A high-fidelity physics-based model of mixed-gas transport coupled with kinetic and equilibrium adsorption is derived, and experiments were performed in order to calibrate and exercise the model. In the literature, a continuum-scale model that couples Fickian diffusion with Henry's law absorption, and kinetic Langmuir adsorption was previously developed to describe the diffusion and sorption of moisture in porous materials. Here, we expand the model to gases, rather than moisture, derive, and implement a competitive adsorption mechanism into the model to enable mixed-gas sorption. This model facilitates a mechanistic-based understanding of the sorption and diffusion processes of mixed gases in polymeric materials. Diffusion and sorption experiments were conducted for a range of partial pressures; model validation and calibration were carried out by comparing modeled mass uptake and experimental data considering the uncertainties of conceptualized (or assumed) physical processes and system parameters. Uncertainty quantification and sensitivity analysis methods are described and exercised here to demonstrate the capability of this predictive model.