D39.4 Titration of Polyprotic Acids and Bases

When a polyprotic acid is titrated, there are usually multiple equivalence points. For example, when H2SO3 is titrated with NaOH, there are two equivalence points corresponding to the two acidic protons from the H2SO3 molecule. There are also as many midpoints as there are equivalence points.

When a strong monoprotic base is added to a solution of a polyprotic acid, the neutralization reaction occurs in stages. The most acidic proton (Ka,1) is titrated first, followed by the next most acidic (Ka,2), and so forth. If the Ka values differ by at least three orders of magnitude, then the overall titration curve will show well-resolved “steps” corresponding to the titration of each acidic proton.

Consider the titration of a generic weak polyprotic acid H3A with NaOH as shown below. The first equivalence point corresponds to the point where 1 mole of NaOH has been added per mole of H3A in the solution being titrated. As more titrant is added, the titration curve crosses another midpoint and reaches the second equivalence point, corresponding to a total of 2 moles of NaOH being added per mole of H3A in the solution. The titration is finally complete when all three equivalence points have been reached.

Figure: Polyprotic acid titration. Titration of a weak polyprotic acid by a strong base is shown. Move the slider to see the different stages of titration.

It is not always possible to detect all the equivalence points in the titration of a polyprotic acid. An actual titration of the triprotic acid H3PO4 with NaOH is illustrated in the figure below. It shows two well-defined steps, and the first midpoint corresponds to pKa,1 while the second midpoint corresponds to pKa,2. Because HPO42− is a very weak acid, pKa,3 has a high pH value, and the third step cannot be resolved using 0.100 M NaOH as the titrant.

Figure: Titration Curve for Phosphoric Acid. The curve for the titration of 25.0 mL of 0.100-M H3PO4 solution with 0.100-M NaOH. Species in solution at each midpoint are shown. Note the two distinct equivalence points corresponding to deprotonation of H3PO4 at pH ≈ 4.6 and H2PO4– at pH ≈ 9.8. Because HPO42- is a very weak acid, the third equivalence point, at pH ≈ 13, is not well defined. (This is because the maximum pH that can be achieved with 0.100-M NaOH is 13.)

The titration curve for the reaction of a polyprotic base with a strong acid is similar, but inverted on the pH scale. The initial pH is high; as acid is added, the pH decreases in steps if the successive pKb values are well separated.

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