Examples for Some Simple Reactions

Section 19 provides discussion about advantages and disadvantages of CSTRs versus PFR and BR for various reaction systems. 

TABLE 7-3 Consecutive and Parallel First-Order Reactions in an Isothermal Constant-Volume Ideal CSTR 

Global or complex reactions are not usually well represented by mass action kinetics because the rate results from the combined effect of several simultaneous elementary reactions (each subject to mass action kinetics) that underline the global reaction. The elementary steps include short-lived and unstable intermediate components such as free radicals, ions, molecules, transition complexes, etc. 

The reason many global reactions between stable reactants and products have complex mechanisms is that these unstable intermediates have to be produced in order for the reaction to proceed at reasonable rates. Often simplifying assumptions lead to closed-form kinetic rate expressions even for very complex global reactions, but care must be taken when using these since the simplifying assumptions are valid over limited ranges of compositions, temperature, and pressure. These assumptions can fail completely—in that case the full elementary reaction network has to be considered, and no closed-form kinetics can be derived to represent the complex system as a global reaction. 

These simplifying assumptions allow elimination of some reaction steps, and representation of free radical and short-lived intermediates concentrations in terms of the concentration of the stable measurable components, resulting in complex non-mass action rate expressions. 

Accordingly, the change in concentration (or in temperature) across the reactor can be made as small as desired by increasing the recycle ratio. Eventually, the reactor can become a well-mixed unit with essentially constant concentration and temperature, while substantial differences in composition will concurrently arise between the fresh feed inlet and the product withdrawal outlet, similar to a CSTR. Such an operation is useful for obtaining experimental data for analysis of rate 

Reaction network Material balances Concentration profiles 

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The lUPAC has not explicitly defined the symbols and terminology for equilibrium constants of reactions in aqueous solution. The NBA has therefore adopted the conventions that have been used in the work Stability Constants of Metal ion Complexes by Sillen and Martell [64SIL/MAR], [71S1L/MAR]. An outline is given in the paragraphs below. Note that, for some simple reactions, there may be different correct ways to index an equilibrium constant. It may sometimes be preferable to indicate the number of the reaction to which the data refer, especially in cases where several ligands are discussed that might be confused. For example, for the equilibrium ... 

For some simple reactions however, the exponents in the rate law correspond exactly to the stoichiometric coefficients in the balanced equation. Such reactions are called elementary. For example, the initial rate of the gaseous reaction... 

The observant reader will notice that some of the equations in this book are not balanced. Although unbalanced chemical equations can be distracting, there are times when trying to balance them is even more distracting. Chemical equations involving polymers certainly can be balanced, but doing so often leads to confusion. For example, consider this simple reaction from Chapter 2 indicating the formation of nylon-6 ... 

The knowledge currently available allows us to make useful predictions of which metals (pure or alloyed) and in which form (small or large particle size) have the best chance to be good catalysts for a new reaction with simple (monofunctional) molecules which have not yet been studied. However, much less can be predicted at the moment with regard to the polyfunctional molecules, in which (for example) a C=C bond stands in the neighbourhood of a C=0, C=N or other bond. The only general theory of selectivity in these reactions is that of Ballandin [86], but this theory does not seem to be satisfactory from the modern point of view. However, useful information is available for some individual reactions. For example, with regard to the a,(1-unsaturated aldehydes, of which acrolein is the simplest example. Let us describe this in more detail. 

Certain hydrides behave as acids in aqueous solution, in particular the simple carbonyl hydrides. This property in aqueous solution, however, does not necessarily indicate the direction of polarity of the M—H bond in the neutral hydride. For example, in some addition reactions of HCo(CO)4 to olefins the behavior of the hydrogen is sometimes protonic and sometimes hydridic (see Section III,B,3). Therefore it is unwise to classify metal hydrides as acidic or basic without reference to the particular conditions. 

Table I lists a few representative examples of estimated A-factors for some hydrocarbon reactions proceeding through six-membered ring, cyclic transition states. We see that although the simple rotor rule is fairly effective in estimating A-factors, it generally errs on the high side. The more complex analysis (10) which takes into account all the changes in frequencies in going to the cyclic complex does a somewhat better job of estimating the A-factors.

Inadequate stoichiometry and poor calibration of the analytical device are interconnected problems. The kinetic model itself follows the stoichiometric rules, but an inadequate calibration of the analytical instrument causes systematic deviations. This can be illustrated with a simple example. Assume diat a bimolecular reaction, A + B P, is carried out in a liquid-phase batch reactor. The density of the reaction mixture is assumed to be constant. The reaction is started with A and B, and no P is present in the initial mixture. The concentrations are related by cp=CoA-Cj=Cob -Cb, i e. produced product, P, equals with consumed reactant. If the concentration of the component B has a calibration error, we get instead of the correct concentration cb an erroneous one, c n ncs, which does not fulfil the stoichiometric relation. If the error is large for a single component, it is easy to recognize, but the situation can be much worse calibration errors are present in several components and all of their effects are spread during nonlinear regression, in the estimation of the model parameters. This is reflected by the fact that the total mass balance is not fulfilled by the experimental data. A way to check the analytical data is to use some fonns of total balances, e.g. atom balances or total molar amounts or concentrations. For example, for the model reaction, A + B P, we have the relation ca+cb+cp -c()a+c0 -constant (again c0p=0). 

These examples of some simple types of chemical reactions show the general solution methodology for determining the behaviour of chemical reactions over time. Especially the modelling of catalytic and reversible reactions requires more sophisticated mathematical methods to determine the concentration rates. However, in the end more or less complicated systems of differential equations have to be solved. 

In such cases the rate constant may be controlled either by diffusion or by chemical factors depending on the conditions. Evidence for the simultaneous roles of diffusion and activation control has also been found for some other reactions in highly viscous solvents, in that they show curved Arrhenius plots, indicating that the rate is controlled by diffusion at low temperatures where the viscosity is highest, but by chemical activation at ordinary temperatures. Examples include the reactions of CO with haemoglobin and myoglobin in aqueous glyerol [10,c,d]. Reactions of simple radicals such as H- and HO- with solvated electrons... 

Thus, we have an opportunity to calculate A from theoretical perspectives and compare it to experimentally determined values (as determined, for example, by graphing In k versus 1/7). Table 20.2 lists some simple reactions and their experimental and calculated pre-exponential factors. Agreements are typically about the correct order of magnitude. 

This is the first example where we have tested to see if the concentration of a product affects the rate of a reaction. It may seem intuitive that products should not be involved in rate laws, but as we show in Section 15-1. a product may influence the rate of a reaction. In careful rate studies, this possibility must be considered. It is common for some reagents in a chemical system to have no effect on the rate of chemical reaction. Although it is unusual for none of the reagents to affect the rate, there are some reactions that are zero order overall. Such reactions have a particularly simple rate law Rate = t. 

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