Environmental Engineering Reference
In-Depth Information
The estimated fraction [ML]/
C
L
is applied to the approach of Ruzic (
1982
). The
conditional stability constants (
K
′
ML
) for complex formation between M and the
ligand, L, assuming simple 1:1 equilibrium can be written as follows (Eq.
3.2
):
[ML]
[
M
]
·
[ML
· α
M
]
(
C
M
−
[ML]
)(
C
L
−
[ML]
)
K
′
ML
=
L
′
=
(3.2)
where
K
′
ML
is the constant with regard to the concentration of free metal ion, [M];
[M′] and [L′] are the total concentrations of all inorganic forms of M and of L
unbound to M, respectively;
α
M
is the inorganic side-reaction coefficient for M
that is estimated to be
α
M
=
[M′]/[M]
=
11 at pH 8.15 under the same conditions
(Midorikawa et al.
1990
).
Substituting for [ML]
=
C
L
X
, Eq. (
3.2
) can be rewritten as (Eq.
3.3
)
1
−
X
X
α
M
K
′
ML
C
M
·
=
C
L
· (
1
−
X
) +
(3.3)
By plotting of
C
M
(1
−
X
)/
X
versus. (1
−
X
), a linear regression is observed by
the least-squares analysis that will give the best-fit values of
C
L
from the slope, and
the conditional stability constant
K′
ML
from the intercept. For the nonlinear diagram,
two 1:1 complexes by two discrete ligand classes with different stability constants
are assumed, which can be treated by another model (van Den Berg
1984
).
3.4 Theory for Protonation Constants of DOM in M-DOM
Complexation
The protonation constants of organic ligands are estimated from the changes in
fluorescence according to the changes in pH with regard to single protonation
(Midorikawa and Tanoue
1998
). The fluorescence (
F
) of the ligand (L) during the
acid-base titration can be expressed by the concentration of each species of the
ligand by the molar fluorescence coefficient (
ε
) as follows (Eqs.
3.4
-
3.6
):
F
H
−
pH
= ε
L
C
L
at high pH
(3.4)
F
L
−
pH
= ε
HL
C
L
at low pH
(3.5)
F
= ε
HL
[
L
]+ε
HL
[
HL
]
at middle pH
(3.6)
where the quantities
F
H-pH
and
F
L-pH
are the limiting fluorescence intensities at either
extreme of the titration:
F
H-pH
is for the free ligand (L) that is dissociated at high pH;
and
F
L-pH
is for HL that is protonated at low pH.
From the mass balance of the ligand,
C
L
=
[L]
+
[HL], the above equations
can be rewritten as follows:
F
H
−
PH
−
F
= (ε
L
− ε
HL
)
[HL]
(3.7)
F
−
F
L
−
PH
= (ε
L
−
ε
HL
)
[L]
(3.8)
