Defining the buffering process by a triprotic acid without relying on stewart-electroneutrality considerations

Upon the addition of protons to an aqueous solution, a component of the H+ load will be bound i.e. buffered. In an aqueous solution containing a triprotic acid, H+ can be bound to three different states of the acid as well as to OH- ions that are derived from the auto-ionization of H2O. In quantifying the buffering process of a triprotic acid, one must define the partitioning of H+ among the three states of the acid and also the OH- ions in solution in order to predict the equilibrium pH value. However, previous quantitative approaches that model triprotic acid titration behaviour and used to predict the equilibrium pH rely on the mathematical convenience of electroneutrality/charge balance considerations. This fact has caused confusion in the literature, and has led to the assumption that charge balance/electroneutrality is a causal factor in modulating proton buffering (Stewart formulation). However, as we have previously shown, although charge balance can be used mathematically as a convenient tool in deriving various formulae, electroneutrality per se is not a fundamental physicochemical parameter that is mechanistically involved in the underlying buffering and proton transfer reactions. The lack of distinction between a mathematical tool, and a fundamental physicochemical parameter is in part a reason for the current debate regarding the Stewart formulation of acid-base analysis. We therefore posed the following question: Is it possible to generate an equation that defines and predicts the buffering of a triprotic acid that is based only on H+ partitioning without incorporating electroneutrality in the derivation? Towards this goal, we derived our new equation utilizing: 1) partitioning of H+ buffering; 2) conservation of mass; and 3) acid-base equilibria. In validating this model, we compared the predicted equilibrium pH with the measured pH of an aqueous solution consisting of Na2HPO4 to which HCl was added. The measured pH values were in excellent agreement with the predictions of our equation. Our results provide further important evidence that one can mathematically model the chemistry of acid-base phenomenology without relying on electroneutrality (Stewart formulation) considerations

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

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