Stoichiometry multiple reactions

For multiple reactions, material balances are required for each stoichiometry. 

The second use of Equations (2.36) is to eliminate some of the composition variables from rate expressions. For example, 0i-A(a,b) can be converted to i A a) if Equation (2.36) can be applied to each and every point in the reactor. Reactors for which this is possible are said to preserve local stoichiometry. This does not apply to real reactors if there are internal mixing or separation processes, such as molecular diffusion, that distinguish between types of molecules. Neither does it apply to multiple reactions, although this restriction can be relaxed through use of the reaction coordinate method described in the next section. 

For multiple reactions, material balances must be made for each stoichiometry. An example is the consecutive reactions, A = B = C, for which problem P4.04.52 develops a closed form solution. Other cases of sets of first order reactions are solvable by Laplace Transform, and of course numerically. 

This is the first time we have encountered multiple reactions. For these in general, if it is necessary to write N stoichiometric equations to describe what is happening, then it is necessary to follow the decomposition of N reaction components to describe the kinetics. Thus, in this system following C, or Cr, or Q alone will not give both ki and k2. At least two components must be followed. Then, from the stoichiometry, noting that + Cr + Q is constant, we can find the concentration of the third component. 

The key to optimum design for multiple reactions is proper contacting and proper flow pattern of fluids within the reactor. These requirements are determined by the stoichiometry and observed kinetics. Usually qualitative reasoning alone can already determine the correct contacting scheme. This is discussed further in Chapter 10. However, to determine the actual equipment size requires quantitative considerations. 

These rates are the rates of production of species A, B, and C (rj = Vjr) so these rates are written as negative quantities for reactants and positive quantities for products. This notation quickly becomes cumbersome for complex reaction stoichiometry, and the notation is not directly usable for multiple reaction systems. 

The stoichiometry of reaction (14) is reminiscent of the electroreduction of 02 to H20. It is of interest that oxygenation of vanadium(III) gives oxovanadi-um(V), whereas multiple one-electron redox centers have been considered to be essential for the incorporation of 02. An explanation for this can be found in... 

Example 6-4 Stoichiometry and Sate Laws for Multiple Reactions... 

A conversion reactor requires a reaction stoichiometry and an extent of reaction, which is usually specified as an extent of conversion of a limiting reagent. No reaction kinetics information is needed, so it can be used when the kinetics are unknown (which is often the case in the early stages of design) or when the reaction is known to proceed to full conversion. Conversion reactors can handle multiple reactions, but care is needed in specifying the order in which they are solved if they use the same limiting reagent. 

Two types of precursor can be used in CVD of superconducting mixed oxides metal halides and metal-organics The use of metal-organic molecules results in some carbon in the films, which can hinder performance, so metal halides gained popularity in early work. Halide precursors call for a much higher deposition temperature. In the case of metal halide reactions, the chemistry follows that presented earlier (see 17.2.5.2.2) but with multiple reactions occurring simultaneously. The gas phase composition and temperature are controlled to obtain the desired stoichiometry. An example of such a reaction would be that used to make Bi2Sr2CaCu20s+ c(or Bi-2212) at 760-820°C ... 

The following format is used. Important physicochemical aspects of CRE (commonly known as reaction analysis) are briefly outlined in Section 11.2, to provide the fundamental framework for the analysis and design of reactors involving one or more phases, referred to generally as singlephase or multiphase reactors, respectively. These include treatment of simple and complex (multiple) reactions, stoichiometry, reaction rates (with a brief reference to the concept of the rate-determining step), and experimental techniques. 

Example 6-5 Stoichiometry aaj Rate Laws for Multiple Reactions Consider the following set of reactioas ... 

For aU reactions on the fullerene, not only the stoichiometry, but also the regi-ochemical course of possible multiple reactions has to be considered. In principle, derivatives of > with 60 addends are conceivable, which would mean complete saturation of the carbon core. Still for the time being molecules like that have not... 

The reactor design equations in this book can be applied to all components in the system, even inerts. When the reaction rates are formulated using Equation 2.8, the solutions automatically account for the stoichiometry of the reaction. This is the simplest and preferred approach, but it has not always been followed in this book. Several examples have ignored product concentrations when they do not affect reactions rates and when they are easily found from the amount of reactants consumed. Also, some of the analytical solutions have used stoichiometry to ease the algebra. The present section formalizes the use of stoichiometric constraints. We begin with a matrix formulation for the reaction rates of the components in multiple reactions. The presentation is rather elegant from a mathematical viewpoint and does have some practical utility. 

In order to quantify the rate of a chemical transformation, we need to introduce some definitions. First, we distinguish between different types of reactions based on the form used to describe eventual chemical transformation, as single or multiple reactions. Usually this can be done from material balance after examining the stoichiometry between reacting materials and products. If a single stoichiometric equation can present the transformation, this is a single reaction. If more than one equation is necessary to present all observed components and their transformations, this it is a case of multiple reactions. The examples are as following ... 

A Case of Multiple Reactions with Slightly More Complex Stoichiometry... 

Chapter 1 begins with a review of the stoichiometry of chemical reactions, which leads into a discussion of various definitions of the reaction rate. Both homogeneous and heterogeneous systems are treated. The material in this chapter recurs throughout the book, and is particularly useful in Chapter 7, which deals with multiple reactions. 

When multiple reactions are considered, each reaction has its own corresponding extent of reaction, Thus, we must keep track of the stoichiometry of each species i for each of the k separate chemical reactions. Reaction (9.5) can be written for each separate reaction (1, 2,.. . k. . . R) thus, we must now sum over all of the i species for each of the k reactions. Mathematically, we accomplish this task by using a double sum, as follows ... 

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