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Permeation of multilayered graphene oxide (GO) membranes by polar solvents is known to correlate with their swelling properties and amount of sorbed solvent. However, quantitative estimation of sorption using standard (e.g., gravimetric) methods is technically challenging for few nanometers thick GO membranes/films exposed to solvent vapors. Neutron reflectivity (NR) was used here to evaluate the amount of solvents intercalated into the film which consists of only ∼31.5 layers of GO. Analysis of NR data recorded from the GO film exposed to vapors of polar solvents provides information about change of film thickness due to swelling, amount of intercalated solvent, and selectivity in sorption of solvents from binary mixtures. A quantitative study of GO film sorption was performed for D₂O, d-methanol, ethanol, dimethyl sulfoxide (DMSO), acetonitrile, dimethylformamide (DMF), and acetone. Using isotopic contrast, we estimated selectivity in sorption of ethanol/d-methanol mixtures by the GO film. Estimation of sorption selectivity was also performed for D₂O/DMF, D₂O/DMSO, and D₂O/acetonitrile binary mixtures. Sorption of polar solvents was compared for the thin GO film, micrometer thick free standing GO membranes, and graphite oxide powders.