The chemisorption of H-2 over a set of gallia polymorphs (alpha-, beta-, and gamma-Ga2O3) has been studied by temperature-programmed adsorption equilibrium and desorption (TPA and TPD, respectively) experiments, using in situ transmission infrared spectroscopy. Upon heating the gallium oxides above 500 K in 101.3 kPa of H-2, two overlapped infrared signals developed. The 2003- and 1980-cm(-1) bands were assigned to the stretching frequencies of H bonded to coordinatively unsaturated (cus) gallium cations in tetrahedral and octahedral positions [v(Ga(t)-H) and v(Ga(o)-H), respectively]. Irrespective to the gallium cation geometrical environment, (i) a linear relationship between the integrated intensity of the whole v(Ga-H) infrared band versus the Brunauer-Emmett-Teller surface area of the gallia was found and (ii) TPA and TPD results revealed that molecular hydrogen is dissociatively chemisorbed on any bulk gallium oxide polymorph following two reaction pathways. An endothermal, homolytic dissociation occurs over surface cus-gallium sites at T > 450 K, giving rise to Ga-H(I) bonds. The heat and entropy of this type I hydrogen adsorption were determined by the Langmuir's adsorption model as Deltah(I) = 155 +/- 25 kJ mol(-1) and Deltas(I) = 0.27 +/- 0.11 kJ mol(-1) K-1. In addition, another exothermic, heterolytic adsorption sets in already in the low-temperature region. This type of hydrogen chemisorption involves surface Ga-O-Ga species, originating GaO-H and Ga-H(II) bonds which can only be removed from the gallia surface after heating under evacuation at T > 650 K. The measured desorption energy of this last, second-order process was equal to 77 +/- 10 kJ mol(-1). The potential of the H-2 chemisorption as a tool to measure or estimate the specific surface area of gallia and to discern the nature and proportion of gallium cation coordination sites on the surface of bulk gallium oxides is also analyzed.