Page 125 - Hydrogeology Principles and Practice

HYDC03 12/5/05 5:37 PM Page 108

108 Chapter Three

Table 3.9 Examples of oxidation states for various compounds that occur in groundwater. The oxidation state of free elements, whether
in atomic or molecular form, is zero. Other rules for assigning oxidation states include: the oxidation state of an element in simple ionic
form is equal to the charge on the ion; the sum of oxidation states is zero for molecules; and for ion pairs or complexes it is equal to the
formal charge on the species. After Freeze and Cherry (1979).
Carbon compounds Sulphur compounds Nitrogen compounds Iron compounds

Substance C state Substance S state Substance N state Substance Fe state

HCO − 3 +IV S 0 N 2 0 Fe 0
CO 2− +IV H S −II SCN − +II FeO +II
3
2
CO 2 +IV HS − −II N O −III Fe(OH) 2 +II
2
CH O 0 FeS 2 −I NH 4 + +III FeCO 3 +II
2
C H O 0 FeS −II NO − 2 +V FeO 3 +III
6 12 6
CH 4 −IV SO 2− +IV NO − 3 −III Fe(OH) 3 +III
3
CH OH −II SO 2− +VI HCN −I FeOOH +III
4
3
and expresses the net effect of the electron transfer oxidized forms and electrons are written on the left
with the absence of free electrons, thus: and the reduced products on the right.
Rearrangement of equation 3.33 gives the electron
1 2+ + 3+ −
/2O + 2Fe + 2H = 2Fe + H O eq. 3.30 activity [e ] for a half-reaction as:
2 2
By expressing redox reactions as half-reactions, the [ ⎧ reductants] ⎫ 1 /n
−
=
concept of pe is used to describe the relative electron [] ⎨ ⎬ eq. 3.34
e
activity where: ⎩ [oxidants] K ⎭
−
pe =−log [e ] eq. 3.31 Rewriting equation 3.34 by taking the negative log-
10
arithm of both sides yields:
pe is a dimensionless quantity and is a measure of the
−
oxidizing or reducing tendency of the solution where −log [e ] = pe
10
pe and pH are functions of the free energy involved in
the transfer of 1 mole of electrons or protons, respect- 1 ⎧ [reductants] ⎫
ively, during a redox reaction. = ⎨ log K − log 10 ⎬
10
n ⎩ [oxidants] ⎭
For the general half-reaction:
eq. 3.35
−
oxidants + ne = reductants eq. 3.32
When a half-reaction is written in terms of a single
where n is the number of electrons transferred, then, electron transfer, or n = 1, the log K term is written
10
o
from the law of mass action: as pe such that:
=
o
=
K [reductants] n eq. 3.33 pe pe − log 10 [reductants] eq. 3.36
−
[oxidants][ e ] [oxidants]
A numerical value for such an equilibrium constant Tabulations of thermodynamic data for redox reac-
o
can be computed using Gibbs free energy data for con- tions are commonly expressed as pe values. A set of
ditions at 25°C and 1 atmosphere pressure. By con- reduction reactions of importance in groundwater,
o
vention, the equilibrium constant for a half-reaction together with their respective pe values, is listed
is always expressed in the reduction form. The in Table 3.10. The reactions are listed on the basis