Hammett equation

The Hammett equation in organic chemistry 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 a 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:

${\displaystyle \log {\frac {K}{K_{0}}}=\sigma \rho }$

relating the equilibrium constant, K, for a given equilibrium reaction with substituent R and the reference K₀ constant when R is a hydrogen atom to the substituent constant σ which depends only on the specific substituent R and the reaction constant ρ which depends only on the type of reaction but not on the substituent used.

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