Chapter 11

1. Chapter 11 Polyprotic Acid-Base Equilibria

2. Focus of Chapter Determination of pH of polyprotic systems Buffers made from polyprotic systems Determination of the principle species in solution at any given pH

3. Common Polyprotic Systems Diprotic Sulfuric Acid Oxalic Acid Triprotic Phosphoric Acid Amino Acids Minimum - Diprotic Systems

4. Polyprotic Systems Polyprotic Acids and Bases - compounds that can donate or accept more than one proton Diprotic Acids and Bases - a compound that can donate or accept two protons

5. Diprotic Acids and Bases Amino Acid Structure Neutral molecule is a zwitterion, a molecule that have both a positive and negative charge This form is due to the acidity of the carboxylic acid functional group compared to that of the ammonium group forcing the amino acid to rearrange to give the zwitterion. Low pH - both the ammonium and carboxyl groups are protonated High pH - neither group is protonated

6. Diprotic Acid and Base - pH Determination Example Calculate the pH and composition of individual solutions of 0.0500 M H2L+, 0.0500 M HL, and 0.0500 M L-.

7. Diprotic Acid and Base - pH Determination Example 0.0500 M H2L+ Diprotic system - can dissociate twice From pKa�s - K1=4.69 x 10-3 and K2=1.79 x 10-10 H2L+ from K1 is a weak acid - partial dissociation HL from K2 hardly dissociates at all Approximation - H+ from H2L+ >> H+ from HL - behaves as a monoprotic acid

8. Diprotic Acid and Base - pH Determination Example 0.0500 M L- Diprotic System - hydrolyze twice From KaKb=Kw - Kb1= Kw/K2=5.59 x 10-5; Kb2= Kw/K1=2.13 x 10-12 L- from Kb1 is a weak base HL from Kb2 hardly hydrolyzes at all Approximation - L- behaves as a monoprotic base

9. Diprotic Acid and Base - pH Determination Example Diprotic System more complicated can react to give H2L+ or L- (amphiprotic) HL ? H+ + L- Ka2=1.79 x 10-10 HL + H2O ? H2L+ + OH- Kb2=2.13 x 10-12 Use the systematic treatment of equilibria

10. Diprotic Acid Calculation Summary Solution H2A K1 = x2 / F - x where x = [H+] = [HA] [H2A+] = F - x and [A2-] calculated using K2 Solution HA- [H+] = ?{(K1K2F + K1Kw) / (K1 + F)} should be close to 1/2(pK1 + pK2) [HA-] = F use K1, K2, [H+], and [HA] to solve for [H2A+] and [A2-]

11. Diprotic Acid Calculation Summary Solution of A2- Kb1 = x2 / F - x where x = [OH-] = [HA-[H2A+] = F - x and [A2-] calculated using K2

12. Diprotic Acid and Base - pH Determination Example Potassium hydrogen phthalate, KHP, is a salt of the intermediate for of phthalic acid. Calculate the pH of both 0.10 M and 0.010 M KHP. (pK1 = 2.950; pK2 = 5.408)

13. Diprotic Buffers Calculated the same was as for monoprotic buffers pH = pK1 + log [HA-] / [H2A] pH = pK2 + log [A2-] / [HA-]

14. Diprotic Buffer Example Find the pH of a solution prepared by dissolving 1.00 g of potassium hydrogen phthalate and 1.20 g of disodium phthalate in 50.0 mL of water. How many milliliters of 0.800 M KOH should be added to 3.38 g of oxalic acid to give a pH of 4.40 when diluted to 500.0 mL.

15. Polyprotic Acids and Bases Extension of the treatments completed for the diprotic systems Example - Triprotic System

16. Polyprotic Acids and Bases Triprotic System Equations H3A ? H+ + H2A- H2A- ? H+ + HA2- HA2- ? H+ + A3- A3- + H2O ? HA2- + OH- HA2- + H2O ? H2A- + OH- H2A- + H2O ? H3A + OH-

17. Polyprotic Acids and Bases A solution of H3A Treat like a monoprotic weak acid H3A ? H+ + H2A- [H3A] ? F(H3A) [H+] = [H2A-] = x K1 = x2 / ([H3A] - x) [HA2-] = value from K2 [A3-] = value from K3

18. Polyprotic Acids and Bases A solution of H2A- H2A- ? H+ + HA2- H2A- + H2O ? H3A + OH- [H2A-] ? F(H2A-) [H+] = ?[(K1K2F + K1Kw) / (K1 + F)] [H3A] = value from K1 [HA2-] = value from K2 [A3-] = value from K3

19. Polyprotic Acids and Bases A solution of HA2- HA2- ? H+ + A3- HA2- + H2O ? H2A- + OH- [HA2-] ? F(HA2-) [H+] = ?[(K2K3F + K2Kw) / (K2 + F)] [H2A-] = value from K2 [A3-] = value from K3 [H3A] = value from K1

20. Polyprotic Acids and Bases A solution of A3- Treat like a monoprotic weak acid A3- + H2O ? HA- + OH- [A3-] ? F(A3-) [OH-] = [HA2-] = x Kb1 = x2 / ([A3-] - x) [H2A-] = value from Kb2 [H3A] = value from Kb3 [H+] = Kw / [OH-]

21. Polyprotic Acids and Bases Find the pH of 0.10 M H3His2+, 0.10 M H2His+, 0.10 M HHis, and 0.10 M His-, where His stands for the amino acid histidine.

22. Principle Species in Solution? How do you identify the primary species in solution? Evaluate the pK�s of the system. If the pH < pK1, then the most acidic species is the predominant species If the pH > pKb1, then the species with the least number of protons is predominant If the pH resides between two pK values then the intermediate that lies within that region will be predominant

23. Principle Species in Solution? What is the principle species of benzoic acid at pH = 8? What is the predominant form of ammonia in a solution of pH 7.0? Approximate what fraction is in this form

24. Principle Species in Solution? What is the principle species of oxalic acid in solution at a pH = 4.00? What is the principle form of arginine at pH 10.0? Approximately what fraction is in this form? What is the second most abundant form at this pH?

25. Principle Species in Solution? In the pH range 1.82 - 8.99, H2Arg+ is the principal form of arginine. Which is the second most prominent species at pH 6.O? at pH 5.0?