Our group has developed five fundamental equations that help provide a broad understanding of different aspects of catalysis research. These will be explained. The “degree of rate control” (DRC) is a mathematical approach for analysing multi-step reaction mechanisms that has proven very useful in catalysis research.1 It identifies the “rate-controlling transition states and intermediates” (i.e., those whose DRCs are large in magnitude). Even in mechanisms with over 30 intermediates and transition states, these are generally just a few distinct chemical species whose energies, if they could be independently changed, would achieve a faster net reaction rate to the product of interest. For example, when there is a single “rate-determining step”, the DRC for its transition state is 1. Since the (relative) energies of these key adsorbed intermediates and transition states can be adjusted by modifying the catalyst or solvent, the DRC values provide important ideas for catalyst improvement. The species with large DRCs are also the ones whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. The apparent activation energy is a weighted average of the enthalpies of all the species in the mechanism, each weighted by its DRC.2 The logarithm of the kinetic isotope effect is a weighted average of the standard-state free energy difference between isoptopes of all the species, each weighted by its DRC.2 In heterogeneous catalysis, the effect of different solvents on the adsorption energies of (some) adsorbed reaction intermediates can be estimated from the surface area required per adsorbate times the solvent’s adhesion energy to the catalyst surface. Solvent adhesion energies can be estimated from their integral heat of adsorption up to multilayer coverage. For supported metal nanoparticle catalysts, the chemical potential of the metal atoms varies with particle size and support material, and correlates with sintering rates and surface reactivity. This size dependence is well modelled by a Gibbs-Thomson-like equation that adds in the effect of the adhesion energy between the nanoparticle and its support, and adjusts for the fact that both the metal’s surface energy and its adhesion energy increase with decreasing diameter (D) as (1-D0/D), with D0 ~5 atomic diameters.

Five new equations that provide fundamental understanding in catalysis research

ACS Fall 2021

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.