How many data points and how large an R-squared value is essential for Arrhenius plots?

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Arrhenius plots estimate the apparent activation energy (Ea) of catalytic reactions. The R-squared value (r2) often accompanies the Arrhenius plot to support its validity. However, no paper has quantitatively presented the minimum data points and the minimum r2 to validate the Ea. In this study, statistical analysis quantitatively visualized the relationship between the number of data points (np), r2, and the reliability of Ea. When np ≧ 5, the risk of underestimating the variance of Ea is suppressed significantly, making the Ea and its variance more reliable. Furthermore, to claim that two values of Ea are statistically different, the minimum required r2 was formulated and plotted as a function of Ea and np. The proposed formulas couple np and r2 to validate Ea quantitatively. This method is superior to the empirical method using r2 alone. This study produces tangible and quantitative guidance to control the reliability of the Arrhenius plot.
Original languageEnglish
Pages (from-to)26-36
Number of pages11
JournalJournal of Catalysis
Publication statusPublished - Mar 2023


  • Arrhenius plot
  • Activation energy
  • R-squared value
  • Statistical analysis
  • Confidence intervals
  • Monte Carlo simulation

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