The Hammett Equation Class II

Linear correlations (Equation 1) between the logarithms of rate constants for reactions of meta- and /7ara-substituted phenyl derivatives (log x) and pA values of the correspondingly substituted benzoic acids were reported by Hammett. The equation for the unsubstituted derivative (H, Equation 2) can be combined with Equation (1) for the X-substituted derivative to yield Equations (3) and (4) where a = pX, - 

The Hammett relationship only applies to systems where substituents are attached to the reaction centre via aromatic rings and are situated meta or para-, ortho substituents are not included in the Hammett equation owing to steric and through-space interactions (Chapter 6). 

The use of Hammett s a often gives uninterpretable results in reactions where the substituent is located on aliphatic carbon and transmission of charge is through sigma bonds. Another polarity parameter, analogous to the Hammett a, must therefore be sought for aliphatic systems. 

In Taft s treatment the acid- and base-catalysed hydrolysis of substituted esters X-COOR are employed as combined reference reactions for defining polar and steric effects for the substituent X. Equation (5) governs the combined inductive, steric (5) and resonance (R) effects on the rate of a reaction.Equations (6) and (7) can be written for base-and acid-catalysed hydrolysis using methyl (Me) as the standard substituent. 

If S and A are the same for acid and base reactions, Equations (6) and (7) can be combined to give Equation (8)  

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