We used density functional theory to study the electrochemical conversion of nitrogen to ammonia on the (001), (100/010), (101), and (111) surfaces of γ-Mo2N. Based on the calculated free energy profiles for the reduction of nitrogen by the associative and dissociative mechanisms, reactivity was found to decrease in the order (111) > (101) > (100/010) ≈ (001). Namely, the cell potentials needed to drive the reduction to ammonia increase in the following order: -0.7 V on (111), -1.2 V on (101), and -1.4 V on (100/010) and (001) surfaces. The (111) surface was found to be the most reactive for nitrogen due to (i) its ability to adsorb the N2 in the side-on position which activates N-N bonding and (ii) its high affinity for N-adatoms which also prevents accumulation of H-adatoms on the catalytic surface at low cell potentials. We have also calculated vibrational frequencies of different NxHy species adsorbed on various γ-Mo2N surfaces. The frequencies are found to depend strongly on the type of the binding sites available on the crystal facets. A comparison of the calculated frequencies with the frequencies of the corresponding species in transition metal complexes and other metal surfaces shows that the frequencies of several signature modes fall in a similar region and might be used to assign the spectra of hydrogen and nitrogen containing surface species on different metal surfaces.