Accurate prediction of the bubble-enhanced mass transport rate of dissolved water from a layer of aqueous nitric acid ("aqueous phase") to an overlying, reactive layer of tri-n-butyl phosphate and nitric acid ("organic phase") is crucial to assessing the conditions for a runaway reaction in the organic phase. This paper presents a rational, predictive model of the concentration profile history of a dissolved species in a vertical column comprising an organic phase overlying an aqueous phase. The model incorporates both interfacial and axial dispersion limitations to species transport. Open-literature correlations on enhanced heat transfer in bubbling pools, after conversion to mass transfer correlations, provide the model's needed interfacial resistance coefficients. The model shows that in laboratory-scale systems interfacial limitations to dissolved species mass transport are controlling while in full-scale columns mass transport is axial dispersion controlled. The model is capable of rationalizing available measurements of dissolved species mass transfer between the organic and aqueous phases. A previous interpretation of the measurements is shown to be incorrect.