Suggested Forms for Kinetic Models

With two adjustable constants, you can fit a straight line. With six, you can fit an elephant. With eight, you can fit a running elephant or a cosmological model of the universe (Hogan, 2000). 

For enzymatic and other heterogeneously catalyzed reactions, there is competition for active sites. This leads to rate expressions with forms such as 

All the rate constants should be positive so the denominator in this expression will always retard the reaction. The same denominator can be used with Equation 7.3 to model reversible heterogeneous reactions. Although the dimensions of the numerator rate constant k depend on the overall reaction order, all the denominator rate constants have dimensions of inverse concentration. 

More complicated rate expressions are possible. For example, the denominator may be squared or square roots can be inserted here and there based on theoretical considerations. The denominator may include a term, / /[/], to account for compounds that are nominally inert and do not appear in Equation 7.1 but occupy active sites on the catalyst and thus retard the rate. The various rate constants will be functions of temperature and are usually modeled using an Arrhenius form. This doubles the number of adjustable parameters. The more complex kinetic models have enough adjustable parameters to fit a stampede of elephants. Careful analysis is needed to avoid being crushed underfoot. 

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