Disagreements Between Calorimetric and Van't Hoff Enthalpies of Adsorption: A New Langmuir-like Model to Account for the Effect of Solvent Displacement Stoichiometry.

The reported inconsistencies between calorimetry and the van't Hoff equation hinder the utility of thermodynamics in pharmaceutical research. In ligand binding or adsorption assays, it is believed that the van't Hoff equation falls short because of the lack of stoichiometric treatment in the equilibrium constant. A new modified Langmuir-Like equation that accounts for the stoichiometry of solute adsorption and solvent displacement is proposed in this work. The performance of the model was evaluated by studying the adsorption of phenobarbital from aqueous solutions by commercial activated carbon. The amount of water occupying the adsorption sites was estimated by graphical analysis of the 'knee point' of water-vapor adsorption isotherms and was found to correlate well with the relative percentage of hydroxyl and carbonyl surface groups. It was found that one phenobarbital molecule displaces 2-6 water molecules from the adsorption site. It is shown that adsorption enthalpy was not affected by the adjustment for stoichiometry, supporting the notion that the van't Hoff enthalpy is intrinsic and is independent of the stoichiometry of solvent displacement in Langmuir-based binding. The widely reported disparities between the van't Hoff and calorimetric enthalpies are unlikely to be from a stoichiometric origin.