Predictions of reactive transport in the subsurface are routinely compromised by both model (structural) and parametric uncertainties. We present a set of computational tools for quantifying these two types of uncertainties. The model uncertainty is resolved at the molecular scale where epistemic uncertainty incorporates aleatory uncertainty. The parametric uncertainty is resolved at both molecular and continuum (Darcy) scales. We use the proposed approach to quantify uncertainty in modeling the sorption of neptunium through a competitive ion exchange. This radionuclide is of major concern for various high-level waste storage projects because of its relatively long half-life and its high-solubility and low-sorption properties. We demonstrate how parametric and model uncertainties affect one's ability to estimate the distribution coefficient. The uncertainty quantification tools yield complete probabilistic descriptions of key parameters affecting the fate and migration of neptunium in the subsurface rather than the lower statistical moments. This is important, since these distributions are highly skewed.