Differences of ionic concentrations across lipid bilayers are some of the primary energetic driving forces for cellular electrophysiology. While macroscopic models of asymmetric ionic solutions are well-developed, their connection to ion, water, and lipid interactions at the atomic scale are much more poorly understood. In this study, we used molecular dynamics to examine a system of two chambers of equal ionic strength, but differing amounts of NaCl and KCl, separated by a lipid bilayer. Our expectation was that the net electrostatic potential difference between the two chambers should be small or zero. Contrary to our expectation, a large potential difference (-70 mV) slowly evolved across the two water chambers over the course of our 172-ns simulation. This potential primarily originated from strong Na+ binding to the carbonyls of the phosphatidylcholine lipids. This ion adsorption also led to significant structural and mechanical changes in the lipid bilayer. We discuss this surprising result in the context of indirect experimental evidence for Na+ interaction with bilayers as well as potential caveats in current biomembrane simulation methodology, including force-field parameters and finite size effects.