Thermal equilibrium determination dissociation energies

In this model, A2 molecules are first adsorbed on the surface non-dissociatively. The A2 molecular precursor might dissociate if there is a free active site adjacent to it, and if it is capable of climbing the dissociation energy barrier due to thermal excitation, or the precursor could be thermally activated to desorb as A2 into the gas phase again. It is still assumed that the dissociation (now from the precursor state and not from the gas phase) is the rate-determining step. If the reaction proceeds to a steady-state, but the over-all gas phase reactants and products are kept out of equilibrium, the precursor state will be in equilibrium with the gas phase reactant, but not with the dissociated state. This model will have a turnover frequency given by ... 

DETERMINATION OF BOND DISSOCIATION ENERGIES BY THERMAL EQUILIBRIUM METHODS... 

To determine the kinetic behavior of the model, we first prepared the system in its molecular form in thermal equilibrium at a low temperature. Then we rapidly heated the system, in 10 to 40 time steps, at constant volume, to raise the temperature to the desired level. After heating, we allowed the system to evolve without interference, while we continuously monitored the energies of the system, the number of dissociated molecules, etc., until the dissociation reached an equilibriim state in several thousand time steps (6,000 to 10,000). In some cases we also applied a correction to keep the total energy of the system constant to within narrow limits (O.OOOSe). The cumulative corrections in 2000 or more time steps (at Ar=0.01 per time step) were found to remain small, typically under 0.3% of the total energy of the system. We obtained constant pressure conditions by adjusting the volume of the system by trial and error. 

Recombination of adsorbed hydrogen atoms leads to the reverse process of thermal desorption whose rate is governed by Ead + E, where E is the activation energy for dissociative adsorption. If a hydrogen-covered Fe surface is heated up in vacuo, desorption will be completed at 500 Under the conditions of ammonia synthesis (>700 K) this step will hence be so rapid that the steady-state coverage of Had will be determined by the adsorption-desorption equilibrium H2+ 2Had, where the concentration of free surface sites is, of course, affected by the presence of all other surface intermediates. 

In this section we summarize methods for solution of the master equation, which couples the collisional relaxation of the highly excited unimolecular species with the microcanonical dissociation rates to determine, for a given temperature and pressure, the non-equilibrium probability distribution for the molecular population over energies and angular momenta, and thence the thermal rate coefficient k(T, P). The separability of molecular interactions in the gas phase into unimolecular events and bimolecular events enables the overall thermal dissociation process to be modeled by the two-dimensional master equation, expressed in continuum notation as... 

---