A theory of surface charging of colloidal particles suspended in an electrolyte solution is presented. The charging at the particle surface is assumed to originate from the adsorption and desorption of protons and is therefore strongly dependent on the acidity of the solution. The surface binding of protons occurs locally at sites of occupancy zero or one that are described by a binding energy u(0) and a three-dimensional vibration of frequency v. The diffuse screening of ions at the surface is described by the corrected Debye-Huckel analysis assuming linear response. The model contains a capacitor layer close to the charged surface and the finite size of the electrolyte ions is taken into account. The theory has been applied to titrated surface charge data on goethite (alpha-FeOOH) at NaClO4 background concentrations ranging from 0.01 to 1.0 M. The protonation mechanism used in the modeling of these data corresponds to the 1-pK approach. A very good description of the experimental data was obtained at the highest ionic strength. Close to the pH(pzc) the theory also gave a good description at lower ionic strengths. However, at low salt concentrations and pH values far away from the pH(pzc) the electrostatic potential outside the capacitor layer becomes so high that nonlinear electrostatic effects become important and the theory therefore underestimates the surface charge. These results were compared with model calculations obtained using existing surface complexation models.