Module 8

Lesson 4.2  Polyprotic pH Curves



Key Concepts


In Lesson 4.1, you studied monoprotic titration curves.


However, some substances can donate or accept more than one proton. These entities are referred to as polyprotic substances.

Polyprotic acid - an acid that can lose more than one proton (H2CO3 is an example of a polyprotic acid.)

Polyprotic base - a base that gains more than one proton (CO32- is an example of a polyprotic base.)

When a polyprotic substance is titrated, a series of single-proton transfers occurs. The shape of the resulting pH curve communicates a great deal of information regarding the reactions that are occurring. Study the pH curve showing the titration of phosphoric acid (H3PO4) with sodium hydroxide (NaOH).

The phosphoric acid has three protons to donate, but the pH curve shows only two equivalence points. Why is this?


To write the reaction for the transfer of the first proton, apply the five-step method that you learned in Lesson 2.


  1. List all entities initially present as they exist in aqueous solution.


    \( \mathrm { Na^+(aq), OH^-(aq), H_3PO_4 (aq), H_2O(l) } \)


  2. Using the Bronsted-Lowry definition, identify and label all possible aqueous acids and bases.
    \( \mathrm { Na^+(aq) } \)
    \( \mathrm { OH^-(aq) } \) B
    \( \mathrm { H_3PO_4 (aq) } \) A
    \( \mathrm { H_2O(l) } \) A or B

  3. Identify the strongest acid (SA) and the strongest base (SB) present, using the table of Relative Strengths of Aqueous Acids and Bases. These will be the reactants.


    \( \mathrm { OH^-(aq) } \) SB
    \( \mathrm { H_3PO_4(aq) } \) SA

  4. Write an equation showing a transfer of one proton from the strongest acid to the strongest base, and predict the products. The products are the conjugates located beside the SA and SB on the table of Relative Strength of Acids and Bases.


    \( \mathrm { OH^-(aq) + H_3PO_4 (aq) \rightarrow H_2O(l) + H_2PO_4^-(aq) } \)


    The transfer of the first proton is quantitative.


To write the reaction for the transfer of the second proton, follow the same steps. Because the transfer of the first proton is quantitative, assume that only H2PO4- (aq) remains after the first equivalence point (that is, no H3PO4 (aq) remains). H2PO4- (aq) is a much weaker acid than H3PO4 (aq); therefore, the pH rises sharply after the first equivalence point.


  1. List all entities as they exist in aqueous solution.


    \( \mathrm { Na^+(aq), OH^-(aq), H_2PO_4^- (aq), H_2O(l) } \)


  2. Using the Bronsted-Lowry definition, identify and label all possible aqueous acids and bases.


    \( \mathrm { Na^+(aq) } \)
    \( \mathrm { OH^-(aq) } \) B
    \( \mathrm { H_2PO_4^- (aq) } \) A or B
    \( \mathrm { H_2O(l) } \) A or B

  3. Identify the strongest acid (SA) and the strongest base (SB) present, using the table of Relative Strengths of Aqueous Acids and Bases. These will be the reactants.


    \( \mathrm { OH^-(aq) } \) SB
    \( \mathrm { H_2PO_4^- (aq) } \) SA

  4. Write an equation showing a transfer of one proton from the strongest acid to the strongest base, and predict the products. The products are the conjugates located beside the SA and SB on the table of Relative Strength of Acids and Bases.


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    The transfer of the second proton is quantitative.


To write the reaction for the transfer of the third proton, follow the steps again to identify the strongest acid and the strongest base. For this reaction, the strongest acid and strongest base are HPO42- (aq) and OH- (aq).


Hydrogen phosphate is an extremely weak acid and does not quantitatively lose protons to the hydroxide ion; instead, an equilibrium is established. The fact that this reaction never goes to completion accounts for the fact that there is no third equivalence point. Only quantitative reactions produce detectable equivalence points in acid-base titrations.





 Read pages 755 to 758 to better understand the reactions of polyprotic entities. Study carefully how the five-step reaction is used to predict accurately the sequential proton transfers that occur.

Check Your Understanding


Complete Practice Question 9 on page 759 of your textbook.

Page 759 Practice Question 9

  1. Two reactions occur:


    \( \mathrm { PO_4^{3-}aq) , Na^+(aq) , H_3O^+(aq), Cl^-(aq), H_2O(l) } \)


    strongest base = \( \mathrm { PO_4^{3-}(aq) } \)


    strongest acid = \( \mathrm { H_3O^+(aq) } \)


    \( \mathrm { PO_4^{3-}(aq) + H_3O^+(aq) \rightarrow HPO_4^{2-}(aq) + H_2O(l) } \)


    Because the first reaction is quantitative, we can assume that no PO43-(aq) remains after the first equivalence point.


    \( \mathrm { HPO_4^{2-}(aq) , Na^+(aq) , H_3O^+(aq), Cl^-(aq), H_2O(l) } \)


    strongest base = \( \mathrm { HPO_4^{2-}(aq) } \)


    strongest acid = \( \mathrm { H_3O^+(aq) } \)


    \( \mathrm { HPO_4^{2-}(aq) + H_3O^+(aq) \rightarrow H_2PO_4^-(aq) + H_2O(l) } \)


    The second reaction is quantitative as well.


    The positions of H2PO4-(aq) and H3O+(aq) do not indicate a quantitative reaction would occur in a third reaction although the reaction favours the products. The reaction establishes an equilibrium that shifts gradually to the right as more hydrochloric acid is added.


    Because there are two quantitative reactions, there would be two equivalence points on a pH curve.



  2. reaction 1: \( \mathrm { PO_4^{3-}aq) + H_3O^+(aq) \rightarrow HPO_4^{2-}aq) + H_2O(l) } \)


    reaction 2: \( \mathrm { HPO_4^{2}aq) + H_3O^+(aq) \rightarrow H_2PO_4^-(aq) + H_2O(l) } \)


    reaction 3: \( \mathrm { HPO_4^{2-}aq) + H_3O^+(aq) \overset{>50\%}{\leftrightarrows} H_3PO_4(aq) + H_2O(l) } \)


    (Reaction 3 establishes an equilibrium that shifts gradually as more hydrochloric acid is added.)