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
- 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
- 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.