### 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 + H_{2}O_{2} = HO_{2} + H_{2} and O + HO_{2} = OH + O_{2} were used as examples.

Original language | English |
---|---|

Pages (from-to) | 1798-1809 |

Number of pages | 12 |

Journal | Journal of Mathematical Chemistry |

Volume | 49 |

Issue number | 8 |

DOIs | |

Publication status | Published - Sep 2011 |

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### Keywords

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

### ASJC Scopus subject areas

- Chemistry(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Chemistry*,

*49*(8), 1798-1809. https://doi.org/10.1007/s10910-011-9859-7

**Numerical investigation of the uncertainty of Arrhenius parameters.** / Varga, Lászĺ; Szabó, Botond; Zsély, I.; Zempléni, András; Turányi, T.

Research output: Contribution to journal › Article

*Journal of Mathematical Chemistry*, vol. 49, no. 8, pp. 1798-1809. https://doi.org/10.1007/s10910-011-9859-7

}

TY - JOUR

T1 - Numerical investigation of the uncertainty of Arrhenius parameters

AU - Varga, Lászĺ

AU - Szabó, Botond

AU - Zsély, I.

AU - Zempléni, András

AU - Turányi, T.

PY - 2011/9

Y1 - 2011/9

N2 - 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.

AB - 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.

KW - Arrhenius equation

KW - Chemical kinetics

KW - Probability density function

KW - Rate coefficient

KW - Uncertainty parameter

UR - http://www.scopus.com/inward/record.url?scp=79960892353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960892353&partnerID=8YFLogxK

U2 - 10.1007/s10910-011-9859-7

DO - 10.1007/s10910-011-9859-7

M3 - Article

AN - SCOPUS:79960892353

VL - 49

SP - 1798

EP - 1809

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 8

ER -