Density functional theory has been used to gain molecular understanding of various catalytic processes involving N species on Rh(111). These include CN, N2, and HCN formation and N2O decomposition. Our calculations substantiate the conclusion that, starting from chemisorbed C and N atomic species, CN formation is preferred over N2 formation, because of the lower activation energy of the former process (1.73 vs. 2.10 eV). HCN formation has been studied starting from adsorbed CH and N species, with a computed activation barrier of 1.35 eV. The process of binding CH to N is more favorable than recombination of C and N atoms into CN followed by hydrogenation. Concerning the adsorption and dissociation of N2O on Rh, two pathways have been investigated, leading to N2 or NO. From thermodynamic considerations, N2 can be concluded to be the preferred product resulting from N2O dissociation. Our results also support the participation of N2O as a reaction intermediate during reduction of nitric oxide to nitrogen over Rh surfaces by reaction of adsorbed NO and N atoms.