Term: Hammett equation (Hammett relation)
https://doi.org/10.1351/goldbook.H02732

Definition:
The equation in the form: \[\log _{10}(\frac{k}{k_{0}}) = \rho \ \sigma \] or \[\log _{10}(\frac{K}{K_{0}}) = \rho \ \sigma \] applied to the influence of meta- or para-substituents X on the reactivity of the functional group Y in the benzene derivative m- or p-XC6H4Y. k or K is the rate or equilibrium constant, respectively, for the given reaction of m- or p-XC6H4Y; k0 or K0 refers to the reaction of C6H5Y, i.e. X = H; is the substituent constant characteristic of m- or p-X: is the reaction constant characteristic of the given reaction of Y. The equation is often encountered in a form with log 10 k 0 or log 10 K 0 written as a separate term on the right hand side, e.g. \[\log _{10}k = \rho \ \sigma +\log _{10}k_{0}\] or \[\log _{10}K = \rho \ \sigma +\log _{10}K_{0}\] It then signifies the intercept corresponding to X = H in a regression of log 10 k or log 10 K on σ.

Related Terms:
1) <i>ρ</i>-value (http://doi.org/10.1351/goldbook.V05019).
2) σ-constant (http://doi.org/10.1351/goldbook.C05438).
3) taft equation (http://doi.org/10.1351/goldbook.T06247).
4) yukawa–tsuno equation (http://doi.org/10.1351/goldbook.Y06734).
5) functional group (http://doi.org/10.1351/goldbook.F02555).
6) equilibrium constant (http://doi.org/10.1351/goldbook.E02177).

Source: PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1119 (https://doi.org/10.1351/pac199466051077)

Citation: 'Hammett equation (Hammett relation)' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.H02732

License: The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms.

Disclaimer: The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.