This work gives a van't Hoff law expression of Langmuir constants of different species for determining their occupancy in the nanocavities of clathrate hydrates. The van't Hoff law's parameters are derived from a fit with Langmuir constants calculated using a pairwise site-site interaction potential to model the anisotropic potential environment in the cavities, as a function of temperature. The parameters can be used for calculating clathrates compositions. Results are given for nineteen gas species trapped in the small and large cavities of structure types I and II [1]. The accuracy of this approach is based on a comparison with available experimental data for ethane and cyclo-propane clathrate hydrates. The numerical method applied in this work, was recently validated from a comparison with the spherical cell method based on analytical considerations [1]