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 − pK a ) and abs(log C b − log C a ). 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.

Is Your Henderson–Hasselbalch Calculation of Buffer pH Correct?

“…The fundamental test to determine if eq is valid is whether [H + ] and [OH – ] are small (e.g., <5%) relative to F HA and F A – . ,− For acidic buffers, [H + ] > [OH – ], and so, the greatest deviation occurs on the acidic side of the p K a . As the buffering agent becomes more acidic (lower p K a ), the Henderson–Hasselbalch approximation becomes increasingly poor over a greater portion of its buffering range.…”

“…Textbooks state that eq is a reasonable approximation either without qualification − or within limits ,− such as if the buffer concentration (i.e., F HA + F A – ) is greater than 1 mM; if K a is less than 10 –3 ; if K a < 100 F HA and K a < 100 F A – ; if the buffer concentration is more than 200 times K a . The limits of eq can also be visualized by including H + and OH – in pH versus log C graphs …”

Development of Acid–Base Indicators from Natural Pigments in Agar Gel

“…First, solutions with pH values ranging from 2 to 12 were prepared, as outlined in Table . Each solution was mixed and adjusted to the desired pH using HCl or NaOH, with the final pH measured using a pH meter . Second, a few drops of each extracted indicator were added to 3 mL of each solution, and their colors were observed and recorded, as shown in Table .…”

Visualization of Validity Ranges for Acid Approximations: Error Contour Plots as a Function of Concentration and Ka

“…Mathematical approximations − are commonly employed in calculations involving acids and bases. For example, working out the exact equilibrium pH of a monoprotic acid (assuming ideal solution behavior) requires solving a complicated cubic equation: false[ normalH + false] 3 + K normala false[ normalH + false] 2 − ( K a C 0 + K W ) [ H + ] − K normala K normalW = 0 Here, C 0 refers to the initial concentration of the acid and K a and K W are the dissociation constants of the acid and water, respectively.…”