Chemical Kinetics Conclusion

Detailed balance is a chemical application of the more general principle of microscopic reversibility, which has its basis in the mathematical conclusion that the equations of motion are symmetric under time reversal. Thus, any particle trajectory in the time period t = 0 to / = ti undergoes a reversal in the time period t = —ti to t = 0, and the particle retraces its trajectoiy. In the field of chemical kinetics, this principle is sometimes stated in these equivalent forms ... 

The subject of flame extinction at the forward stagnation point of the liquid sphere under forced-convection conditions has also been analyzed in some detail (56). Basing his conclusion on theoretical considerations of the chemical kinetics and the hydrodynamics at the forward stagnation point, Spalding stated that for specified physical conditions the flame extinction velocity is proportional to the sphere diameter. This relationship was confirmed by his experimental observations but not by work performed subsequently (1). 

The conclusion itself suggests that from the point of view of formal chemical kinetics both energy transfer and the Frenkel defect recombination with... 

The conclusion suggests itself that the decay law n(t) oc t l obtained earlier in terms of standard chemical kinetics (2.1.8) is replaced by a slower decay. 

Based on a consideration of the possible reactions between catalase and C2H5OH from chemical kinetics positions, Kremer [105] drew conclusions about the high probability of the following mechanism ... 

In conclusion, the chemical equilibrium model suggests that the process may be feasible. However, the insertion of chemical kinetics is necessary to get a more realistic description. 

Nonequilibrium thermodynamics was chosen as a main object for comparison, though an essential part of conclusions drawn below is useful in MEIS comparison with the models of chemical kinetics, synergetics, theory of dynamic systems and other models, model engineering and theories of motions. Comparison is made from two standpoints (1) a scope of areas of effective applications and (2) simplicity and fruitfulness of computing experiments. 

In conclusion, pseudo-kinetic models cannot be extrapolated beyond the range of the experimental data they are derived from, cannot incorporate the progress achieved in the whole field of fundamental chemical kinetics, both experimental and theoretical, and cannot be used for designing new reactors. In all these domains, mechanistic simulation is obviously superior, at least theoretically, and this seems also to be true in practice. Indeed, Goossens et al. [77—79] have carried out a comparison of the value for prediction of their mechanistic model and of the molecular reaction schemes proposed by Ross and Shu [55] and Sundaram and Froment [60]. Goossens et al. concluded that there is an actual superiority of the mechanistic model. Froment himself now seems to agree with this conclusion since, after having developed the molecular reaction schemes with co-workers [57—61], he and Sundaram [186] have lately proposed free radical schemes for pyrolysis reactions. 

Due to the progress in chemical kinetics, with regard to both experimental methods and theoretical interpretations, more and more complex reaction mechanisms are written by kineticists. It is clear that confronting theoretical models and experimental results, in any case, can only be achieved by computer modelling. Let us now briefly summarize the conclusions we have arrived at concerning model building and identification. 

In conclusion, the fact that a correct reactor model is as important as a correct reaction model in order to be able either to elucidate reaction mechanisms and determine rate coefficients (chemical kinetics problem) or to simulate the operation of a reactor (chemical reaction engineering problem) cannot be too strongly emphasized. 

It is instructive to compare the three transport processes (conduction, tracer diffusion and chemical diffusion) by using chemical kinetics and for simplicity concentrating on the electron-rich electron conductor, i.e., referring to the r.h.s. of Fig. 52. The results of applying Eq. (97) are summarized in Table 5 and directly verify the conclusions. Unlike in Section VI.2. ., we now refer more precisely to bimolecular rate equations (according to Eqs. 113-115) nonetheless the pseudo-monomolecular description is still a good approximation, since only one parameter is actually varied. This is also the reason why we can use concentrations for the regular constituents in the case of chemical diffusion. In the case of tracer diffusion this is allowed because of the ideality of distribution. 

It is true that in chemical kinetics one can disprove, but never definitely prove. A theory or model is conclusively disproved by experimental evidence to the contrary, but compatibility with such evidence is no proof because alternative explanations are always possible and new experiments might support those. ... 

Many important conclusions concerning chemical kinetics in specific flames have been obtained in the references cited (for example, [63]-[85]) and in related work. Since these are too numerous to be discussed here, the reader is referred to the references. 

With this replacement of the strong collider assumption now commonplace, the term RRKM theory has become largely synonymous with quantum TST for unimolecular reactions, and we use this terminology here. The foundations of RRKM theory have been tested in depth with a wide variety of inventive theoretical and experimental studies [9]. While these tests have occasionally indicated certain limitations in its applicability, for example to timescales of a picosecond or longer, the primary conclusion remains that RRKM theory is quantitatively valid for the vast majority of conditions of importance to chemical kinetics. The H + O2 HO2 OH + O reaction is an example of an important reaction where deviations from RRKM predictions are significant [10, 11]. The foundations of RRKM theory and TST have been aptly reviewed in various places [7, 9, 12-15]. Thus, the present chapter begins with only a brief... 

A consideration of the characteristic times for chemical kinetic and heat transfer phenomenon within a rapidly pyrolyzing particle indicate that heat transfer (not chemical kinetics) is the rate limiting step. However, the thermochemical and optical properties of biomass materials are poorly understood and much more experimental work must be completed before definitive conclusions in this important area can be made. 

From the Korzukhin theorem follows an important conclusion. Any dynamical systems of the form (4.58) may be regarded as those corresponding to slow dynamics of a standard kinetic system. In other words, the behaviour of dynamical systems can be modelled using chemical reactions. In particular, any of the gradient systems may be modelled in this way. As will be shown in Chapter 5, catastrophes occurring in complex dynamical systems are equivalent to catastrophes appearing in much simpler systems. The latter can be classified — these are so-called standard forms. The standard forms are of the form (4.58) and it follows from the Korzukhin theorem that they can be modelled by the standard equations of chemical kinetics (4.27), corresponding to a realistic mechanism of chemical reactions. 

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