A new hierarchical MOF consisting of Cu(II) centers connected by benzene-tricarboxylates (BTC) is prepared by thermoinduced solid transformation of a dense CuBTC precursor phase. The mechanism of the material formation has been thoroughly elucidated and revealed a transformation of a ribbon-like 1D building unit into 2D layers and finally a 3D network. The new phase contains excess copper, charge compensated by systematic hydroxyl groups, which leads to an open microporous framework with tunable permanent mesoporosity. The new phase is particularly attractive for molecular separation. Energy consumption of adsorptive separation processes can be lowered by using adsorbents that discriminate molecules based on adsorption entropy rather than enthalpy differences. In separation of a 11-component mixture of C1-C6 alkanes, the hierarchical phase outperforms the structurally related microporous HKUST-1 as well as silicate-based hierarchical materials. Grand canonical Monte Carlo (GCMC) simulation provides microscopic insight into the structural host-guest interaction, confirming low adsorption enthalpies and significant entropic contributions to the molecular separation. The unique three-dimensional hierarchical structure as well as the systematic presence of Cu(II) unsaturated coordination sites cause this exceptional behavior.