Gross-Butler equation

Consider a system with more than one equivalent exchangeable site, each of which contributes a factor of this form in the numerator for such sites on the transition state and in the denominator for those on the reactant. That is, for n such sites the factor is (l - d + xni)"/(1 - d + d< r) Then, if there are other sites inequivalent to these, corresponding factors for them also appear. The final expression, referred to as the Gross-Butler equation,23 is... 

Gross-Butler equation is that the reactant is in isotopic equilibrium with the solvent. Given that the process under consideration occurs on an exceptionally short time scale, the assumption is not necessarily valid. A very thorough analysis of the isotopic possibilities was used to show that the interpretation presented here is nonetheless correct.25... 

Measurements in mixtures of H2O and D2O give information about the number of protons ehanging their fraetionation faetors between ground state and transition state. The analysis is eondueted in terms of the Gross-Butler equation, whose modern form is given as equation 1.17, where kn is the rate eonstant at atom fraetion deuterium n, that in pure H2O, and and are the fractionation factors of the fth exchangeable proton in the transition state and the ground state, respectively. 

For more detailed discussion of the Gross-Butler equation see refs. 7, 18 and 19. 

Finally, these results clearly show yet again that attachment of hydrogen to the aromatic is not a fast step, thereby eliminating the A-l mechanism yet the data in mixed solvents followed the prediction of the Gross-Butler cubic equation, and once again this test turns out to be valueless. 

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