Abstract
The Arrhenius plot (logarithmic plot vs. inverse temperature) is represented by a straight line if the Arrhenius equation holds. A curved Arrhenius plot (mostly concave) is usually described phenomenologically, often using polynomials of T or 1/T. Many modifications of the Arrhenius equation based on different models have also been published, which fit the experimental data better or worse. This paper proposes two solutions for the concave-curved Arrhenius plot. The first is based on consecutive A→B→C reaction with rate constants k1 ≪ k2 at higher temperatures and k1 ≫ k2 (or at least k1 > k2) at lower temperatures. The second is based on the substitution of the temperature T the by temperature difference T − T0 in the Arrhenius equation, where T0 is the maximum temperature at which the Arrheniusprocess under study does not yet occur.
Highlights
The Arrhenius equation was published in 1889 [1]
The Arrhenius equation is used in materials science and biology, for example in describing the kinetics of austenitization [2], the respiration rate of plant leaves [3], or the heartbeat rate of terrapins [4]
This seems to be one of the main reasons for the invalidity of the Arrhenius equation, which is manifested by the curved Arrhenius plot
Summary
The Arrhenius equation was published in 1889 [1]. It describes very accurately the temperature dependence of the kinetics of chemical reactions of simple chemicals (cane sugar was studied in the cited paper). The author of this paper attempted to use Equation (6) as a regression function in many cases of curved Arrhenius or Kissinger plots, but values of m = 0.5 or m = 1 did not noticeably change the linearity of these plots. This temperature characterizes the end of the transformation returns to its constant value after reaching the maximum value, namely for the highest process From this point of view, Equation (7) can hardly be considered a useful result of heating rate. In other words, this temperature characterizes the end of the transformation theoretical derivation, rather it is a phenomenological equation of the type: process.
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