Linear Control of Temperature with Time—A New Approach to Reaction Kinetics

Abstract

The temperature dependence of the rate of chemical reactions has been known for a long time; very often it is characterized by the Arrhenius plot. However, kinetic methods that take this phenomenon into account in one measurement in a planned manner have been applied to reactions in solution only in isolated examples-with the exception of the temperature jump method developed by Eigen et al. for fast reactions, based on a stepped temperature program. A mathematical analysis, however, reveals to the chemist that from the point of view of information theory the course of the reaction rate versus time under conditions of constantly increasing temperature is the measured signal which should lead to the most effective understanding of the reaction mechanism. Analysis of the measured peaks, which may overlap, allows the characterization of reactions either in the solid state or in solution by "mechanistic coordinates", which extend the concept of reaction order. Their behavior allows further experiments to be planned, enabling elementary steps to be eliminated. Each reacting system can be characterized kinetically by one series of experiments using different starting concentrations for each reactant and, additionally, using different heating rates. The experimental verification of these considerations can be seen in ca. 1400 DTA and UV experiments for ca. 120 different systems. Furthermore, the example of the oscillating Belousov-Zhabotinsky reaction shows that "fast" reactions frequently may also be recognized. A test for proposed reaction mechanisms is provided by integration programs which allow immediate comparison between experimental and theoretical signal curves.

New strategies for studies on the kinetics and energetics of the Belousov‐Zhabotinskii reaction

“…Table 2a). The numerous dependences of various parameters on the reactant concentrations, especially the MCC's, yield a compendious material for discussions [20,23,32], but we can only deal with a small collection here.…”

“…This phenomenon is associated with the typical shifts of the mechanistic coordinates (Fig. 5a), beginning in the zero-order range (small shape index, <0.58, and high M-index, >0.019 kJ/mol K), which is typical for autocatalytic processes [23]. Using 0.0345 M bromide, the scenario during the main peak is rather similar to a true first-order situation.…”

“…after subdividing the x-range into the same optimized number of sections (5-10) for all y-parameters; it was proven to be most effective to choose the logarithm of the initial concentration of the component varied (cf. [23,39,42]. Therefore, the "translation" of such symbol chains into models is possible for all twostep models [14,21], and we expect an essential progress in solving this problem of pattern recognition in the near future.…”

“…50 input and response parameters, were accumulated in our data bank. Further, theoretical DTA and rate curves for special mechanisms were generated by our integration program METEX [19,21,23, and were subjected to the same routine evaluation program (comparative one-step strategy [19,32,33]) as the experiments. For the DTA experiments, the reaction enthalpy AH was calculated from the temperature difference B(t) sample/reference using VOLDs equation [34] c c , ra The assumptions for the determination of the reference rate coefJcients were [19,35,36]: 1) The bimolecular rate law for the reaction between bromate and bromide (lo-' M Br-assumed for the bromide-free experiments); 2) Arrhenius equation; 3) Proportionality of rate and heat flow; 4) First-order heat decay in the calorimeter equation (Tian-equation) [19,29,37].…”