Applicability of single-site rate equations for reactions on inhomogeneous surfaces

Single-site rate laws are broadly applicable to surface mediated chemical kinetics even though most surfaces are strongly inhomogeneous. We defined the best single-site approximation for an inhomogeneous rate law by square error minimization and, using this definition, examined the limits of the applicability of the single-site approximation and the nature of the errors that arise when inhomogeneity is ignored. We found that (i) correlation between kinetic inhomogeneity and sorptive inhomogeneity does not affect the success of the single-site approximation, (ii) many types of inhomogeneity produce similar macroscopic kinetic behavior, (iii) ignoring inhomogeneity in a single kinetic experiment causes rates to be overestimated at high and low concentrations and underestimated at intermediate concentrations, (iv) it is difficult to obtain detailed information about inhomogeneity from a single kinetic experiment, and (v) kinetic experiments over varying concentration ranges may be used to diagnose the existence of inhomogeneity and to parametrize an inhomogeneous rate law.