Brønsted relation

https://doi.org/10.1351/goldbook.B00746
The term applies to either of the equations: \[\frac{k_{\textrm{HA}}}{p}=G\left ( \frac{q\: K_{\textrm{HA}}}{p} \right )^{\alpha}\] \[\frac{k_{\textrm{A}}}{q}=G\left ( \frac{q\: K_{\textrm{HA}}}{p} \right )^{-\beta} \] (or their logarithmic forms) where \(\alpha\), \(\beta\) and \(G\) are constants for a given reaction series (\(\alpha\) and \(\beta\) are called 'Brønsted exponents'), \(k_{\textrm{HA}}\) and \(k_{\textrm{A}}\) are @C00885@ (or rate coefficients) of reactions whose rates depend on the concentrations of HA and/or of A. \(K_{\textrm{HA}}\) is the acid @D01801@ constant of the acid HA, \(p\) is the number of equivalent acidic protons in the acid HA, and \(q\) is the number of equivalent basic sites in its conjugate base A. The chosen values of \(p\) and \(q\) should always be specified. (The charge designations of H and A are only illustrative.) The Brønsted relation is often termed the 'Brønsted @C00875@' (or the '@C00875@'). Although justifiable on historical grounds, this name is not recommended, since Brønsted relations are known to apply to many uncatalysed and pseudo-catalysed reactions (such as simple @P04915@ @P04915@). The term 'pseudo-Brønsted relation' is sometimes used for reactions which involve @N04250@ instead of acid–base @C00874@. Various types of Brønsted parameters have been proposed such as \(\beta_{\textrm{lg}}\), \(\beta_{\textrm{nuc}}\), \(\beta_{\textrm{eq}}\) for @L03493@, nucleophile and equilibrium constants, respectively.
See also:
linear free-energy relation
Sources:
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1091 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 154 [Terms] [Paper]