pH and Acid-Base Equilibrium Calculations via a Matrix Representation of Solutions of Acids and/or Bases

In this article we implement the idea of representing an aqueous solution of acids and/or bases with a matrix from which the pH and equilibrium concentrations of all species in any described solution can be extracted. Given that this matrix can be readily generated using an ad hoc MS Excel sheet, whatever pH calculation is reduced to the problem of selecting a row from the matrix by using as a guide the proton balance equation in the solution. A special scheme is presented allowing the needed proton balance relation to be derived from the specified solution data in all cases. This preserves the fundamental unity of the topic without sacrificing chemical understanding and simplicity. By consequence, the presented calculation technique is eminently suitable to be used in introductory courses as a complement, an extension or a substitute whenever the usual way of dealing with the topic (which, in general, consists in developing a menu of special cases, formulas and/or algebraic procedures) is judged insufficient. A MS Excel file named <matrixGenerator.xlsx>, attached to the present paper as supporting material, allows the matrix representation of any given solution to be developed in a very short time.