The rate law for the reaction A + B → P is:
Unlike the 2nd order reaction of the type A → P with a rate law of , eq11 cannot be integrated unless we express [B] in terms of [A], or [A] and [B] in terms of a third variable x. Since A and B react in a ratio of 1:1, the remaining concentrations of A and B at any time of the reaction are:
where [A0] and [B0] are the initial concentrations of A and B respectively.
Differentiating both sides of [A] = [A0] – x with respect to time, we have
Therefore, we can rewrite eq11 as
where a = [A0] and b = [B0]
Integrating eq12 using the partial fraction expression of ,
After some algebra, we have,
which is equivalent to