The structures and compositions of Pb(II) adsorption complexes and surface binding sites on alpha-Al2O3 (0001) and (1 (1) over bar 02) surfaces were investigated in the presence of water using grazing-incidence X-ray absorption fine structure (GI-XAFS) spectroscopy. Pb(II) ions were found to adsorb in an inner-sphere mode on alpha-Al2O3 (1 (1) over bar 02) but as outer-sphere complexes on alpha-Al2O3 (0001). The distance between the outer-sphere complexes and the surface places useful constraints on double-layer properties of water. A bond-valence model is described that relates the reactivities of surface functional groups and adsorption complexes to their molecular structures and compositions, and places constraints on the stoichiometries of adsorption reactions, including proton release. The EXAFS and modeling results suggest that Pb(II) and Co(II) ions bond to [Al-Al(Al) --> O-1/2--> and [Al-OH2+1/2] surface functional groups. In contrast, [(Al)(Al) > OH] groups complex Co(II) but not Pb(II). The results indicate the importance of using structurally defined surface sites to describe reactions at oxide-water interfaces.