Abstract
<jats:p> The Gibbs equation (∆ <jats:italic toggle="yes">G</jats:italic> = ∆ <jats:italic toggle="yes">H</jats:italic> – <jats:italic toggle="yes">T</jats:italic> ∆ <jats:italic toggle="yes">S</jats:italic> ) remains a cornerstone of chemical thermodynamics. Yet the scope and origins of the widely observed correlations between the enthalpies (∆ <jats:italic toggle="yes">H</jats:italic> ) and entropies (∆ <jats:italic toggle="yes">S</jats:italic> ), or Gibbs energies (∆ <jats:italic toggle="yes">G</jats:italic> ) and enthalpies, have long been debated. This study systematically analyzes over 4,500 experimental thermodynamic values at 298.15 K to establish quantitative principles governing the ∆ <jats:italic toggle="yes">G</jats:italic> <jats:italic toggle="yes">vs.</jats:italic> ∆ <jats:italic toggle="yes">H</jats:italic> relationship across solvation, vaporization, and molecular complexation processes. By classifying systems according to hydrogen-bonding capabilities, we demonstrate that non-associated solute–solvent pairs universally follow a baseline linear correlation (the Barclay–Butler line). Systematic deviations from this baseline are quantitatively attributed to distinct physical contributions: conformational flexibility in long-chain aliphatics (hindered internal rotation), a constant entropic penalty per directional hydrogen bond, and predominantly entropic solvophobic effects in associated solvents. Through thermodynamic transformations, these solvation/vaporization rules are extended to yield a universal linear ∆ <jats:italic toggle="yes">G</jats:italic> –∆ <jats:italic toggle="yes">H</jats:italic> relationship with an invariant slope of 0.660 for both solution- and gas-phase molecular complexation, encompassing hydrogen bonding, charge transfer, and dispersion interactions. The framework is successfully applied to <jats:italic toggle="yes">α</jats:italic> -cyclodextrin host–guest systems, where it can be used as a diagnostic tool for detecting anomalous or non-inclusion binding modes and for deeper analysis of the complexation mechanism. Ultimately, this work transforms the Gibbs equation into a predictive instrument, enabling accurate estimation of enthalpies from single-temperature Gibbs energy measurements and providing a unified, mechanism-independent foundation for analyzing intermolecular interactions in systems of varying complexity. </jats:p>