Environmental Engineering Reference
In-Depth Information
It is clear from the above discussion that the surface charge density is the differ-
ence in surface concentration (mol/m
2
)of
M-OH
2
and
M-O
−
moieties on the
≡
≡
surface. Thus,
σ
e
=[≡
M
−
OH
2
]−[≡
M
−
O
−
]
.
(4.64)
The above equation gives the overall alkalinity or acidity of the surface. If the
species concentrations are expressed in mol/kg, then the overall charge balance can
be written as
OH
−
]−[
H
+
]={≡
OH
2
}−{≡
O
−
}
C
A
−
C
B
+[
M
−
M
−
,
(4.65)
where
C
A
and
C
B
are the added aqueous concentrations of a strong acid and a strong
base, respectively. [OH
−
] and [H
+
] are the aqueous concentrations of base and acid
added. Note that
{}
denotes mol/kg, whereas [ ] represents mol/m
2
for M-OH
2
and
M-O
−
species.
When
σ
e
is zero, there are equal surface concentrations of both species. The pH at
which this happens is called pH
pzc
, the point of zero charge.At the pH
pzc
, the surface
potential,
0. Now, one can relate the pH
pzc
to the intrinsic surface activities by
equating the concentrations of the surface species, [
Ψ →
M-OH
2
] and [
M-O
−
].
≡
≡
p
K
intr
1
p
K
int
2
.
1
2
pH
pzc
=
+
(4.66)
If pH
<
pH
pzc
, the surface has a net positive charge, whereas for pH
>
pH
pzc
, the
surface is negatively charged.
Getting back to the equation for
σ
e
and utilizing the equations for intrinsic
equilibrium constants, one obtains
OH]
H
+
K
intr
1
.
exp
exp
F
K
intr
2
F
RT
RT
H
+
σ
e
=
[
≡
M
−
−
−
(4.67)
We can now substitute in the above expression the equation for
Ψ
in terms of
σ
e
and
getanexplicitequationrelatingthesurfacehydroxylconcentrationto
σ
e
throughionic
strength
I
. A listing of the characteristic values of
K
intr
1
,
K
int
2
, and pH
pzc
for several
commonoxidemineralsisgiveninTable4.11.Inthepresenceofotherionsinaqueous
solution (in addition to H
+
and OH
−
)
, the influence of the specifically sorbed ions
on the surface introduces some complexity into this analysis. These concepts have
been discussed by Stumm (1993) and should be consulted for an in-depth discussion.
The mathematical treatment of surface charges and surface ionization come under the
so-called
surfacecomplexationmodels
(Stumm and Morgan, 1996). The metal cation
adsorption data over a wide range of pH values can be represented by an equation of
the form
ln
D
=
a
+
b
·
pH,
(4.68)
where
D
φ
soln
.
K
sw
is the distribution (partition) constant between
the solid and water,
C
s
is the mass of adsorbent per unit volume of aqueous solution,
=
K
sw
C
s
= φ
sorb
/
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