Chemical kinetics series-parallel reactions

The chemical composition of many systems can be expressed in terms of a single reaction progress variable. However, a chemical engineer must often consider systems that cannot be adequately described in terms of a single extent of reaction. This chapter is concerned with the development of the mathematical relationships that govern the behavior of such systems. It treats reversible reactions, parallel reactions, and series reactions, first in terms of the mathematical relations that govern the behavior of such systems and then in terms of the techniques that may be used to relate the kinetic parameters of the system to the phenomena observed in the laboratory. 

Additions of these two simple cases can lead to series parallel networks of chemical reaction. When we encounter a problem like this one, we have to handle the kinetics carefully. This is just what we will do in the case of this problem. 

Chapter 2 covers the basic principles of chemical kinetics and catalysis and gives a brief introduction on classification and types of chemical reactors. Differential and integral methods of analysis of rate equations for different types of reactions—irreversible and reversible reactions, autocatalytic reactions, elementary and non-elementary reactions, and series and parallel reactions are discussed in detail. Development of rate equations for solid catalysed reactions and enzyme catalysed biochemical reactions are presented. Methods for estimation of kinetic parameters from batch reactor data are explained with a number of illustrative examples and solved problems. 

It is quite possible that a series of intermediate phases forms during the electrochemical process, their exact nature being controlled by the differences in the kinetics of the diffusion of the different ions or atoms in the system. Parallel reactions to products with similar thermodynamic stability may lead to a degradation of the reversible properties, if one of the products is not electrochemically reversible. Hence, knowledge of the real reaction partners and of their properties is the key for understanding the electrochemical processes in the system and elucidating the reaction mechanism. This is possible by making ex situ and/or in situ experiments with methods that supply information about the chemical composition, structural, and thermal properties of the compounds in the reaction mixture. A number of examples have been presented in literature based on the various methods as listed in Table 3.5. 

Chemical reactions occurring because of a single kinetic act, i.e., because of a single collision between two molecules, are defined as elementary reactions. More complex laws of dependence on concentrations can be explained by complex reaction mechanisms, i.e., by the idea that most reactions occur as a sequence of many elementary reactions, linked in series or in parallel. As an example, the following... 

If a chemical reaction is operated in a flow reactor under fixed external conditions (temperature, partial pressures, flow rate etc.), usually also a steady-state (i.e., time-independent) rate of reaction will result. Quite frequently, however, a different response may result The rate varies more or less periodically with time. Oscillatory kinetics have been reported for quite different types of reactions, such as with the famous Belousov-Zha-botinsky reaction in homogeneous solutions (/) or with a series of electrochemical reactions (2). In heterogeneous catalysis, phenomena of this type were observed for the first time about 20 years ago by Wicke and coworkers (3, 4) with the oxidation of carbon monoxide at supported platinum catalysts, and have since then been investigated quite extensively with various reactions and catalysts (5-7). Parallel to these experimental studies, a number of mathematical models were also developed these were intended to describe the kinetics of the underlying elementary processes and their solutions revealed indeed quite often oscillatory behavior. In view of the fact that these models usually consist of a set of coupled nonlinear differential equations, this result is, however, by no means surprising, as will become evident later, and in particular it cannot be considered as a proof for the assumed underlying reaction mechanism. 

A series of rapid chemical quench experiments under single enzyme turnover conditions using radiolabeled S3P or PEP revealed that the tetrahedral ketal phosphate enzyme intermediate was formed as a new peak upon HPLC analysis with detection of the radiolabel. The time course revealed that the formation of the tetrahedral intermediate species paralleled the disappearance of PEP substrate and formation of the EPSP product thus establishing that it was a kinetically competent species. Isolation of the tetrahedral ketal phosphate intermediate using C-2 PEP and S3P as substrates coupled with rapid chemical quench was carried out in conjunction with H-, C-, and P- NMR to provide a definitive structure proof Thus with these studies we have satisfied the criteria for a true reaction intermediate in terms of a chemically plausible mechanism, structure proof, and kinetic competence. Additional studies support the mechanism for EPSP synthase described (Scheme 4, pathway a) including observation of the intermediate bound to the enzyme at internal equilibrium using solution NMR and C-2 PEP as well as using rapid freeze-quench/solid-state NMR studies. ... 

For competing reactions, both in series and parallel, adjust the temperature, pressure, and catalyst to obtain high yields of the desired products. In the initial distribution of chemicals, assume that these conditions can be satisfied. Before developing a base-case design, obtain kinetics data and check this assumption. 

Therefore we attempted to simulate advanced pyrolysis using a multi-step model (MSM). This model was developed using TGA- and DSC-derived kinetic coefficients, determined for chemically and thermally treated oil shale samples by modelling particular reaction steps. The MSM is based on the reaction scheme shown in Fig. 4-116 which displays a series of parallel and consecutive first order reactions. K and B denote the kerogen and bitumen originally present in the oil shale B, B, and to /Jj are non-volatilized intermediates and products (solids and liquids) to are volatilized products (gases and vapors) and/j to/jg are the stoichiometric coefficients that fulfil the condition ... 

Figure 1.14. Schematic of steps that are part of an overall reaction from initial reactants to final products via intermediate species. indicates a reaction intermediate and the different -values indicate that there are many resistances for processes in parallel and in series. A chemical reaction is analogous to a network of resistors in circuits a chemical conversion rate is comparable to a current. The overall kinetics are determined by the lowest k-value in the reaction series that has the highest rate of production of end products compared to other reaction series running in parallel. The scheme presupposes a small driving force AG.

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