Reaction rates stoichiometry

Choosing a reactor for a given reaction is based on several considerations and combines reaction analysis with reactor analysis. Thus, we consider in this chapter the following aspects of reactions and reactors, much of which should serve as an introduction to chemists and a refresher to chemical engineers reaction rates, stoichiometry, rate equations, and the basic reactor types. 

A study of the kinetics of a chemical reaction begins with the measurement of its reaction rate. Consider, for example, the general reaction shown in the following equation, involving the aqueous solutes A, B, C, and D, with stoichiometries of a, b, c, and d. 

The stoichiometric relationship between chlorine dioxide added and color removed during bleaching is nonlinear, but it is independent of temperature, pH, and pulp concentration under conditions normally used. Models used to explain the kinetics and stoichiometry show a strong dependence on chromophore concentration that probably results from differences in the reaction rates of the various chromophores present in the pulps (80). 

A gas decomposition reaction with stoichiometry 2A —> 2B -i- C follows a second order rate law rj(mol / m s) = kC, where C is the reactant concentration in mol/m. The rate constant k varies with the reaction temperature according to the Arrhenius law ... 

The choice of solvent is not trivial and, generally, the reaction medium must be a good solvent for both monomers and polymer product. In addition, to obtain high molecular weight, water needs to be removed from the system to avoid hydrolyzing the activated substrate, since hydrolysis reduces the reaction rate and upsets the stoichiometry of the monomers.61 63... 

In the calculation in Example 13.1, we used the units micromoles per liter per second (pmol-L 1 -s 1) to report the reaction rate, but other units for time (such as minutes or even hours) are commonly encountered for slower reactions. Note, too, that, when we report a reaction rate, we must specify the species to which the rate refers. For example, the rate of consumption of HI is twice the rate of formation of H2 in the reaction in Example 13.1, because two HI molecules are used to make one H2 molecule. The various ways of reporting the rate of a given reaction are related by the reaction stoichiometry. Therefore, in our example, we conclude that... 

Similar expressions can be written for third-order reactions. A reaction whose rate is proportional to [A] and to [B] is said to be first order in A and in B, second order overall. A reaction rate can be measured in terms of any reactant or product, but the rates so determined are not necessarily the same. For example, if the stoichiometry of a reaction is2A-)-B—>C- -D then, on a molar basis, A must disappear twice as fast as B, so that —d[A]/dt and -d[B]/dr are not equal but the former is twice as large as the latter. 

The functional form of the reaction rate in Equation (1.14) is dictated by the reaction stoichiometry. Equation (1.12). Only the constants kf and k can be adjusted to fit the specific reaction. This is the hallmark of an elementary reaction its rate is consistent with the reaction stoichiometry. However, reactions can have the form of Equation (1.14) without being elementary. 

This reaction is complex even though it has a stoichiometric equation and rate expression that could correspond to an elementary reaction. Recall the convention used in this text when a rate constant is written above the reaction arrow, the reaction is assumed to be elementary with a rate that is consistent with the stoichiometry according to Equation (1.14). The reactions in Equations (2.5) are examples. When the rate constant is missing, the reaction rate must be explicitly specihed. The reaction in Equation (2.6) is an example. This reaction is complex since the mechanism involves a short-lived intermediate, B. 

The numerical methods 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. We have not always followed this approach. For example, several of the examples have ignored product concentrations when they do not affect reaction rates and when they are easily found from the amount of reactants consumed. Also, some of the analytical solutions have used stoichiometry directly to ease the algebra. This section formalizes the use of stoichiometric constraints. 

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 balanced equation shows that three molecules of oxygen are consumed for every two molecules of propene and two molecules of ammonia. Thus, the rate of C3 Hg and NH3 consumption is only two-thirds the rate of O2 consumption. Those seven molecules of starting materials produce two molecules of CH2 CHCN and six molecules of H2 O. Thus, CH2 CHCN is produced at the same rate as C3 Hg is consumed, whereas H2 O is produced three times as fast as CH2 CHCN is. The link between relative reaction rates and reaction stoichiometry is Equation. Therefore,... 

When a reaction proceeds in a single elementary step, its rate law will mirror its stoichiometry. An example is the rate law for O3 reacting with NO. Experiments show that this reaction is first order in each of the starting materials and second order overall NO + 03- NO2 + O2 Experimental rate = i [N0][03 J This rate law is fully consistent with the molecular view of the mechanism shown in Figure 15-7. If the concentration of either O3 or NO is doubled, the number of collisions between starting material molecules doubles too, and so does the rate of reaction. If the concentrations of both starting materials are doubled, the collision rate and the reaction rate increase by a factor of four. 

Reactions for which the rate equations follow the stoichiometry as given in Equations 5.23 to 5.26 are known as elementary reactions. If there is no direct correspondence between the reaction stoichiometry and the reaction rate, these are known as nonelementary reactions and are often of the form ... 

Acids are selected based on the nature of the well treatment and the mineralogy of the formation. The critical chemical factors in properly selecting an acid are stoichiometry (how much formation material is dissolved by a given amount of acid), the equilibrium constant (complete reaction of the acid is desired), and reaction rate between the acid and the formation material (106). 

From a knowledge of the reaction stoichiometry and measurements of the total pressure as a function of time, it is possible to determine the extent of reaction and the partial pressures or concentrations of the various reactant and product species at the time at which the measurement is made. Illustration 3.3 indicates how pressure measurements can be used to determine a reaction rate function. 

When integral methods are used in data analysis, measured concentrations are used in tests of proposed mathematical formulations of the reaction rate function. One guesses a form of the reaction rate expression on the basis of the reaction stoichiometry and assumptions concerning its mechanism. The assumed expression is then integrated to give a relation between the composition of the reaction mixture and time. A number of such relations were developed in... 

Use of Excess Concentrations—The Isolation Method. The method of isolation for elucidating the form of the reaction rate expression is based on the simplifications that occur when the concentration of one or more of the reactants appearing in the rate expression is much greater than that called for by the stoichiometry of the reaction. 

Preliminary Criteria for Testing a Proposed Reaction Mechanism— Stoichiometry and Derivation of a Rate Expression for the Mechanism... 

First consider mechanism A. Addition of reactions C and D gives reaction A, so the stoichiometry of the mechanism is consistent. Reaction C is the rate limiting step, so the overall reaction rate is given by... 

Although reaction rate expressions and reaction stoichiometry are the experimental data most often used as a basis for the postulation of reaction mechanisms, there are many other experimental techniques that can contribute to the elucidation of these molecular processes. The conscientious investigator of reaction mechanisms will draw on a wide variety of experimental and theoretical methods in his or her research program in an attempt to obtain information about the elementary reactions taking... 

Extension of the analysis developed above to cases where the stoichiometry of the surface reaction differs from that considered is relatively simple and straightforward. An interesting case is that where the overall conversion rate is limited by adsorption of a species that dissociates on adsorption. Consider a reaction whose stoichiometry can be represented by... 

The principles of stoichiometry may be used to write the reaction rate in terms of the fraction conversion. The desired conversion level is expressed in terms of the initial substrate level. Thus CAo = 24 kg/m3. At any time the instantaneous concentration of substrate can be written as... 

An exothermic reaction with the stoichiometry A 2B takes place in organic solution. It is to be carried out in a cascade of two CSTR s in series. In order to equalize the heat load on each of the reactors it will be necessary to operate them at different temperatures. The reaction rates in each reactor will be the same, however. In order to minimize solvent losses by evaporation it will be necessary to operate the second reactor at 120 °C where the reaction rate constant is equal to 1.5 m3/kmole-ksec. If the effluent from the second reactor corresponds to 90% conversion and if the molal feed rate to the cascade is equal to 28 moles/ksec when the feed concentration is equal to 1.0 kmole/m3, how large must the reactors be If the activation energy for the reaction is 84 kJ/mole, at what temperature should the first reactor be operated ... 

Diphenylmethane reacts with dioxygen in the presence of potassium 1,1-dimethylethoxide in various solvents (dimethylformamide [DMF], hexamethylphosphoramide [HMPA], pyridine) to produce nearly 100% yields of benzophenone [284]. The adduct of benzophenone with dimethylsulfoxide (DMSO) [l,l-diphenyl-2-(methylsulfinyl)ethanol] is formed as the final product of the reaction. The stoichiometry of the reaction and the initial rate depends on the solvent (conditions 300 K, [Ph2CH2] = 0.1mol L [Me3COK] = 0.2mol L 1,p02 = 97kPa). 

A plug flow reactor is used for a reaction with stoichiometry, 2A = 3B, in the gas phase. The rate equation is... 

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