A linear relationship between the behavior (-phi vs. E) of the phase shift (0 degrees <= - phi <= 90 degrees) for the optimum intermediate frequency and that (theta vs. E) of the fractional surface coverage (1 >= theta >= 0) of over-potentially deposited hydrogen (OPD H) for the cathodic H-2 evolution reaction (HER), i.e., the phase-shift method, at the poly-Pt/0.5 M H2SO4 aqueous electrolyte interface has been verified using cyclic voltammetric, differential pulse voltammetric, and ac impedance techniques. The phase-shift method for determining the suitable adsorption isotherm (Langmuir, Frumkin, Temkin) of OPD H for the cathodic HER at the interface also has been proposed. At the poly-Pt/0.5 M H2SO4 aqueous electrolyte interface, the Langmuir adsorption isotherm (theta vs. E) of OPD H, the equilibrium constant (K = 1.3 x 10(-4)) for OPD H and the standard free energy (Delta G(ads)(0) = 22.2 kJ/mol) ad of OPD H are determined using the phase-shift method. At the same interface, the Temkin adsorption isotherm (theta vs. E) of OPD H, the equilibrium constant (1.3 x 10(-3) >= K >=, 1.3 x 10(-5) with theta, i.e., 0 <= theta <= 1) for OPD H, and the standard free energy (16.5 <= Delta G(theta)(0) <= 27.9 kJ/mol with theta, i.e., 0 <= theta <= 1) of OPD H are also determined using the phase-shift method. At the 0 intermediate values of theta, i.e., 0.2 < theta < 0.8, the Langmuir and Temkin adsorption isotherms of OPD H for the cathodic HER at the interface are converted to each other. The equilibrium constant (K-0) for the Temkin adsorption isotherm (theta vs. E) is ca. 10 times greater than that (K) for the corresponding Langmuir adsorption isotherm (theta vs. E). The interaction parameter (g) for the Temkin adsorption isotherm (theta vs. E) is ca. 4.6 greater than that (g) for the corresponding Langmuir adsorption isotherm (theta vs. E). These numbers (10 times and 4.6) can be taken as constant conversion factors between the corresponding adsorption isotherms (Temkin, Langmuir, Frumkin). The Temkin adsorption isotherm corresponding to the Langmuir or the Frumkin adsorption isotherm, and vice versa, can be effectively converted using the constant conversion factors. Both the phase-shift method and constant conversion factors can be effectively used as a new electrochemical method to determine the suitable adsorption isotherms (Langmuir, Frumkin, Temkin) of H for the cathodic HER in electrochemical systems. (c) 2005 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.