric composition can exist in different structural forms, then it is possible for each form to have a different micro-log P [224,243,273,275], When logP is determined by the potentiometric method (below), the constant determined is the macro-log P. Other log/1 methods may also determine only the macroscopic constant. 

In this subsection we have treated a variety of higher-order simple parallel reactions. Only by the proper choice of initial conditions is it possible to obtain closed form solutions for some of the types of reaction rate expressions one is likely to encounter in engineering practice. Consequently, in efforts to determine the kinetic parameters characteristic of such systems, one should carefully choose the experimental conditions so as to ensure that potential simplifications will actually occur. These simplifications may arise from the use of stoichiometric ratios of reactants or from the degeneration of reaction orders arising from the use of a vast excess of one reactant. Such planning is particularly important in the early stages of the research when one has minimum knowledge of the system under study. 

There are few short-cut methods for analyzing simple parallel systems. One useful technique, however, is to use stoichiometric ratios of reactants so that the ratio of the time derivatives of the extents of reaction simplifies where possible. For higher-order irreversible simple parallel reactions represented by equations 5.2.41 and 5.2.42, the degenerate form of the ratio of reaction rates becomes... 

Independent Parallel Reactions of the Same Species. Independent parallel reactions of the same species may be represented in stoichiometric form as... 

Locate the LOC on the oxygen axis, and draw a line parallel to the fuel axis until it intersects with the stoichiometric line. Draw a point at this intersection. 

In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

Compounds are made up of atoms of more than one chemical element. The point defects that can occur in pure compounds parallel those that occur in monatomic materials, but there is an added complication in this case concerning the composition of the material. In this chapter discussion is confined to the situation in which the composition of the crystal is (virtually) fixed. Such solids are called stoichiometric compounds. (The situations that arise when the composition is allowed to vary are considered in Chapter 4 and throughout much of the rest of this book. This latter type of solid is called a nonstoichiometric compound.) The composition problem can be illustrated with respect to a simple compound such as sodium chloride. 

Antisite defects in the pyrochore structure Er2Ti207 were mentioned previously (Section 1.10). These defects also occur in the nonstoichiometric compound Er2.09Ti194O6.952, which is slightly Er203-rich compared to the stoichiometric parent phase. The formation of the antisite pair is now accompanied by the parallel formation of oxygen vacancies ... 

In most experimental investigations involving parallel reactions, species B is in stoichiometric excess, so that fsi < f) 1. In this range, only Yfff is non-zero, and thus its value serves as a measure of the rate of micromixing. Ideally, in order to maximize the range of possible values of Cs = Cq s2Y2oo, the flow rates and inlet concentrations... 

Of course, all the appropriate higher-temperature reaction paths for H2 and CO discussed in the previous sections must be included. Again, note that when X is an H atom or OH radical, molecular hydrogen (H2) or water forms from reaction (3.84). As previously stated, the system is not complete because sufficient ethane forms so that its oxidation path must be a consideration. For example, in atmospheric-pressure methane-air flames, Wamatz [24, 25] has estimated that for lean stoichiometric systems about 30% of methyl radicals recombine to form ethane, and for fuel-rich systems the percentage can rise as high as 80%. Essentially, then, there are two parallel oxidation paths in the methane system one via the oxidation of methyl radicals and the other via the oxidation of ethane. Again, it is worthy of note that reaction (3.84) with hydroxyl is faster than reaction (3.44), so that early in the methane system CO accumulates later, when the CO concentration rises, it effectively competes with methane for hydroxyl radicals and the fuel consumption rate is slowed. 

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