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 H4SiO4o + C H3SiO4- + C H2SiO42-

Case for dissolved potassium species:

C K
+ = C K+ + C KSO4-

Case for dissolved calcium species:

C Ca
2+ = C Ca2+ + C CaSO4- + C CaCO3o + C CaHCO3+

Using this convention, the activity coefficient
g becomes the total activity coefficient gT, where:


gT = a /CT

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

 gT

 Cl-

0.681

 Na+

0.652

 Mg2+

0.215

 SO42-

 0.121

 Ca2+

 0.201

 K+

0.618

HCO3-  

0.500

 CO32-  

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
gT is determined using the relationship

gT= (m / mT)g*

where:

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:

Ionic strength is defined as:


where,

mi= 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.
taken from figure 2-1 from Berner 1971.

A simple 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 :

SiO2 + H2O <----> H4SiO4o


At 25° C:

K = a H4SiO4o = 2 x 103

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,



this simplifies the activity equation and introduces the concentration solubility product




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/Kc

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.