1. Ch 16: Acid-Base Equilibria Brown, LeMay Ch 16 AP Chemistry

2. 2 16.1: Acids and Bases * Defined by Svante Arrhenius in 1880’s Arrhenius acids: produce protons; increase [H + ] HCl (aq) → H + (aq) + Cl - (aq) Arrhenius bases: produce hydroxides; increase [OH - ] NaOH (aq) → Na + (aq) + OH - (aq) or NH 3 (aq) + H 2 O (l) ↔ NH 4 + (aq) + OH - (aq)

3. 3 16.2: Dissociation of Water Autoionization of water: H 2 O (l) ↔ H + (aq) + OH - (aq) K W = ion-product constant for water H 3 O + (aq) or H + (aq) = hydronium

4. 4 16.3: The pH Scale pH = -log [H + ] = -log [H 3 O + ] or [H + ] = 10 -pH [H + ][OH - ] = K W = 1.0x10 -14 -log ([H + ][OH - ]) = -log K W -log [H + ] + -log[OH - ] = -log (1.0x10 -14 ) pH + pOH = 14.00 pOH = -log [OH - ] or [OH - ] = 10 -pOH pX = -log [X]

5. 5 16.3: The pH Scale If [H + ]<[OH - ], then [H + ]<1.0x10 -7 Ex: pH = -log[1.0x10 -10 ] = 10.00 (basic) If [H + ] = [OH - ] Since[H + ][OH - ] = 1.0x10 -14 [H + ] = [OH - ] = 1.0x10 -7 pH = -log[1.0x10 -7 ] = 7.00 (neutral) If [H + ]>[OH - ], then [H + ]>1.0x10 -7 Ex: pH = -log [1.0x10 -3 ] = 3.00 (acidic) pH 14 7 0 pOH 0 7 14

6. 6 Johannes Brønsted (Denmark) Thomas Lowry (England), 1923 Brønsted-Lowry acids: H + donor Brønsted-Lowry bases: H + acceptor NH 3 (aq) + H 2 O (l) ↔ NH 4 + (aq) + OH - (aq) Base Acid 16.4: Brønsted-Lowry Acids & Bases

7. 7 Amphoterism Amphoteric: capable of acting as either an acid or base H 2 O (l) ↔ Acting as an acid Acting as a base Al(OH) 3 (aq) ↔ Al(OH) 4 - (aq) + H + (aq) Al(OH) 2 + (aq) + OH - (aq) Al(OH) 3 (aq) + H 2 O(l) ↔ OH - (aq) + H + (aq) * Amphiprotic: can accept or donate a p +

8. 8 Conjugated Acid-Base Pairs For acid “HA”: HA (aq) + H 2 O (l) ↔ A - (aq) + H 3 O + (aq) acidbase conjugate base For base “B”: B (aq) + H 2 O (l) ↔ HB + (aq) + OH - (aq) baseacid conjugate acid conjugate base conjugate acid

9. 9 Relative Acid-Base Strengths The stronger an acid (the greater its ability to donate p + ), the weaker its conjugate base (the lesser its ability to accept p + ). The stronger a base, the weaker its conjugate acid. In an acid-base equilibrium, the p + is transferred from the strongest acid to the strongest base. HSO 4 - + CO 3 2- ↔ SO 4 2- + HCO 3 - Stronger acid Stronger base

10. 10 16.5: Strong Acids and Bases Strong acids and bases fully ionize in water (equilibrium is shifted “entirely” toward ions). Strong acids: HI, HBr, HCl, HClO 4, HClO 3, H 2 SO 4, HNO 3 Ex: In 6M HCl solution, 0.004% exist as molecules Strong bases: LiOH, NaOH, KOH, RbOH, CsOH, Ca(OH) 2, Sr(OH) 2, and Ba(OH) 2

11. 11 16.6: Weak Acids Weak acids partially ionize in water (equilibrium is somewhere between ions and molecules). HA (aq) ↔ A - (aq) + H + (aq) K a = acid-dissociation constant in water  Weak acids generally have K a < 10 -3  See Appendix D for full listing of K a values

12. 12 Ex: Calculate the pH of 2.0 M HCl solution (K a ≈10 6 ) Strong acid, completely dissociated HCl (aq) → H + (aq) + Cl - (aq) HCl (aq)H + (aq)Cl - (aq) Initial Change Final 2.0 M - 2.0 M 0 M + 2.0 M 2.0 M So: [HCl] initial = [H + ] final = [Cl - ] final = 2.0 M pH = - log [H + ] = - log [2.0] = -0.30

13. 13 Ex: Calculate pH of 2.0 M HF solution (K a =7.2x10 -4 ) Weak acid, partially dissociated HF (aq) ↔ H + (aq) + F - (aq) HF (aq)H + (aq)F - (aq) Initial Change Equilibrium 2.0 M - x M (2.0 – x) M 0 M + x M x M Using quadratic eq’n, 0 = x 2 + 7.2 x 10 -4 x – 1.44 x 10 -3 x = 3.7229 x 10 -2 or – 3.8669 x 10 -2 = [H + ] pH = - log [H + ] = - log [3.7 x 10 -2 ] = 1.43

14. 14 Or, since weak acids partially dissociate, assume that [HF] init >> [H + ] eq Then, [HF] init – [H + ] ≈ [HF] init pH = - log [H + ] = - log [3.8 x 10 -2 ] = 1.42  General rule: if [H + ]  5% of [HA], it is better to use quadratic formula.

15. 15 Percent Ionization of an Acid Ex: Calculate the % ionization of: 2.0 M solution of HCl 2.0 M solution of HF

16. 16 Polyprotic acids: have more than one H + to “donate” Ex: H 2 SO 3 (aq) ↔ HSO 3 - (aq) + H + (aq) K a1 = 1 st acid-dissociation constant= 1.7 x 10 -2 HSO 3 - (aq) ↔ SO 3 2- (aq) + H + (aq) K a2 = 2 nd acid-dissociation constant = 6.4 x 10 -8 K a1 >K a2 ; 1 st H + dissociates more easily than the 2 nd.

17. 17 * Polyprotic Acids Ascorbic acid (Vitamin C): Citric acid:

18. 18 16.7: Weak Bases Partially ionize in water. B (aq) + H 2 O (l) ↔ BH + (aq) + OH - (aq) K b = base-dissociation constant in water In practice, where x = [OH - ]

19. 19 16.8: Relationship between K a and K b Weak base: NH 3 (aq) + H 2 O(l) ↔ NH 4 + (aq)+OH - (aq) Conjugate acid: NH 4 + (aq) ↔ NH 3 (aq) + H + (aq)

20. 20 NH 3 (aq) + H 2 O (l) ↔ NH 4 + (aq) + OH - (aq) + NH 4 + (aq) ↔ NH 3 (aq) + H + (aq) H 2 O (l) ↔ H + (aq) + OH - (aq) And: Therefore: For a conjugate acid-base pair

21. 21 In general, when two reactions are added to give a 3 rd, the equilibrium constant for the 3 rd reaction equals the product of the equilibrium constants of the two added reactions. Furthermore: For a conjugate acid-base pair

22. 22 16.9: Salt Solutions as Acids & Bases Hydrolysis: acid/base reaction of ion with water to produce H + or OH - Anion (A - ) = a conjugate base A- (aq) + H 2 O (l) ↔ HA (aq) + OH- (aq) Cation (B + ) = a conjugate acid B + (aq) + H 2 O (l) ↔ BOH (aq) + H + (aq)

23. 23 Predicting pH of Salt Solutions Salt typeCationAnion Hydrolyzes to produce pH Consider the relative strengths of the acid and base from which the salt is derived: Strong electrolyte Ex: Ca(NO 3 ) 2 Ca 2+ conjugate acid of strong base Ca(OH) 2 NO 3 - conjugate base of strong acid HNO 3 Neither H + nor OH - 7

24. Salt typeCationAnion Hydrolyzes to produce pH ClO - (aq) + H 2 O (l) ↔ HClO (aq) + OH - (aq) Weak electrolyte Ex: NaClO Na + conjugate acid of strong base, NaOH ClO - conjugate base of weak acid, HClO OH - > 7 where x = [OH - ]

25. Salt typeCationAnion Hydrolyzes to produce pH NH 4 + (aq) + H 2 O (l) ↔ NH 3 (aq) + H 3 O + (aq) Weak electrolyte Ex: NH 4 Cl NH 4 + conjugate acid of weak base, NH 3 Cl - conjugate base of strong acid, HCl H+H+ < 7 where x = [H + ]

26. 26 16.10: Acid-Base Behavior & Chemical Structure Stronger acids, HA, have: 1.H with a higher  + 2.Weaker H-A covalent bond (smaller bond enthalphy) 3.More stable conjugate bases A - Stronger oxyacids, H x O z -Y, have: 1.Central nonmetal “Y” with higher electronegativity 2.More O atoms Ex: Rank these in order from strongest to weakest: HClO, HClO 2, HCl, HBr

27. 27 16.11: Lewis Acids & Bases Lewis acid: “e- pair acceptor” Brønsted-Lowry acid = H + donor Arrhenius acid = produces H + Lewis base: “e- pair donor” B-L base = H + acceptor Arrhenius base = produces OH - Ex: NH 3 + BF 3 → NH 3 BF 3 Lewis baseLewis acidLewis salt 6 CN - + Fe 3+ → Fe(CN) 6 3- Lewis baseLewis acidCoordination compound Gilbert N. Lewis (1875 – 1946)