Geology Reference
In-Depth Information
concentrations
a
i
) is the quantity in brackets above, and
this can vary in non-ideal solutions according to the
values of the activity coefficients.
Why does the charge of each ion
z
i
appear in this for-
mula as
z
i
2
rather than just
z
i
? A rigorous explanation
would require a digression into electrostatic field the-
ory (Atkins and de Paula, 2009), but we can see that
the appearance of
z
i
2
is plausible in the following way.
The force attracting ion
i
to one of its oppositely
charged neighbours is proportional to
z
i
: if
z
i
= 2, the
ion will be twice as strongly attracted at a given dis-
tance as it would be if
z
i
= 1. But the stronger attraction
will tend to draw ion
i
closer to the neighbour, increas-
ing the attraction still further, making it more than
twice as strong as that felt by a singly charged ion.
This relationship is represented more faithfully by
m
i
2
than
m
i
z
i
.
Natural waters span a considerable range of ionic
strength, as these representative figures show:
Ionic strength
The activity coefficient
γ
i
for a particular species
i
depends upon the concentrations of all the solutes
present in the solution. How is this overall 'strength'
of the solution to be expressed?
Because departures from ideality arise from electro-
static interaction between ions, it is logical to devise a
parameter that combines the amount of each type of
ion present in solution and the charge on the ion. This
is accomplished by the
ionic strength,
introduced by
the American chemists G.N. Lewis and M. Randall in
1921. The ionic strength
I
of a solution is given by the
formula
I
/mol kg
−1
River water
<0.01
Seawater
0.7
=
∑
2
I
ii
i
1
2
(4.28)
Brines
1-10
Different values of the integer subscript
i
(1, 2, 3, etc.)
identify in turn the various ionic species present in
the solution.
m
i
is the molality of ionic species
i
(which
can be established from a chemical analysis of the
solution) and
z
i
is the charge on the ion concerned,
expressed as a multiple of the charge on an electron.
The summation symbol Σ
i
means adding together
the
m
i
2
terms for all the values of
i
(i.e. for every ion
species in solution).
Consider a solution in which NaCl is present at a
molality of 0.1 mol kg
−1
and BaF
2
has a molality of
0.005 mol kg
−1
(i.e. below saturation). The ionic strength
I
of this solution is given by:
Natural waters
There is no universal theoretical treatment capable of
predicting non-ideal behaviour across the whole range
of ionic strengths given above. The degree of inter-
ionic attraction and repulsion and their influence on
the properties of a solution change considerably as the
ionic strength increases. It will be helpful to divide the
spectrum of natural waters into smaller ranges of ionic
strength, for which different assumptions and approxi-
mations apply.
River water (
I
< 0.01 mol kg
−1
):
Debye-Hückel Theory
Values in equation
What they represent
(
)
2
2
I
=
1
2
.
01 1
.
×
1
2
.
m
⋅
z
+
+
Na
Na
Table 4.2 shows the principal dissolved constituents of
average river water. The reader can confirm that its
ionic strength is about 0.002 mol kg
−1
. Solutions as dilute
as this exhibit the weakest ionic interactions, because
the ions are widely separated from each other. There is
nevertheless a tendency for each ion to attract a diffuse,
continually changing jumble of oppositely charged
⋅
(
)
2
+×
01 1
.
2
mz
−
−
Cl
Cl
⋅
(
)
2
+
×
2
0 005 2
.
mz
(4.29)
2
+
2
+
Ba
Ba
⋅
(
)
2
(
)
2
+×
20005
.
×
1
mz
F
−
−
F
=
0 115
. mol kg
−
1
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