18 - Lecture notes for Clay Mineralogy
The Geochemistry of clay minerals
Suggested reading:
Background reading on principles of chemistry of natural waters.
Drever, James I., 1997 The Geochemistry of Natural Waters: Surface
and Groundwater Environments. Prentice Hall, Upper Saddle River, NJ.436
P.
Langmuir, Donald, 1997 Aqueous Environmental Geochemistry. Prentice
Hall, Upper Saddle River, NJ.600 P.
Determination of activity coefficients - primary concern is with
the determination of g for dissolved species
in interstitial solutions.
Several simplifying assumptions:
Assume that concentration (C) represents the sum of free ions plus
ion pairs and complexes.
For example for dissolved silica species:
C Si 4+ = C H 4 SiO
4 o + C H 3 SiO 4
- + C H 2SiO 4 2-
Case for dissolved potassium species:
C K + = C K +
+ C KSO 4 -
Case for dissolved calcium species:
C Ca 2+ = C Ca 2+
+ C CaSO 4 - + C
CaCO 3 o + C CaHCO 3+
Using this convention, the activity coefficient g
becomes the total activity coefficient g
T , where:
g T = a /C T
This effect is important under conditions of high concentrations of dissolved
ions, such as in sea water.
* see Table below from Berner 1980. Total activity coefficients for the
major ions in seawater. T = 25°C, P = 1 atm., Salinity = 35 parts per
thousand.
Ion |
g T |
Cl - |
0.681 |
Na + |
0.652 |
Mg 2+ |
0.215 |
SO 4 2- |
0.121 |
Ca 2+ |
0.201 |
K + |
0.618 |
HCO 3 - |
0.500 |
CO 3 2- |
0.030 |
The activity is therefore, going to be a function of the ionic strength
of the solution.
For ground water with total dissolved solids (i.e., salinity) up to the
levels of sea water the g T is determined
using the relationship
g T = (m / m
T ) g*
where:
- m T = total molality for a given element
- m = molality of the free ion
- g * = activity given by the Debye-Hückel
limiting law
The molality of the free ion is calculated from mass balance expressions
and ion-pair equilibrium expressions using an iterative method.
The value of g * is determined using the Debye-Hückel
equation:
where:
- A, B = constants that are f (T).
- a o i = ion size parameter for ion i
- Z i = valance of the ion i
- I = ionic strength
Ionic strength is defined as:
where,
m i= molality of the ith species (mol . kg -1 )
A 1 m solution of CaCl 2 will have an ionic strength of
I = 1/2 [(1)(2) 2 + (2)(1) 2 ] = 3 m
A general plot of activity coefficient versus ionic strength for some common
ion species in clays is shown below.
A common reaction that occurs in soils and sediments is that between solid
SiO 2 and its ion complexes in solution. At pH values below
8 the only effective form of dissolve silica is orthosilisic acid.
Consider the reaction involving amorphous SiO 2 :
SiO 2 + H 2 O <----> H
4SiO 4 o
At 25° C:
K = a H 4 SiO 4 o
= 2 x 10 3
where:
K = equilibrium solubility product.
recall that activity can be expressed in terms of concentration by the expression:
recall r* w is the mass of
water per volume of interstitial solution.
Therefore,
which simplifies the activity equation and introduces the concentration
solubility product. Be careful to note the differences between the various
forms of activity coefficents that are used in the literature.
Saturation index
Once the ion activity product is known, then the actual ion activity product
can be used to create a dimensionless parameter called the saturation index
( W) such that,
W= IAP/K = ICP/K c
where:
IAP = actual ion activity product
ICP = actual ion concentration product
K = equilibrium ion activity product (solubility product)
K c = equilibrium ion concentration product.
It is now possible to express the state of saturation for a particular reaction
by W , where:
if W > 1, then the solution is supersaturated.
if W = 1, then the solution is saturated.
if W< 1, then the solution is undersaturated.