Environmental Engineering Reference
In-Depth Information
E
XAMPLE
5.15 S
ILICA
D
ISSOLUTIONIN
W
ATER
—AH
ETEROGENEOUS
R
EACTION
Mineral weathering is the process of congruent dissolution (without the formation
of new phases) and incongruent dissolution (where new solid phases are formed).
An example of the latter is an aluminosilicate mineral and an example of the former
is a carbonate mineral. The origin of major ions in seawater over geologic times can
be explained as a result of these two processes. The discussion of heterogeneous solid
reactions in this section has a direct bearing on this topic. The five steps involved in the
heterogeneous reaction that we alluded to earlier occur over long periods of time and
cover large surface areas (of sediments) and volumes (of water) and proceed inexorably
toward equilibrium. To illustrate this process, let us consider the dissolution of silica
that forms the most prevalent mineral on earth. From a geochemistry point of view, it
occurs near shores (surface sediments) at ambient temperatures and in the interior of
the earth at exorbitant temperatures. Stumm and Morgan (1996) identified four major
species of silica—quartz,
-cristobolite, and amorphous silica in the order of
stability. The relevant hydration reaction of interest is
α
- and
β
2H
2
O
k
diss
SiO
2
(
s
)
+
k
prec
Si(OH)
4
(
aq
)
(5.147)
with an equilibrium constant
[
Si
(
OH
)
4
]γ
Si
(
OH
)
4
a
H
2
O
·
a
SiO
2
(
s
)
K
eq
=
.
(5.148)
Solid SiO
2
has unit activity (
a
SiO
2
=
1), and since the solution is dilute (
a
H
2
O
=
1).
We also note that the activity coefficient of Si(OH)
4
is one. Thus
K
eq
[
Si
(
OH
)
4
]
.
(5.149)
Hence, the equilibrium constant is the molar solubility of silica. At the ambient
temperature (298 K) and a natural pH of 9.5, the Si(OH)
4
remains undissociated. Since
the above reaction is reversible, the net rate of change of Si(OH)
4
concentration is the
balancebetweendissolution(rateconstant,
k
diss
)andprecipitation(rateconstant,
k
prec
).
Therefore, the following equation was proposed (Rimstidt and Barnes, 1980; Brezonik,
1994):
d
[
Si
(
OH
)
4
]
d
t
A
s
V
w
(k
diss
[
−
=
SiO
2
][
H
2
O
]−
k
prec
[
Si
(
OH
)
4
]
)
.
(5.150)
In dilute solutions we have [SiO
2
][H
2
O
]=
1, using the definition
K
eq
=
k
diss
/k
prec
,
and noting that
β =[
Si
(
OH
)
4
]
/K
eq
is the
saturation ratio
in the aqueous phase
d
d
t
=
A
s
V
w
k
prec
(
1
− β
)
,
−
(5.151)
where
A
s
/V
w
is the surface area of silica per unit volume of water.
The above differential equation can be integrated using the initial condition that at
t
=
0,
β =
0 to obtain
β =
1
−
e
−
((A
s
/V
w
)
·
k
prec
)t
.
(5.152)
continued
Search WWH ::
Custom Search