The prerequisites for a statistical mechanical treatment of phase transitions of adsorbed layers on electrode surfaces to give results compatible with both classical thermodynamics and experiment are studied. It is shown that the use of the charge density as the independent electrical variable, either in the canonical ensemble or the grand ensemble partition function of simple models, leads to artifacts which are at variance with thermodynamics. In contrast, the generalised ensemble Delta, presented in Nikitas et al. (J. Electroanal. Chem., 317 (1991) 43), which uses the potential drop across the layer which undergoes the transition as independent variable, gives results compatible with both experiment and thermodynamics under all circumstances. The results obtained are compared with the predictions of Guidelli and Aloisi’s three-dimensional lattice model of TIP4P water molecules. It is shown that in this case the choice of the charge density as independent variable leads to an incomplete description of the two-dimensional phase transition properties, since the vertical steps obtained in the adsorption isotherms at constant charge density may either indicate a new type of phase transition which has not been observed experimentally yet or they are artifacts which do not represent the properties of the phase transition.