3-D Surface Visualization of pH Titration “Topos”: Equivalence Point Cliffs, Dilution Ramps, and Buffer Plateaus

Abstract

3-D topographic surfaces (“topos”) can be generated to visualize how pH behaves during titration and dilution procedures. The surfaces are constructed by plotting computed pH values above a composition grid with volume of base added in one direction and overall system dilution on the other. What emerge are surface features that correspond to behavior in aqueous solutions. Equivalence point breaks become cliffs that pinch out with dilution. Buffer effects become plateaus. Dilution alone generates 45° ramps. Limitations of the Henderson–Hasselbalch equation can be seen by noting the conditions over which a plateau remains relatively flat. Because dissociation is driven by dilution, the surfaces demonstrate when the solution of a weak acid becomes indistinguishable from that of a strong acid. Surfaces are presented for hydrochloric acid, HCl (a strong acid); acetic acid, CH3COOH (a weak monoprotic acid); oxalic acid, HOOCCOOH (a weak diprotic acid) and l-histidine dihydrochloride, C6H9N3O2·2HCl (a weak triprotic acid). Supplementary materials include suggested use of topos in lecture, as worksheets and in support of laboratory activities for first-year college courses and third-year analytical chemistry courses. Also provided is pH TOPOS, the macro-enabled spreadsheets that quickly generate surfaces for any mono-, di-, or triprotic acid desired. Only a change of acid dissociation constants, Ka values, is required.