Disagreements Between Calorimetric and Van't Hoff Enthalpies of Adsorption II: Effect of pH and pH Buffers on Phenobarbital Adsorption to Activated Carbon.

The reported inconsistencies between the van't Hoff equation and calorimetry hinder the utility of thermodynamics in biochemical and pharmaceutical research. A novel thermodynamic approach is developed herein for ligand adsorption with a focus on the interpretation of calorimetric data in the presence of concurrent proton exchange reactions. Such exchange reactions typically result in a pH-dependence of calorimetric measurements that obscures intrinsic binding enthalpies. It is shown that for the adsorption of phenobarbital to activated carbon, the measured calorimetric enthalpy is a result of three linked acid/base equilibria. A model was established to predict the intrinsic binding enthalpy using 1) the adsorbate's pKa and 2) the adsorbate's enthalpy of protonation. The observed calorimetric enthalpy of binding exhibited both pH and buffer-dependence and was between -5 and -42 kJ/mol. Meanwhile, the predicted intrinsic enthalpy (-25.1 kJ/mol) of binding was in excellent agreement with the measured intrinsic enthalpy (-25.6 kJ/mol). Corrections to the observed calorimetric enthalpies allowed comparisons with enthalpies obtained from the van't Hoff method. It is shown that the predicted intrinsic calorimetric enthalpy agrees well with the van't Hoff enthalpies in instances where observed enthalpies significantly deviated. This treatment is general and is not specific to phenobarbital or activated carbon.