High pressure x-ray studies on the rhodium-hydrogen system have been performed up to 8 GPa at ambient temperature. Formation of the hydride phase has been observed at 3.8 GPa of hydrogen pressure, accompanied by a rapid increase of the lattice volume of rhodium metal. Decomposition pressure has been determined as 2.5 GPa. This value has been used for the calculation of the standard free energy of formation of the rhodium hydride, giving a value of 11 500 cal/mol H-2. The thermodynamic properties of the RhH have been discussed. The pressure-concentration isotherm has been calculated, using the x-ray data and the "universal" volume increase during the hydride phase formation.