Efficient purification and storage of hydrogen are becoming increasingly important as we head towards hydrogen economy. Pd-based membranes are highly selective for hydrogen separation. However, these membranes suffer from the lack of stability and they are easily poisoned by impurities, such as sulfur, CO, hydrocarbons, and various trace elements. The stability can be enhanced by formulating Pd-containing alloy membranes. In this work we have employed quantum chemical density functional theory (DFT) calculations to investigate the elementary steps associated with hydrogen separation through Pd and Pd-alloy membranes. This molecular information was further employed in an efficient lattice-based kinetic Monte Carlo (KMC) method. The KMC simulations allow us to connect the DFT calculations to macroscopic observables such as tracer diffusivities and fluxes. We find that the diffusivity of hydrogen obtained in our KMC simulations are in excellent agreement with the experimental data. We will elaborate on the proposed approach that combines first principles quantum calculations and KMC simulations and demonstrate that this methodology can not only explain experimental observations but also it can be utilized as an efficient predictive tool.