Theoretical quantum calculations and molecular beam experiments of the dissociative chemisorption of N-2 molecules on catalytic active metal surfaces have given new insight in the fundamental process of the ammonia synthesis. This new approach to the study of catalytic process supplements the conclusions based on a traditional kinetic analysis and may resolve some existing ambiguities in the analysis of the kinetic data. In this paper we address two controversial questions concerning the dissociative chemisorption of N-2, namely: The existence of a precursor state, and the existence of a barrier to dissociation. Our analysis of the dissociation process suggests that it is not possible to define, in some well specified way, a precursor state at typical temperatures in the technical ammonia synthesis. The kinetic scheme for the complete ammonia synthesis without the precursor state can still account for the observed conversion to ammonia. We have constructed an empirical potential energy surface for N-2/Fe(111) which has barriers to dissociation even larger than for the previously studied N-2/Re system. It is shown that the presence of barriers is consistent with the observation that the activation energy, determined from an Arrhenius plot of the rate constant, is close to zero. This is due to tunneling through the barrier and energy exchange between the molecule and metal.