Experimental findings indicate that the impressively low friction and wear of diamond in humid environments are determined by the surface passivation. In this paper, we investigate the relationship between the surface chemistry and the nanotribological properties of diamond surfaces. We consider the (2x1)-C(001) surface taking into account different terminations constituted of hydrogen, oxygen, and hydroxyl groups. We analyze the adsorbate geometry and the polarization of the surface bonds. We discuss the stability of the different surface terminations in different conditions, which account for the presence in the environment of H-2, O-2, and H2O molecules in different concentrations and we present the surface phase diagram. Finally, we report the calculated adhesion energy between the passivated surfaces and analyze its variation as a function both of the surface separation and of the surface relative lateral position. In this way, we provide information on the effect of the different adsorbates on the interaction between diamond surfaces and on the magnitude and anisotropy of friction forces.