Appendix V
159 APPENDIX V
Determination of the acidity dependence of the apparent equilibrium constant for complex formation
The reaction to form the ML complex is expressed by the apparent reaction
M f + L f ML T K app
(V.1)
whose equilibrium constant is
] [ ] [
] [
f f app T
L M K ML
= × (V.2)
where [M f ]=[M 3+ ]+[MOH 2+ ]+[M(OH) 2+ ] and [L f ]=[H 2 L + ]+[HL]+[L - ] are the total concentrations of uncomplexed metal and ligand respectively, whereas [ML T ]=[MH 2 L 4+ ]+[MHL 3+ ]+[ML 2+ ] is the sum of the complexes which can be formed according to reactive scheme of the Ga(III)-HQ system:
M 3+ MH 2 L 4+
MHL 3+
M(OH) 2+ +
HL ML 2+
H 2 L +
M(OH) 2+ + H 2 L + +
k 2
k 3 k -3
k -2
k -1
k 1
K A1 K C2
K C1 K H1
H +
H +
H + H +
( I )
( II )
( III )
Appendix V
160
substituting the definition of [ML T ] into equation (V.2) one obtains
] [L ] [M
] [ML ]
[L ] [M
] [MHL ]
[L ] [M
] L [MH ]
[L ] [M
] [ML ] [MHL ]
L K [MH
f f
2
f f
3
f f
4 2 f
f
2 3
4 2
app + ×
+ ×
= ×
×
+
= + + + + + + + (V. 3)
now define
) ] ([
] [ ]
[ ] [ 2
2
f A L
H H K
H L
L H
= +
= + + +
α (V.4)
) ]
([
] [ ]
[ ] [
1 3
f H
M H K
H M
M
= +
= + + +
β (V.5)
] [ ] [
] [
2 3
4
1 + 2 +
+
= ×
L H M
L
K MH (V.6)
] [ ] [
] [
2 2
3
2 + +
+
= ×
L H MOH
K MHL (V.7)
] [ ] [
] [
2 2
3 MOH HL
K ML
= + + × (V.8)
] [
] [ ] [
2
1 +
× +
= H L H
K
AHL (V.9)
] [
] [ ] [
3 2
1 +
+
+ ×
= M
H
K
HMOH (V.10)
Introducing equation (V.4) and (V.5) into equation (V. 3), the latter is reduced to
] [
] [
] [ ]
[ ] [
] [
] [
] [
] [
3 2 2
3 2 3
3 2 2 4 app
2
