Consecutive Chemical Reactions

Sets of first-order rate equations are solvable by Laplace transform (Rodiguin and Rodiguina, Consecutive Chemical Reactions, Van Nostrand, 1964). The methods of linear algebra are applied to large sets of coupled first-order reactions by Wei and Prater Adv. Catal., 1.3, 203 [1962]). Reactions of petroleum fractions are examples of this type. 

Because the rates of chemical reactions are controlled by the free energy of the transition state, information about the stmcture of transition states is crucial to understanding reaction mechanism. However, because transition states have only transitory existence, it is not possible to make experimental measurements that provide direct information about their structure.. Hammond has discussed the circumstances under which it is valid to relate transition-state stmcture to the stmcture of reactants, intermediates, and products. His statements concerning transition-state stmcture are known as Hammond s postulate. Discussing individual steps in a reaction mechanism, Hammond s postulate states if two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have neariy the same energy content, their interconversion will involve only a small reorganization of molecular stmcture. ... 

In the case of coupled heterogeneous catalytic reactions the form of the concentration curves of analytically determined gaseous or liquid components in the course of the reaction strongly depends on the relation between the rates of adsorption-desorption steps and the rates of surface chemical reactions. This is associated with the fact that even in the case of the simplest consecutive or parallel catalytic reaction the elementary steps (adsorption, surface reaction, and desorption) always constitute a system of both consecutive and parallel processes. If the slowest, i.e. ratedetermining steps, are surface reactions of adsorbed compounds, the concentration curves of the compounds in bulk phase will be qualitatively of the same form as the curves typical for noncatalytic consecutive (cf. Fig. 3b) or parallel reactions. However, anomalies in the course of bulk concentration curves may occur if the rate of one or more steps of adsorption-desorption character becomes comparable or even significantly lower then the rates of surface reactions, i.e. when surface and bulk concentration are not in equilibrium. 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

To this point we have focused on reactions with rates that depend upon one concentration only. They may or may not be elementary reactions indeed, we have seen reactions that have a simple rate law but a complex mechanism. The form of the rate law, not the complexity of the mechanism, is the key issue for the analysis of the concentration-time curves. We turn now to the consideration of rate laws with additional complications. Most of them describe more complicated reactions and we can anticipate the finding that most real chemical reactions are composites, composed of two or more elementary reactions. Three classifications of composite reactions can be recognized (1) reversible or opposing reactions that attain an equilibrium (2) parallel reactions that produce either the same or different products from one or several reactants and (3) consecutive, multistep processes that involve intermediates. In this chapter we shall consider the first two. Chapter 4 treats the third. 

Formulation of the Solution Steps for the Gauss-Newton Method Two Consecutive Chemical Reactions... 

As an example for precise parameter estimation of dynamic systems we consider the simple consecutive chemical reactions in a batch reactor used by Hosten and Emig (1975) and Kalogerakis and Luus (1984) for the evaluation of sequential experimental design procedures of dynamic systems. The reactions are... 

Figure 12.2 The operability region for the consecutive chemical reactions example [reprinted from the Canadian Journal of Chemical Engineering with permission].

Table 12.1 Consecutive Chemical Reactions Effect of Final Time on the Selection of the Best Grid Point Using the Volume Criterion ...

Table 12.2 Consecutive Chemical Reactions Selection of the Best Grid Point Based on the Volume Criterion and Through the Use of the Information Index...

Figure 11.3 is the representation of the case study that is used to demonstrate the performance of the proposed model it is taken from directly from Chapter 10. To facilitate understanding, this case study is described in some detail in this chapter. The plant, which constitutes 30% of production and consumes 55% of utility steam in the multinational agrochemical facility of choice, involves the manufacture of an herbicide. The saturated steam is produced from a coal fired boiler at 10 bar absolute pressure and 3 t/h, although it is only used at 4 bar in the chosen process. The process entails 3 consecutive chemical reactions which take place in 4 reactors. The first reaction, which uses water as a solvent, takes place in reactors R1 and R2. 

Ans. (a) We simplify this process by imagining that it takes place in two consecutive steps. The first step is the chemical reaction, which liberates heat. (AH is negative.) This heat is the cause of the temperature rise. (b) The second step is the addition of that heat to the solution, causing the temperature rise. The solution takes in the heat. AH is positive for this step. If no heat escapes to the surroundings, the overall A H is 0. 

Comparison of the fractional yields of V in mixed and plug flow reactors for the consecutive first-order reactions. A A- V W. (Adapted from Chemical Reaction Engineering, Second Edition, by O. Levenspiel. Copyright 1972. Reprinted by permission of John Wiley and Sons, Inc.)... 

Liquid phase chlorination work in the former U.S.S.R. has been summarized by Vereshchinskii (1972). With tetradecane, the reaction is nearly or partially diffusion-controlled at a dose rate of 0.1-0.4 rad s-1. However, during the chlorination process, the liquid phase properties change continuously because of chlorine absorption accompanying the chemical reactions. Due to long chain reactions the chlorination G value is high and can reach 105 per 100 eV of energy absorption. At around 10-30°C the reaction rate is found to vary as the square root of the dose rate. A set of consecutive reactions has been reported in the liquid phase chlorination of 1,1,1,5-tetrachloropentane (Vereshchinskii, 1972). 

Isopropylbenzene (A) is alkylated with propylene (P) using HF catalyst. The mono (B), di (C), tri (D) and tetra (E) derivatives are formed. Relative specific rates are given by Rodiguin Rodiguina (Consecutive Chemical Reactions, 1964) for the case of a large excess of propylene which makes the reactions pseudo first order. The relative specific rates used here are kx = 1.0, k2 = 0.5, k3 = 0.3 and k4 0.2. The system of linear differential... 

As briefly discussed in Section 1.2, chemical-reaction engineers recognized early on the need to predict the influence of reactant segregation on the yield of complex reactions. Indeed, the competitive-consecutive and parallel reaction systems analyzed in the previous section have been studied experimentally by numerous research groups (Baldyga and Bourne 1999). However, unlike the mechanical-engineering community, who mainly focused on the fluid-dynamics approach to combustion problems, chemical-reaction... 

N.M. Rodiguin, E.N. Rodiguina. Consecutive Chemical Reactions. Mathematical Analysis and Development. D. van Nostrand New York 1964... 

Biochemical reactions are interesting but they are not magic . Individual chemical reactions that comprise a metabolic pathway obey, obviously, the rules of organic chemistry. All too often students make fundamental errors such as showing carbon with a valency of 3 or 5, or failing properly to balance an equation when writing reactions. Furthermore, overall chemical conversions occur in relatively small steps, that is there are usually only small structural changes or differences between consecutive compounds in a pathway. 

One important type of complex mechanism in electrode reactions is a series of consecutive reactions. One example of this type is electrochemical deposition from complexed ions. In this case the electrochemical reaction is preceded by a chemical reaction. Another example is that of inclusion of cathodic hydrogen evolution. We discuss these two cases next. 

Reaction stoichiometry and mechanism. This process, which selectively produces linear alcohols ranging fhom to about C ,is based on the chemical reactions of Table IT. Main reactions (fa,b) produce alcohols and their related unavoidable by-products, CO and H O, the former being favored at low H /CO ratios due to side or consecutive shift reaction (c). Secondary reactions produce light hydrocarbons (d,e). The reactions stoichiometry (H /CO) varies between 0.6 and 3, depending on the nature of the products and the number of carbon atoms involved. Most of these reactions are strongly exothermic. 

Using the dropping zinc amalgam microelectrode, detailed kinetic data were obtained [40], and the two consecutive electron transfers followed by a chemical reaction (EEC) mechanism of Zn(II) reduction could be revealed. 

We take the simplest kinetic scheme for our requirements two consecutive first-order chemical reactions converting an initial reactant P into a final product B through a single intermediate species A... 

They proposed a polymerization scheme closely related to other well-known chemical reactions of metal alkoxide with carbonyl compounds (20). In Scheme 2, complex [A] is converted to [B] by hydride ion transfer from the alkoxyl group to the carbon atom of aldehyde (Meerwein-Ponndorf reduction). Addition of one molecule of monomer to the growing chain requires transfer of the alkoxide anion to the carbonyl group to form a new alkoxide [C]. Repetition of these two consecutive processes, i.e., coordination of aldehyde and transfer of the alkoxide anion, constitutes the chain propagation step. 

Some experimental methods to compensate or to minimize the influence of the capacitive current have been reviewed by MacDonald [22]. The reader is directed to the same reference for the theoretical treatments of more complex systems involving parallel and consecutive charge transfer reactions, coupled chemical reactions, as well as of more sophisticated performances of large amplitude galvanostatic techniques, e.g. current reversal and cyclic methods. 

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