We have used embedded clusters to model the abstraction of oxygen from N2O over the (001) terraces of BaO. At low coverage, we find a very low barrier (16 kcal/mol) in strong contradiction with experiment (33 kcal/mol). Regeneration of the surface through surface diffusion of oxygen and recombination is excluded by high barriers. At low coverage, the direct reaction of N2O with surface peroxide ion through an Elay-Rideal (ER) mechanism has a computed barrier of 20.6 kcal/mol, which at full coverage increases to 34.3 kcal/mol. The reaction will use the lower-barrier direct abstraction as long as there are free anions available and will switch to the ER mechanism at high coverage of peroxide ions.