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Numerical investigation of the uncertainty of Arrhenius parameters


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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  1. 1

    Nagy T, Turányi T: Int. J. Chem. Kinet. 43, 359 (2011)

    Article  CAS  Google Scholar 

  2. 2

    Baulch D.L., Bowman C.T., Cobos C.J., Cox R.A., Just T., Kerr J.A., Pilling M.J., Stocker D., Troe J., Tsang W., Walker R.W., Warnatz J.: J. Phys. Chem. Ref. Data 34(3), 757 (2005)

    Article  CAS  Google Scholar 

  3. 3

    Brown M.J., Smith D.B., Taylor S.C.: Combust. Flame 117, 652 (1999)

    Article  CAS  Google Scholar 

  4. 4

    Turányi T., Zalotai L., Dóbé S., Bérces T.: Phys. Chem. Chem. Phys. 4, 2568 (2002)

    Article  Google Scholar 

  5. 5

    Zsély I.G., Zádor J., Turányi T.: Int. J. Chem. Kinet. 40, 754 (2008)

    Article  Google Scholar 

  6. 6

    Zsély I.G., Zádor J., Turányi T.: Proc. Combust. Inst. 30, 1273 (2005)

    Article  Google Scholar 

  7. 7

    Zádor J., Zsély I.G., Turányi T., Ratto M., Tarantola S., Saltelli A.: J. Phys. Chem. A 109, 9795 (2005)

    Article  Google Scholar 

  8. 8

    Zádor J., Zsély I.G., Turányi T.: Reliab. Eng. Syst. Safe. 91(10–11), 1232 (2006)

    Article  Google Scholar 

  9. 9

    Sheen D.A., You X., Wang H., Løvås T.: Proc. Combust. Inst. 32, 535 (2009)

    Article  CAS  Google Scholar 

  10. 10

    Sheen D.A., Wang H.: Combust. Flame 158, 645 (2011)

    Article  CAS  Google Scholar 

  11. 11

    Cvetanović R., Overend R., Paraskevopoulos G.: Int. J. Chem. Kinet. S1, 249 (1975)

    Google Scholar 

  12. 12

    Cvetanović R.J., Singleton D.L.: Int. J. Chem. Kinet. 9, 481 (1977)

    Article  Google Scholar 

  13. 13

    Cvetanović R.J., Singleton D.L., Paraskevapoulos G.: J. Phys. Chem. 83, 50 (1979)

    Article  Google Scholar 

  14. 14

    Héberger K., Kemény S., Vidóczy T.: Int. J. Chem. Kinet. 19, 171 (1987)

    Article  Google Scholar 

  15. 15

    Klička R., Kubáček L.: Chemomet. Intell. Lab. Syst. 39, 69 (1997)

    Article  Google Scholar 

  16. 16

    Sundberg R.: Chemom. Intell. Lab. Syst. 41(2), 249 (1998)

    Article  CAS  Google Scholar 

  17. 17

    Rodriguez-Aragon L.J., Lopez-Fidalgo J.S.: Chemom. Intell. Lab. Syst. 77(1–2), 131 (2005)

    CAS  Google Scholar 

  18. 18

    Schwaab M., Pinto J.C.: Chem. Eng. Sci. 62(10), 2750 (2007)

    Article  CAS  Google Scholar 

  19. 19

    Schwaab M., Pinto J.C.: Chem. Eng. Sci. 63, 4631 (2008)

    Article  CAS  Google Scholar 

  20. 20

    Najm H., Debusschere B.J., Marzouk Y.M., Widmer S., Le Maître O.P.: Int. J. Numer. Meth. Eng. 80, 789 (2009)

    Article  Google Scholar 

  21. 21

    Rao C.R.: Linear Statistical Inference and Its Applications, 2nd edn. Wiley, New York (1973)

    Book  Google Scholar 

  22. 22

    Skodje R.T., Tomlin A.S., Klippenstein S.J., Harding L.B., Davis M.J.: J. Phys. Chem. A 114(32), 8286 (2010)

    Article  CAS  Google Scholar 

  23. 23

    Ziehn T., Hughes K.J., Griffiths J.F., Porter R., Tomlin A.S.: Combust. Theor. Modell. 13, 589 (2009)

    Article  CAS  Google Scholar 

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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).

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