Simultaneous Determination of Forward and Reverse Rate Constants for Gas−Liquid Oxygen Transport by Real-Time Phosphorescence Monitoring

Abstract

Conventional net-flux descriptions of gas−liquid interfacial transport intrinsically couple the forward and reverse exchange processes, leaving the individual directional rate constants unidentifiable when the gas-phase boundary condition is not independently specified. Here we introduce an analytical platform that overcomes this limitation by directly controlling the gas-phase boundary conditions, transforming the measurement problem from structurally underdetermined to overdetermined and enabling simultaneous determination of the two rate constants. The platform combines real-time phosphorescence monitoring of dissolved oxygen with a precision gas-mixing system delivering O2/Ar mixtures of defined composition. Applied to oxygen transport at the gas−water interface, it yields the solvent-to-bubble (kSB) and bubble-to-solvent (kBS) rate constants over a wide range of gas-phase compositions: kSB = (2.99 ± 0.11) × 10−2 s−1 and kBS = (6.6 ± 1.1) × 10−7 s−1, where the uncertainties are combined standard uncertainties incorporating experimental run-to-run reproducibility and Monte Carlo-propagated input uncertainty. These values define the characteristic timescales of forward and reverse oxygen transport and yield a ratio, kSB/kBS = (4.54 ± 0.83) × 104, consistent with equilibrium partitioning within the two-state kinetic description. Extension to acetonitrile and toluene resolves both directional constants and further shows that kSB in water is approximately two-fold lower despite water’s lower equilibrium oxygen solubility, providing a physically grounded interpretation of the observed underperformance of freeze−pump−thaw deoxygenation in water relative to organic solvents. The boundary-controlled strategy can in principle be extended to other gas−liquid systems by coupling controlled gas-phase conditions with an appropriate gas-selective readout.