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Numerical investigation of the uncertainty of Arrhenius parameters

Abstract

The temperature dependence of rate coefficient k is usually described by the Arrhenius expression ln k = ln A − (E/R)T −1. Chemical kinetics databases contain the recommended values of Arrhenius parameters A and E, the uncertainty parameter f (T) of the rate coefficient and temperature range of validity of this information. Taking ln k as a random variable with known normal distribution at two temperatures, the corresponding uncertainty of ln k at other temperatures was calculated. An algorithm is provided for the generation of the histogram of the transformed Arrhenius parameters ln A and E/R, which is in accordance with their 2D normal probability density function (pdf). The upper and the lower edges of the 1D normal distribution of ln k correspond to the two opposite edge regions of the 2D pdf of the transformed Arrhenius parameters. Changing the temperature, these edge regions move around the 2D cone. The rate parameters and uncertainty data belonging to reactions H + H2O2 = HO2 + H2 and O + HO2 = OH + O2 were used as examples.

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Correspondence to Tamás Turányi.

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Varga, L., Szabó, B., Zsély, I.G. et al. Numerical investigation of the uncertainty of Arrhenius parameters. J Math Chem 49, 1798 (2011). https://doi.org/10.1007/s10910-011-9859-7

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Keywords

  • Chemical kinetics
  • Arrhenius equation
  • Rate coefficient
  • Uncertainty parameter
  • Probability density function