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 dat...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.展开更多
文摘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.
