We present an analytical thermodynamic model of a surface in contact with a gas phase which enables us to determine the surface coverage of the adsorbate depending on the temperature, pressure and chemical potential of the gas. This model is applied to both the W(110) and W(100) surface of tungsten in contact with hydrogen. The thermodynamic model is built upon data computed by density functional theory that provide the complete electronic and vibrational energetics of both surfaces. It is further compared to experimental measurements of hydrogen coverage during isobar exposure at various temperature acquired via low energy ion scattering and direct recoil spectroscopy techniques. On W(110), the agreement is quantitative provided that an additional degree of freedom is added to the model. This degree of freedom accounts for the translational motion of the adsorbate along 1D channel on the surface. On W(100), surface reconstruction makes the energetics of the system more complex; the full details of the experimental isobar are not well reproduced, although the overall consistency is obtained. We end-up with a thermodynamic model based on DFT data having accurate predictive capabilities to determine the hydrogen coverage of tungsten at any p and T.