The relation may be derived as follows,
If ΔGo is the free energy change for the dissociation of substituted benzoic acid it must be a combination of free energy change of unsubstituted benzoic acid and the influence due to the substituent which can be represented as an equation
A parameter σ is defined for each substituent in order to express the relation in more convenient form.
Thus the relation can be expressed as
The relation between free energy and equilibrium constant is
Using the above relation and substituting in the first equation.
This is the same as
Thus substituents should influence similarly on other processes as well.