The Langmuir adsorption isotherms of the under-potentially deposited hydrogen (UPD H) and the over-potentially deposited hydrogen (OPD H) at the poly-Pt/0.5M $H_2SO_4$ and 0.5 M LiOH aqueous electrolyte interfaces have been studied using cyclic voltammetric and ac impedance techniques. The behavior of the phase shift $(0^{circ}{leq}{-phi}{leq}90^{circ})$ for the optimum intermediate frequency corresponds well to that of the fractional surface coverage $(1{geq}{ heta}{geq}0)$ at the interfaces. The phase-shift method, i.e., the phase-shift profile $({-phi};vs.;E)$ for the optimum intermediate frequency, can be used as a new electrochemical method to determine the Langmuir adsorption isotherms $({ heta};vs.;E)$ of the UPD H and the OPD H for the cathodic $H_2$ evolution reactions at the interfaces. At the poly-Pt/0.5M $H_2SO_4$ aqueous electrolyte interface, the equilibrium constant (K) and the standard free energy $({Delta}G_{ads})$ of the OPD H are $2.1 imes10^{-4}$ and 21.0kJ/mol, respectively. At the poly-Pt/0.5M LiOH aqueous electrolyte interface, K transits from 2.7(UPD H) to $6.2 imes10^{-6}$ (OPD H) depending on the cathode potential (E) and vice versa. Similarly, ${Delta}G_{ads}$ transits from -2.5kJ/mol (UPD H) to 29.7kJ/mol (OPD H) depending on I and vice versa. The transition of K and ${Delta}G_{ads}$ is attributed to the two distinct adsorption sites of the UPD H and the OPD H on the poly-Pt surface. The UPD H and the OPD H on the poly-Pt surface are the independent processes depending on the H adsorption sites themselves rather than the sequential processes for the cathodic $H_2$ evolution reactions. The criterion of the UPD H and the OPD H is the H adsorption sites and processes rather than the $H_2$ evolution reactions and potentials. The poly-Pt wire electrode is more efficient and useful than the Pt(100) disc electrode for the cathodic $H_2$ evolution reactions in the aqueous electrolytes. The phase-shift method is well complementary to the thermodynamic method rather than conflicting.