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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Article
Methods for Calculating Activation Energies of Ideal Gases
Author(s)
Richard Martin Gibbons
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DOI:10.17265/1934-8975/2018.02.003
Affiliation(s)
4 Little Acre, Beckenham, Kent BR3 3ST, UK
ABSTRACT
The previous paper Ref. [1] showed
how to calculate activation energies for ideal gas reactions from the CDF (cumulative
distribution function) of the MBD (Maxwell Boltzmann Distribution) and the heat
capacity data of the components. The results presented here show comparisons of
activation energies of four ideal gases calculated in that way with those calculated
from the ND (Normal Distribution) and its CDF. The evaluation of the CDF for the MBD in Ref. [1] required extensive numerical integrations for each substance. In this paper this method
of calculating activation energies is generalised, by showing the CDF is a unique
function, independent of temperature and composition,
enabling the CDF
to be presented graphically or in tabular form. These activation energies
are compared to those calculated from the ND and its CDF. The MBD is related to
the ND because it has a generating function which is shown here to have the simple form (1-kT)-1.5. The activation energies
obtained from the CDF of the ND are shown to agree
ca. 5-7% with those obtained directly
from the MBD. Because existing thermodynamic
treatments are based
on average properties, they cannot give either a complete account of thermodynamic controlled
and kinetic controlled equilibrium states or explain transitions between them. Complete
treatments must include effects from the MBD which are
the causes of kinetic controlled equilibrium. The basis for
a complete treatment is outlined, which includes the standard deviations and activation
energies.
KEYWORDS
Thermodynamics, statistical mechanics, equilibrium, reactions of ideal gases.
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