A large surface area, wide band gap, and unique bonding property between Zn and O atoms make the hexagonal ZnO monolayer attractive as a gas sensor. In the present work, the adsorption and evolution of nitrogen (N2) molecules over a ZnO monolayer have been studied using two different theoretical methods: van der Waals density functional theory (vdW-DFT) and kinetic Monte-Carlo (kMC) simulation. The adsorption and diffusion (hopping over the surface) energy of a N2 gas molecule has been calculated considering the different sites over the ZnO substrate using the revPBE-vdW functional. Bader charge, electron localization function analysis, density of states and band structure plotting have been used to understand the adsorption mechanism. Lateral repulsive interaction between two N2 molecules limits the maximum packing number of gas molecules within one hexagonal ring. The output of the vdW-DFT calculation has been fed to the kMC code to predict the rate of adsorption, desorption, and diffusion, along with the overall surface coverage at different temperatures and pressures. Finally, the change in the N2 adsorption energy has been predicted with the increase of the ZnO layer number.