Abstract In this paper, we report a first-principles Molecular Dynamics (FPMD) study of interfacial structures and acidity constants of goethite. The pKa values of the groups on (010), (110), and (021) surfaces (space group Pbnm) are derived with the FPMD based vertical energy gap technique. The results indicate that major reactive groups include ≡Fe2OH2 and ≡FeOH2 on (010), ≡FeOH2, ≡Fe3OLH, and ≡Fe3OUH on (110), and ≡FeOhH2 and ≡Fe2OH on (021). The interfacial structures were characterized in detail with a focus on the hydrogen bonding environment. With the calculated pKa values, the point of zero charges (PZCs) of the three surfaces are derived and the overall PZC range of goethite is found to be consistent with the experiment. We further discuss the potential applications of these results in future studies toward understanding the environmental processes of goethite.