### Visual approach to acid-base systems

Most students in General Chemistry are never taken beyond the traditional, algebraic treatment of acid-base equilibria. This is unfortunate for the following reasons:

• It can be an awful lot of work. Have you ever noticed that many of the acid-base systems most commonly encountered (phosphate, citrate, salts such as ammonium acetate, amino acids, EDTA) are rarely treated in standard textbooks? Treadting these analytically requires setting up a series of mass- and charge-balance expressions which must be solved simultaneously.
• Most algebraic teatments are approximations anyway. Did you know, for example, that the exact calculation of the pH of a solution of a monoprotic weak acid requires the solution of a cubic equation? Carrying out the same operation for H3PO4 requires solution of a fifth-order polynomial! To simplify the calculations, approximations are made, sometimes unwittingly. The algebraic calculations that we actually carry out are almost never exact in the first place!
• Equilibrium constants are not really. Even if you carry out an exact calculation, the results will never be any more reliable than the equilibrium constants you use. But the values of these vary with the temperature and especially with the ionic content of the solution. The values listed in tables are rarely applicable to practical applications.
• All you get is a number: Algebraic approaches contribute almost nothing to the larger view of how an acid-base system behaves as the pH is changed.

Yes, I still teach my students how to set up a quadratic equation to calculate the pH of an acetic acid solution, but I insist that they also be able to do the same thing graphically. The major advantages of the graphical approach:

• Easy to do: the graphs are easily constructed and generally give pH values as good as those from algebra. Even if you sketch out the graph on the back of an envelope and without a straightedge, you can get results to within half a pH unit. A good way to amaze your friends!
• Provides an overall picture of the acid-base system. A glance at the graph shows you the approximate concentrations of all species present over a range of pH values, thus providing a bird's-eye view of the acid-base system as s whole.
• Reinforces important principles. In learning to sketch out and interpret log-concentration vs. pH plots, the student must consider such things as the nature of the equilibria occurring in solutions of the pure acid and of its conjugate base, conservation of protons, and the significance of the pK.
• Allows treatment of a wider range of systems. Graphical estimation of the pH of solutions of acids, bases and ampholytes of such as phosphate, citrate, amino acids, EDTA etc. are not all that much more difficult than treating a monoprotic or diprotic system.