Hydrogen storage materials form a crucial research topic for future energy utilization employing hydrogen and among those of interest magnesium diboride (MgB₂) has shown its prevalence. In this study, a first-principles analytical adsorption model of one hydrogen molecule in the vicinity of various magnesium diboride crystal surfaces was developed in order to obtain surface thermodynamic properties as a function of molecular and lattice properties. Henry's law constant (K_H) and isosteric heat of adsorption (ΔH_ads) indicators of the affinity between a gaseous molecule and a solid surface are thus calculated. The results in this paper not only address questions pertaining to the first stage of hydrogen storage processes but also advance the understanding of physisorption thermodynamics of a neutral molecule (H₂) coming in contact with a layered metallic-like surface (MgB₂). Although the model is built from a framework of classical calculations, quantum effects are incorporated as the fractional charge of the ions on the free surfaces, which is essential for the calculation of analytic thermodynamic values that approximate calculations from other methods. To benchmark our theoretical models, periodic density functional calculations were performed to determine the interactions between H₂ and different MgB₂ surfaces from first-principles. By considering both the top and sublayers of MgB₂ in calculating interaction energy, we have analytically and computationally calculated the interaction energies of H₂ molecules and MgB₂'s terminated planes, and witnessed the strong dependence of interaction energies on surface charges. We have also observed a dipole flipping phenomenon which explains the discontinuity seen in the interaction energy graph of Mg(0001). Both analytical and computational results showed heat of adsorption at zero coverage varying at a very low range (<7 kJ mol⁻¹).