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

Abstract

The analytical expression for deviations from linear behavior of logarithmic product ratios as a function of the reciprocal temperature (modified Eyring-plots) depends on the reason for the displacement. Therefore no generally valid formula exists that describes the experimentally observed inversion temperatures. In the case of the disturbance of the establishment of preequilibria, general conditions for the existence of inversion temperatures associated with maxima and minima are deduced. In addition it is shown that the inversion temperature is independent of the activation entropy values for the reaction of the starting materials to the intermediates (ΔS₁₁^‡ and ΔS₁₂^‡), but is dependent on the corresponding activation enthalpy values.

The examples discussed show that the limiting conditions intersecting points of the absolute rates are not suitable for a general description of the complex behavior of the nonlinear temperature dependency.

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38. $$\eqalign{T_{{\rm lcip}} & \equals {{\Delta H_{21} ^\ddag \minus \Delta H_{ \minus 11} ^\ddag \minus \lpar \Delta H_{22} ^\ddag \minus \Delta H_{ \minus 12} ^\ddag \rpar } \over {\Delta S_{21} ^\ddag \minus \Delta S_{ \minus 11} ^\ddag \minus \lpar \Delta S_{22} ^\ddag \minus \Delta S_{ \minus 12} ^\ddag \rpar }} \cr & \equals {{\lpar 24000 \minus 38000\rpar \minus \lpar 27000 \minus 38000\rpar } \over {\lpar 0 \minus 60\rpar \minus \lpar 0 \minus 60\rpar }} \cr} $$ (1)

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