Unit 09a : Advanced Hydrogeology
Chemical Reactions
Chemical Reactions
• A wide variety of chemical reactions can take
place between gases, solutes and solids in
groundwater systems:
–
–
–
–
–
–
Acid-base
Solution-precipitation
Complexation.
Redox
Hydrolysis
Isotopic processes
Hydrogen Ion Activity
• [H+] represents the activity of hydrogen ions
in solution:
pH = - log[H+] = -log[H3O+]
– since hydrogen ions exist in solution in the
hydrated form as H3O+
– this allows us to distinguish between hydrogen
ions and protons
• pH is a “master variable” controlling chemical
systems.
• pH is controlled by acid-base reactions.
Acids and Bases
• An acid is a substance with a tendency to
lose protons
• A base is a substance with a tendency to gain
protons.
• Acids react with bases to transfer protons
• In acid-base reactions, because no free
protons are produced, there must be two
acid-base systems involved:
Acid1 + Base1 = Acid2 + Base2
Bicarbonate Reaction
HCO3- + H2O = H3O+ + CO32• A proton is transferred (donated) from the
bicarbonate ion to the water molecule to
create an hydrogen ion.
K = [H3O+ ] [CO32-] = [H+ ] [CO32-]
[HCO3- ] [H2O]
[HCO3- ]
– assuming the activity of water is unity and
abandoning our “hydrogen ion” distinction.
• Remember the reaction is nevertheless an
acid-base reaction with water as a base:
HCO3- = H+ + CO32-
Ammonia Reaction
•
•
•
•
H2O + NH3 = NH4+ + OHAmmonia is a base that ionizes in water by
accepting a proton.
In this case, water is the proton donor and
water acts as an acid.
The concept of acid or base is simple: the
proton donor is the acid the proton
acceptor is a base.
In the first reaction water accepted a proton
from the bicarbonate ion. In this reaction
water donates a proton.
Strong and Weak Acids
HA + H2O = H3O+ + A• The strength of an acid depends on its
ability to drive the ionization reaction
from left to right.
• Strong acids donate protons freely in
spite of the fact that water is a weak
base (proton acceptor).
Weak Acid-Base Reactions
• There are a few weak acid reactions
that are important in groundwater
systems:
– dissociation of water
– dissociation of carbonic acid (dissolution of
gaseous CO2)
– dissociation of silicic acid (dissolution of
silicate minerals)
Dissociation of Water
H20 + H2O = H3O+ + OH• The equilibrium constant for this acid-base
reaction, where water is both acid and base,
is 10-14
Kw = [H+] [OH-]
– again we assume [H2O] is unity and don’t bother
to include it explicitly in the equations
• Just as pH represents –log[H+], it is
convenient to use pK to represent –log[K]
• For the dissociation of water pKw = 14
– because [H+] = [OH-], the pH of pure water is 7.0
Carbonic Acid
CO2(g) + H20 = H2CO3*  CO2(aq)
• The equilibrium constant pKCO2 for the
solution of carbon dioxide in water to produce
carbonic acid is 1.46.
H2CO3* = H+ + HCO3• The first dissociation constant pK1 = 6.35
HCO3- = H+ + CO32• The second dissociation constant pK2 = 10.33
Carbonate Speciation Example p.1
• Calculate the distribution of mass between carbonate
species at pH 7 given [CO2]T = 10-3 M.
• Step 1: Identify the species.
[CO2]T = [H2CO3*] + [HCO3-] + [CO32-]
• Step 2: Calculate [H+] and [OH-]
pH = 7 therefore [H+] = 10-7
[OH-] = Kw / [H+] = 10-14 / 10-7 = 10-7
• Step 3: Write [HCO3-] using K1
[HCO3-] = [H2CO3*] (K1 / [H+])
= [H2CO3*] (10-6.35 / 10-7) = [H2CO3*] (100.65)
• Step 4: Write [CO32-] using K2
[CO32-] = [HCO3-] (K2 / [H+]) = [H2CO3*] (K1 / [H+]) (K2 / [H+])
= [H2CO3*] (100.65) (10-10.33 / 10-7) = [H2CO3*] (10-2.68)
Carbonate Speciation Example p.2
• Step 5: Write [CO2]T in terms of [H2CO3*] to find [H2CO3*]
[CO2]T = [H2CO3*] + [HCO3-] + [CO32-]
[CO2]T = [H2CO3*] + [H2CO3*] (100.65) + [H2CO3*] (10-2.68)
[CO2]T = [H2CO3*] ( 1 + 100.65 + 10-2.68 )
[CO2]T = [H2CO3*] (5.47)
[H2CO3*] = [CO2]T / (5.47)
[H2CO3*] = 10-3 / 5.47 = 10-3.74
• Step 6: Calculate [HCO3-]
[HCO3-] = [H2CO3*] K1 / [H+] = 10-3.74(10-6.35 / 10-7) = 10-3.09
• Step 7: Calculate [CO32-]
[CO32-] = [HCO3-] K2 / [H+] = 10-3.09(10-10.33 / 10-7) = 10-6.42
• The carbonate species [H2CO3*], [HCO3-] and [CO32-]
have concentrations of 10-3.74, 10-3.09 and 10-6.42 M
respectively at pH 7. Bicarbonate is the dominant ion.
Carbonate in Solution
0
OH-
-2
H+
-4
H2CO3*
CO32-
-6
log [C]
-8
HCO3-
HCO3-
-10
-12
H+
OH-
-14
-16
-18
H2CO3*
CO32-
-20
-22
0
1
2
3
4
5
6
7
8
pH
9
10
11
12
13
14
15
(CO2)T = 10-3 M
Carbonate in Solution
0
H+
-2
OH-
-4
CO32-
H2CO3*
-6
log [C]
-8
-10
HCO3-
HCO3-
-12
-14
H+
OH-
-16
-18
H2CO3*
-20
CO32-
-22
0
1
2
3
4
5
6
7
8
pH
9
10
11
12
13
14
15
(CO2)T = 10-4 M
Carbonate System
• Plotted for (CO2)T = 10-3 M or about 100 mg/L
• Crossover points
– pK1 = 6.35 where [HCO3-] = [H2CO3*]
– pK2 = 10.33 where [HCO3-] = [CO32-]
• Carbonate species
H2CO3*
HCO3CO32-
is dominant for pH < 6.35
is dominant for 6.35 > pH < 10.33
is dominant for pH > 10.33
Silicic Acid
• Carbon and silicon both form strong covalent
bonds with oxygen.
• Silicic acid is also a weak acid like carbonic
acid.
H2SiO3 = H+ + HSiO3• The first dissociation constant pK1 = 9.86
HSiO3- = H+ + SiO32• The second dissociation constant pK2 = 13.1
Silica in Solution
0
OHSiO32-
H+
-2
-4
H2SiO3
-6
HSiO3-
log [C]
-8
-10
HSiO3-
H2SiO3
-12
-14
OH-
H+
-16
-18
-20
SiO32-
-22
0
1
2
3
4
5
6
7
8
pH
9
10
11
12
13
14
15
(SiO2)T = 10-4 M
Silica System
• Plotted for (SiO2)T = 10-4 M or about 10 mg/L
• Crossover points
– pK1 = 9.86 where [HSiO3-] = [H2SiO3]
– pK2 = 13.1 where [HSiO3-] = [SiO32-]
• Silicate species
H2SiO3
HSiO3SiO32-
is dominant for pH < 9.86
is dominant for 9.86 > pH < 13.1
is dominant for pH > 13.1
Alkalinity
• The Bjerrum plots (log[C] against pH) show
the effect of pH alone on speciation but in
“real world” systems there are additional
factors to consider.
• The equilibria are influenced by strong bases
added through the dissolution of carbonates
and silicates.
• Alkalinity is the net concentration of strong
bases in excess of strong acids with a pure
water – CO2 system as a reference point
(zero alkalinity).
Charge Balance
• When CO2 is dissolved in water (at a fixed
PCO2 ) the charge balance is:
[H+] = [OH-] + [HCO3-] + 2[CO32-]
– the cations must balance the anions
• Adding a strong base (NaOH) and a strong
acid (HCl) to the system will add Na+ and H+
cations and OH- and Cl- anions so the charge
balance becomes:
[Na+] + [H+] = [OH-] + [HCO3-] + 2[CO32-] + [Cl-]
Alkalinity Defined
• The net excess contribution of ions from the
strong base is the alkalinity (for Na+ > Cl-)
given by:
[Na+] - [Cl-] = [OH-] + [HCO3-] + 2[CO32-] - [H+]
• If we generalize to any base and any acid
(rather than NaOH and HCl) we can write:
Alkalinity = S [i+]sb – S [i-]sa
= [OH-] + [HCO3-] + 2[CO32-] - [H+]
• For the pure water-CO2 reference system, the
alkalinity is zero.
Net Alkalinity and Net Acidity
• In most natural systems, the generation of net
positive charges from dissolution of
carbonates and silicates usually exceeds the
contribution of negative charges from the
ionization of strong acids. Most natural
groundwaters are alkaline.
• When strong acids are present (for example
from pyrite oxidation) groundwaters may
display net acidity. Such cases are often
associated with sulphide mineralization or
contamination by acid rock drainage (ARD).
Mineral Dissolution
• Increasing alkalinity results from an increase in
positive ions on the LHS of the alkalinity equation
from mineral dissolution.
• An equal number of negative ions are added to the
RHS to maintain neutrality and some of these ions
come from ionization of H2CO3* to HCO3- and H2SiO3
to HSiO3-.
• The equilibria for ionization of the weak acids
removes hydrogen ions as HCO3- and HSiO3- are
produced since the dissociation constant is invariant.
• In most natural groundwater systems, pH increases
along the flow path as minerals are dissolved.
Solute Mass Loadings
• Water is an excellent solvent.
• Mineral dissolution is primarily responsible for
the mass loadings in groundwater.
• Other processes contribute to the reduction of
solute mass loadings. These include:
– gas exsolution
– volatilization
– precipitation
Henry’s Law
• Henry’s law does not strictly apply to gases (like CO2
and NH3) that react in solution.
• Very little [CO2]aq reacts and H2CO3 concentrations
are very low such that [CO2]aq  [H2CO3*]
• Henry’s law thus adequately approximates the
distribution of CO2 between the aqueous and
gaseous phases:
KH = PCO2
[CO2]aq
– KH is the Henry’s law constant with units of kPa.L.mol-1 or
atm.L.mol-1.
Carbon Dioxide Solution
• Changes in PCO2 directly effect [CO2]aq and
hence [H2CO3*]
• Changes in [H2CO3*] through the dissociation
constants pK1 and pK2 influence [HCO3-],
[CO32-], [OH-] and pH.
• Addition of CO2 to groundwater through the
unsaturated zone increases [HCO3-] and pH
and enhances the ability of the solution to
dissolve silicate minerals.
Volatilization
• Volatilization is the process of liquid or solid
phase evaporation at a liquid-gas or solid-gas
interface.
• The process of volatilization of solutes is
controlled by Henry’s law.
– NOTE: we are not discussing any non-aqueous
phase liquids.
• Volatilization can create problems in
sampling. When samples have access to the
atmosphere, loss of volatiles to the vapour
phase can be significant.
Dissolution and Precipitation
• Dissolution and precipitation of solids are two
of the most import processes controlling
groundwater chemistry.
• Groundwater systems evolve towards the
equilibrium state either from undersaturation
(most natural systems) or oversaturation (some
contaminated systems).
• In natural systems, dissolution proceeds and
pH rises as waters evolve along the flow path.
• In contaminated systems, precipitation can
remove metals as pH rises along the flow path.
Mineral Solubility
• Solubility reflects the extent to which the
reactant (mineral) and products (ions and/or
secondary minerals) are favoured in a
dissolution-precipitation reaction.
• Because the activity of the reacting solid is
taken to be unity, the magnitude equilibrium
constant pK provides a relative measure of
mineral solubility (in pure water).
• When other ions are present, absolute and
relative solubilities can change.
Common Mineral Solubilities
Mineral
Halite
Sylvite
Quartz
Gypsum
Magnesite
Aragonite
Calcite
Na-Montmorillonite
Kaolinite
Siderite
Brucite
Ferrous Hydroxide
Dolomite
Pyrrhotite
Spalerite
Galena
Gibbsite
IAP
pK
[Na+][Cl-]
[K+][Cl-]
[H2SiO3]
[Ca2+][SO42-]
[Mg2+][CO32-]
[Ca2+][CO32-]
[Ca2+][CO32-]
[Na+][H4SiO4]4
[H4SiO4]2
[Fe2+][CO32-]
[Mg2+][OH-]2
[Fe2+][OH-]2
[Ca2+][Mg2+][CO32-]2
[Fe2+][S2-]
[Zn2+][S2-]
[Pb2+][S2-]
[Al3+][OH-]3
-1.54
-0.98
4.00
4.62
7.62
8.22
8.35
9.10
9.40
10.70
11.10
15.10
16.70
18.10
23.90
27.50
33.50
Ionic Strength Effect
• Generally solubility increases with
increasing ionic strength.
• The presence of other ions reduces the
activity of ions involved in the reaction.
• This increases the number of ions
needed in solution to achieve the
equilibrium IAP.
Common Ion Effect
• When a solution contains the ion that is
released when a solid dissolves, the
presence of that ion means that less
dissolution is required to reach the
equilibrium IAP.
• This phenomenon decreases the
solubility and is called the common ion
effect.
Complexation
• A complex is an ion that forms by combining
simpler anions, cations and molecules.
• The cation (or central atom) is typically a
metal.
• The anion (or ligand) is almost any simple
anion (halide, sulphate, carbonate,
phosphate, etc)
• A simple complexation reaction involves a
metal and a ligand:
Zn2+ + Cl- = ZnCl-
Complex Complexes
• Sometimes complexes combine with ligands
and metals are distributed among a large
number of cation complexes.
• For example, the hydrolysis of the trivalent
chromium ion:
Cr3+ + OH- = Cr(OH)2+
Cr(OH)2+ + OH- = Cr(OH)2+
Cr(OH)2+ + OH- = Cr(OH)30
General Complexes
• Most reactions involving complexes are “fast” in a
kinetic sense.
• A general complexation reaction involves a metal
cation (M), b ligands (L) and c hydrogen ions (H):
aM + bL + cH = MaLbHc
• The stability constant for the complex KMLH is given
by the association reaction:
KMLH = [MaLbHc]
[M]a[L]b[H]c
or pKMLH = a.log[M] + b.log[L] + c.log[H] – log[MaLbHc]
• The larger the value of KMLH, the more stable the
complex
More about Complexes
• Most complexes involve a single cation:
ZnCl+, Cr(OH)2+
• Polynuclear complexes are relatively unusual:
Cr3(OH)45+, Cu2(OH)22+
• Complexation facilitates the transport of
potentially toxic metals such as Cd, Cu, Cr,
Mo, Pb, and U. For example, U forms
complexes with many ligands including F,
CO3, SO4 and PO4.
Complex Speciation Example p.1
• A solution contains a trace of chromium (10-5 M) at a
pH of 5. Determine the speciation among the Cr
hydroxyl complexes given stability constants (where
pK = -log K) pK2 = -10.0, pK1 = -18.3 and pK0 = -24.0
• Step 1: Identify the species
[Cr]T = [Cr3+] + [Cr(OH)2+] + [Cr(OH)2+] + [Cr(OH)30]
• Step 2: Calculate [H+] and [OH-]
pH = 5 therefore [H+] = 10-5
[OH-] = Kw / [H+] = 10-14 / 10-5 = 10-9
• Step 3: Use the association reactions to find [C] for complexes
[Cr]T = [Cr3+] + K2[Cr3+][OH-] + K1[Cr3+][OH-]2 + K0[Cr3+][OH-]3
Complex Speciation Example p.2
•
•
•
•
Step 4: Solve for [Cr3+]
[Cr]T = [Cr3+] + K2[Cr3+][OH-] + Ki[Cr3+][OH-]2 + K0[Cr3+][OH-]3
[Cr]T = [Cr3+] (1 + K2[OH-] + Ki[OH-]2 + K0[OH-]3)
[Cr3+] = [Cr]T / (1 + K2[OH-] + Ki[OH-]2 + K0[OH-]3)
[Cr3+] = 10-5 / (1 + 1010.10-9 + 1018.3.10-18 + 1024.10-27)
[Cr3+] = 10-5 / (1 +101 + 100.3 + 10-3)
[Cr3+] = 10-5 / (1 + 10 + 1.995 + 0.001) = 10-5 / (12.996) = 10-6.12
Step 5: Solve for [Cr(OH)2+]
[Cr(OH)2+] = K2[Cr3+][OH-] = 1010.10-6.12.10-9 = 10-5.12
Step 6: Solve for [Cr(OH)2+]
[Cr(OH)2+] = Ki[Cr3+][OH-]2 = 1018.3.10-6.12.10-18 = 10-5.82
Step 7: Solve for [Cr(OH)2+]
[Cr(OH)30] = K0[Cr3+][OH-]3 = 1024.10-6.12.10-27 = 10-9.12
• The chromium species [Cr3+], [Cr(OH)2+], [Cr(OH)2+], and
[Cr(OH)30] have molar concentrations of 10-6.12, 10-5.12, 10-5.82
and 10-9.12 M respectively at pH 5. Cr(OH)2+ is the dominant ion.
Major Ion Complexation
• When we calculated IAP/K ratios and saturation
indices earlier, we used total concentrations.
• The true concentrations are significantly reduced by
complexation.
• Even at relatively low ionic strength >0.02 M, the
error in determining mineral saturations can be
substantial if complexation is neglected.
• In seawater, for example, only 40% of the total SO4
exists as SO42-, 37% exists as NaSO4+ and 19% as
MgSO40
Metal Mobility
• Generally, in groundwater, metals are most
mobile at low pH.
• Ignoring surface reactions, metal
concentrations begin to decline when pH
increases to the point where equilibrium is
reached with a solid phase.
• The solid phases are usually metalhydroxides, metal-sulphides or metalcarbonates.
Uranium Complexes
• Complexes can enhance the transport of
metals at low concentrations.
• Uranium is a good example, forming many
uranyl (UO22+) complexes with ligands
including F-, CO32-, SO42- and PO43-.
• At pH 7, (UO2)(HPO4)22- is the dominant
uranyl species and increases the solubility of
some uranium minerals by several orders of
magnitude (Langmuir, 1978).
Surface Reactions
• When water containing a trace constituent is
mixed with a disseminated solid and allowed
to equilibrate, mass partitions between the
solution and the solid surface.
S = (Co – C).V / Ms
where S is the mass sorbed on the surface
(M/M); Co is the initial concentration in
solution (ML-3) and C is the equilibrium
concentration in solution (ML-3), V is the
solution volume (L3) and Ms is the mass of
solid (M).
Freundlich Isotherm
1.0
n = 0.1
0.9
n = 0.2
0.8
0.7
Mass Sorption
• The function S(C)
describing the surface
sorption for various
equilibrium concentrations
is called a sorption
isotherm.
• Isotherms functions have
no theoretical form and
have be derived
empirically.
S = K.Cn
is a form suggest by
Freundlich where K and n
are empirical constants.
n = 0.5
0.6
0.5
0.4
n=1
0.3
n=2
0.2
n=5
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Concentration
0.7
0.8
0.9
1.0
Langmuir Isotherm
1.0
K = 20
0.9
0.8
0.7
Mass Sorption
• The Langmuir isotherm
has a more complex form:
S = Q.K.C / (1 + K.C)
where Q is the maximum
sorptive capacity of the
surface and K is a
partition coefficient.
• The value of K controls
the extent of sorption.
• The Langmuir isotherm
limits the maximum mass
sorption through the
parameter Q.
0.6
K = 0.5
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Concentration
0.7
0.8
0.9
1.0
Linear Isotherm
1.0
0.9
0.8
0.7
Mass Sorption
• The Freundlich isotherm
for n =1 is called a linear
isotherm
S = Kd.C
where Kd is the distribution
coefficient.
• This special case has
been widely used to
represent sorption of
metals.
• Finding a single value Kd
to characterize the
sorption process has
proved difficult and more
complex models are
demanded by experience.
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Concentration
0.7
0.8
0.9
1.0
Surface Reactions
• For surface reactions, it is possible to account for the
properties of the solution and the solid surfaces.
• Cation exchange is the best-known surface reaction.
• The process is driven by electrostatic attraction
between charged cations and the surface charge on
clay mineral and oxide/hydroxide surfaces.
• Clay mineral surfaces have significant negative fixed
charges due lattice substitutions and broken bonds at
the edges of the minerals.
• Cations bind to the surfaces to balance the charge.
Cation Exchange Capacity
• Cation exchange capacity (CEC)
describes the quantity of exchangeable
cations sorbed onto a surface.
• CEC has units of meq per 100 g of
sample.
• CEC varies from one mineral to another
but is strongly related to surface area.
Clay Mineral CEC
Mineral
Kaolinites*
Illites
Chlorites
Vermiculites
Montmorillonites
CEC
Surface Area
(meq/100g)
(m2/g)
5-15
15
25
80
10-40
80
100-150
100
80-100
800
Cation Affinity
• Clay minerals exhibit a preference for specific ions
occupying exchange sites:
Li+ < Na+ < H+ < K+ < NH4+ < Mg2+ < Ca2+ < Al3+
• In general, cation affinity for exchange sites increases
with ionic charge.
• At high concentrations, ion hydration and
complexation can influence cation affinities.
• In general, monovalent ions have hydration energies
of around 100 kcal/mol compared with 400-500
kcal/mol for divalent ions and >1000 kcal/mol for Al3+
and Fe3+
Exchange Reactions
• The general form of a cation exchange reaction is:
nMX + mNn+ = nMm+ + mNX
where M and N are metal cations with charges m+ and n+
respectively and MX and NX are the corresponding metals
sorbed on the solid phase.
• For example:
Na-clay + K+ = Na+ + K-clay
n1Ca2+ + n2Mg2+ + n3Fe2+ + 2(n1+n2+n3)Na-clay =
2(n1+n2+n3)Na+ + Ca-Mg-Fe-clay
Ca2+ + 2Mg2+ + Fe2+ + 8Na-clay = 8Na+ + Ca-Mg-Fe-clay
Other Sorption Reactions
• A second group of sorption reactions involve
solids whose surface charge depends on
groundwater composition.
• Hydrated metal oxides and hydroxides (Si, Al,
Fe) and kaolinites are the most important
solids in this group.
• Surfaces typically carry a positive charge at
low pH but become negatively charged cation
exchangers at higher pH.
Oxides and Hydroxides
XOH = H+ + XOXOH + H+ = XOH2+
• At low pH, XOH2+ is the dominant
surface species whereas at higher pH,
XO- is dominant.
• The neutral point for a surface in terms
of pH is called the isoelectric point
Isoelectric Points
Mineral
Quartz
Kaolinite
Hematite
Magnetite
Goethite
Corundum
Gibbsite
pH
2.0 - 3.5
1.8 - 4.6
5.0 - 9.0
6.5
6.0-7.0
9.1
~9
Redox
• The hydrogen ion activity (H+) and the
availability of electrons (e-) are the master
variables of groundwater reactions.
• Unlike H+ ions, electrons are not 'free
forming'; they are contained within atoms or
molecules. Electrons are only transferred
between species.
• Redox, short for reduction-oxidation, is the
termed used to denote reactions involving the
transfer of electrons.
Microorganisms
• Oxidation-reduction reactions differ from
many other reactions because they are
frequently mediated by microorganisms.
• The role of the microorganisms is usual to act
as a catalyst and increase the rate of
reaction.
• Microbial films on grains and fracture
surfaces use redox reactions as a source of
energy.
Redox Reactions
• Oxidation-reduction reactions involve
electron (e-) exchange
• An element changes oxidation state
• There are no free electrons an
electron transfer occurs
• The process is described by paired (or
coupled) half-reactions involving
oxidation and reduction together.
Oxidation Number
• The oxidation number of an element indicates
the number of electrons lost, gained, or
shared as a result of chemical bonding.
• The change in the oxidation state of a
species lets you know if it has undergone
oxidation or reduction.
• Oxidation can be defined as "an increase in
oxidation number".
• Reduction can be defined as "a decrease in
oxidation number".
Simple Reaction
2Na + Cl2 > 2NaCl
• The sodium starts out with an oxidation number of
zero (0) and ends up having an oxidation number of
+I. It has been oxidized from a sodium atom to a
positive sodium ion.
• The chlorine also starts out with an oxidation number
of zero (0), but it ends up with an oxidation number of
-I. It, therefore, has been reduced from chlorine
atoms to negative chloride ions.
Oxidizing and Reducing Agents
• The substance bringing about the oxidation of
the sodium atoms is the chlorine, thus the
chlorine is called an oxidizing agent.
• The substance bringing about the reduction
of the chlorine is the sodium, thus the sodium
is called a reducing agent.
• Oxidation is ALWAYS accompanied by
reduction.
• Reactions in which oxidation and reduction
are occurring are called Redox reactions.
Oxidation Numbers (I)
• Oxidation numbers are often written as roman
numerals.
Example: Cr(VI), Mn(IV), Fe(III)
• The oxidation number of an atom in the elemental
state is zero.
Example: Cl2, Al and N2 are all 0
• The oxidation number of a monatomic ion is equal to
its charge.
Example: In the compound NaCl, the Na+ has an oxidation
number of +I and the Cl- has an oxidation number of -I.
• The algebraic sum of the oxidation numbers in the
formula of a compound is zero.
Example: the oxidation numbers in the NaCl above add up to 0
Oxidation Numbers (II)
• The oxidation number of hydrogen in a compound is
+I, except when hydrogen forms compounds called
hydrides with active metals, and then it is -I.
Example: H is +I in H2O, but -I in NaH (sodium hydride).
• The oxidation number of oxygen in a compound is -II,
except in peroxides when it is -I, and when combined
with fluorine. Then it is +II.
Example: In H2O the oxygen is -II, in H2O2 it is -I.
• The algebraic sum of the oxidation numbers in the
formula for a polyatomic ion is the charge on that ion.
Example: in the sulphate ion, SO42-, the oxidation numbers of
the sulphur and the oxygens add up to -II. The oxygens are -II
each, and the sulphur is +VI.
Oxidation States
Carbon
+VI
+V
+IV
+III
+II
+I
0
-I
-II
-III
-IV
Nitrogen
Sulphur
SO42-
Iron
NO3CO2, HCO3-
SO32-
NO2-
C
N2
CH2O,CH3OH
NH4+
CH4
Fe(OH)3, FeO(OH)
Fe(OH)2
S
FeS2
H2S,FeS
Fe
Oxidation and Reduction
• When an oxidation or reduction reaction is
written independently; for example, the
reduction of CO2
CO2 + 4e- + 4H+ = CH2O + H2O
or for the oxidation of H2O
2H2O = O2 + 4e- + 4H+
a ‘free’ electron (e-) is written in the equation.
• An overall redox reaction will never have an
(e-) shown:
CO2 + H2O = CH2O + O2
Half Reactions
• Reduction of elemental oxygen:
½O2 + 2H+ + 2e- = H2O
• Oxidation of ferrous iron:
Fe2+ = Fe3+ + e• Combining the two half-reactions gives
a balanced redox reaction:
2Fe2+ + ½O2 + 2H+ = 2Fe3+ + H2O
Electron Donors
• By far the most prevalent electron donor in
the shallow subsurface is organic carbon.
CH2O + H2O = CO2 + 4e- + 4H+
• This half reaction is what supplies energy to
microorganisms within soils.
• The electron donor (organic carbon) is the
reducing agent and is oxidized to CO2.
Inorganic Electron Donors
• Common electron donors that participate in
chemical redox couples in groundwaters
include:
• Mn(II) = Mn(IV) + 2e• Fe(II) = Fe(III) + e• S2- = SO42- + 8e• As(III) = As(V) + 2e-
Redox Chain
• Groundwaters follow a chain of redox
reactions during infiltration that involve
consuming organic matter
• Each redox step is generally controlled by the
availability of an oxidant (bacterial catalysts
are ubiquitous)
• The redox state of the groundwater is usually
controlled by the dominant redox pair
• Redox state affects the mobility (solubility) of
redox-sensitive metals
Common Redox Pairs
Reduced Form
H2S
NH4+
CH4
Fe2+
Mn2+
As3+
hydrogen sulphide
ammonium
methane
ferrous iron
Oxidized Form
SO42- sulphate
NO3- nitrate
CO2 carbon dioxide
Fe3+ ferric iron
Mn4+
As5+
Electron Activity
• For equilibrium reactions:
Ox + n e- = Red
K = [Red] / [Ox][e-]n
• For the electron transfer reaction:
pE = (1/n) ( log K - log [Red] / [Ox] )
pE is analogous to pH such that pE = -log[e-]
• If reactions are always written such that n=1:
pE = log K - log [Red] / [Ox]
pE = pEo - log [Red] / [Ox]
Expressions for pE
• For example:
½O2 + 2H+ + 2e- = H2O
pE = ½ ( log K - log 1 / PO21/2[H+]2 )
pE = ½ ( log K + log PO21/2[H+]2 )
pE = ½ ( log K + log PO21/2 + 2 log [H+] )
pE = ½ ( log 1041.55 + ½ log PO2 - 2 pH )
pE = 20.78 + 1/4 log PO2 - pH
• For example:
Fe2+ = Fe3+ + epE = log K + log [Fe3+] / [Fe2+]
pE = log 1012.53 + log [Fe3+] / [Fe2+]
pE = 12.53 + log [Fe3+] / [Fe2+]
Electrode Potential
• While pE is a convenient way to 'view' redox
reactions, it is not real.
• Since electrons do not exist in solution we
need a separate way of measuring their
reactivity in a system.
• This is done with electrode potential: the
potential for an electron to participate in a
reaction measured as a voltage relative to a
reference (hydrogen) electrode.
pE and Eh
• pE, represents the negative logarithm of the electron
activity
• Eh is the thermodynamic redox potential expressed
in terms of millivolts.
• pEo = 59.2 Eho (at 25oC)
• For measurement purposes, the Eh of a system may
be defined as the potential developed at an inert
metallic electrode expressed relative to the standard
hydrogen electrode in a reversible redox system.
• Eh is dependent on pH and so the pH at which any
measurement of Eh is made must be stated.
Redox State of Soils
• Soils have been broadly classified into three
redox states based on their pE (or Eh) values:
• Oxic:
pE > 7
Eh > 400 mV
• Suboxic pE 2-7
Eh < 100-400 mV
• Anoxic pE < 2
Eh < 100 mV
• This classification ignores pH.
• A better classification associates suboxic
zones with the reduction of Fe and Mn
oxides, but not the reduction of sulphate and
anoxic zones with sulphate reduction.
pE and Eh in Natural Systems
• Interpreting the Eh or pE of a system, especially a
natural system, is extremely difficult.
• Measurements rely on the assumptions that the
redox system is reversible, i.e. the kinetics of the
relevant reaction are fast, and that the system is in
equilibrium.
• Neither of these assumptions are likely to be true in
most cases.
• Additionally, any number of reactions could contribute
to the measured value, further complicating
interpretation.
Free Oxygen
• The presence of O2 increases the redox potential of a
system and makes it more oxidized.
• Coupling oxygen’s reduction half-reaction (Eho =
1229 mV) with any redox couple having a lower Eh
value will result in an energetically favourable redox
reaction.
• In the shallow subsurface, micro-organisms control
the redox potential along with the redox couple of the
electron acceptor.
• Oxygen is the preferred acceptor because it is most
easily reduced to water of the available acceptors.
Electron Acceptors
• Alternate electron acceptors, in order of
preference (based on Eho values) are:
• Mn(III) > Mn(II)
• NO3- > N2 (or other reduced N forms)
• Mn(IV) > Mn(II)
• Fe(III) > Fe(II)
• SO42- > S2- (or H2S)
• The order of preference is due to the redox
potentials for the half-reactions.
Redox Potentials
Half Reaction
Mn3+ + e- = Mn2+
MnO(OH)(s) + 3 H+ + e- = Mn2+ + 2 H2O
0.2 NO3- + 1.2 H+ + e- = 0.1 N2(g) + 0.6 H2O
0.5 MnO2 + 2 H+ + e- = 0.5 Mn2+ + H2O
0.25 O2(g) + H+ + e- = 0.5 H2O
Fe(OH)3(s) + 3 H+ + e- = Fe2+ + 3 H2O
0.5 NO3- + H+ + e- = 0.5 NO2- + 0.5 H2O
Fe3+ + e- = Fe2+
0.5 O2(g) + H+ + e- = 0.5 H2O2
0.125 SO42- + 1.25 H+ + e- = 0.125 H2S + 0.5 H2O
0.167 N2(g) + 1.333 H+ + e- = 0.333 NH4+
0.125 CO2(g) + H+ + e- = 0.125 CH4 + 0.25 H2O
H+ + e- = 0.5 H2(g)
Eho (mv) pEo
1510 -25.51
1450 -24.49
1245 -21.03
1230 -20.78
1229 -20.76
1057 -17.85
834 -14.09
742 -12.53
682 -11.52
303
-5.12
279
-4.71
169
-2.85
0
0.00
pH and Eh Stability Fields
+1.0
oxygen
+0.8
+0.6
+0.4
water
Eh
+0.2
0.0
-0.2
-0.4
-0.6
-0.8
hydrogen
-1.0
0
2
4
6
8
pH
10
12
14
pH and Eh
• As groundwaters become reduced, their pH tends to
move toward neutrality.
• When the pH is initially low, H+ consumption in the
reduction reactions increases the pH.
• For example:
MnO2(s) + 4H+ + 2e- = Mn2+ + 2H2O
• If the pH is initially basic, then precipitation of metal
ions such as Fe2+ and Mn2+ as hydroxides,
carbonates, or sulphides tends to lower the pH.
• For example:
Fe2+ + 2H2O = Fe(OH)2(s) + 2H+
Fe2+ + HCO3 = FeCO3(s) + H+
Redox Kinetics
• Redox reactions tend to be “slow” because:
– numbers of microorganisms are small
– reactants are not easily metabolized
• Large pEo values make reactions essentially
irreversible (hard to get [Red]/[Ox] to exceed pEo)
– dissolved oxygen will continue to oxidize organic
carbon until all organic matter is destroyed
• pE can be calculated from many couples and is rarely
the same because of disequilibrium (ie Fe(II)/Fe(III)
may give a different pE to S2-/SO42-)
Dominant Couples
• Constant Eh (or pE) exists when the
concentration of one of the couples is much
greater than the other:
CH2O + O2 = CO2 +H2O
• The O2/H2O couple dominates CH2O/CO2 in
natural systems such that the dissolved
oxygen concentration only changes
marginally to oxidize all the organic matter.
Sulphate/Sulphide System
• The sulphate/sulphide couple controls the mobility of
many metals.
• (ST) exists as SO42-, H2S, HS-, S2- with concentration
controlled by equilibrium relationships (like carbonate
and silicate systems).
• In sulphate the oxidation state of S is S(+VI) and in
the other species S(-II).
• In oxic environments (Eh > 400 mV) SO42- dominates
• Under anoxic conditions (Eh < 100 mV) the S(-II)
species prevail.
Redox and Metals Mobility
• When SO42- dominates metal concentrations are high
because there are no significant solubility constraints
for Fe, Ni, Co, Cu, Zn etc
• Under anoxic conditions where S2- is present almost
all the sulphur and metals are precipitated because of
the very low solubilities of metal sulphides.
• pH changes the system significantly and Eh-pH
diagrams are useful to examine metal mobilities in
aqueous solutions.
• For example, Fe3+ is stable in solution only at high Eh
>790 mV and low pH < 3.
Iron Stability Fields
+1.0
Fe3+
+0.8
+0.6
Fe2+
+0.4
Eh
+0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
2
4
6
8
pH
10
12
14