Kinetics of multiple reactions

The multiple reactions involve parallel, series, and mixed reactions. They consist of complex reactions in which the specific rates of each reaction should be determined. They often occur in industrial processes. These reactions can be simple, elementary, irreversible and reversible, or even nonelementary. Some cases are  

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The recycle reactor is used to control the reaction kinetics of multiple reaction systems. By controlling the concentration present in the reactor, one can shift selectivity toward a more desired product for nonlinear reaction kinetics. 

Solid-phase peptide synthesis products Near-IR multispectral imaging based on scanning acousto-optic tunable filter Simultaneous determination of kinetics of multiple reactions 29 ... 

Chapter 1 treated single, elementary reactions in ideal reactors. Chapter 2 broadens the kinetics to include multiple and nonelementary reactions. Attention is restricted to batch reactors, but the method for formulating the kinetics of complex reactions will also be used for the flow reactors of Chapters 3 and 4 and for the nonisothermal reactors of Chapter 5. 

Except for the recent developments in measurement of electrode kinetics of multiple-electron charge transfer reactions and in... 

For reactor design purposes, the distinction between a single reaction and multiple reactions is made in terms of the number of extents of reaction necessary to describe the kinetic behavior of the system, the former requiring only one reaction progress variable. Because the presence of multiple reactions makes it impossible to characterize the product distribution in terms of a unique fraction conversion, we will find it most convenient to work in terms of species concentrations. Division of one rate expression by another will permit us to eliminate the time variable, thus obtaining expressions that are convenient for examining the effect of changes in process variables on the product distribution. 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

In practice, most industrial processes are staged with multiple reaction processes and separation units as sketched in Figure 4-15. A is the key raw material and is the key product, it is clear that many factors must be included in designing the process to maximize the yield of E. The effectiveness of the separations are obviously critical as well as the kinetics of the reactions and the choice of reactor type and conversion in each reactor. If separations are perfect, then the yields are equal to the selectivities, so that the overall... 

This source of multiplicity is probably the most intrinsic one in catalytic and biocatalytic reactors, for it occurs due to the nonmonotonic dependence of the intrinsic rate of reaction upon the concentration of reactants and products. Although a decade ago, nonmonotonic kinetics of catalytic reactions were considered the exceptional case, today it is clear that nonmonotonic kinetics in catalytic reactions are much more widespread than previously thought. The reader can learn more about various examples from the long list of catalytic reactions exhibiting nonmonotonic kinetics [71-76]. 

Furthermore, the short scan times of EPR (usually 500 ms or less) and the ability to measure species in diamagnetic matrices, for example, aqueous solutions, enable the time-resolved monitoring of chemical reactions involving radical reactants or intermediates. In this way, kinetics of such reactions can be studied even if multiple magnetic species are involved, as their characteristic signals typically differ sufficiently to deconvolute the resulting EPR spectra. Commercial pulsed EPR spectrometers are also available, enabling the study of spin dynamics, that is, the relaxation of the excited system via spin-spin and spin-lattice mechanisms. 

In the case of technetum, this is the most practically used element among non-/ radioactive ones for medical and technical purposes [283], so the permanent interest in its coordination chemistry (in particular, the structural aspect of its compounds [547] and kinetics of substitution reactions [548]) is not surprising [549]. The theoretical interest in Tc is provoked, in particular, by the fact that this is a rhenium analogue. This element (Re) forms multiple metal-metal bond complexes and has been studied intensively in order to achieve a better understanding of the physical and chemical properties of multiple bonds between metal atoms [533],... 

Another subject that captured the attention of researchers in the 1970s was the identification of reaction conditions under which catalyzed and uncatalyzed reactions exhibit multiple steady states and/or oscillatory behavior. Theoretical investigations demonstrated that such behavior could arise from the nonlinear character of the reaction kinetics or from an interplay between the kinetics of a reaction and mass transport processes. A rich body of literature has now emerged detailing the space of reaction conditions and parameters within which multiple steady states and oscillations can be expected [15]. 

The contents of the present contribution may be outlined as follows. Section 6.2.2 introduces the basic principles of coupled heat and mass transfer and chemical reaction. Section 6.2.3 covers the classical mathematical treatment of the problem by example of simple reactions and some of the analytical solutions which can be derived for different experimental situations. Section 6.2.4 is devoted to the point that heat and mass transfer may alter the characteristic dependence of the overall reaction rate on the operating conditions. Section 6.2.S contains a collection of useful diagnostic criteria available to estimate the influence of transport effects on the apparent kinetics of single reactions. Section 6.2.6 deals with the effects of heat and mass transfer on the selectivity of basic types of multiple reactions. Finally, Section 6.2.7 focuses on a practical example, namely the control of selectivity by utilizing mass transfer effects in zeolite catalyzed reactions. 

This chapter, after introducing the equilibrium constant, discusses briefly the rate of entropy production in chemical reactions and coupling aspects of multiple reactions. Enzyme kinetics is also summarized. 

Elder [45] has modelled several multiple reaction schemes, including mutually independent concurrent first-order reactions, competitive first-order reactions, mutually independent n-th order reactions, and mutually independent Avrami-Erofeev models with n = 2 or 3. The criteria identified for recognizing the occurrence of multiple reactions were (i) the apparent order of reaction, n, varies with the method of calculation, and (ii) the kinetic parameters, A and vary with the extent of reaction, a. 

For a comprehensive assessment of electrocatalytic specificity, a quantitative determination of the rate and the kinetics of each possible path is necessary under various conditions. We recently discussed a phenomenological analysis of multiple reactions in parallel or in series to obtain electrode kinetic information and criteria for selectivity control (60, 61. Previous... 

A number of homogeneous models have been proposed to interpret kinetics of ionic reactions on inorganic and organic soil constituents. These include zero-order equations (with the rate of release of the ionic species independent of the amount left in the exchanger material) (Keeney, 1973 Reddy et al., 1978), classical first-order (Sawhney, 1966 Sparks and Jardine, 1984) and multiple first-order equations (Griffin and Jurinak, 1974 . lardine and Sparks, 1984 Carski and Sparks, 1987) (the multiple terms are attributed... 

To eliminate errors resulting from mixing or due to the exothermic reaction heat, so-called 1C adhesives were developed. These EP resins are only single-component adhesives in a procedural sense Chemically they are stiU two-component or multiple-component adhesives. These resins frequently contain additional catalysts that influence the course and kinetics of the reaction. 

Bloomfield, V., Peller, L., Alberty, R. A. (l%2b). Multiple intermediates in steady-state enzyme kinetics III. Analysis of the kinetics of some reactions catalyzed by dehydrogenases. J. Amer. Chem. Soc. 84,4375-4384. 

The elementary (or simple) reaction is one of the key concepts in the modeling of complex processes. An elementary reaction can be defined as a totality of all chemically identical elementary acts in which reordering of chemical substances and/or change of their state are taking place (see, for instance, Emanuel and Knorre, 1984). Since the following discussion deals with the development of kinetic schemes consisting of multiple reactions to which such elementary sense is attributed, a clear definition of this term is required. We will further call the reaction elementary if it passes through not more than one potential barrier in both directions (forward and reverse). 

Most of the studies reported in this chapter fail to include the phase behavior of the reacting mixture. Since multiple phases can occur in the mixture critical region, reaction studies need to be complemented with phase behavior studies so that we may gain an understanding of the fundamentals of the thermodynamics and kinetics of chemical reactions in solution. Chapter 5 describes how a simple cubic equation of state can be used to extend and complement the phase behavior studies. An equation of state can be used to determine the location of phase-border curves in P-T space and, with transition-state theory, to correlate the pressure dependence of the reaction rate constant when the pressure effect is large (i.e., at relatively high pressures). 

In Sect. 7.4.3, the reduction of dihydroxyphenylpyruvic acid (DHPP) to dihydrox-yphenyllactic acid (DHPL) was used as an example for discussion of the kinetics of multiple enzyme systems (Eq. (49)). The rate equations for the reduction reaction of DHPP to DHPL (v>i) and the regeneration of PEG-NAD+ to PEG-NADH (v2) have been introduced (Eqs. (50) and (51)). 

Bond (1987) covers the basic principles of catalysis, adsorption on solid surfaces, chemisorption at metal and oxide surfaces, the kinetics of catalyzed reactions, the quantitative aspects of catalysis by metals and the structure, preparation and use of heterogeneous catalysts. The book also discusses the application of catalysts in different fields including energy conservation, production of hydrocarbon feedstocks, bifunctional catalysts in petroleum industry, oxidation catalysts in the petrochemical industry, heavy inorganic industry, hydrogenation of multiple bonds and catalysts used in atmospheric pollution control. 

When the kinetics of the reaction are non-monotonic and at the same time the system is non-isothermal, the situation may become complex especially for exothermic reactions. For non-monotonic kinetics multiplicity of the steady states may arise for isothermal as well as for mildly endothermic reactions =0, P <0. For exothermic reactions both concentration multiplicity (resulting from the nonmonotonic kinetics) as well as thermal multiplicity (resulting from the exothermicity of the reaction) are combined to give a slightly more complicated multiplicity phenomenon than discussed previously,... 

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