A microgravimetric technique for the determination of solubility, cΒ°, of hygroscopic solid is proposed. The method allows the determination of the critical concentration of supersaturated solution, cβ, where spontaneous nucleation of the solid phase takes place. The two concentrations, cΒ°and cβ, delimit the metastable domain of supersaturated solutions wherein growth of crystals is realisable. Ammonium nitrate is used as a model of hygroscopic solid. The kinetics of absorption of water vapor is followed by high precision microbalance (Dynamic Vapor Sorption). Powder sample is placed in an atmosphere of constant temperature and of relative humidity superior to the critical relative humidity while mass of absorbed water vapor is monitored continuously. As long as solid phase is present in the sample holder, the rate of absorption is constant and determined by the imposed relative humidity. The absorption of water continues even after all solid is dissolved, but, due to continuous dilution of the obtained solution, by continuously decreasing rate. The change of kinetics of water sorption is used as an indicator for the determination of the solid/liquid equilibrium concentration (or solubility), cΒ°. The concentration cβ is determined by subsequently performed measurements but at relative humidity lower then the critical relative humidity for a given temperature: water evaporates at continuously decreasing rate because the concentration of solute in solution increases; highly supersaturated solutions can be obtained in such a way. When finally the solid phase appears in the supersaturated solution evaporation suddenly accelerates; this change of regime is used for the determination of the critical supersaturation concentration, cβ. The evaporation accompanied by growth of crystals proceeds until all water is evacuated from the sample. In present paper we compare thus obtained solubility curve to the known literature data for ammonium nitrate.