We present measurements of the net electrical surface charge of silicon dioxide (SiO2) in contact with solvents of dielectric constants between 5 and 80. Our experimental approach relies on observing the thermal motion of single silica particles confined in an electrostatic fluidic trap created by SiO2 surfaces. We compare the experimentally measured functional form of the trapping potential with that from free energy calculations and thereby determine the net surface charge in the system. Our findings clearly demonstrate that contrary to popular perception, even in the absence of surfactants, the net electrical charge of ionizable surfaces in contact with apolar solvents can be large enough to lead to significant repulsive forces. A charge regulation model for SiO2 surfaces with a single tunable parameter explains our measurements. This model may find general applicability in estimating the net charge of ionizable surfaces, given system parameters such as the dissociation or association constants of the ionizable groups and the pH, ionic strength, and dielectric constant of the solvent phase.