Environmental Engineering Reference
In-Depth Information
3.2.4 I
ONIC
S
TRENGTH AND
A
CTIVITY
C
OEFFICIENTS
The activities of dissociating (ionic) and nondissociating (neutral) species in aqueous
solutions are influenced by the
ionic strength
of the solution. Ionic strength is the
combined effect of all ionic species in water.
The ionic strength (denoted
I
)isgivenby
1
2
·
m
i
z
i
,
I
=
(3.14)
i
where
m
i
is the molality of species
i
(mol/kg) and
z
i
is the charge of species
i
in solu-
tion. Ionic strength has units of mol/kg. For example, if we consider a 1:1 electrolyte
(
z
+
=
m
. Note that
I
is always a positive
quantity and is additive for each species in solution.
Theactivityofdissociating(ionic)speciesisrelatedto
I
throughtheDebye-Huckel
equation, which is described in Section 3.4.3.5. It is based on the fact that long-range
and Coulombic forces between ions are primarily responsible for departures from
ideality in solutions. It suffices to summarize the final equation in this context. The
Debye-Huckel theory has been modified and extended to higher ionic strength values.
These are summarized in Table 3.3 (Pankow, 1992; Stumm and Morgan, 1996).
For nondissociating (neutral organic) species, the effect of ionic strength
I
on
activity coefficient is given by the McDevit-Long theory, which predicts an equation
whose general form is log
1;
z
−
=−
1), then
I
=
0.5
(m
+
+
m
−
)
=
γ
i
=
kI
, where
k
depends on the type of ionic species in
solution and also on the temperature and pressure.
k
is specific to the species
i
of
concern. Because of the dependence of
k
on both the nature of the species
i
and the
ions, a universal equation for the effect of
I
on the activity coefficients of neutral
species is not likely. Positive
k
values indicate that salts tend to make the solvent less
TABLE 3.3
Relationships between Ionic Strength (
I
) and Mean Ionic Activity
Coefficient (
γ
±
)
Name
Equation
Range of
I
log
γ
±
=−
Az
i
√
I
I <
10
−
2.3
Debye-Huckel
√
I
1
+
B
√
I
log
γ
±
=−
Az
i
I <
10
−
1
Extended Debye-Huckel
√
I
1
+
√
I
γ
±
=−
Az
i
I <
10
−
1
Guntelberg
log
√
I
1
+
√
I
−
0.2
I
log
γ
±
=−
Az
i
Davies
I <
0.5
Source:
FromPankow,J.F.1991.
AquaticChemistryConcepts
.Chelsea,MI:LewisPublishers.
Note:
Parameters
A
and
B
depend on temperature and di-electric constant of the liquid. For
water at 298 K,
A
=
0.51 and
B
=
0.33. The parameter
a
is an ion size parameter and
is listed by Pankow (1992). Note that
z
i
=|
z
+
||
z
−
|
.
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