Bubble-mediated mass transfer is of major importance for the gas exchange between soil air and groundwater. The presence of entrapped air bubbles in the upper, quasisaturated aquifer zone can crucially affect the interpretation of atmospheric trace gas concentrations in groundwater and associated fluids as well as intrinsic and enhanced bioremediation procedures that rely on the actual dissolved gas content of gases such as oxygen or nitrogen. To describe the bubble-mediated gas exchange in detail, a kinetic multi-species model for dissolved gas transport in a porous medium including inter-phase mass transfer with entrapped gas bubbles was developed. It takes into account changes in the entrapped gas bubble sizes resulting from the mass exchange and therefore allows the quantification of mass transfer between bubbles of any gas composition and flowing or stagnating water in a substrate column. Considering the dissolution of entrapped air bubbles, the resulting concentrations of dissolved atmospheric gases significantly exceed their solubility equilibrium concentrations. The temporal evolution of the composition of this excess gas is controlled by the solubility and the molecular diffusivity of the gases considered, by the flow conditions, and by the physical properties of the aquifer such as the ratio of entrapped air to water in the pore space. In the case of noble gases in a through-flow system, solubility differences appear to be more important for the composition of the gas excess than the differences between molecular diffusivities.