Autocatalytic and Enzymatic Reactions The adiabatic elimination

The simplest form of catalysis may be represented by a reaction of the type 

Although the stoichiometry of the reaction is effectively equivalent to the simplest B — C, we assume that the rate is influenced by the presence of the catalyst A, and that the elementary molecular form of the reaction is (3.17). An autocatalytic reaction is one in which the product (or one of the products) of the reaction is the catalyst itself, e.g. C = A, so that 

In addition to strictly chemical catalysis processes, Eq. (3.18) may represent other situations such as for example combustion (the combustion of B requires of heat A, but the reaction is exothermic, so that more heat A is produced), or secondary crystallization from a solution (B is the substance in solution which crystalizes in form A if some nuclei of A are already present). If B is kept at constant concentration we have the simplest autocatalytic reaction  

In the absence of any other mechanism, this leads to the exponential unlimited growth of A. 

We note that this last equation, the logistic equation, is formally identical to (3.9). However, the constants Q3 and Q have a different expression in terms of the initial conditions (see (3.8) and (3.22)). From the exact solution 

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