CH 16: ACID-BASE EQUILIBRIA
Brown, LeMay Ch 16
AP Chemistry
Monta Vista High School
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
NH3 (aq) + H2O (l) ↔ NH4+ (aq) + OH- (aq)
2
16.2: DISSOCIATION OF WATER

Autoionization of water:
H2O (l) ↔ H+ (aq) + OH- (aq)


[ H ][OH ]
Kc 
[ H 2O ]


-14
 [ H ][OH ]  1.0 x 10  K w
KW = ion-product constant for water

H3O+ (aq) or H+ (aq) = hydronium
1000 g 1 mol

 55.6 M
[H 2 O (l)] 
1 L 18.0 g
3
16.3: THE PH SCALE
pX = -log [X]
pH = -log [H+] = -log [H3O+]
or [H+] = 10-pH
pOH = -log [OH-] or [OH-] = 10-pOH
[H+][OH-] = KW = 1.0x10-14
-log ([H+][OH-]) = -log KW
-log [H+] + -log[OH-] = -log (1.0x10-14)
pH + pOH = 14.00
4
pOH
pH
0
14
[H+] = [OH-]
7
Since
[H+][OH-] = 1.0x10-14
[H+] = [OH-] = 1.0x10-7
pH = -log[1.0x10-7] = 7.00 (neutral)
7
16.3: THE PH SCALE
 If
[H+]<[OH-], then [H+]<1.0x10-7
Ex: pH = -log[1.0x10-10] = 10.00 (basic)
 If
 If
[H+]>[OH-], then [H+]>1.0x10-7
14
Ex: pH = -log [1.0x10-3] = 3.00 (acidic)
5
0
16.4: BRØNSTED-LOWRY ACIDS & BASES
 Johannes
Brønsted (Denmark)
Thomas Lowry (England),
1923
 Brønsted-Lowry
acids: H+ donor
 Brønsted-Lowry bases: H+ acceptor
NH3 (aq) + H2O (l) ↔ NH4+ (aq) + OH- (aq)
Base
Acid
6
CONJUGATED ACID-BASE PAIRS

For acid “HA”:
HA (aq) + H2O (l) ↔ A- (aq) + H3O+ (aq)
conjugate conjugate
acid
base
base

acid
For base “B”:
B (aq) + H2O (l) ↔
base
acid
HB+ (aq) + OH- (aq)
conjugate
acid
conjugate
base
7
AMPHOTERISM

Amphoteric: capable of acting as either an acid or base
H2O (l) ↔
OH- (aq) + H+(aq)
Acting as a base
Acting as an acid
8

* Amphiprotic: can accept or donate a p+
Amphoterism Contd.
Many transition metal oxides and hydroxides act as
amphoteric substances. Most common amphoteric
substance is water.
Zinc Oxide acting amphoteric:
 In acid: ZnO + 2H+ → Zn2+ + H2O
 In base: ZnO + H2O + 2OH- → [Zn(OH)4]2Al(OH)3 acting amphoteric:
 Base (neutralizing an acid): Al(OH)3 + 3
HCl → AlCl3 + 3H2O
 Acid (neutralizing a base): Al(OH)3 +
NaOH → Na[Al(OH)4]
9
Partner Activity:
Write balanced net ionic equations
with a partner showing how Al(OH)3
behaves as an acid and a base
Ex:
Al (OH)3 + OH-  Al (OH) 4- + H2O
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.

HSO4- + CO32- ↔ SO42- + HCO3Stronger acid
Stronger base
11
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, HClO4, HClO3, H2SO4, HNO3
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
12
16.6: WEAK ACIDS

Weak acids partially ionize in water
(equilibrium is somewhere between ions and
molecules).
HA (aq) ↔ A- (aq) + H+ (aq)


[ H ][ A ]
Ka 
[ HA]eq
Ka = acid-dissociation constant in water
 Weak acids generally have Ka < 10-3
 See Appendix D for full listing of Ka values
13
Ex: Calculate the pH of 2.0 M HCl solution (Ka≈106)
 Strong acid, completely dissociated
 HCl (aq) → H+ (aq) + Cl- (aq)
HCl (aq)
H+ (aq)
Cl- (aq)
Initial
2.0 M
0M
0M
Change
- 2.0 M
+ 2.0 M
+ 2.0 M
Final
0M
2.0 M
2.0 M
So:
[HCl]initial = [H+]final = [Cl-]final = 2.0 M
pH = - log [H+] = - log [2.0] = -0.30
14
Ex: Calculate pH of 2.0 M HF solution (Ka=7.2x10-4)
 Weak acid, partially dissociated
 HF (aq) ↔ H+ (aq) + F- (aq)
HF (aq)
H+ (aq)
F- (aq)
Initial
2.0 M
0M
0M
Change
-xM
+xM
xM
+xM
xM
(2.0 – x) M


2
[
H
][
F
]
(
x
)(
x
)
x
-4
Ka  7.2  10 


[ HF ]eq
[ HF ]initial  x
2 .0  x
Equilibrium
Using quadratic eq’n, 0 = x2 + 7.2 x 10-4x – 1.44 x 10-3
x = 3.7229 x 10-2 or – 3.8669 x 10-2 = [H+]
15
pH = - log [H+] = - log [3.7 x 10-2] = 1.43
Or, since weak acids partially dissociate, assume
that [HF]init >> [H+]eq
Then, [HF]init – [H+] ≈ [HF]init
2
2
x
x
7.2 10 

2.0  x 2.0
3
2
1.4 10  x
4
x  1.4 103  3.8 102  [ H  ]
pH = - log [H+] = - log [3.8 x 10-2] = 1.42
16
 General rule: if [H+]  5% of [HA], it is better to use
quadratic formula.

Percent Ionization of an Acid

% Ionization 
[H ]eq
[HA] in it
100%
Ex: Calculate the % ionization of:
•2.0 M solution of HCl
[2.0]
% Ionization 
100%  100%
[2.0]
•2.0 M solution of HF
-2
[3.8x10 ]
% Ionization 
100%  1.9%
[2.0]
17

Polyprotic acids: have more than one H+ to
“donate”
Ex: H2SO3 (aq) ↔ HSO3- (aq) + H+ (aq)
Ka1 = 1st acid-dissociation constant
10-2
= 1.7 x
HSO3- (aq) ↔ SO32- (aq) + H+ (aq)
Ka2 = 2nd acid-dissociation constant = 6.4 x 10-8

Ka1>Ka2; 1st H+ dissociates more easily than the
18
2nd.
* POLYPROTIC ACIDS

Ascorbic acid (Vitamin C):

Citric acid:
19
16.7: WEAK BASES

Partially ionize in water.
B (aq) + H2O (l) ↔ BH+ (aq) + OH- (aq)


[ BH ][OH ]
Kb 
[ B ]eq
Kb = base-dissociation constant in water
In practice,


2
x
( x)( x)
[ BH ][OH ]


Kb 
[ B ]initial  x [ B]initial
[ B ]eq
20
where x = [OH-]
16.8: RELATIONSHIP BETWEEN KA AND KB
Weak base: NH3(aq) + H2O(l) ↔ NH4+(aq)+OH(aq)


[ NH 4 ][OH ]
Kb 
[ NH 3 ]
Conjugate acid: NH4+(aq) ↔ NH3(aq) +
H+(aq)

[ H ][ NH 3 ]
Ka 

[ NH 4 ]
21
NH3 (aq) + H2O (l) ↔ NH4+ (aq) + OH- (aq)
+
NH4+ (aq) ↔ NH3 (aq) + H+ (aq)
H2O (l) ↔ H+ (aq) + OH- (aq)
And:



[ NH 4 ][OH ] [ NH 3 ][ H ]
Kb  K a 


[ NH 3 ]
[ NH 4 ]

Therefore:

 [OH ][ H ]
K b  K a  K w  1.0 10
14
For a
22
conjugate
acid-base pair

In general, when two reactions are added to give
a 3rd, the equilibrium constant for the 3rd reaction
equals the product of the equilibrium constants of
the two added reactions.
Furthermor
Kb  K a
e:
14
 K w  1.0 10
14
 log( K b  K a )   log K w   log( 1.0 10 )
 log Kb   log K a   log K w  14.00
pKb  pK a  pK w  14.00
For a
23
conjugate
acid-base pair
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) + H2O (l) ↔ HA (aq) + OH(aq)
 Cation
(B+) = a conjugate acid
B+ (aq) + H2O (l) ↔ BOH (aq) + H+
(aq)
24
PREDICTING PH OF SALT SOLUTIONS
Consider the relative strengths of the acid
and base from which the salt is derived:
Salt type
Cation
Anion
Strong electrolyte
Ca2+
NO3-
Ex: Ca(NO3)2
conjugate acid
of strong base
Ca(OH)2
conjugate base
of strong acid
HNO3
Hydrolyzes
pH
to produce
Neither H+ nor
OH-
7
25
Salt type
Cation
Anion
Na+
ClO-
conjugate acid
of strong base,
NaOH
conjugate base
of weak acid,
HClO
Hydrolyzes
pH
to produce
Weak electrolyte
Ex: NaClO
OH-
ClO- (aq) + H2O (l) ↔ HClO (aq) + OH- (aq)

( x)( x)
[ HClO ][OH ]

Kb 


[ClO ]initial  x
[ClO ]eq
2
Kw
x
Kb 

-]

where
x
=
[OH
K a [ClO ]initial
>7
Salt type
Weak electrolyte
Ex: NH4Cl
Cation
Anion
NH4+
Cl-
conjugate acid
of weak base,
NH3
conjugate base
of strong acid,
HCl
Hydrolyzes
pH
to produce
H+
NH4+ (aq) + H2O (l) ↔ NH3 (aq) + H3O+ (aq)

[ NH 3 ][ H ]
Ka 

[ NH 4 ]eq
( x)( x)


[ NH 4 ]initial  x
Kw
x2
Ka 

where x = [H+]

K b [ NH 4 ]initial
<7
16.10: ACID-BASE BEHAVIOR & CHEMICAL
STRUCTURE



Strength of acids and bases explained by proton source
and sink
Stability of their anions, factors affecting stability of
anions
Stronger acids, HA, have:
1.
2.
3.

H with a higher d+
Weaker H-A bonds (smaller bond energies)
More stable conjugate bases A-
Stronger oxyacids, HxOz-Y, have:
1.
2.
Central nonmetal “Y” with higher electronegativity
More O atoms
28
Ex: Rank these in order from strongest to weakest: HClO,
HClO2, HCl, HBr
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 OHGilbert N. Lewis
(1875 – 1946)
Ex:
NH3 +
BF3
→
Lewis baseLewis acid
NH3BF3
Lewis salt
6 CN+
Fe3+
Lewis baseLewis acid
→
Fe(CN)6329
Coordination compound