Chemical kinetics, simplification defined

In the strict sense, the real reacting system could be mathematically described by chemical kinetic equations only taking into account the processes of diffusion and convection in self-generated non-uniform temperature fields. However, this problem, as we mentioned above, can be solved only at the expense of significant simplification of the chemical description. It is usually acceptable in studies of combustion and explosion processes where the chemical part may be reduced to a very schematic description, which defines the rate of heat... 

In the equation above tot is the total concentration of enzyme (total amount, if we are talking about the chemicals dissolved in the same volume of solvent). Like in the case of ligand-receptor, under the chapter on chemical equilibrium, we define it as a sum of free enzyme and enzyme bound in complex [ ]tot = [filfree + [ S]. Of course you want to have as little [ ]free 3S possible. There are also a number of assumptions and simplifications used in developing the relations that help us process the enzyme kinetics data. 

A mathematical simplification of rate behavior of a multistep chemical process assuming that over a period of time a system displays little or no change in the con-centration(s) of intermediate species (i.e., d[intermedi-ate]/df 0). In enzyme kinetics, the steady-state assumption allows one to write and solve the differential equations defining fhe rafes of inferconversion of various enzyme species. This is especially useful in initial rate studies. 

Our discussion up to this point has dealt with the use of kinetics to describe the rates of chemically well-defined reactions and to explore the mechanism of reactions. Kinetic formulations can be used in what one might call the opposite sense—that is, to provide an empirical mathematical framework in which data from complex reactions can be analyzed. The objective here is a simplification of complex situations, not the discovery of exact mechanism from kinetic analysis. Two examples of this use of kinetic formulations that are relevant to aquatic systems will be given here. The first concerns treatment of data from the biochemic ... 

Simplification not only is a means for the easy and efficient analysis of complex chemical reactions and processes, but also is a necessary step in understanding their behavior. In many cases, to understand means to simplify. Now the main question is Which reaction or set of reactions is responsible for the observed kinetic characteristics The answer to this question very much depends on the details of the reaction mechanism and on the temporal domain that we are interested in. Frequently, simplification is defined as a reduction of the original set of system factors (processes, variables, and parameters) to the essential set for revealing the behavior of the system, observed through real or virtual (computer) experiments. Every simplification has to be correct. As a basis of simplification, many physicochemical and mathematical principles/methods/approaches, or their efficient combination, are used, such as fundamental laws of mass conservation and energy conservation, the dissipation principle, and the principle of detailed equilibrium. Based on these concepts, many advanced methods of simplification of complex chemical models have been developed (Marin and Yablonsky, 2011 Yablonskii et al., 1991). 

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