We investigated the dependence of ion transport through perforated graphene on the concentrations of the working ionic solutions. We performed our measurements using three salt solutions, namely, KCl, LiCl, and K2SO4. At low concentrations, we observed a high membrane potential for each solution while for higher concentrations we found three different potentials corresponding to the respective diffusion potentials. We demonstrate that our graphene membrane, which has only a single layer of atoms, showed a very similar trend in membrane potential as compared to dense ion-exchange membranes with finite width. The behavior is well explained by Teorell, Meyer, and Sievers (TMS) theory, which is based on the Nernst-Planck equation and electroneutrality in the membrane. The slight overprediction of the theoretical Donnan potential can arise due to possible nonidealities and surface charge regulation effects.