Mathematical Characterization of Simple Reaction Systems

The term reaction rate constant is actnally a misnomer, because k may vary with temperature, the solvent for the reaction, and the concentrations of any catalysts that may be present in the reaction system. The term is in nniver-sal use, however, because it implies that the parameter k is independent of the concentrations of reactant and prodnct species. 

The reaction rate is properly defined in terms of the time derivative of the extent of reaction [eqnation (3.0.1)]. One must define /c in a similar fashion to ensnre nniqneness. Definitions of k in terms of the various r, would lead to rate constants that would differ by the ratios of their stoichiometric coefficients. The units of the rate constant will vary depending on the overall order of the reaction. These units are those of a rate divided by an mth power of concentration (where m is the overall order of the rate law). Thns, from examination of equations (3.0.17) and (3.0.18), 

1 Mathematical Characterization of Simple Constant Volume Reaction Systems 

1 First-Order Reactions in Constant Volume Systems 

For a first-order reaction the rate is proportional to the first power of the concenffation of one of the reacting substances  

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Mathematical Characterization of Simple Variable Volume Reaction Systems... 

Simple Parallel Reactions. The simplest types of parallel reactions involve the irreversible transformation of a single reactant into two or more product species through reaction paths that have the same dependence on reactant concentrations. The introduction of more than a single reactant species, of reversibility, and of parallel paths that differ in their reaction orders can complicate the analysis considerably. However, under certain conditions, it is still possible to derive useful mathematical relations to characterize the behavior of these systems. A variety of interesting cases are described in the following subsections. 

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