For a generic reaction:
where [A] and [B] express the concentration of the species A and B, respectively (usually in moles per liter (molarity, M)); x and y are the respective stoichiometric coefficients of the balanced equation; they must be determined experimentally. k is the rate coefficient or rate constant of the reaction. The value of this coefficient k depends on conditions such as temperature, ionic strength, surface area of the adsorbent or light irradiation. For elementary reactions, the rate equation can be derived from first principles using collision theory. Again, x and y are not always derived from the balanced equation.
A reaction is said to be second order when the overall order is two. The rate of a second-order reaction may be proportional to one concentration squared, or (more commonly) to the product of two concentrations. For a second order reaction, its reaction rate is given by:
Conflating the 2 inside the constant for the first derivative form will only make it required in the second integrated form. The option of keeping the 2 out of the constant in the derivative form is considered more correct because it is almost always used in peer-reviewed literature, tables of rate constants, and simulation software.
Consider then a second order reaction, such as butadiene dimerization. The general second order reaction A→products has the rate law:
We can use Calculus to find the function [A](t) from the above equation. The result is most easily written as:
Note that, as t increases,
This shows that, unlike a first order reaction, the half-life for a second order reaction depends on how much material we start with. The more concentrated the reactant is, the shorter the half-life.
An example of an second order reaction is the process of nitrogen dioxide turning into nitric oxide and oxygen .