1. CHAPTER 15
Titration Curves for Complex Acid/Base Systems

2. Two acids or bases of different strengths
In this chapter, we describe methods for calculating curves for complex acid/ base systems.
Two acids or bases of different strengths
An acid or base that has two or more acidic or basic functional groups
An amphiprotic substance
Equations for more than one equilibrium are required to describe the characteristics of any of these system
395

3. § 15A Mixtures of strong and weak acids or strong and weak bases
It is possible to determine each of the components in a mixture containing a strong acid and weak acid (or a strong base and weak base) provided that the concentrations of the two are of the same order of magnitude and that the dissociation constant for the weak acid or base is < 10-4

4. Ex 15-1 Calculate the pH of a 25mL mixture acid that is 0
Ex 15-1 Calculate the pH of a 25mL mixture acid that is M in hydrochloride acid and M in the weak acid HA (Ka = 1.00 x 10-4) during its titration with M KOH. Compute results for additions of the following volumes of base; (a) 0.00 mL and (b) 5.00 mL (CASE I )
25mL 的混合酸液( M in HCl 與 M 的弱酸 HA )，以0.1000M的KOH滴定，試求pH值

5. Ex 15-2 Calculate the pH of the solution that results when 29
Ex 15-2 Calculate the pH of the solution that results when mL of M NaOH is added to mL of the solution described in Ex 15-1 (CASE II)
延續Ex15-1，25 mL 的混合酸液( M in HCl 與 M 的弱酸 HA )，以29 mL M的KOH滴定，試求pH值

6. CASE III : the amount of base added = the amount of HCl
～～～ appropriate quantities of the weak acid and sodium chloride in a suitable volume of water
強鹼與強酸到達當量點後，滴定曲線可視為
弱酸強鹼的滴定， pH值受到弱酸解離的影響

7. Figure 15-1
Curves for the titration of strong acid/weak acid mixtures with M NaOH. Each titration is on mL of a solution that is M in HCl and M in HA
399

8. § 15B Polyfunctional acids and bases
Poly:多，polyfunctional acids：多質子酸
~~ generally, the two groups differ in strength and exhibit two or more end points in a neutralization titration

9. The phosphoric acid system
Ka1 > Ka2 > Ka3

11. The carbon dioxide carbonic acid system

13. Ex 15-3 Calculate the pH of a solution that is 0.02500M CO2.
求 M CO2 溶液的 pH值

14. § 15C Buffer Solutions Involving Polyprotic Acids
Free acid H2A + its conjugate base salt NaHA
The acic NaHA + its conjugate base salt Na2A
The pH of 2) is higher than 1)
401

15. Ex Calculate the hydronium ion concentration for a buffer solution that is 2.00M in phosphoric acid and 1.50M in potassium dihydrogen phosphate.
求下列緩衝溶液的[H3O+]，
2.00 M H3PO4 磷酸與1.50 M KH2PO4 磷酸二氫鉀
402

16. Ex Calculate the hydronium ion concentration of a buffer that is 0.050M in potassium hydrogen phthalate (KHP) and 0.150M in potassium phthalate (K2P).
求下列緩衝溶液的[H3O+]， M KHP 與0.150 M K2P
403

17. § 15D Calculation of the pH of Solution of NaHA
Calculate the pH of solutions of salts that have both acidic and basic properties
~~ amphiprotic salts
The pH of the solution is determine by
404

18. CNaHA = [HA-] + [H2A] + [A2-]
[Na+] + [H3O+] = [HA-] + 2[A2-] + [OH-] ……charge-balance
CNaOH + [H3O+] = [HA-] + 2[A2-] + [OH-]
CNaOH = [H2A] +[HA-] + [A2-] ……..mass balance
[H3O+] = [A2-] + [OH-] – [H2A]

20. Ex 15-6 Calculate the hydronium concentration of a 1
Ex 15-6 Calculate the hydronium concentration of a 1.00X 10-3M Na2HPO4 solution. The pertinent dissociation constant are Ka2 and Ka3, which both contain [HPO42-]. Their value are Ka2 = 6.32X10-8 and Ka3 = 4.5X10-13.
求下列溶液的[H3O+]， 1.00x10-3M Na2HPO4

21. 求下列溶液的[H3O+]， M NaH2PO4
Ex Find the hydronium ion concentration of a M NaH2PO4 solution.

22. 求下列溶液的[H3O+]， M NaHCO3
Ex Calculate the hydronium ion concentration of a 0.100M NaHCO3 solution.

23. § 15E Titration Curves For Polyfunctional Acids
Compounds with two or more acid functional groups yield multiple end points in a titration curve.
407

24. Figure 15-2
Titration of mL of M H2A with M NaOH. For H2A, Ka1=1.00×10-3 and Ka2=1.00×10-7. The method of pH calculation is shown for several points and regions on the titration curve.
407

25. HOOC-CH=CH-COOH, with 0.1000M NaOH.
Ex Construct a curve for the titration of 25.00mL of M maleic acid,
HOOC-CH=CH-COOH, with M NaOH.
建構下列酸鹼滴定的曲線：以 M NaOH 滴定25.00mL M 的丁烯二酸
408

26. Figure 15-3
Titration curve for mL of M maleic acid, H2M, with M NaOH.
414

27. Figure 15-4
Curves for the titration of polyprotic acids. A M NaOH solution is used to titrate ML of M H3PO4(curve A), M oxalic acid (curve B), and M H2SO4 (curve C).
414

28. The dissociation of sulfuric acid
H2SO4 ~~ one proton is a strong acid
~~ one proton is a weak acid
Ka2 = 1.02 x 10-2
Example: How the [H3O+] is computed in M solution.
Ans: [H3O+] is computed in M

29. § 15F Titration Curves For Polyfunctional Bases
Consider the titration of sodium carbonate solution with standard HCl

30. Figure 15-5
Curve for the titration of mL of M Na2CO3 with M HCl.
417

31. § 15G Titration Curves For Amphiprotic Species
An amphiprotic substance, when dissolved in a suited solvent, behaves both as a weak acid and as a weak base.

32. Example: sodium dihydrogen phosphate solution NaH2PO4 Na+ + H2PO4-
acid
base

33. § 15H The Composition of Solutions of a Polyprotic Acid as a Function of pH

34. Composition of H2M solutions as a function of pH.
Figure 15-6
Composition of H2M solutions as a function of pH.
421

35. Figure 15-7
Titration of mL of M maleic acid with M NaOH. The solid curves are plots of alpha values as a function of volume. The broken curve is a plot of pH as a function of volume.
421