Lewis Acid-Base
C. P. Huang
University of Delaware
1
Content
1.
2.
3.
4.
5.
6.
7.
8.
Definition
Complex formation equilibrium
Inorganic complexes
Metal ion as Lewis acid
Metal ion hydrolysis
Chelates
Conditional stability constants
pM as a master variable
2
1.0 Definition
• By C. N. Lewis in 1923
• Lewis acid: electron pair acceptor
• Lewis base: electron pair donor
http://www.meta-synthesis.com/index.html
3
Definition
Species in which central atom is involved in multiple
bonds to (electronegative) terminal atoms are potential
Lewis acids
H
|
+
H + :N--H-- H 
|
H
..
Co2+ + :O --H 
|
H
H
|
H-- N --H
|
H
Co2+ 
..
:O --H
|
H
H
|
H-- N: +
|
H
H+ +
F
H F
|
| |
B --F  H-- N -- B --F
| |
|
H F
F
..
..
|
H
|
H
:O --H  H -- O --H
4
Definition
Species in which central atom is involved in
multiple bonds to (electronegative) terminal
atoms are potential Lewis acids
Cu2+
+
H
|
4 :N --H 
|
H
H
|
H-- N --H
|
H
H
|
|
|
H-- N---- Cu ----N--H
|
|
H
|
H
|
H-- N-- H
|
H
5
Definition
LA + LB = Complex
Hemoglobin (Iron complex)
Chlorophyll (Magnesium complex)
Vitamin B12 (Cobalt complex)
6
Chlorophyll a
Vitamin B12
hemoglobin
7
8
Lewis Base-Ligand
..
NH2
..
NH2
bidentate
NH
.. 2
..
NH2
tridentate
NH
.. 2
• Central atom: metal ion (LA)
• Ligand: anion or molecule that forms coordination
compounds (LB)
• Ligand atoms: atoms of ligand that donating free
pairs of electron
• Monodentate: ligand occupying only 1 position.
• Bidentate:ligand occupying 2 positions
• Tridentate:ligand occupying 3 positions
• Chelation: complex formation with multidentate
ligand.
9
Type of complexes
• Ion pairs: ions of opposite charge that approach within a
critical distance effectively form an ion pair and are no
longer electrostatically effective. Metal ion and the base
are separated by one or more water molecules (Outer
sphere complexes)
• Complexes: Most stable entities that result from the
formation of largely covalent bonds between a Lewis
acid and a Lewis base (inner sphere complexes)
• Chelates: Metal ion and base form 3D framework with
multiple ligand atoms.
10
2.0 Complex Formation Equilibrium
M + L = ML; K1
ML + L = ML2; K2
ML2 + L = ML3; K3
M+ L = ML; β1
M + 2 L = ML2; β2
M + 3L = ML3; β3
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Stumm & Morgan
M + HL = H+ +ML; *K1
ML + HL = H+ + ML2; *K2
ML2 + HL = H+ + ML3; *K3
M+ HL = H+ ML; *β1
M + 2HL = 2H+ + ML2; *β2
M + 3HL = 3H+ + ML3; *β3
12
mM + nL = MmLn; βnm
mM + nHL = MmLn + nH+; *βnm
13
Formation Curve
M + iL = ML i ; β i
β1 [L] + β 2 [L]2 + β 3 [L]3 + β 4 [L]4 + ... + β N [L]N
n=
1 + β1 [L] + β 2 [L]2 + β 3 [L]3 + β 4 [L]4 + ... + β N [L]N
[MLi ]
β i=
[M ][L]i
n = (1 − n )β1 [L] + ( 2 − n )β 2 [L]2 + ....(N − n )β N [L]N
N
MT = [M ] + ∑ [MLi ]
1
N
MT = [M ] + ∑ β i [M ][L]
1
N
n=
∑ [ML ]
i
1
MT
N
= ∑ iα i
i
N
n = ∑ (i − N )β i [L]
i
1
1
α i = α 0 β i [L]i
14
Stability Constant
When N = 2
n
1 − n [L]
(
β1 [L] + β 2 [L]2
n=
1 + β1 [L] + β 2 [L]2
(
β 2 [L ] 2 − n
n
− β1 =
1− n
1− n
(
)
(
)
)
β2
)
β1
(2 − n )[L]
(1 − n )
15
Log K= 8; 5; 2
Log β = 8, 13, 15
16
Log K = 5; 4.5; 4
Log β = 5, 9.5, 13.5
17
Log K =7; 3; 4
Log β = 7, 10, 14
18
Log K = 4; 5; 6
Log β = 4, 9, 15
19
Formation Curve
20
3.0 Inorganic Complexes
21
Al(III)-F(-I) System
Al3+ +F- =AlF2+; log β1 =6.164
Al3+ + 2F- =AlF2+; log β2 =5.053
Al3+ + 3F- = AlF3; log β3 = 3.91
Al3+ +4F- = AlF4-; log β4 = 2.71
Al3+ + 5F- = AlF52-; log β5 = 1.46
Al3+ + 6F- = AlF63-; log β6 = 2.7
22
Al(III)-F(-I) System
[Al(III)] = [Al3+] + [AlF] +[AlF2] +[AlF3] +[AlF4] +[AlF5] + [AlF6]
[Al(III)] = [Al3+] +K1[Al3+][F-] +β2[Al3+][F-]2 +β3[Al3+][F-]3 +β4[Al3+][F-]4
+β5[Al3+][F-]5 +β6[Al3+][F-]6
[Al(III)] =[Al3+](1+β1[F-]+β2[F-]2+β3[F-]3+β4[F-]4+β5[F-]5+β6[F-]6)
α0=[Al3+]/[Al(III)]=1/(1+β1[F-]+β2[F-]2+β3[F-]3+β4[F-]4+β5[F-]5+β6[F-]6)
α1=[AlF]/[Al(III)]=β1[F-]α0
α2=[AlF2]/[Al(III)]=β2[F-]2α0
α3=[AlF3]/[Al(III)]=β3[F-]3α0
α4=[AlF4]/[Al(III)]=β4[F-]4α0
α5=[AlF5]/[Al(III)]=β5[F-]5α0
α6=[AlF6]/[Al(III)]=β6[F-]6α0
23
Al(III)-F(-I) System
Log K1 = 6.16
Log K2 = 5.05
Log K3 = 3.91
Log K4 = 2.71
Log K5 = 1.46
Log K6 = 2.7
Log β1 = 6.16
Log β2 =log (K1K2) = 11.21
Log β3=log (K1K2K3) = 15.13
Log β4 = log (K1K2K3K4) =17.84
Log β5 = log (K1K2K3K4 K5) = 19.30
Log β6 = log (K1K2K3K4K5K6) = 22.0
24
K1 = 101.5
K2 = 100.7
K3 = 10-0.1
K4 = 10-0.07
Cd(II)-Cl(-I)
β1= 1.5
β2= 2.2
β3 = 2.3
β4 = 1.6
25
Cd(II)-Cl(-I) System
6
[i]/[Cd] vs. log[Cl]
4
2
0
[i]/[Cd]
-12
-10
-8
-6
-4
-2
0
-2
Cd/Cd
CdCl/Cd
CdCl2/Cd
CdCl3/Cd
CdCl4/Cd
-4
2
[Cd]/[Cd]=1
[CdCl]/[Cd]=α1/α0
[CdCl2]/[Cd]=α2/α0
[CdCl3]/[Cd]=α3/α0
[CdCl4]/[Cd]=α4/α0
-6
-8
-10
log[Cl]
26
27
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4.0 Metal Ions as Lewis Acid
29
Occurrence of forms of metal species
30
Proton and meal ions
31
32
Acidity of metal ions
33
Mn+ + H2O = MOHn-1 + H+; *K1
pK1*
Hg2+
Pb2+
Ca2+
Cu2+
Zn2+
Co2+
Ni2+
-5
-8
-9
-9
-10
-11
-11.5
34
Stumm & Morgan
35
Stumm & Morgan
36
37
38
39
5.0 Metal Ions Hydrolysis
40
41
Metal ion Hydrolysis
42
Hg(II)-H2O System
Log β1=10.0
Log β2 =21.8
Log β3 = 20.9
43
Al(III)-H2O system
1.2
1
a
0.8
b1
b2
9.01
b3
17.8
a1
a2
b4
25.5
a0
0.6
33.4
0.4
a3
0.2
a4
0
0
2
4
6
8
10
12
14
12
14
pH
a
n
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
a1
a2
a3
a4
n
n
a0
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
n
0
0
2
4
6
8
pH
10
12
14
2
4
6
8
10
pH
44
45
46
47
48
Metal Ion Hydrolysis
FeT=[Fe3+] +[Fe(OH)2+] +[Fe(OH)2+] + 2[Fe2(OH)24+]

* K1
* β2
2[ Fe3+ ] * β 22 

+
+
FeT = [ Fe ]1 +
+
+ 2
+ 2
[H ]
 [H ] [H ]

3+

* K1
* β2
2[ Fe3+ ] * β 22 

α 0 = 1 + + + + 2 +
+ 2
[H ]
 [H ] [H ]

−1
2α 0 [ Fe3+ ] * β 22
* β2
 * K1

+
+
+
α
1

 −1 = 0
0
+
+ 2
[ H + ]2
[
]
[
]
H
H


α 22 = 2 [[ H ]]
α 0 Fe3+ β 22
+ 2
α1 =
α 0 * K1
[H + ]
α0 * β 2
α2 =
[ H + ]2
FeT = [ Fe3+ ](1 + β1[OH − ] + β 2 [OH − ]2 + 2 β 22 [ Fe3+ ][OH − ]2 )
α 0 = (1 + β1[OH − ] + β 2 [OH − ]2 + 2 β 22 [ Fe3+ ][OH − ]2 )
−1
α 0 (1 + β1[OH − ] + β 2 [OH − ]2 ) + α 0 (2 β 22 [ Fe3+ ][OH − ]2 ) = 1
49
FeT = [ Fe3+ ](1 + β1[OH − ] + β 2[OH − ]2 + β 3[OH − ]3 + β 4 [OH − ]4 + 2[ Fe3+ ]β 22 [OH − ]2 + β 43[ Fe3+ ]2 [OH − ]4 )
50
Fe(III) =10-9 M
51
Fe(III)= 10-4 M
Fe(III) = 10-2 M
52
53
54
55
6.0 Chelates
56
57
58
59
60
Stumm & Morgan
61
62
63
64
7.0 Conditional Stability Constant
[CuY 2− ]
K=
[Cu2+ ][ Y 4 − ]
[CuY 2− ]
=
Y
CuT α Cu
Y
α
0
T 4
[CuY 2− ]
Y
= Kα Cu
α
o
4 = K'
CuT YT
65
66
67
68
Example
Calculate the conditional stability of Al(III)-EDTA
complexes at pH 10
Al(III): log K1 = 9.01; log β2 = 17.8; log β3 = 25.5 log β4 = 33.4
Y(IV): log K1 =2.07; log K2 = 2.74; log K3=6.24; log K4 = 10.34
At pH = 10
K=1016.1
1.57x10
−2
[ AlY −1 ]
=
AlT YT
α0 =
1
1 + K1[OH− ] + β 2 [OH− ]2 + β 3 [OH− ]3 + β 4 [OH− ]4
= 3.98x10 −18
α Y4 =
K 1K 2K 3K 4
[H+ ]4 + K 1[H+ ]3 + K 1K 2 [H+ ]2 + K 1K 2K 3 [H+ ] + K 1K 2K 3K 4
= 0.3137
K' = Kα 0Alα 0Y = 1016.110 −17.4 (0.3137) = 1.57x10 −2
69
8.0 pM as a Master Variable
pM = -log[M]
M + L = ML
LT = [L] + [ML]
MT = [M] + [ML]
MT = [M] + [ML]
= [M] + K[M][L]
= [M] (1+ K[L])
70
pM as a Master Variable
pM = -log[M]
M + L = ML
LT = [L] + [ML]
MT = [M] + [ML]
MT = [M] + [ML]
= [M] + K[M][L]
= [M] (1+ K[L])
71
Metal ion buffers
72
Mg + L = MgL; K=108.69
α(L) = 0.45
73
∑ [H Y ] = [Y
i
T
− CaT ]
[Ca2+] = 4.12x10-5 (pCa=4.39)
74
75
76
CaT = 9.82x10-3 M
CaT = 9.80x10-3 M
dCaT= 2x10-5 M
[Ca2+] = 4.12x10-5 M [Ca2+] = 4.027x10-5 M
pCa = 4.395
dpCa = 0.005
pCa= 4.390
=(2x10-5)/(0.005) = 4x10-3 M/pCa
77
Metal ion buffer capacity
dL T
dMT
βM = −
=
dpM dpM
MT = [M ] + [ML]
= [M ] + LT α ML
= [M ] + MT α ML
α ML =
[M ]
1
+ [M ]
K
=
[L ]
1
+ [L ]
K
pM = − log[M]
d[M]
dpM = −
2.3[M]
1

1
 + [M]  − [M]
dα ML  K

K
=
=
2
2
d[M]
1

1

 + [M] 
 + [M] 
K


K

1
2.3[M ] 
LT dα ML
 K  = −2.3L α α
=−
T ML L
2
dpM
1


 + [M ] 

K
dMT
d [M ] d [ML]
βM = −
=−
−
dpM
dpM dpM
= 2.3([M ] + LT α MLα L )
= 2.3([M ] + LT α ML (1 − α ML ))
78
Metal ion buffer capacity
K = 105
K = 103
79
80