second order reaction
A second order reaction depends on the concentrations of one second order reactant, or two first order reactants.
The reaction rate is given by
or by 
For a reaction of type
(where 
is the product or products), the rate is defined as
.
The derivative of 
with respect to time is equal to minus one half of the derivative of
with respect to time is equal to minus one half of the derivative of 
with respect to time, because for each that is formed, two
react. Thus the speed with which l disappears is twice the speed with which appears.
In terms of the concentration of the reactant , the rate of a reaction which is second-order in A is then:
, the rate of a reaction which is second-order in A is then:
For this case, the integrated second order rate law is
If a reaction of type A + B → P is first-order in both reactants A and B, the rate is
.
In this case the integrated rate law is
,
provided that the two initial concentrations [A]0 and [B]0 are not equal.
For the special case of equal concentrations
, the rate 
, and the integrated second order rate law is 
, the rate , and the integrated second order rate law is
The half-life equation for a second order reaction dependent on one second order reactant is
.
.
For such a reaction, the half-life progressively doubles as the concentration of the reactant falls to half its initial value.
Another way to present the above rate laws is to take the log of both sides:
Examples of a Second order reaction
