Complex catalytic reactions

The procedure for solving the relations between concentrations has been used in kinetic studies of complex catalytic reactions by many authors, among the first of them being Jungers and his co-workers 17-20), Weiss 21, 22), and others [see, e.g. 23-25a). In many papers this approach has been combined with the solution of time dependencies, at least for some of the single reactions. Also solved were some complicated cases [e.g. six-step consecutive reaction 26,26a) 3 and some improvements of this time-elimination procedure were set forth 27). The elimination of time is... 

The kinetics of a complex catalytic reaction can be derived from the results obtained by a separate study of single reactions. This is important in modeling the course of a catalytic process starting from laboratory data and in obtaining parameters for catalytic reactor design. The method of isolation of reactions renders it possible to discover also some other reaction paths which were not originally considered in the reaction network. 

Shinnar, R. and Feng, C. A., Structure of complex catalytic reactions thermodynamic constraints in kinetic modeling and catalyst evaluation, I EC Fundam., 24, 153-170 (1985). 

The major problem in accomplishing water splitting via the pathway of Scheme 4 is how to suppress the back recombination reaction + A -> D + A, which is a simple exothermic bimolecular process and therefore typically proceeds much more rapidly than complex catalytic reactions of H2 and O2 evolution. 

T. Yamamoto, T. Murauyama, Z.-H. Zhou, T. Ito, T. Fukuda, Y. Yoneda, F. Begum, T. Ikeda, S. Sasaki, H. Takezoe, A. Fukuda, and K. Kubota, -ir-Conjugated poly(pyridine-2,5-diyl), poly(2,2 -bipyridine-5,5 -diyl), and their alkyl derivatives. Preparation, linear structure, function as a ligand to form their transition metal complexes, catalytic reactions, //-type electrically conducting properties, optical properties, and alignment on substrates, J. Am. Chem. Soc., 116 4832-4845,... 

Muller, J. M., and Gault, F. G., Presented at the Fourth Int. Congr. Catal., Moscow, 1968. Symposium Kinetics and Mechanism of Complex Catalytic Reactions," Paper 15. 

Overall Reaction Rate Equation of Single-Route Complex Catalytic Reaction in Terms of Hypergeometric Series... 

The non-linear theory of steady-steady (quasi-steady-state/pseudo-steady-state) kinetics of complex catalytic reactions is developed. It is illustrated in detail by the example of the single-route reversible catalytic reaction. The theoretical framework is based on the concept of the kinetic polynomial which has been proposed by authors in 1980-1990s and recent results of the algebraic theory, i.e. an approach of hypergeometric functions introduced by Gel fand, Kapranov and Zelevinsky (1994) and more developed recently by Sturnfels (2000) and Passare and Tsikh (2004). The concept of ensemble of equilibrium subsystems introduced in our earlier papers (see in detail Lazman and Yablonskii, 1991) was used as a physico-chemical and mathematical tool, which generalizes the well-known concept of equilibrium step . In each equilibrium subsystem, (n—1) steps are considered to be under equilibrium conditions and one step is limiting n is a number of steps of the complex reaction). It was shown that all solutions of these equilibrium subsystems define coefficients of the kinetic polynomial. 

A single-route complex catalytic reaction, steady state or quasi (pseudo) steady state, is a favorite topic in kinetics of complex chemical reactions. The practical problem is to find and analyze a steady-state or quasi (pseudo)-steady-state kinetic dependence based on the detailed mechanism or/and experimental data. In both mentioned cases, the problem is to determine the concentrations of intermediates and overall reaction rate (i.e. rate of change of reactants and products) as dependences on concentrations of reactants and products as well as temperature. At the same time, the problem posed and analyzed in this chapter is directly related to one of main problems of theoretical chemical kinetics, i.e. search for general law of complex chemical reactions at least for some classes of detailed mechanisms. 

As for the quasi (pseudo)-steady-state case, the basic assumption in deriving kinetic equations is the well-known Bodenshtein hypothesis according to which the rates of formation and consumption of intermediates are equal. In fact. Chapman was first who proposed this hypothesis (see in more detail in the book by Yablonskii et al., 1991). The approach based on this idea, the Quasi-Steady-State Approximation (QSSA), is a common method for eliminating intermediates from the kinetic models of complex catalytic reactions and corresponding transformation of these models. As well known, in the literature on chemical problems, another name of this approach, the Pseudo-Steady-State Approximation (PSSA) is used. However, the term "Quasi-Steady-State Approximation" is more popular. According to the Internet, the number of references on the QSSA is more than 70,000 in comparison with about 22,000, number of references on PSSA. 

Some examples of kinetic equations of complex catalytic reactions are presented in Appendix 1. 

When the complex catalytic reaction is irreversible, a typical form of the corresponding kinetic equation, i.e. LH equation, is written as follows ... 

As previously mentioned, the QSSA is a common method for eliminating intermediates from the kinetic models of complex catalytic reactions and corresponding transformation of these models. Mathematically, it is a zero-order approximation of the original (singularly perturbed) system of differential equations, which describes kinetics of the complex reaction. We simply replace... 

Yablonskii, G. S., Spivak, S. 1., and Lazman, M. Z., Modeling of complex catalytic reactions, in "Proceedings of the 4th International Symposium on Systems Analysis and Simulation (Berlin, Germany)" (A. Sydow Ed.), pp. 651-656. Elsevier, New York. (1992). 

Yablonsky, G. S., and Lazman, M. Z., Non-Linear Steady-State Kinetics of Complex Catalytic Reactions Theory and Experiment, Dynamics of Surfaces and Reaction Kinetics in Heterogeneous Catalysis, Proceedings of the International Symposium, Antwerpen, September 371-378 (1997). 

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