The dissolution of hydrogen sulfide in water was studied by measuring the heat of mixing Delta H-mix at conditions of interest for geologic storage of acid gases in deep aquifers. The measurements were performed with a new mixing unit equipped with a Hastelloy tubing, developed specifically for an isothermal differential heat flux calorimeter of Setaram. The heats of mixing were determined at target temperatures of 323, 353, and 393 K and pressures up to 31 MPa in the regions where the solution is unsaturated or saturated by H2S, that is, gaseous, liquid, or supercritical states. The concentration dependence of Delta H-mix allowed the simultaneous determination of the limiting enthalpy of solution Delta H-sol and the gas solubility limit. The agreement between our solubility results and the data from the direct phase equilibrium measurements reported in literature was good. Although no calorimetric data exist for verifying the correctness of Delta H-sol values, their internal consistency was tested by conversion to the low pressure enthalpies of hydration Delta H-hyd. These values agreed reasonably well with those derived from the temperature derivative of the Henry's law constants calculated from representative correlations in the literature. The solubility and enthalpic data for aqueous H2S as a function of temperature and pressure were compared with analogous data for CO2 in water that we have published earlier.