An **autocatalytic reaction** is one in which a product catalyses the reaction. An example is the *Mn ^{2+}*-catalysed oxidation of oxalic acid by potassium manganate (VII):

The equation can be reduced to *A + P* → 2*P*, or simply, *A *→ *P*, with the rate law:

Using the same logic described in a previous article, we can rewrite the rate law as:

where *a* = [*A _{0}*] and

*p*= [

*P*].

_{0}Integrating throughout, we have

Substituting the partial fraction expression in eq14 and after some algebra, we have,

which is equivalent to

###### Question

The mechanism of the above reaction is found to include the following steps:

With this in mind, derive the rate law and show that it is consistent with eq13a.

###### Answer

We can write the rate law as:

where *K* is the equilibrium constant for the 1st step and *k* = 2*k _{rds}K*. Furthermore, the overall reaction is

*A*→

*P*, which means that