Buffer Squares: A Graphical Approach for the Determination of Buffer pH Using Logarithmic Concentration Diagrams

Abstract

Teaching the concept of pH buffers is considered to be important both in the final high-school years and at the early undergraduate level. Here, we propose the use of pH–log C diagrams to investigate the properties of pH buffers. This graphical approach is extremely simple to employ because it only requires drawing a simple square that can then be used to determine relevant pH-buffer parameters. This square is based on the Henderson–Hasselbalch equation with the length of each of its sides equal to abs(pH – pKa) and abs(log Cb – log Ca). In addition, the “buffer square”, as we propose naming it, can be used by instructors as a pedagogical tool to introduce the concept of buffer capacity, to help determine pH change upon the addition of an acid or base, and to easily calculate the required concentrations for preparing a pH buffer with specific properties. Finally, we consider this approach to be especially powerful for helping students visualize the location of a buffer system on a full pH–log C diagram and, thus, help them evaluate if the Henderson–Hasselbalch equation is valid for accurate pH determination as an alternative to the more complex cubic or quadratic equations that are needed to describe acid–base equilibria more precisely in some cases.