The reaction mechanism for nitrous oxide decomposition has been studied on hydrated and dehydrated mononuclear iron sites in Fe-ZSM-5 using density functional theory. In total, 46 different surface species with different spin states (spin multiplicity M(S) = 4 or 6) and 63 elementary reactions were considered. Heats of adsorption, activation barriers, reaction rates, and minimum energy pathways were determined. The approximate minimum energy pathways and transition states were calculated using the "growing string method" and a modified "dimer method". Spin surface crossing (e.g., O(2) desorption) was considered. The minimum potential energy structure on the seam of two potential energy surfaces was determined with a multiplier penalty function algorithm by Powell and approximate rates of spin surface crossings were calculated. It was found that nitrous oxide decomposition is first order with respect to nitrous oxide concentration and zero order with respect to oxygen concentration. Water impurities in the gas stream have a strong inhibiting effect. In the concentration range of 1-100 ppb, the presence of water vapor influences the surface composition and the apparent rate coefficient. This is especially relevant in the temperature range of 600-700 K where most experimental kinetic studies are performed. Apparent activation barriers determined over this temperature range vary from 28.4 (1 ppb H(2)O) to 54.8 kcal/mol (100 ppb H(2)O). These results give an explanation why different research groups and different catalyst pretreatments often result in very different activation barriers and preexponential factors. Altogether perfect agreement with experimental results could be achieved.