We report extensive density functional calculations of the energetics of N-2 adsorption and dissociation on a Fe(lll) surface. From the calculations we can present a detailed picture of the rate limiting step in the ammonia synthesis which is consistent with available experimental observations. Four different molecularly adsorbed states are identified, including a new state not seen by experiment. The new state is the true precursor to dissociation. We find that there are two dissociation channels, one going through all the molecular states sequentially with a low energy barrier, but a high entropy barrier, and the other a direct channel into the new precursor, which is highly activated. In this way we can explain both the measured sticking probability for a thermal gas of N-2 above a Fe(lll) surface and the molecular beam scattering experiments. During ammonia synthesis conditions the low barrier channel is expected to dominate, but at the highest synthesis temperatures, the high barrier channels may become the most effective. The origin of the alkali promotion of the N-2 dissociation process is also discussed.