Hammett equation information

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.^[1]^[2] This equation was developed and published by Louis Plack Hammett in 1937^[3] as a follow-up to qualitative observations in his 1935 publication.^[4]

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.^[5] This notion does not follow from elemental thermochemistry or chemical kinetics and was introduced by Hammett intuitively.^[a]

The basic equation is:

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

where

{K}_{0}

= Reference constant

\sigma

= Substituent constant

\rho

= Reaction rate constant

relating the equilibrium constant, ${K}$ , for a given equilibrium reaction with substituent R and the reference constant ${K}_{0}$ 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.^[4]^[3]

The equation also holds for reaction rates k of a series of reactions with substituted benzene derivatives:

\log {\frac {k}{k_{0}}}=\sigma \rho

In this equation ${k}_{0}$ is the reference reaction rate of the unsubstituted reactant, and k that of a substituted reactant.

A plot of $\log {\frac {K}{K_{0}}}$ for a given equilibrium versus $\log {\frac {k}{k_{0}}}$ for a given reaction rate with many differently substituted reactants will give a straight line.

^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Hammett equation (Hammett relation)". doi:10.1351/goldbook.H02732
^ Keenan, Sheue L.; Peterson, Karl P.; Peterson, Kelly; Jacobson, Kyle (2008). "Determination of Hammett Equation Rho Constant for the Hydrolysis of p-Nitrophenyl Benzoate Esters". J. Chem. Educ. 85 (4): 558. Bibcode:2008JChEd..85..558K. doi:10.1021/ed085p558.
^ ^a ^b Hammett, Louis P. (1937). "The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives". J. Am. Chem. Soc. 59 (1): 96–103. doi:10.1021/ja01280a022.
^ ^a ^b ^c Louis P. Hammett (1935). "Some relations between Reaction Rates and Equilibrium Constants". Chem. Rev. 17 (1): 125–136. doi:10.1021/cr60056a010.
^ Carey, Francis A.; Sundberg, Richard J. (1983). Advanced Organic Chemistry Part A, 2nd edition. Plenum Press. ISBN 9780306410871. OCLC 1064985344.

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[goldbook-1] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Hammett equation (Hammett relation)". doi:10.1351/goldbook.H02732

[2] Keenan, Sheue L.; Peterson, Karl P.; Peterson, Kelly; Jacobson, Kyle (2008). "Determination of Hammett Equation Rho Constant for the Hydrolysis of p-Nitrophenyl Benzoate Esters". J. Chem. Educ. 85 (4): 558. Bibcode:2008JChEd..85..558K. doi:10.1021/ed085p558.

[Hammett1937-3] Hammett, Louis P. (1937). "The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives". J. Am. Chem. Soc. 59 (1): 96–103. doi:10.1021/ja01280a022.

[Hammett1935-4] Louis P. Hammett (1935). "Some relations between Reaction Rates and Equilibrium Constants". Chem. Rev. 17 (1): 125–136. doi:10.1021/cr60056a010.

[Carey1983-5] Carey, Francis A.; Sundberg, Richard J. (1983). Advanced Organic Chemistry Part A, 2nd edition. Plenum Press. ISBN 9780306410871. OCLC 1064985344.

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