Hammett equation

In organic chemistry, the Hammett equation describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para-substituents to each other with just two parameters: a substituent constant and a reaction constant. This equation was developed and published by Louis Plack Hammett in 1937 as a follow-up to qualitative observations in his 1935 publication. The basic idea is that for any two reactions with two aromatic reactants only differing in the type of substituent, the change in free energy of activation is proportional to the change in Gibbs free energy. This notion does not follow from elemental thermochemistry or chemical kinetics and was introduced by Hammett intuitively. The basic equation is: where = Reference constant = Substituent constant = Reaction rate constant relating the equilibrium constant, , for a given equilibrium reaction with substituent R and the reference constant when R is a hydrogen atom to the substituent constant σ which depends only on the specific substituent R and the reaction rate constant ρ which depends only on the type of reaction but not on the substituent used. The equation also holds for reaction rates k of a series of reactions with substituted benzene derivatives: In this equation is the reference reaction rate of the unsubstituted reactant, and k that of a substituted reactant. A plot of for a given equilibrium versus for a given reaction rate with many differently substituted reactants will give a straight line. The starting point for the collection of the substituent constants is a chemical equilibrium for which the substituent constant is arbitrarily set to 0 and the reaction constant is set to 1: the deprotonation of benzoic acid or benzene carboxylic acid (R and R' both H) in water at 25 °C. Having obtained a value for K0, a series of equilibrium constants (K) are now determined based on the same process, but now with variation of the para substituent—for instance, or .