Features of the Gibbs Equation (∆G = ∆H - T∆S) Applied to Solvation, Vaporization, and Complexation Thermodynamics
Year: 2026
Type: preprint
Abstract: The Gibbs equation (∆ G = ∆ H – T ∆ S ) remains a cornerstone of chemical thermodynamics. Yet the scope and origins of the widely observed correlations between the enthalpies (∆ H ) and entropies (∆ S ), or Gibbs energies (∆ G ) 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 ∆ G vs. ∆ H 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 ∆ G –∆ H 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 α -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.
Source: ChemRxiv
Authors: Boris N. Solomonov, Mikhail I. Yagofarov
Institution: Kazan Federal University
Language: English
Subfield: Organic Chemistry
Field: Chemistry
Domain: Physical Sciences
Open Access status: green
Funder: Kazan Federal University
Award: G3098198495
OpenAlex ID: W7220393728