Features of the Gibbs Equation (∆G = ∆H - T∆S) Applied to Solvation, Vaporization, and Complexation Thermodynamics
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.
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BibTeX
@misc{solomonov2026features,
title = {{Features of the Gibbs Equation (∆G = ∆H - T∆S) Applied to Solvation, Vaporization, and Complexation Thermodynamics}},
author = {Boris N. Solomonov and Mikhail I. Yagofarov},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15006218/v2},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15006218/v2},
note = {CC BY},
}
RIS
TY - UNPB
TI - Features of the Gibbs Equation (∆G = ∆H - T∆S) Applied to Solvation, Vaporization, and Complexation Thermodynamics
AU - Boris N. Solomonov
AU - Mikhail I. Yagofarov
PY - 2026
DA - 2026/10/05
PB - ChemRxiv
DO - 10.26434/chemrxiv.15006218/v2
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15006218/v2
AB - 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.
ER -