14
Acids and bases
※ Definition
 Arrhenius (1859-1927) acid and base (1887)
Acid
A molecule ionizes in water to form a solution
containing H ions
Base
A molecule ionizes in water to form a solution
containing OH ions
 Brønsted acid and base (1923 by Brønsted and Lowry)
Acid: A proton (H+) donor
Base: A proton acceptor

NH3(aq) + H2O(l)  NH4 (aq) + OH(aq)
 Lewis acid and base
Acid: An electron-pair acceptor
Base: An electron-pair donor
Ex.
BF3 + NH3  F3BNH3
Lewis acid
Lewis base
1
※ Acid strength
Hydronium ion
HA(aq) + H2O(l)  H3O(aq) + A(aq)
acid
base
conjugate conjugate
acid
base
 conjugate (共軛) acid-base pair 
Can be represented as
HA(aq)  H(aq) + A(aq)
Dissociation constant
[H3O  ][ A  ] [H ][ A  ]
Ka 

[HA]
[HA]
HA is a strong acid
when Ka is large
or equilibrium lies far to the right
Ka is a measurement of acid strength
Strong acid gives weak conjugate base
Weak acid gives strong conjugate base
pKa = logKa
Ex.
H2O
NH4+
H3O+
H2SO4
HCl
HI
15.7
9.25
1.7
3
6 ~ 7
9.5 ~ 10
2
※ The pH
pH = log[H+]
At neutral condition
pH < 7.00
pH > 7.00
[H+] = 1.0 × 107
pH = 7.00
acidic
basic
※ Calculating pH
 Strong acid: complete dissociation
 The pH of a mixture of weak acids
Ex.
1.00 M HCN
5.00 M HNO2
Ka = 6.2 × 1010
Ka = 4.0 × 104
H2O(l)  H+(aq) + OH(aq)
pH?
Kw = 1.00 × 1014
HNO2 is the strongest acid, the other two can be neglected
3
HNO2 (aq)  H+(aq) + NO2(aq)
ini
final
5.00
5.00－x
0
x
K a  4.0  10  4 
0 (M)
x
x2
x2

5.00  x 5.00
small
x = 4.5 × 102 M = [H+]
pH = 1.35
Check: [H+] is indeed small compared to 5.00 M
(tolerance: ±5%)
HCN (aq)  H+(aq) + CN(aq)
final
1.00－x
4.5 × 102
K a  6.2  10 10 
x
(M)
( 4.5  10 2 ) x ( 4.5  10 2 )x

1.00  x
1.00
x = 1.4 × 108 M = [CN]
Check: [CN] is small indeed
also [H+] is mainly from HNO2
4
※ Percent dissociation
amt dissociated
 100%
initial conc
For weak acid: more dilute higher percent dissociation


HA(aq)  H (aq) + A (aq)
Ka 
x2
x2

[HA ]o  x [HA ]o
x  K a [HA ]o
percent dissociation 
Ka
x
100%  (
)100%
[HA]o
[HA ]o
[HA]o ↓  percent dissociation↑
※ Bases
NaOH(aq), KOH(aq) dissociate completely in H2O
 Strong bases
Ca(OH)2 : similar but solubility is small
does not produce high [OH]
Slaked lime (熟石灰)
Removal of Ca2+ in hard water
CaO + Na2CO3 (the soda lime method)
CaO(s) + H2O(l)  Ca(OH)2(aq)
CO32(aq) + H2O(l)  HCO3(aq) + OH(aq)
Ca(OH)2(aq) + Ca2+(aq) + 2HCO3(aq)  2CaCO3(s) + 2H2O(l)
in hard water
5
◎ Other bases

NH3 (aq) + H2O(l)  NH4 (aq) + OH(aq)
ammonia
pKa = 9.25
Amine bases
N
H
H
methylamine
H3C
N
CH3
H
dimethylamine
H3C
N
C2H5
C2H5
triethylamine
C2H5
N
pyridine
In general
B(aq) + H2O(l)  BH(aq) + OH(aq)
Kb 
[BH ][OH ]
[B]
Kb ↑  base strength ↑
Kw = Ka･Kb
In practice
the base strength is often measured
by the pKa of its conjugate acid
pKa ↑  base strength ↑
6
※ Polyprotic acids
H2SO4, H3PO4 ···
Dissociate stepwise

H3PO4(aq)  H(aq) + H2PO4 (aq)
Ka1 = 7.5 × 103
H2PO4(aq)  H(aq) + HPO42(aq)
Ka2 = 6.2 × 108
HPO42(aq)  H(aq) + PO43(aq)
Ka3 = 4.8 × 1013
In general
Ex.
Ka1 >> Ka2 >> Ka3
For a 5.0 M H3PO4 solution
H3PO4(aq)  H(aq) + H2PO4(aq)
ini
final
5.0
5.0－x
0
x
K a1  7.5  10 3 
0
x
(M)
x2
x2

5 .0  x 5 .0
x = 1.9 × 101 M
Within 5% error
2
2
K a2
[H ][HPO 4 ] (0.19)[HPO 4 ]
2


 [HPO 4 ]  6.2  10 8 M

(0.19)
[H2PO 4 ]
K a3
[H ][PO 4 ] (0.19)[PO 4 ]


2
(6.2  10 8 )
[HPO 4 ]
3
3
[PO43] = 1.6 × 1019 M
7
Ex.
pH of a 1.00 × 10-2 M H2SO4
Complete dissociation for the 1st step
HSO4(aq)  H(aq) + SO42(aq)
ini
0.0100
final 0.0100－x
0.0100
0.0100＋x
K a 2  1.2  10 2 
0
x
(M)
(0.0100  x )x
(0.0100  x )
x = 0.012
Assume 0.0100 >> x
incorrect
x2 + (2.2 × 10-2)x – (1.2 × 10-4) = 0
x = 4.5 × 10-3 M
[H+] = 0.0100 + 0.0045 = 0.0145
pH = 1.840
※ Acid-base properties of salts
 Conjugate base of strong acid
Conjugate acid of strong base
no effect on pH
Conjugate base of a weak acid
NaC2H3O2, KCN, KF ···
Ex.
0.30 M NaF(aq)
Ka for HF: 7.2 × 104
∵ Kw = Ka Kb ∴ Kb = 1.4 × 1011
ini
final


F (aq) + H2O(l)  HF(aq) + OH (aq)
0.30
0
0
(M)
0.30－x
x
x
K b  1.4  10 11 
x2
x2

0.30  x 0.30
x = 2.0 × 106 M = [OH]
8
 Conjugate acid of a weak base
Ex.
Ammonium salt
NH4Cl


NH4 (aq)  H (aq) + NH3(aq)
Ka = 5.6 × 1010
A 0.10 M solution  pH = 5.13
 With highly charged metal ion
Ex.
Al(H2O)63+
AlCl3(s) + 6H2O(l)  Al(H2O)63+(aq) + 3Cl(aq)
3+
2+

Al(H2O)6 (aq)  Al(OH)(H2O)5 (aq) + H (aq)
Ka = 1.4 × 105
A 0.010 M solution  pH = 3.43
 Both ions affect the pH
Ex.
+

NH4 C2H3O2
ammonium acetate
Basic; Kb = 5.6 × 1010
Acidic; Ka = 5.6 × 1010
Ka > Kb
Ka < Kb
Ka = Kb
Ex.
acidic
basic
neutral
NH4+CN
basic
Kb = 1.6 × 105
9
Ex.
pH of a 0.100 M NH4CN


NH4 (aq)  H (aq) + NH3(aq)
Ka = 5.6 × 1010
CN(aq) + H2O(l)  HCN(aq) + OH(aq)
Kb = 1.6 × 105
H2O(l)  H+(aq) + OH(aq)
Kw = 1.0 × 1014
NH4(aq) + CN(aq)  NH3(aq) + HCN(aq)
K
K a(NH  )
[NH3 ][HCN] [NH3 ][H ]
[HCN]
4



 0.90





[
H
][
CN
]
K
[NH4 ][CN ]
[NH4 ]
a(HCN )
The dominate process
※ The effect of structure
◎ Brønsted-Lowry acid
XH
Potentially acidic
Two major factors
the strength: stronger bond  weaker acid
the polarity: more polar  stronger acid
Ex.
In the same period
HCH3
HNH2
HOH
Least polar
Weakest bond
HF
Most polar
Strongest bond
Acidity (polarity factor)
10
Ex.
Down a group
HF
HCl
HBr
Most polar
Strongest bond
HI
Least polar
Weakest bond
Fact: HI is the strongest acid in water
Q: Is it due to bond strength factor?
BE of H-X Hosolvation for Sosolvation for electron affinity
(kJ/mol)
X (kJ/mol) X (J/K･mol)
(kJ/mol)
F
565
510
159
327.8
Cl
427
366
96
348.7
X
Br
I
334
291
363
295
HX(aq)
G
81
64
H(aq) + X(aq)
G1
HX(g)
324.5
295.2
G5
G6
G2
G3
H(g)
e + H(g)
+
G4
X(g) + e
G1: reverse of the solvation of HX
G2: bond energy data
G3: ionization data of H atom
G4: electron affinity data of X atom
G5: solvation of proton
G6: solvation of halide
X(g)
G = G1 + G2 + G3 + G4 + G5 +G6
Overall: the halide solvation entropy change is the
determinant factor
Note: in the same period the sizes of Xs are similar
11
◎ Oxyacids
containing H-O-X structure
O
H O Cl O
O
Ex.
~107
Ka
O
H O Cl
O
H O Cl O
H O Cl
~1
1.2 × 102
3.5 × 108
 More oxygen attached to the central atom
 more acidic
Ex.
HOCl
HOBr
Ka
4 × 108
2 × 10
HOI
2 × 1011
 With more electronegative atom attached to O
 more acidic
◎ Oxides
H-O-X can also behave as a base
Releasing OH: NaOH, KOH, ····
(X is electropositive or O-X is weak)
Basic
oxide
CaO(s) + H2O(l)  Ca(OH)2(aq)
Actually Ca2+ and O2
12
Acidic
oxide
SO3(g) + H2O(l)  H2SO4(aq)


O
O
S
More covalent
O
O
H O S O H
O
Based on Lewis acid-base model
SO3 is a Lewis acid
H2O is a Lewis base
13