For surface-mediated processes in general, such as epitaxial growth and heterogeneous catalysis, a constant slope in the Arrhenius diagram of the rate of interest, R, against inverse temperature, log R vs 1/T, is traditionally interpreted as the existence of a bottleneck elementary reaction (or rate-determining step), whereby the constant slope (or apparent activation energy, [Formula: see text]) reflects the value of the energy barrier for that elementary reaction. In this study, we express [Formula: see text] as a weighted average, where every term contains the traditional energy barrier for the corresponding elementary reaction plus an additional configurational term, while identifying each weight as the probability of executing the corresponding elementary reaction. Accordingly, the change in the leading (most probable) elementary reaction with the experimental conditions (e.g. temperature) is automatically captured and it is shown that a constant value of [Formula: see text] is possible even if control shifts from one elementary reaction to another. To aid the presentation, we consider kinetic Monte Carlo simulations of submonolayer growth of Cu on Ni(111) and Ni on Cu(111) at constant deposition flux, including a large variety of single-atom, multi-atom and complete-island diffusion events. In addition to analysing the dominant contributions to the diffusion constant of the complete adparticle system (or tracer diffusivity) and its apparent activation energy as a function of both coverage and temperature for the two heteroepitaxial systems, their surface morphologies and island densities are also compared.