Geometric-algebraic approach to acid-base equilibrium

TL;DR

This paper derives exact algebraic formulas for calculating the pH of weak acid and buffer solutions, enabling precise analysis of common approximations and pH stability without numerical methods.

Contribution

It introduces a unified algebraic framework for pH calculation in weak acid systems using computer algebra, improving accuracy and understanding of pH behavior.

Findings

Closed-form pH expressions for weak acids and buffers.

Analytical evaluation of approximation accuracy.

Unified expression for pH in terms of effective parameters.

Abstract

Closed-form expressions for the pH of ideal weak acid and weak acid buffer solutions (and their titration with a strong base) were obtained and analyzed with the aid of computer algebra systems. These expressions are used to evaluate, without the use of numerical approximations, the precision and accuracy of different approximations commonly employed to calculate the pH. The closed-form expression for the pH of a buffer solution is used to obtain an analytical expression for the pH stability when a strong base is added. Finally, it is shown that the pH expressions for all the systems under study can be obtained from an unique closed-form expression in terms of an effective weak acid constant and an effective acid concentration.