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Calculation of the equilibrium pH in a multiple-buffered aqueous solution based on partitioning of proton buffering: a new predictive formula

Department of Medicine, University of California, Los Angeles, California

Submitted 31 October 2008 ; accepted in final form 30 March 2009

Upon the addition of protons to an aqueous solution containing multiple buffers, the final H⁺ concentration ([H⁺]) at equilibrium is determined by the partitioning of added H⁺ among the various buffer components. In the analysis of acid-base chemistry, the Henderson-Hasselbalch equation and the Stewart strong ion formulation can only describe (rather than predict) the equilibrium pH following a proton load since these formulas calculate the equilibrium pH only when the reactant concentrations at equilibrium¹ are already known. In this regard, it is simpler to directly measure the equilibrium pH rather than measure the equilibrium reactant concentrations to calculate the equilibrium pH. As these formulas cannot predict the final equilibrium [H⁺] following a proton load to a multiple-buffered aqueous solution, we developed a new quantitative approach for predicting the equilibrium [H⁺] that is based on the preequilibrium² concentrations of all buffers in an aqueous solution. The mathematical model used to derive our equation is based on proton transfer buffer equilibria without requiring the incorporation of electroneutrality considerations. The model consists of a quartic polynomial equation that is derived based solely on the partitioning of H⁺ among the various buffer components. We tested the accuracy of the model using aqueous solutions with various buffers and measured the equilibrium pH values following the addition of HCl. Our results confirmed the accuracy of our new equation (r² = 1; measured pH vs. predicted pH), indicating that it quantitatively accounts for the underlying acid-base phenomenology.

acid-base chemistry; proton; bicarbonate; Stewart; Henderson-Hasselbalch