Consider a general polyprotic acid system with equilibria between species H2A+, HA, and A-. Rather than starting with the diprotic form of the acid (as in Problem 1), suppose that you made a solution by adding the monoprotic form HA to water.
Derive an expression for the concentration of H+ (or H3O+) ions in terms of the two acid dissociation constants (Ka1 and Ka2), the water dissociation constant (Kw), and the initial concentration of added acid F (stands for Formality).
To help you with this process, here is a suggested outline: a) Set up your system of equations (you should have 5) b) Express [H+] in terms of [HA] using 4 of the equations c) Ka2 and Kb2 are almost invariably small. So make an assumption about how [HA]
compares to F! [Hint: Look at your mass balance] This will allow you to derive a final expression.
EXTRA CREDIT: You can derive a simple expression for the pH of this solution by making two more assumptions:
Assume Ka2F >> Kw (usually true, but not guaranteed) Assume Ka1 << F (true unless very dilute, or an unusually strong/weak acid)