The state of protonation/deprotonation of surfaces has far-ranging implications in all areas of chemistry: from acid-base catalysis$^1$ and the electro- and photocatalytic splitting of water$^2$, to the behavior of minerals$^3$ and biochemistry$^4$. The acidity of a molecule or a surface site is described by its proton affinity (PA) and pK$_\mathrm{a}$ value (the negative logarithm of the equilibrium constant of the proton transfer reaction in solution). For solids, in contrast to molecules, the acidity of individual sites is difficult to assess. For mineral surfaces such as oxides they are estimated by semi-empirical concepts such as bond-order valence sums$^5$, and also increasingly modeled with first-principles molecular dynamics simulations$^{6,7}$. Currently such predictions cannot be tested - the experimental measures used for comparison are typically average quantities integrated over the whole surface or, in some cases, individual crystal facets$^8$, such as the point of zero charge (pzc)$^9$. Here we assess individual hydroxyls on In$_2$O$_3$(111), a model oxide with four different types of surface oxygen atoms, and probe the strength of their hydrogen bond with the tip of a non-contact atomic force microscope (AFM). The force curves are in quantitative agreement with density-functional theory (DFT) calculations. By relating the results to known proton affinities and pK$_\mathrm{a}$ values of gas-phase molecules, we provide a direct measure of proton affinity distributions at the atomic scale.
