Understanding/visualizing the established interactions between gases and adsorbents is mandatory to implement better performance materials in adsorption/separation processes. Here we report the unique behavior of a rare example of a hemilabile chiral three-dimensional metal-organic framework (MOF) with an unprecedented qtz-e-type topology, with formula CuII2(S,S)-hismox·5H2O (1) (hismox = bis[(S)-histidine]oxalyl diamide). 1 exhibits a continuous and reversible breathing behavior, based on the hemilability of carboxylate groups from l-histidine. In situ powder (PXRD) and single crystal X-ray diffraction (SCXRD) using synchrotron radiation allowed us to unveil the crystal structures of four different host-guest adsorbates (Ar@1, N2@1, CO2@1, and C3H6@1), rationalize the breathing motion, and unravel the mechanisms governing the adsorption of these gases. Then this information was transferred to implement efficient separations of mixtures of industrial and environmental relevance, CO2/N2, CO2/CH4, and C3H8/C3H6, using 1 in packed columns as the stationary phase and dispersed in a mixed matrix membrane.