Geology Reference
In-Depth Information
ions around itself, aptly described by chemists as the
ionic atmosphere
of the ion concerned. Around each cat-
ion there is a slight statistical preponderance of anions,
and vice versa. Like the phenomenon of hydration
(Box 4.1), this tenuous ion-ion association is sufficient
to depress the free energy of the ions in solution, mak-
ing them less likely to take part in chemical reactions
such as precipitation. The extent of this non-ideality
can be estimated using a simple equation derived by
physicists P.J.W. Debye and E. Hückel in 1923, from a
consideration of the free-energy change associated with
the electrostatic properties of the ionic atmosphere:
Thus in river water the behaviour of univalent ions
(Na
+
, K
+
, HCO
3
−
and Cl
−
) is only marginally non-ideal:
=095. /
o
a
m m
i
i
and assuming ideal behaviour would introduce an
error of only 5% for each of these ions.
The appearance of
z
i
2
in Equation 4.28 (for reasons
similar to those explained in the preceding section)
suggests that divalent ions will show a larger depar-
ture from ideality. For
z
i
= 2,
z
i
2
= and:
log
γ
i
=−0 0937
.
and therefore γ
i
= 0.81
The activity of each divalent ion will therefore be
about 20% below its molality. Thus even at an ionic
strength as low as 0.002 mol kg
−1
, river water is percep-
tibly non-ideal. For example, from equations 4.29 and
4.17 we would expect that sparingly soluble species
like BaSO
4
would be about 25% more soluble than in
pure water.
In addition to dissolved material and sediment, riv-
ers transport some products of weathering and erosion
in the form of colloidal suspension (Box 4.4).
1
2
2
log
10
γ
i
=−
Az I
(4.30)
i
where
γ
i
is the activity coefficient of ionic species
i
;
z
i
is
the charge on ion
i
(±1, 2, 3, etc.);
A
is a constant which
is characteristic of the solvent (
A
=
1
2
1
2
−
. gmol for
water at 25 °C); and
I
is the ionic strength of the solution.
This equation is known as the
Debye-Hückel equation
,
which works accurately for non-ideal solutions of ionic
strength up to 0.01 mol kg
−1
. Conveniently, most fresh
waters fall into this category (broadly
I
< 0.01 mol kg
−1
).
For univalent ions in Table 4.2:
0 509
1
2
1
2
Seawater (
I
= 0.7 mol kg
−1
)
A
=
0 509
. gmol
−
2
z
=±
1
,
therefore
z
=
1
Seawater, as the principal medium of sediment deposi-
tion and the ultimate sink for the dissolved products of
erosion and anthropogenic pollution, is geologically
the most important category of natural water. Analyses
show that it has remarkably constant composition
across the world. Confining attention to the open
oceans, both the
salinity
(the total salt content) and the
concentration ratios between elements vary by less
than 1%. In enclosed basins the composition of sea-
water may vary more widely owing to evaporation or
freshwater runoff.
Table 4.3 shows the global average composition of
seawater. Calculation of the ionic strength, assuming
all the constituents shown are fully ionized, gives
0.686 mol kg
−1
. This is well outside the range of comp-
osition to which Debye-Hückel theory is applicable.
The population of the ionic atmosphere around an
ion in fresh water is essentially transient: ions are too
dispersed for permanent associations between ions to
i
i
I
= 0.0021 mol kg
−1
for average river water.
1
2
1
2
1
2
−
Therefore
I
=
0 046
. mol kg
Thus
log γ
i
= − 0.0234
and so
γ
i
= 0.95
Table 4.2
Composition of average river water
Ion
Concentration
(ppm = mg kg
−1
)
Molality m
i
(10
−3
mol kg
−1
)
HCO
3
−
58.3
0.955
Ca
2+
15.0
0.375
Na
+
4.1
0.274
Cl
−
7.8
0.220
Mg
2+
4.1
0.168
SO
4
2−
11.2
0.117
K
+
2.3
0.059
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