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Am J Physiol Renal Physiol (April 1, 2009). doi:10.1152/ajprenal.90651.2008
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Submitted on October 31, 2008
Revised on March 6, 2009
Accepted on March 30, 2009

Calculation of the Equilibrium pH in a Multiple-Buffered Aqueous Solution Based on Pre-Equilibrium Reactant Concentrations: A New Predictive Formula

Minhtri Khac Nguyen1*, Liyo Kao1, and Ira Kurtz2

1 UCLA
2 Ronald Reagan UCLA Medical Center

* To whom correspondence should be addressed. E-mail: mtnguyen{at}mednet.ucla.edu.

Upon the addition of protons to an aqueous solution containing multiple buffers, the final [H+] at equilibrium is determined by the partitioning of added H+ among the various buffer components. Current approaches to the analysis of acid-base chemistry (Henderson-Hasselbalch equation and the Stewart strong ion formulations) 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 equilibrium are already known. In this regard, it is simpler to directly measure the equilibrium pH rather than measuring the equilibrium reactant concentrations in order to calculate the equilibrium pH. As none of the current formulas can 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 for the first time on the pre-equilibrium concentrations of all buffers in an aqueous solution. The mathematical model used to derive our equation is based on proton transfer buffer equilibria and does not require 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.







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