Apparent activation energies on catalysts with heterogeneous surfaces: III. Atomically-flat surfaces on body and face-centered cubic lattices

Abstract

The heterogeneity of a catalyst surface has been estimated using hard sphere models. The number of sites of different free bond number was calculated for atomically-flat surfaces on body or face-centered cubic lattices. By substituting this theoretical heterogeneity into the equations derived previously the apparent activation energy and pre-exponential factor for simple first or zero-order reactions catalyzed by a single ( hkl) plane or polycrystalline surfaces were found. The model predicts that, despite the heterogeneity of the surface, the apparent rate constant will still appear to obey the Arrhenius equation. The apparent activation energy derived from this equation will, however, be very sensitive to the range of temperature used in its determination. The activation energy for a first-order reaction will be independent of surface orientation. For a zero-order reaction, depending upon some assumptions, the activation energy for low-index planes is different from that for high-index planes or polycrystalline surfaces. If the true activation energy and pre-exponential factor on individual types of site show the compensation effect, then a series of catalysts of different orientation or composition will also show compensation between apparent activation energy and pre-exponential factor. It is not necessary to postulate some special site distribution to obtain this result.