Here it is shown that graphene membranes that separate 2 gases at identical pressure are deflected by osmotic pressure. The osmotic pressure is a consequence of differences in gas permeation rates into a graphene enclosed cavity. The deflection of the few layer graphene membranes is detected by an interferometric technique for measuring their tension-induced resonance frequency. Using a calibration measurement of the relation between resonance frequency and pressure, the time dependent osmotic

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... ressure on the graphene is extracted. The osmotic pressure for different combinations of gases shows large differences that can be accounted for by a model based on the different gas permeation rates. Thus a graphene membrane based gas osmometer with a responsitivity of ~60 kHz/mbar and nanoscale dimensions is demonstrated.