The sensing properties of an α phase black phosphorus carbide (P2C2) monolayer for the adsorption of CO2, H2, H2O, N2, H2S, NH3, O2 and NO2 gases are theoretically investigated using first-principles calculations. We calculate the adsorption energy, equilibrium distance, Mulliken charge transfer, electron localization function, and work function to explore whether P2C2 is suitable for detecting NO2 gas. The results demonstrate that the P2C2 monolayer is highly sensitive and selective to NO2 gas molecules with robust adsorption energy and superior charge transfer due to the existence of strong orbital hybridization between the NO2 molecule and monolayer P2C2. In addition, the results of the work function calculations indicate that field effect transistor type NO2 gas sensors based on P2C2 monolayers are also feasible. Furthermore, the current-voltage curves reveal that the adsorption of NO2 can greatly modify the resistance of the P2C2 monolayer. Our results show that gas sensors based on P2C2 monolayers could be better than those based on black phosphorene (BP) for detecting NO2 molecules in an air mixture. In addition, the recovery time of the P2C2 sensor at T = 300 K was estimated to be short (and even shorter at higher temperatures) for NO2 which satisfies the demands for sustainable use.