Geology Reference
In-Depth Information
aqueous systems, it is first necessary to consider the relationship between
solute concentration and solute activity.
The activity of a solute is a measure of its observed chemical
behaviour in (aqueous) solution. Interactions between the solute and
other species in solution lead to deviations between solute activity {i} and
concentration [i]. An activity coecient, g
i
, is therefore defined as a
correction factor, which interrelates solute activity and concentration.
{i}
¼
g
i
[i]
(3.1)
Concentration and activity of a solute are only the same for very dilute
solutions, i.e. g
i
approaches unity as the concentration of all solutes
approaches zero. For non-dilute solutions, activity coecients must be
used in chemical expressions involving solute concentrations.
w
Although
freshwaters are suciently dilute to be potable (containing less than
about 1000 mg L
1
total dissolved solids (TDS)),
8
it cannot be assumed
that activity coecients are close to unity.
Calculation of activities using the expression in Equation (3.1) would
appear to be straightforward, requiring only a value for the activity
coe
cient and the concentration of the solute, i. The activity coe
cients
for individual ions, g
i
, cannot, however, be measured. The presence of
both cations and anions in solution means that laboratory experiments
quantifying either the direct (e.g. salt solubility) or indirect (e.g. elevation
of boiling point, depression of freezing point, etc.) effects of the presence
of solutes in aqueous solution generally lead to the mean ion activity
coecients, g
. Traditionally, single-ion activity coecients have been
obtained from the mean values, e.g. using the mean-salt method (Example
3.1),
9,10
but this approach has been shown to be inadequate because it
ignores ion pairing effects at higher solute concentrations.
11,12
This is
generally more significant for anions than for cations because the extent
of anion association at higher solute concentration is much greater.
13
Example 3.1: Determination of single-ion activity coecients for Ca
21
from mean values for CaCl
2
using the mean-salt method.
The solubility of calcium chloride in water can be expressed as
CaCl
2(s)
Ca
2
þ
(aq)
þ
2Cl
(aq)
"
K
SP
w
Concentration is expressed on the molar scale in terms of mol L
1
of solvent or on the molal scale
in terms of mol kg
1
of solvent. The molal scale gives concentrations that are independent of
temperature and pressure. In this chapter, the molar scale will be used on the basis that molarity
and molality are almost identical for the low ionic strengths commonly associated with fresh-
waters.
