A Thermodynamically Consistent Formulation of the Fundamental Equation in Inverse Gas Chromatography for an Accurate Determination of Solid Surface Properties

The classical theory of inverse gas chromatography (IGC) assumes that adsorbed probe molecules behave as a perfect two-dimensional gas, a simplification that leads to large systematic errors in the surface energy and Lewis acid-base calculations. We introduce a corrected formulation for the Gibbs free energy of adsorption, Δ<i>G</i> _<i>a</i> ⁰(<i>T</i>) = Δ<i>G</i> _<i>a</i> ^0*(<i>T</i>) + <i>f</i>(<i>T</i>, Σ), where <i>f</i>(<i>T</i>, Σ) accounts for temperature and specific surface area effects. Applied to 17 solid surfaces and 19 solvents, the deviation function proved essential, as the classical models produced errors exceeding 1000%. Errors decreased with an increasing surface area, confirming the physical origin of the deviation. This framework redefines the thermodynamic foundation of IGC, enabling accurate determination of dispersive and polar surface energies and necessitates a reevaluation of decades of published data. Although both van der Waals and Redlich-Kwong equations correct the classical IGC formulation, the Redlich-Kwong model yields the best agreement with experimental data with discrepancies between models diminishing as the solid surface area increases.