  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 pressure 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.
