Grunwald-Winstein equation

In physical organic chemistry, the Grunwald–Winstein equation is a linear free energy relationship between relative rate constants and the ionizing power of various solvent systems, describing the effect of solvent as nucleophile on different substrates. The equation, which was developed by Ernest Grunwald and Saul Winstein in 1948, could be written

where the k_{x, sol} and k_{x, 80% EtOH} are the solvolysis rate constants for a certain compound in different solvent systems and in the reference solvent, 80% aqueous ethanol, respectively. The parameter m is a parameter measuring the sensitivity of the solvolysis rate with respect to Y, the measure of ionizing power of the solvent.

The Hammett equation (Equation 1) provides the relationship between the substituent on the benzene ring and the ionizing rate constant of the reaction. Hammett used the ionization of benzoic acid as the standard reaction to define a set of substituent parameters σ_X, and then to generate the ρ values, which represent ionizing abilities of different substrates. This relationship can be visualized through a Hammett Plot.

${\displaystyle \log {\frac {k_{{\ce {X}}}}{k_{{\ce {H}}}}}=\rho \sigma _{{\ce {X}}}}$

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