This work reports new measurements of the three-phase (ice + clathrate hydrate + vapor) equilibrium in the systems of water and each of the following guest species: xenon from (167.20 to 246.16) K, carbon dioxide from (172.28 to 182.15) K, and methane from (145.75 to 195.74) K. The results are compared with the corresponding data reported in the literature and are used to determine empirical laws allowing the equilibrium pressure of these pure clathrates to be calculated at any temperature relevant to the astrophysical environments below the freezing point of water. These relations can be used in astrophysical models such as those devoted to the studies of the cooling and condensation of the solar nebula or to the ones of the physical evolution and gas production from cometary nuclei.

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