Two Acid Titration with Strong Base
Two weak acid analytes HA1, and HA2 have acid equilibrium constants of Ka1 and Ka2 and initial concentrations F1 and F2 repectively. Strong base titrant is NaOH, with concentration FNaOH
Use the systematic approach to solving chemical equilibrium problems...
Chemistry:
Charge Balance:
Mass Balance:
Equilibrium Equations:
Solve for concentration of A1- and A2- using a...
Substitute [A1,2-], [OH-]=Kw/[H3O+], and [Na+]=FNaOH into the charge balance equation
and solve for [H3O+]...
Formal concentrations are adjusted for the volume change upon titration.
Mixed-Acid
Relative fractions as a function of pH
The titration curve may be difficult to calculate obtain owing to the high power dependence on [H3O+]. However, the relative acid and conjugate base fractions can still be obtained, accurately, with the a expressions.
For these plots, we only need the a expressions
It is important to realize that since the a only depend only on [H3O+], the relative concentration two acids do not affect each other (except perhaps through acitivity). So these a are valid even when one of the acids is at a very much lower concentration than the other. This situation is quite common in everyday Titrimetric analysis since the indicator is an acid (albeit with a low concentration relative to the analyte acid).
When the acid pKa are different by more than 3 units,
a pH dependent plot of the relative fractions (a) show that there are only 2 principle species at any pH. Since there are only 2
principle species, the titration curve will exhibit two distinct equivalence points if the
two acid concentrations are in the order of magnitude and if neither acid has too small of
a Ka. Shown below are the a and titration curves for 10 mL each of 0.1 F solution of two acids, with
pKa of 3 and 7, being titrated with a 0.1 F strong base. 
When the acid pKa are similar, the a plots show that there is significant concentrations of more than two species in some pH ranges. This means that one acid may buffer the large pH change that would occur at the equivalence point.
Shown here are the a and titration curves for 10 mL each of 0.1 F
solution of two acids with pKa of 6 and 8. Again, the titrant is 0.1 F
strong base, such as NaOH or KOH.
Notice that the fraction plot shows significant concentrations of both HA2 and A2- at the point where HA1 is being converted to A1-, at pH~6.5
The reason why the first equivalence point is not observed with a large change in pH as a function of added titrant is that the weaker acid, HA2, has a significant fraction as the conjugate base at this pH. The combined acid/conjugate base concentration buffers the pH at the first equivalence point.
Nonetheless, the total amount of acid can be determined since the total
base volume required to reach the second equivalence point is the sum of volumes
(equivalents) needed to neutralize both acids.
Lesson: The effect of having more than 2 dominant species present at an equivalence point also affects the titration curves obtained for polyprotic acids and bases. If more than two species have significant concentration, then the titration curves will not exhibit a sharp change in pH with added titrant.
This page was created by Professor Stephen Bialkowski, Utah State University.
Last Updated Tuesday, August 03, 2004