Tender X-ray operando photoemission spectroscopy has been used to directly analyze the energetics of the double layer at a metal-water interface in a dilute electrolyte having a Debye length of several nanometers. The data are compared to a theoretical evaluation of the potential of the solution near the electrode. Due to its noble nature, Ir was chosen as a working electrode material, and KOH(aq) at varied concentrations and thicknesses constituted the electrolyte. Shifts in peak width and binding energy of the water O 1s core level were analyzed by modeling based on Debye-Hückel approximations. The data are consistent with electrochemical formulations of the double layer that provide a foundation to electrochemistry.