Surface effects limit the performance of hypersonic vehicles, micro-electro-mechanical devices, and directed energy systems. This research develops methods to predict adsorption, scattering, and thermal desorption of molecules on a surface. These methods apply to physisorptive (adsorption and scattering) and chemisorptive (thermal desorption) gas-surface systems, and are developed under the Direct Simulation Monte Carlo construct. The novel adsorption and scattering contribution, the Modified Kisliuk with Scattering method, predicts angular and energy distributions, and adsorption probabilities. These results agree more closely with experiment than the state-of-the-art Cercignani-Lampis-Lord scattering kernel. Super-elastic scattering is predicted. Gas-adlayer interactions are included for the first time. The new thermal desorption model accurately predicts angular and energy distributions. The equations of motion are non-dimensionalized. Accurate timing is included. Initial conditions are chosen from a new truncated Maxwell- Boltzmann distribution. The absorption energy barrier is shown to significantly contribute only to translational energy