The phase-shift method for the Frumkin adsorption isotherms at the Pd/acidic (H2SO4) and alkaline (KOH) solution interfaces has been studied using an ac impedance method. The phase shift (phi) depends on the cathode potential (E < 0) and is inversely proportional to the fractional surface coverage (theta) of the adsorbed hydrogen atom (H-ads). The phase-shift profile (phi vs. E) at the intermediate frequencies (ca. 130 Hz for the 0.1 M H2SO4 solution and ca. 63 Hz for the 0.1 M KOH solution) can be used as an experimental method to estimate or plot the Frumkin adsorption isotherm (theta vs. E). The rates (r) of change of the free energy of adsorption with theta at the Pd/0.1 M H2SO4 and 0.1 M KOH solution interfaces are 7.4 and 49.6 kJ/mol, respectively. The equilibrium constant (K) and the standard free energy (Delta G(0)) of H-ads at the Pd/0.1 M H2SO4 solution interface are 5.0 x 10(-7) < K < 1.0 x 10(-5) and 35.9 > Delta G(0) > 28.5 kJ/mol, respectively. The equilibrium constant (K) and the standard free energy (Delta G(0)) of H-ads at the Pd/0.1 M KOH solution interface are 2.1 x 10(-15) < K < 1.0 x 10(-6) and 83.8 > Delta G(0) > 34.2 kJ/mol, respectively. The electrode kinetic parameters (r, K, Delta G(0)) depend on theta (0 < theta < 1).