Hammett equation
Linear free energy relationship

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

Derivation of Hammett equation

A parameter σ is defined for each substituent in order to express the relation in more convenient form.

Hammett equation

Thus the relation can be expressed as

hammett equation

The relation between free energy and equilibrium constant is

Hammett equation

Using the above relation and substituting in the first equation.

Hammett equation

This is the same as

Hammett equation

Thus substituents should influence similarly on other processes as well.

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