If the products of a reaction act as a catalyst for the reaction, it is referred to as autocatalysis. Reactions that show autocatalysis start slowly and as more of the reactants get converted to the products there is an increase in the rate of the reaction. Later, there is a fall in the rate as the concentration of the reactants decreases and the reaction finally comes to an end.
A second order autocatalytic reaction: A + B --> 2B proceeds at a rate given by R = k*(A)(B) where (A) and (B) are the concentrations of A and B.
The graph of the rate at which an autocatalytic reaction proceeds forms a sigmoid curve.
An example of an autocatalytic reaction is the reaction of permanganate with oxalic acid. This reaction is catalyzed by Mn2+ ions. When potassium permanganate undergoes a reaction with acidified oxalate solution, the rate of the reaction is initially slow. It slowly increases in rate due to the formation of Mn2+ ions as follows:
2 MnO4-(aq ) + 5 H2C2O4(aq ) + 6 H3O+(aq ) --> 2Mn2+(aq ) + 10 CO2(aq ) + 14 H2O
If a little Mn2+ is added to the reactants initially, the reaction proceeds at a fast rate right from the beginning. If that is not done, the rate of the reaction follows a sigmoid curve with more Mn2+ being created as one of the products.