Conditions for maxima and minima as inversion points in the temperature dependence of selection processes

The analytical expression for deviations from linear behavior of Logarithmi c product ratios as a function of the reciprocal temperature (modified Eyri ng-plots) depends on the reason for the displacement. Therefore no generall y Valid formula exists that describes the experimentally observed inversion temperatures, In the case of the disturbance of the establishment of preeq uilibria, general conditions for the existence of inversion temperatures as sociated with maxima and minima are deduced. In addition it is shown that t he inversion temperature is independent of the activation entropy values fo r the reaction of the starting materials to the intermediates (Delta S(11)d ouble dagger and Delta S(12)double dagger), but is dependent on the corresp onding activation enthalpy values. The examples discussed show that the limiting conditions intersecting point s of the absolute rates are not suitable for a general description of the c omplex behavior of the nonlinear temperature dependency.