Suggested reading:

**Background reading on principles of chemistry
of natural waters.
**Drever, James I., 1997

Langmuir, Donald, 1997 *Aqueous Environmental
Geochemistry.* Prentice Hall, Upper Saddle River, NJ.600 P.

Several simplifying assumptions:

Assume that concentration (

For example for dissolved silica species:

Case for dissolved potassium species:

Case for dissolved calcium species:

Using this convention, the activity coefficient g becomes the total activity coefficient g

g

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 |

Cl |
0.681 |

Na |
0.652 |

Mg |
0.215 |

SO |
0.121 |

Ca |
0.201 |

K |
0.618 |

HCO |
0.500 |

CO |
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

g

where:

*m*_{}T = total molality for a given element*m*= molality of the free ion- g*
= activity give 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 ofg* 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.

taken from figure 2-1 from Berner 1971.

A simple common reaction that occurs in soils and sediments is that between solid SiO

Consider the reaction involving amorphous SiO

SiO_{}2
+ H_{}2O <----> H_{}4SiO_{}4^{o}

At 25° C:

K = *a *H_{}4SiO_{}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,

this simplifies the activity equation and introduces the concentration solubility
product

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

where:

IAP = actual ion activity product

ICP = actual ion concentration product

K = equilibrium ion activity product (solubility product)

K

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.