A chemical reaction is called autocatalytic if at least one of the reaction products acts as a catalyst in the same or in one of the coupled reactions. Reactions of this type have the property that the rate equations are nonlinear, that is, the reaction is very slow in the beginning but steadily increases as more product is formed.
The simplest autocatalysis is a reaction in which the product acts as a catalyst for its own production:
A + B → 2B
According to the law of mass actions, the rate of change of the reactant concentration is equal to k+[A][B] and that of the product to k–[B]2 (reverse reaction):
R = d[B] / dt = – d[A] / dt = k+ [A] [B] – k– [B]2
where k+, k– are the reaction constants (velocity coefficients) and [A], [B] are the concentrations of reactant and product. Assuming k+ = k » k–, the rate equation simplifies to
R = – d[A] / dt = k[A] [B],
which can be solved exactly. If [A]0 and [B]0 are the concentration of the reactant and catalyst at the start of the reaction then [A]0 – [A] = [B] – [B]0. Thus the autocatalytic reaction can be written as
– d[A] / dt = k {[A][A]0 + [A]0[B]0 – [A]2},
This equation can be rearranged and converted to the integral form
Integration yields1
These equations describe a sigmoidal variation of reactant and product concentration (see below). The reaction proceeds very slowly at the start (induction period) because there is very little catalyst present, increases steadily as the reaction proceeds and the amount of catalyst increases, and slows down again at the end when the reactant gets depleted.
Many chemical and biochemical reactions are autocatalytic. A common autocatalytic polymeric reaction is the acid-catalyzed hydrolysis of polyester. The rate equation, however, is more complicated since both the molecular acid and the hydrogen ion from its dissociation may function as a catalyst. Other examples of autocatalytic reactions are thiol–epoxy and amine-epoxy step-growth polymerizations. Both are strongly autocatalytic due to the continuous generation of hydroxyl groups that propagate the ring-opening of the epoxy groups.
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