In a simple equilibrium between two species:
where the reaction starts with an initial concentration of reactant A, , and an initial concentration of 0 for product P at time t=0.
Then the equilibrium constant K is expressed as:
where  and  are the concentrations of A and P at equilibrium, respectively.
The concentration of A at time t, , is related to the concentration of P at time t, , by the equilibrium reaction equation:
The term  is not present because, in this simple example, the initial concentration of P is 0.
This applies even when time t is at infinity; i.e., equilibrium has been reached:
then it follows, by the definition of K, that
and, therefore,
These equations allow us to uncouple the system of differential equations, and allow us to solve for the concentration of A alone.
The reaction equation was given previously as:
For  this is simply
The derivative is negative because this is the rate of the reaction going from A to P, and therefore the concentration of A is decreasing. To simplify notation, let x be , the concentration of A at time t. Let  be the concentration of A at equilibrium. Then:
Since:
the reaction rate becomes:
which results in:
A plot of the negative natural logarithm of the concentration of A in time minus the concentration at equilibrium versus time t gives a straight line with slope k + k. By measurement of [A] and [P] the values of K and the two reaction rate constants will be known.