Theoretical studies on the un-catalyzed and catalyzed aminations of ketene with $NH_3$ and $(NH_3)_2$, respectively, were studied using MP2 and hybrid density functional theory of B3LYP at the 6-31+G(d,p) and 6- 311+G(3df,2p) basis sets in the gas phase and in benzene and acetonitrile solvents. In the gas phase reaction, the un-catalyzed mechanism was the same as those previously reported by others. The catalyzed mechanism, however, was more complicated than expected requiring three transition states for the complete description of the C=O addition pathways. In the un-catalyzed amination, rate determining step was the breakdown of enol amide but in the catalyzed reaction, it was changed to the formation of enol amide, which was contradictory to the previous findings. Starting from the gas-phase structures, all structures were re-optimized using the CPCM method in solvent medium. In a high dielectric medium, acetonitrile, a zwitterions formed from the reaction of $CH_2$=C=O with $(NH_3)_2$, I(d), exists as a genuine minimum but other zwitterions, I(m) in acetonitrile and I(d) in benzene become unstable when ZPE corrected energies are used. Structural and energetic changes induced by solvation were considered in detail. Lowering of the activation energy by introducing additional $NH_3$ molecule amounted to ca. ?20 $sim$ ?25 kcal/mol, which made catalyzed reaction more facile than un-catalyzed one.