**Abstract**

Standard thermodynamic treatments of molecular systems are based on thermodynamic properties which are averages of the molecular properties of those systems typically containing an Avogadro’s number of molecules. They contain no information that can account for equilibriums controlled by non-thermodynamic factors arising from the energies of the molecules. This is why two definitions are needed for thermodynamic equilibrium, why there is no discussion about how and why each definition applies to a molecular system for a range of temperatures pressures and composition or why molecular systems may not come to equilibrium at all.

The treatment developed in here states the principle that leads to two definitions of equilibrium. It is based on the average (thermodynamic) properties and the standard deviation of the Maxwell Boltzmann Distribution (MBD). It shows that

(1-kT)^{-1.5 } is the generating function for the MBD for the kinetic energies of ideal gases relating it to the Normal Distribution (ND) by the Central Limit Theorem (CLT). This enables the percentage of molecules involved in a change to be correlated with the molecular energies of the reacting molecules. It is the first method for inferring the activations energies of ideal gas reactions.

It uses this relationship, between the MBD and the ND, to calculate the mole fractions, y_{ign}, that ensure the propagation of the reaction by heating an equal number of molecules in the mixture to the ignition temperature. This is the first method to define the requirements for propagation of a reaction.

Accurate correlations for the heat capacities of the reactants would enable the activation energies to be calculated. The available heat capacity correlations, due to Harmens, are for molecules with electrons in their ground states. The calculated values of y_{ign} from these correlations demonstrate there are no combinations of y_{ign }and associated molecular kinetic energies that can explain the propagation of the reactions for mixtures of air and each of four ideal gases, hydrogen, methane, ethane and propane.

An alternative explanation for reactions is proposed involving excited electronic states which explains also why these mixtures have ignition temperatures. It remains a conjecture until accurate correlations for heat capacity of the reactants including the contributions from excited electrons enable activation energies to be calculated directly.

These results are significant advances in themselves. Two consequences of them may be as important. The first is this analysis makes clear that it is not possible to devise a complete analysis of thermodynamic equilibrium based solely on equilibrium properties.

The second is that the results presented here, combined with those in another paper,

” The “Other” Maxwell Boltzmann Distribution”, provide a basis for a simple introduction to the thermodynamics properties of ideal gas mixtures and their reactions, which is suitable for all students starting chemistry.

These consequences will be discussed further in the presentation.

Keywords: thermodynamics, statistical mechanics, equilibrium, reactions of ideal gases