Kinetic Approach for Assessing Absolute Hydrogen Potential (pH_abs) across Diverse Solvents

The catalytic reactivity of the proton (H⁺) is often governed by its chemical potential, yet quantifying this potential across nonaqueous and mixed-solvent systems remains a fundamental challenge. Here, we present a framework for assessing the absolute potential of hydrogen (pH_abs) using the electrophilic C_ar-D/C_ar-H substitution of phenol-d₆ as a kinetic probe, applicable for wide-ranging solvents with diverse properties, categorized here according to their ability to solvate and stabilize sulfuric acid (H₂SO₄) and its conjugate base (HSO₄^-) as polar HSO₄^- stabilizers, polar HSO₄^- destabilizers, midpolar solvents, bridger solvents, and nonpolar solvents. In midpolar solvents, bridger solvents, and nonpolar solvents, H₂SO₄ molecules form a cluster, whereas in polar HSO₄^- destabilizer solvents, HSO₄^- anions undergo homoassociation. Despite the distinct differences in solvation properties, the electrophilic C_ar-D/C_ar-H substitution rate constants, measured at dilute H₂SO₄ concentrations and normalized to 1 mol L^-1, exhibit a log-linear correlation with the solvent-modulated chemical potential of H⁺, spanning ∼20 pH_abs units and corresponding to a >37,000,000-fold variation in the normalized rate constants at 333 K. The correlation gives estimated pH_abs values for both the nonaqueous and aqueous systems, notably in agreement between the estimated pK_a of H₂SO₄ in methanol (1.4) versus that obtained from electrochemical measurements (1.5). This framework lays the foundation for the prediction of proton reactivity in thermal catalysis.