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- W4247752472 abstract "SummaryThe principal tools for reduction of mathematical bulk by elimination of rate equations are the use of stoichiometric constraints and the concepts of a rate-controlling step, quasi-equilibrium steps, and quasi-stationary states of trace-level intermediates.Each stoichiometric constraint, such as the conservation of carbon or oxygen atoms, allows one rate equation to be expressed in terms of others and so be eliminated.If a step in a pathway is much slower than all others, it constitutes a bottleneck that controls the overall rate. Fast, reversible steps in the pathway have enough time to come to quasi-equilibrium. Such equilibria also affect the overall rate. In either case, all steps must be sequential for the rules to apply.If one or several steps in a pathway or network are much faster than all others, they attain quasi-equilibrium, and their (algebraic) equilibrium conditions can be used to replace rate equations.Any highly reactive intermediate that is and remains at trace level attains a quasistationary state in which its net chemical rate is negligible compared separately with its formation and decay rates. This is the basis of the Bodenstein approximation, which allows the rate equation of the intermediate to be replaced by an algebraic equation for the concentration of the intermediate, an equation which can be used in turn to eliminate that concentration from the set of rate equations. The approximation can be applied in succession for each trace-level intermediate. It is the most powerful tool for reduction of complexity. It is the basis of general formulas to be introduced in Chapters 6 and 8 and widely used in others.Examples include hydroformylation of olefins, nitration of aromatics, the hydrogeniodide reaction, and radioactive decay." @default.
- W4247752472 created "2022-05-12" @default.
- W4247752472 date "2004-01-01" @default.
- W4247752472 modified "2023-09-23" @default.
- W4247752472 title "Chapter 4 tools for reduction of complexity" @default.
- W4247752472 doi "https://doi.org/10.1016/s0069-8040(04)80008-6" @default.
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