The Langmuir adsorption isotherms of the under-potentially deposited hydrogen (UPD H) and the over-potentially deposited hydrogen (OPD H) at the single crystal Pt(100)/0.5 M $H_2SO_4$ and 0.5 M LiOH aqueous electrolyte interfaces have been studied using the phase-shift method. The phase-shift profile $({-varphi};vs.;E)$ for the optimum intermediate frequency can be used as a useful method to estimate the Langmuir adsorption isotherm $( heta;vs.;E)$ at the interfaces. The equilibrium constant (K) for the OPD H and the standard free energy $({Delta}G_{ads})$ of the OPD H at the Pt(100)/0.5M $H_2SO_4$ aqueous electrolyte interface are $1.5 imes10^{-4}$ and 21.8 kJ/mol, respectively. At the Pt(100)/0.5 LiOH aqueous electrolyte interface, K transits from 1.9(UPD H) to $6.8 imes10^{-6}$(OPD H) depending on the cathode potential (E) and vice versa. Similarly, ${Delta}G_{ads}$ transits -1.6 kJ/mol (UPD H) to 29.5 kJ/mol (OPD H) depending on E and vice versa. The transition of K and ${Delta}G_{ads}$ is attributed to the two distinct adsorption sites of the UPD H and OPD H on the Pt(100) surface. The UPD H and the OPD H at the Pt(100) interfaces are the independent processes depending on the H adsorption sites rather than the sequential processes for the cathodic $H_2$ evolution reactions.