The Langmuir adsorption isotherm of the over-potentially deposited hydrogen (OPD H) for the cathodic H-2 evolution reaction (HER) at the Pt-Rh (Pt:Rb; 80:20 wt%) alloy/0.5 M H2SO4 aqueous electrolyte interface has been studied using cyclic voltammetric and ac impedance techniques. The behavior of the phase shift (0degrees less than or equal to - phi less than or equal to 90degrees) for the optimum intermediate frequency can be linearly related to that of the fractional surface coverage (1 greater than or equal to theta greater than or equal to 0) of the OPD H for the cathodic HER at the interface. The phase-shift profile (-phi vs. E) for the optimum intermediate frequency, i.e., the phase-shift method, can be used as a new electrochemical method to determine the Langmuir adsorption isotherm (0 vs. E) of the OPD H for the cathodic HER at the interface. At the Pt-Rh alloy electrode interface, the equilibrium constant (K) and the standard free energy (DeltaGads) of the OPD H are 2.2 x 10(-4) and 20.9 kJ/mol, respectively. At the steady state, the behaviors of the cyclic voltammogram and the Langmuir adsorption isotherm of the OPD H for the cathodic HER at the Pt-Rh alloy electrode interface are similar to those of the pure Pt electrode interfaces. At the steady state, the effect of Rh on the OPD H for the cathodic HER can be neglected at the Pt-Rh (Pt:Rh; 80:20 wt%) alloy/0.5 M H2SO4 aqueous electrolyte interface. (C) 2003 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.