Complex reaction system

Mixed parallel and series reactions producing byproducts. In more complex reaction systems, both parallel and series reactions can occur together. Mixed parallel and series reactions are of the type... 

The importance of numerical treatments, however, caimot be overemphasized in this context. Over the decades enonnous progress has been made in the numerical treatment of differential equations of complex gas-phase reactions [8, 70, 71], Complex reaction systems can also be seen in the context of nonlinear and self-organizing reactions, which are separate subjects in this encyclopedia (see chapter A3,14. chapter C3.6). 

Wei J and Prater C D 1962 The structure and analysis of complex reaction systems Advances in Catalysis (New York Academic) pp 203-392... 

The master equation treatment of energy transfer in even fairly complex reaction systems is now well established and fairly standard [ ]. However, the rate coefficients kjj or the individual energy transfer processes must be established and we shall discuss some aspects of this matter in tire following section. 

For a reaction as complex as catalytic enantioselective cyclopropanation with zinc carbenoids, there are many experimental variables that influence the rate, yield and selectivity of the process. From an empirical point of view, it is important to identify the optimal combination of variables that affords the best results. From a mechanistic point of view, a great deal of valuable information can be gleaned from the response of a complex reaction system to changes in, inter alia, stoichiometry, addition order, solvent, temperature etc. Each of these features provides some insight into how the reagents and substrates interact with the catalyst or even what is the true nature of the catalytic species. 

The strength and interrelation of catalysis, classical promotion and electrochemical promotion is illustrated in Fig. 2.3. The reaction under consideration14 is the reduction of NO by CO in presence of 02. This is a complex reaction system but of great technological importance for the development of efficient catalytic converters able to treat the exhaust gases of lean burn and Diesel engines. 

A complex reaction system cannot be considered completely in most cases. The number of simplifications required for the model increases with the growing complexity of the system. 

Experimental studies, combined with thermodynamic analysis, indicate that the CTA hydropurification process is a complex reaction system including both parallel and tandem reactions wherein 4-CBA hydrogenation is exothermic and its paralleled decarbonylation is endothermic. 

For complex reaction systems the establishment of a reliable kinetic network and accompanying parameters is often difficult or even impossible. Paul (1988, 1990) has categorized complex systems of fine chemistry reactions in the following way ... 

More complex kinetic expressions can be analysed, either in a manner similar to that shown in the above example or using methods discussed in the previous section. More complex reaction systems can also be studied if the reaction mixture is analysed during the course of reaction Tufano (1993) presented a theoretical analysis of such a case. Several examples of the use of a reaction calorimeter for kinetic studies were presented at RC User Forum (see, e.g.. 

For complex reaction systems, the heats of reaction of all individual reactions have to be estimated and the dynamic heat balance equations must include the heats of all the reactions. 

In our laboratory we have utilized multiphoton infrared laser activation of metal ion-hydrocarbon adducts to probe the lowest energy pathways of complex reaction systems (6). Freiser and co-workers have utilized dispersed visible and uv radiation from conventional light sources to examine photochemical processes involving organometallic fragments... 

Reasonable yields (55-85%) of dialkylphosphinic acids have been reported from a complex reaction system beginning with red phosphorus, iodoalkane, and elemental iodine.26 Presumably, the phosphorus trihalide is generated as an intermediate. The reaction is worked up with a nitrous acid system from aqueous HCl/NaN02. 

The interest in the dynamic operation of heterogeneous catalytic systems is experiencing a renaissance. Attention to this area has been motivated by several factors the availability of experimental techniques for monitoring species concentrations both in the gas phase and at the catalyst surface with a temporal resolution and sensitivity not previously possible, the development of efficient numerical methods for predicting the dynamics of complex reaction systems, and the recognition that in selected instances operation of a catalytic reactor under dynamic conditions can yield a better performance than operation under steady-state conditions. 

CSTRCOM - Isothermal Reactor with Complex Reaction System... 

In a complex reaction system occurring in a flow electrolyzer, one of the anode reaction products reacts with the principal constituent of the composite electrolyte, yielding an anionic species whose parasitic reaction at the cathode reduces the cathode efficiency. 

Nonetheless, the topological and stoichiometric analysis of metabolic networks is probably the most powerful computational approach to large-scale metabolic networks that is currently available. Stoichiometric analysis draws upon extensive work on the structure of complex reaction systems in physical chemistry in the 1970s and 1980s [59], and can be considered as one of the few theoretically mature areas of Systems Biology. While the variety and amount of applications of stoichiometric analysis prohibit any comprehensive summary, we briefly address some essential aspects in the following. 

The two routes (one is Eqs. 2-37b and 2-37c the other is Eqs. 2-37a and 2-37d) together constitute a complex reaction system that consists simultaneously of competitive, consecutive and competitive, parallel reactions. 

We should be able to generalize these findings to other more complex reaction systems, such as for two component multistep reactions to polymerizations and to non-Newtonian power law fluids. 

We can use this approximation for many complex reaction systems by assuming many steps to be in thermodynamic equilibrium. Whether or not the expression is a good approximation to the exact expression of course depends on the values of particular rate coefficients. 

Therefore, this method allows for the determination of relative rate constants for the excitation step in a complex reaction system, where this step cannot be observed directly by kinetic measurements. The singlet quantum yield at infinite activator concentrations (high-energy intermediates formed interact with the activator, is also obtained from this relationship (equation 5). 

An indirect method has been used to determine relative rate constants for the excitation step in peroxyoxalate CL from the imidazole (IM-H)-catalyzed reaction of bis(2,4,6-trichlorophenyl) oxalate (TCPO) with hydrogen peroxide in the presence of various ACTs18. In this case, the HEI is formed in slow reaction steps and its interaction with the ACT is not observed kinetically. However, application of the steady-state approximation to the reduced kinetic scheme for this transformation (Scheme 6) leads to a linear relationship of 1/S vs. 1/[ACT] (equation 5) and to the ratio of the chemiluminescence parameters /ic vrAi), which is a direct measure of the rate constant of the excitation step. Therefore, this method allows for the determination of relative rate constants for the excitation step in a complex reaction system, where this step cannot be observed directly by kinetic measurements18. The singlet quantum yield at infinite activator concentrations ( °), where all high-energy intermediates formed interact with the activator, is also obtained from this relationship (equation 5). 

In complex reaction systems the conversion of reactants to products typically takes place through a number of parallel and serial reactions. The reaction path from a reactant through a number of intermediates to the final product naturally occurs in a series of steps. The overall conversion rate and the peak concentrations of the intermediates will depend on the relative rates of the serial reactions. 

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