  Closed-form expressions for the pH of ideal weak acid and weak acid buffer
solutions (and their titration with a strong base) were obtained and analyzed
with the aid of computer algebra systems. These expressions are used to
evaluate, without the use of numerical approximations, the precision and
accuracy of different approximations commonly employed to calculate the pH. The
closed-form expression for the pH of a buffer solution is used to obtain an
analytical expression for the pH stability when a strong base is added.
Finally, it is shown that the pH expressions for all the systems under study
can be obtained from an unique closed-form expression in terms of an effective
weak acid constant and an effective acid concentration.
