Stoichiometry of single reactions

The general stoichiometric relationships for a single reaction in a batch reactor are 

The circumflex over a and b allows for spatial variations. It can be ignored when the contents are perfectly mixed. Equation (2.36) is the form normally used for batch reactors where d = a t). It can be applied to piston flow reactors by setting ao = Ui and d = a z), and to CSTRs by setting ao = and d = Uout- 

There are two uses for Equation (2.36). The first is to calculate the concentration of components at the end of a batch reaction cycle or at the outlet of a flow reactor. These equations are used for components that do not affect the reaction rate. They are valid for batch and flow systems of arbitrary complexity if the circumflexes in Equation (2.36) are retained. Whether or not there are spatial variations within the reactor makes no difference when d and b are averages over the entire reactor or over the exiting flow stream. All reactors satisfy global 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. 

Consider a system with N chemical components undergoing a set of M reactions. Obviously, N M. Define the A x M matrix of stoichiometric coefficients as 

Equation 2.45 applies at every instant of time in a batch reactor. Whether or not there are spatial variations within the reactor makes no difference. All batch reactors satisfy ihe global stoichiometry of Equation 2.45 

Equation 2.45 is frequently used to close the material balance for components that do not affect the reaction rate. A second use of Equation 2.45 is to eliminate some of the composition variables from rate expressions. Divide Equation 2.45 by V 

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Are Side Reactions Important What is the Stoichiometry of the Reaction When a mixture of various species is present in a reaction vessel, one often has to worry about the possibility that several reactions, and not just a single reaction, may occur. If one is trying to study one particular reaction, side reactions complicate chemical analysis of the reaction mixture and mathematical analysis of the raw data. The stoichiometry of the reaction involved and the relative importance of the side reactions must be determined by qualitative and quantitative anal-lysis of the products of the reaction at various times. If one is to observe the growth and decay of intermediate products in series reactions, measurements must be made on the reaction system before the reaction goes to completion. 

The effectiveness depends strongly on the stoichiometry of the reaction, and the single Thiele parameter alone is not sufficient to represent its behavior. But evaluation is feasible for specific cases by integration of equations like Eq (4). The ideal rate is obtained from Eq (2) by replacing f... 

Table II indicates the stoichiometry of the reaction of metal hydro-carbyls with the surface of silicas and aluminas dried at various temperatures. The results indicate that at lower drying temperatures approximately 2 moles of hydrocarbon are liberated per mole of hydrocarbyl compound. Subsequent reaction with the proton source, n-butyl alcohol, generates 1 or 2 moles of hydrocarbon, depending on whether a tris- or tetrahydrocarbyl compound is used. The formation of 2 moles of hydrocarbon can arise as a fortuitous combination of metal species singly, doubly, and triply bonded to the support surface.

When a chemical reaction occurs in a system, the changes in the amounts n, of species are not independent because of the stoichiometry of the reaction that occurs. A single chemical reaction can be represented by the reaction equation... 

A mechanism that is consistent with the data gathered in this study for the oxidation of [Ni(L)CN] by 02 is shown in Scheme 2. This mechanism accounts for the stoichiometry of the reaction, has a major pathway involving incorporation of both atoms of a single 02 molecule, and features a rate-determining step that involves one Ni complex and one 02 molecule. 

We have noted previously that the order of a reaction cannot necessarily be determined from an examination of the stoichiometry of the reaction. Indeed we can define a particular type of reaction—the elementary reaction—which has the special property that its reaction order can be determined from its stoichiometry. Elementary reactions may be mon-omolecular, where a single species reacts and its concentration alone determines the rate of the reaction. Generally stated, if the reaction A -> products is elementary and monomolecular, the rate law will be... 

Step 1 Express the equilibrium concentrations of all species in terms of initial concentrations and a single unknown x, that represents the change in concentration. Let (-x) be the depletion in concentration (mol/L) of HF. From the stoichiometry of the reaction, it follows that the increase in concentration for both and F must be x. Complete a table that lists the initial concentrations, the change in... 

Thus, although reaction 5.2 is apparently a single-step reaction with its own stoichiometry, it is in reality complex. The breakup of this reaction into these mechanistic steps and the study of the controlling mechanism fall in the province of the chemist. The chemical engineer, on the other hand, is concerned primarily with reaction 5.2 per se, and the evaluation of the rate of that reaction in terms of the concentrations of the reacting species, as determined by the stoichiometry of the reaction. This chapter will largely be concerned with the latter approach. 

For single-step reactions elementary reactions), the expression of the relaxation time is readily obtained from the rate equation, taking into accoxmt the stoichiometry of the reaction... 

Because product concentrations increase as the reaction proceeds, the change in concentration of a product is positive. Therefore, when the rate is defined with respect to a product, we do not include a negative sign in the definition—the rate is naturally positive. The factor of j in this definition is related to the stoichiometry of the reaction. In order to have a single rate for the entire reaction, the definition of the rate with respect to each reactant and product must reflect the stoichiometric coefficients of the reaction. For this particular reaction, 2 mol of HI is produced from 1 mol of H2 and 1 mol of I2. 

Reaction mechanism, stoichiometries Rate function of single reactions ... 

Quantitative Calculations In precipitation gravimetry the relationship between the analyte and the precipitate is determined by the stoichiometry of the relevant reactions. As discussed in Section 2C, gravimetric calculations can be simplified by applying the principle of conservation of mass. The following example demonstrates the application of this approach to the direct analysis of a single analyte. 

The Ca-Cu system has been reexamined using thermal analysis and x-ray diffraction methods an independent study of the CaCuj-Cu section has also been completed. The resultant phase diagram, although similar to that in ref. 3 at the Cu-rich end, differs markedly for Ca-rich alloys. Supporting evidence for the modifications has been obtained from the Ca-Mg-Cu ternaiy system. Three intermediate compounds are formed in the system CaCuj (950 C) melts congruently, whereas CajCu (488 C) and CaCu (567°C) are formed in peritectic reactions. Single-crystal x-ray diffraction studies verify the stoichiometry of CajCu and examine the polymorphism of CaCu. ... 

These propagation reactions are circular. They consume a methane radical but also generate one. There is no net consumption of free radicals, so a single initiation reaction can cause an indefinite number of propagation reactions, each one of which does consume an acetaldehyde molecule. Ignoring any accumulation of methane radicals, the overall stoichiometry is given by the net sum of the propagation steps ... 

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