Effect of phase ratio on van't Hoff analysis in reversed-phase liquid chromatography, and phase-ratio-independent estimation of transfer enthalpy

Abstract In analysis of the thermodynamics of the transfer of a solute from the mobile phase to the stationary phase in reversed-phase liquid chromatography, it is nearly always assumed that the phase ratio is constant. This type of analysis is typically performed by applying a form of the van’t Hoff equation, which relates the retention factor to temperature via the enthalpy and entropy of transfer. When non-linear van’t Hoff plots are observed, it is often assumed that the enthalpy and entropy of transfer change with temperature. However, when the possibility of a change in the phase ratio is considered, it becomes apparent that non-linear van’t Hoff behavior may or may not be due to changes in enthalpy or entropy. In this work, we present mathematical evidence that phase ratio changes, if they occur, can cause deviations from linearity in a van’t Hoff plot. We also show that the phase ratio influence can be eliminated by considering the molecular difference between two solutes instead of the solutes themselves. The resulting selectivity van’t Hoff plots may be linear, even when the van’t Hoff plots of the two solutes are non-linear. In such cases, temperature-dependent phase ratio changes, and not necessarily changes in the transfer enthalpy, may be responsible for the curved van’t Hoff plots of the individual solutes. In addition, we present chromatographic evidence that different solutes may “see” different thermodynamic phase ratios. It is clear that the concept of a phase ratio in reversed-phase chromatography is not nearly as well defined as a phase ratio in a bulk system like a liquid–liquid extraction.