Ab initio density functional theory is used to calculate the electrochemical phase diagram for the oxidation and reduction of water over the Pt(111) surface. Three different schemes proposed in the literature are used to calculate the potential-dependent free energy of hydrogen, water, hydroxyl, and oxygen species adsorbed to the surface. Despite the different foundations for the models and their different complexity, they can be directly related to one another through a systematic Taylor series expansion of the Nernst equation. The simplest model, which includes the potential only as a shift in the chemical potential of the electrons, accounts very well for the thermochemical features determining the phase-diagram.