Inverse Chemical Kinetics Problem

Universal Approaches to Inverse Chemical Kinetics Problem... 

Solution of Eq. (2) is only part of the overall problem in mechanistic studies. Indeed, Eq. (2) represents only the first of many sequential inverse problems vthich we commonly lump together and which represent the overall inverse problem in chemical kinetics [110-112]. The next problem is the determination of the moles of all species, the elemental stoichiometries of species, the number of observable reactions, and the balanced stoichiometries for all observable reactions. 

Figure 4.1S Representation of the three primary steps for the generic inverse problem in chemical kinetics including homogeneous catalysis. In situ spectroscopic data is represented by 4kexv Tbe inverse spectroscopic problem (Eq. (2)), which is the focus of this chapter, is represented by S [,s, Ojxv The inverse problem associated with stoichiometries and reaction topology is represented by r rxs moles, reactions, extents of reaction and reaction stoi-...

In short, geochemical kineticists do not have the luxury of chemical kineticists and must deal with real-world and more complicated systems. Geochemists developed the theories and concepts to deal with inverse kinetic problems, reaction kinetics during cooling, and other geologically relevant questions. These new scopes, especially the inverse theories, reflect the special need of Earth sciences, and make geochemical kinetics much more than merely chemical kinetic theories applied to Earth sciences. 

The ultimate goal of kinetics studies is the identification of a (unique) chemical kinetic mechanism, which consists of a reaction scheme such as the one shown in Figure 1.3 and the corresponding numerical values of the rate coefficients, k, which incorporate entropy and enthalpy differences. This is an inverse problem, since only the concentration profile or, in less favorable conditions, only the relaxation times can be observed, and the reaction mechanism must be deduced from this information. Any experimental method that establishes a connection between the signal and the concentration of molecules can be used to investigate kinetics. However, it is necessary that the method has sufficient time resolution since time is the crucial parameter in kinetic experiments. 

In the beginnings of classical physical chemistry, starting with the publication of the Zeitschrift fUr Physikalische Chemie in 1887, we find the problem of chemical kinetics being attacked in earnest. Ostwald found that the speed of inversion of cane sugar (catalyzed by acids) could be represented by a simple mathematical equation, the so-called compound interest law. Nernst and others measured accurately the rates of several reactions and expressed them mathematically as first order or second order reactions. Arrhenius made a very important contribution to our knowledge of the influence of temperature on chemical reactions. His empirical equation forms the foundation of much of the theory of chemical kinetics which will be discussed in the following chapter. 

Methods of elimination and. the problem of nonuniqueness of inverse problem solutions in models of non-s tat ionary chemical kinetics... 

A.G. Pogorelov, An Inverse problem of non-stationary chemical kinetics. Science, Moskow, 1988. 

Determining the activation energy spectrum from Rock-Eval pyrolysis data is an inverse task of mathematical statistics having multiple solutions. Some problems are related to the restoration of chemical-kinetic parameters of effective reactions for organic matter maturation in source rocks. For example, reactions with activation energies of less than 50 Kcal moD do not contribute to the Rock-Eval pyrolysis Sj curve because these reactions can occur during the burial stage and would not contribute to S. ... 

The questions so far (after necessary preliminaries included in (1), (2) and (3)) have dealt with direct problems. These problems have the general form given a differential equation what can we say about its solutions Another set of problems called inverse problems are even more important both in chemical kinetics and in general. It may even be said that solutions of direct problems only have practical importance when used to solve an inverse problem. 

It is believed that one can achieve good lehabihty in describing complex reactions, if one combines computer experiments with detailed laboratory experimental studies. Here, applying the methods of solving inverse problems of chemical kinetics, aimed at updating the rate constant values for individual steps are also relevant [15,63,64],... 

According to Onsager s work, the fluxes near chemical equilibrium are linear functions of potentials and the reciprocal relations state that the matrix of coefficients of these functions is symmetric. It is impossible to measure these coefficients directly. In order to find them, the inverse problem of chemical kinetics, which is often ill posed, needs to be solved. Sometimes it is possible though to find them directly in what we call dual experiments. 

In this paper, both inverse problems and the associated modelling are analysed from a theoretical point of view and subsequently solved. The main results will then be generalised to other Chemical Kinetics applications. 

There are direct and inverse problems of chemical kinetics. 

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