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World Bank & Government of The Netherlands funded
Training module # WQ - 30
Advanced aquatic chemistry:
Redox equilibria
New Delhi, January 2000
CSMRS Building, 4th Floor, Olof Palme Marg, Hauz Khas,
New Delhi – 11 00 16 India
Tel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685
E-Mail: dhvdelft@del2.vsnl.net.in
DHV Consultants BV & DELFT HYDRAULICS
with
HALCROW, TAHAL, CES, ORG & JPS
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 1
Table of contents
Page
1 Module context 2
2 Module profile 3
3 Session plan 4
4 Overhead/flipchart master 5
5 Evaluation sheets 23
6 Handout 25
7 Additional handout 30
8 Main text 33
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 2
1. Module context
This module discusses redox equilibria relationships significant to characterisation of natural
waters. Modules in which prior training is required to complete this module successfully and
other, available related modules are listed in the table below.
While designing a training course, the relationship between this module and the others,
would be maintained by keeping them close together in the syllabus and place them in a
logical sequence. The actual selection of the topics and the depth of training would, of
course, depend on the training needs of the participants, i.e. their knowledge level and skills
performance upon the start of the course.
No. Module title Code Objectives
1. Basic chemistry concepts WQ - 02 • Convert units from one to another
• Discuss the basic concepts of
quantitative chemistry
• Report analytical results with the
correct number of significant digits.
2. Understanding the hydrogen
ion concentration (pH)
WQ - 06 • Discuss about the concept of pH
• Calculate pH
3. The chemistry of dissolved
oxygen measurement
WQ - 11 • Appreciate significance of DO
measurement.
• Understand the chemistry of DO
measurement by Winkler method.
4. Understanding chemical
oxygen demand test
WQ - 18 • Appreciate significance of COD
measurement
• Understand the chemistry of COD
measurement
5. Basic aquatic chemistry
concepts
WQ - 24 • Understand equilibrium chemistry and
ionisation constants.
• Understand basis of pH and buffers
• Calculate different types of alkalinity.
6. Advanced aquatic chemistry:
solubility equilibria
WQ - 29 • Explain the principles of chemical
equilibrium
• Define solubility product and explain
how this relates to water quality
assessment
• Define the octanol-water partition
coefficient and explain how this
relates to water quality assessment.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 3
2. Module profile
Title : Advanced aquatic chemistry: Redox equilibria
Target group : HIS function(s): Q2, Q3, Q5, Q6
Duration : One session of 75 min
Objectives : After the training the participants will be able to:
• Understand the principles of redox reactions
• Understand the significance of redox potential measurement
Key concepts : • Galvanic cells
• Electrode potentials
• Stability field diagrams
Training methods : Lecture, exercises
Training tools
required
: Board, flipchart, OHS
Handouts : As provided in this module
Further reading
and references
: • Chemistry for environmental engineers, C. N. Sawyer, P. L.
McCarty & G. F. Parkin, Mc Graw Hill, Inc., 1994
• Process chemistry for water and wastewater treatment, L. D.
Benefield, J. P. Judkins & B. L. Weand, Prentice-Hall, Inc.,
1982
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 4
3. Session plan
No Activities Time Tools
1 Preparations:
2 Introduction:
• Ask participants to differentiate between different types of
chemical reactions
• Recapitulate reduction and oxidation reactions in the
previous modules
10 min OHS
3. Galvanic Cell:
• Describe component of a galvanic cell
• Explain the arrangement for study of a galvanic cell
• Explain standard hydrogen electrode and standard
electrode potential.
15 min OHS
4. Nernst equation and cell potential
• Explain how to write Nernst equation
• Define cell potential
• Explain how to calculate eqilibrium constant
10 min OHS
5. Stability field diagrams
• Define redox potential
• Discuss relation between Eh and pH
• Explain construction and use of stability field diagrams
15 min OHS
6. Exercise 15 min Additional
handout
7. Wrap out and evaluation 10 min
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 5
4. Overhead/flipchart master
OHS format guidelines
Type of text Style Setting
Headings: OHS-Title Arial 30-36, with bottom border line (not:
underline)
Text: OHS-lev1
OHS-lev2
Arial 24-26, maximum two levels
Case: Sentence case. Avoid full text in UPPERCASE.
Italics: Use occasionally and in a consistent way
Listings: OHS-lev1
OHS-lev1-Numbered
Big bullets.
Numbers for definite series of steps. Avoid
roman numbers and letters.
Colours: None, as these get lost in photocopying and
some colours do not reproduce at all.
Formulas/Equat
ions
OHS-Equation Use of a table will ease horizontal alignment
over more lines (columns)
Use equation editor for advanced formatting
only
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 6
Reduction - Oxidation Equilibria
• Theory of redox reaction
• Equilibrium state
• Stability field diagram
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 7
Recapitulate
• DO & COD determination
• Reduction and oxidation proceed simultaneously
• Gain and loss of electrons
• Change in oxidation state or oxidation number
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 8
Galvanic Cell (1)
• Half-reaction
- oxidation Zn(s) ↔ Zn2+
+ 2e
- reduction Cu2+
+ 2e ↔ Cu(s)
- overall Zn(s) + Cu2
+ ↔ Zn2+
+ Cu(s)
• Flow of electrons can be monitored
- reactions should be separated
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 9
Galvanic Cell (2)
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 10
Galvanic Cell (3)
• Electrodes, anode and cathode
- two half-cells
• Arrangement for migration of ions
• External conductor for flow of electrons
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 11
Electrode potential
• Potential developed at an electrode can be measured against
reference electrode
• Reference hydrogen electrode
- 2H+
+ 2e ↔ H2(g)
- Acts as cathode or anode
- Potential 0.0v
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 12
Standard Electrode Potential (1)
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 13
Standard Electrode Potential (2)
• All species in the two half-cells are at standard state
- P = 1atm, activities = 1
- Flow of electrons from H2 to Cu
- E0
h = +0.334V
• For Zn /H2 cell
- Flow of electrons from Zn to H2
- H2 electrode becomes cathode
- E0
h = -0.763V
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 14
Standard Electrode Potential (3)
O2(g) + 4H+
+4e ↔ 2H2O + 1.229 V
Cu2
+ 2e ↔ Cu(s) + 0.337 V
2H+
+ 2e ↔ H2(g) 0.000 V
Zn2+
+ 2e ↔ Zn(s) - 0.763 V
• Half-reaction always written as reduction
• Oxygen most effective electron acceptor in natural enviroment
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 15
Nernst Equation
aA + bB + … + ne ↔ cC + dD + …
• Gives potential when activities are not 1
• For standard conditions Eh = E0
h
E E
n
C D
A B
at Ch h
c d
a b
= −0 00 0591
25
.
log
...
...
,
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 16
Nernst Equation: Example
Zn2+
+ 2e ↔ Zn(s)
E0
h = -0.763, n = 2, [Zn(s)] = 1
E E
n
Zn s
Zn
h h= − +
0
2
0 0591.
log
bg
E
Zn
h = − − +
0 763 0 0285
1
2
. . log
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 17
Cell Potential
• Ordinarily hydrogen reference cell is not used.
• Any two half-reactions can be combined
• Ecell = Ecathode - Eanode
• Recognise cathode (+) and anode (-) on the basis of E0
h
values or E values when standard conditions do not prevail.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 18
Equilibrium Constant
• Zn - Cu Cell
- Cu electrode acts as cathode, E0
Cu > E0
Zn
• At equilibrium, Ecell = 0
E E
Cu
E
Zn
cell Cu Zn= −
R
S|
T|
U
V|
W|
− −
R
S|
T|
U
V|
W|+ +
0
2
0
2
0 059
2
1 0 059
2
1.
log
.
log
log
.
log
Zn
Cu
E E
K
Cu zn
eq
2
2
0 0
2
0 0591
+
+
=
−
=
d i
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 19
Redox Potential
• At equilibrium all half-cell potentials are equal.
• EZn = Ecu = Esystem (redox potential)
• Potential of an inert electrode against a reference electrode
• Eh (system)
- Oxidising environment ~ +0.3V
- Reducing environment ~ -0.5V
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 20
Stability Field Diagram (1)
• Often redox reactions include H+
or OH-
SO4
2-
+ 10H+
+8e ↔ H2S + 4H2O
• Eh, pH and predominant chemical species can be related
• When [H2S] = [SO4
2-
]
Eh = 0.3 - 0.074pH
E E pH
H S
SO
h h= − − −
0 2
4
2
0 074
0 0591
8
.
.
log
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 21
Stability Field Diagram (2)
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 22
Stability Field Diagram (3)
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 23
5. Evaluation sheets
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 24
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 25
6. Handout
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 26
Reduction - Oxidation Equilibria
• Theory of redox reaction
• Equilibrium state
• Stability field diagram
Recapitulate
• DO & COD determination
• Reduction and oxidation proceed simultaneously
• Gain and loss of electrons
• Change in oxidation state or oxidation number
Galvanic Cell (1)
• Half-reaction
- oxidation Zn(s) ↔ Zn2+
+ 2e
- reduction Cu2+
+ 2e ↔ Cu(s)
- overall Zn(s) + Cu2
+ ↔ Zn2+
+ Cu(s)
• Flow of electrons can be monitored
- reactions should be separated
Galvanic Cell (3)
• Electrodes, anode and cathode
- two half-cells
• Arrangement for migration of ions
• External conductor for flow of electrons
Electrode potential
• Potential developed at an electrode can be measure against reference electrode
• Reference hydrogen electrode
- 2H+
+ 2e ↔ H2(g)
- Acts as cathode or anode
- Potential 0.0v
Standard Electrode Potential (2)
• All species in the two half-cell are at standard state
- P = 1atm, activities = 1
- Flow of electrons from H2 to Cu
- E0
h = +0.334V
• For Zn /H2 cell
- Flow of electrons from Zn to H2
- H2 electrode becomes cathode
- E0
h = -0.763V
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 27
Standard Electrode Potential (3)
O2(g) + 4H+
+4e ↔ 2H2O + 1.229V
Cu2
+ 2e ↔ Cu(s) + 0.337V
2H+
+ 2e ↔ H2(g) 0.000V
Zn2+
+ 2e ↔ Zn(s) - 0.763V
• Half-reaction always written as reduction
• Oxygen most effective electron acceptor in natural environment
Nernst Equation
aA + bB + … + ne ↔ cC + dD + …
• Gives potential when activities are not 1
• For standard conditions Eh = E0
h
Nernst Equation: Example
Zn2+
+ 2e ↔ Zn(s)
E0
h = -0.763, n = 2, [Zn(s)] = 1
Cell Potential
• Ordinarily hydrogen reference cell is not used.
• Any two half-reactions can be combined
• Ecell = Ecathode - Eanode
• Recognise cathode (+) and anode (-) on the basis of E0
h values or E values when
standard conditions do not prevail.
Equilibrium Constant
• Zn - Cu Cell
- Cu electrode acts as cathode, E0
Cu > E0
Zn
• At equilibrium, Ecell = 0
E E
n
Zn s
Zn
h h= − +
0
2
0 0591.
log
bg
E E
n
C D
A B
at Ch h
c d
a b
= −0 00 0591
25
.
log
...
...
,
E
Zn
h = − − +
0 763 0 0285
1
2
. . log
E E
Cu
E
Zn
cell Cu Zn= −
R
S|
T|
U
V|
W|
− −
R
S|
T|
U
V|
W|+ +
0
2
0
2
0 059
2
1 0 059
2
1.
log
.
log
log
.
log
Zn
Cu
E E
K
Cu zn
eq
2
2
0 0
2
0 0591
+
+
=
−
=
d i
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 28
Redox Potential
• At equilibrium all half-cell potentials are equal.
• EZn = Ecu = Esystem (redox potential)
• Potential of an inert electrode against a reference electrode
• Eh (system)
- Oxidising environment ~ +0.3V
- Reducing environment ~ -0.5V
Stability Field Diagram (1)
• Often redox reactions include H+
or OH-
SO4
2-
+ 10H+
+8e ↔ H2S + 4H2O
• Eh, pH and predominant chemical species can be related
• When [H2S] = [SO4
2-
]
Eh = 0.3 - 0.074pH
E E pH
H S
SO
h h= − − −
0 2
4
2
0 074
0 0591
8
.
.
log
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 29
Add copy of Main text in chapter 8, for all participants.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 30
7. Additional handout
These handouts are distributed during delivery and contain test questions, answers to
questions, special worksheets, optional information, and other matters you would not like to
be seen in the regular handouts.
It is a good practice to pre-punch these additional handouts, so the participants can easily
insert them in the main handout folder.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 31
Questions
1. For each cell and given electrode reactions and standard potential, complete
the following table.
Cell Electrode reacions Eo
h, V Cathode Cell potential, V
A.
Cd2+
+ 2e ↔ Cd(s)
Ag+
+ e ↔ Ag(s)
-0.403
+0.799
B.
H2 + 2e ↔ 2H+
Cd + 2e ↔ Cd(s)
0.000
-0.403
C.
H2 + 2e ↔ 2H+
Ag+
+ e ↔ Ag(s)
0.000
0.799
2. A water sample contains both Fe2+
and Fe3+
. If the pH = 7.5 and Eh = +0.25V.
Using Figure 3, indicate which species will predominate.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 32
Questions and Answers
1. For each cell and given electrode reactions and standard potential, complete
the following table.
Cell Electrode reacions Eo
h, V Cathode Cell potential, V
A.
Cd2+
+ 2e ↔ Cd(s)
Ag+
+ e ↔ Ag(s)
-0.403
+0.799
Ag 1.202
B.
H2 + 2e ↔ 2H+
Cd + 2e ↔ Cd(s)
0.000
-0.403
H2 0.403
C.
H2 + 2e ↔ 2H+
Ag+
+ e ↔ Ag(s)
0.000
0.799
Ag 0.7999
2. A water sample contains both Fe2+
and Fe3+
. If the pH = 7.5 and Eh = +0.25V.
Using Figure 3, indicate which species will predominate.
Fe3+
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 33
8. Main text
Contents
1. Introduction 1
2. Galvanic Cells 1
3. Equilibrium state 5
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 1
Advanced aquatic chemistry: Redox equilibria
1. Introduction
Chemical reactions can be divided into two groups: (a) reactions in which no change of
oxidation state occurs, such as precipitation of calcium carbonate when sodium carbonate is
added to water containing calcium ions, neutralisation of carbonate with acid or ionisation of
acetic acid in water and (b) reactions in which changes in oxidation state of the reactants
occurs.
Reduction-oxidation (redox) reactions are involved in the measurement of oxygen and
chemical oxygen demand (see module # 11 and 18). Rules for balancing of redox reactions
were also given in module # 18. This module discusses the basic theory of redox reactions
and its applications in aqueous chemical systems.
2. Galvanic Cells
Redox reactions may be the result of direct transfer of electrons from donor to the acceptor.
Recall that the loss of electrons from the donor results in its oxidation and the gain of
electrons by the acceptor results in its reduction.
Thus, if metallic zinc is immersed in a copper sulphate solution the following reactions occur:
Oxidation : Zn(s) ↔ Zn2+
+ 2e (1)
Reduction: Cu2+
+ 2e ↔ Cu(s) (2)
------------------------------------------
Overall Zn(s) + Cu2+
↔ Zn2+
+ Cu(s) (3)
The individual oxidation and reduction reactions are called half-reactions, copper is
deposited directly on solid zinc surface in the overall reaction.
The flow of electrons from Zn(s) to Cu2+
can be monitored if the two half-reactions are
physically isolated from each other. Such an arrangement is shown in Figure 1 and is called
galvanic or electrochemical cell. The anode of the cell is the electrode at which oxidation
occurs (Zn), while cathode is the electrode at which reduction takes place. The cell can be
considered to comprise two half-cells.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 2
2.1 Standard electrode potentials
It is obvious from Figure 1, that the potential of an electrode can be measured only against
another half cell. An electrode potential is defined as the potential of a cell consisting of the
electrode in question acting as cathode and a standard hydrogen electrode acting as anode.
Figure 2 illustrates a reference hydrogen electrode and a copper electrode for measurement
of the electrode potential for the half-reaction given in Equation (2). Here instead of a
porous disc, as in Figure 1, a salt bridge (a tube containing gelatin and saturated KCl) is
provided to allow migration of negatively charged SO=
4 from copper half cell and positively
charged H+
from hydrogen half cell to maintain electrical neutrality.
The half reaction at the referene electrode is :
H2(g) ↔ 2H+
+ 2e (4)
Note that:
• All species in the standard half-cells are at standard state (P = 1 atm, activities = 1).
• The reference hydrogen half-cell is assigned a potential of 0.0V.
• Copper electrode bears a positive charge and it functions as cathode while the hydrogen
electrode functions as anode.
• The cell develops a potential of 0.334V and by definition is assigned a positive sign.
The standard electrode potential is, therefore, +0.334V.
Replacement of Cu-Cu2+
half-cell with Zn electrode immersed in a solution with a Zn2+
activity of one results in a potential of 0.763V. However, in this case the Zn electrode acts
as anode. The half-reactions become:
Zn(s) ↔ Zn2+
+ 2e (5)
2H+
+ 2e ↔ H2(g) (6)
Since the hydrogen electrode acts as cathode, the electrode potential is assigned a negative
sign and is equal to -0.763V.
Table 1 lists a few standard electrode potentials for the purpose of illustration. A more
complete list may be obtained from chemistry handbooks.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 3
E E
RT
nF
C D
A B
h h
o
c d
a b
= − ln
...
...
Half-reactions for standard electrode potential are always written as reductions. A negative
sign of the numerical value of the potential signifies that the half-reaction when coupled with
the hydrogen reference electrode would be an oxidation reaction.
Table 1 Standard electrode potentials, Eo
h at 250
C
Half-reactions V
O2(g) +4H+
+ 4e ↔ 2H2O + 1.229
Fe3+
+ e ↔ Fe2+
+ 0.771
Cu2+
+ 2e ↔ Cu(s) + 0.337
SO4
2-
+ 10H+
+ 8e ↔ H2S + 4H2O + 0.3
2H+
+ 2e ↔ H2(g) 0.000
Cd2+
+ 2e ↔ Cd(s) - 0.403
Zn2+
+ 2e ↔ Zn(s) - 0.763
Entries in the table are according to the numerical values of the E0
h. Among the listed
reactions oxygen is the most effective electron acceptor.
2.2 The Nernst equation
For the generalised raversible half-reaction
aA + bB + … + ne ↔ cC + dD + … (7)
where capital letters represents formulas for species, e is electron and a,b,c,d and n are
number of moles, the potential Eh is given by
(8)
where
Eo
h = standard electrode potential, V
R = gas constant, 8.316 J.K-1
.mol-1
T = temperature, 298K (25o
C)
F = the faraday, 96487 coulombs
ln = the base for natural logarithms = 2.303 log10
Substitution of numerical values gives:
(9)
(The subscripts h indicate that the potential measurements are against hydrogen reference
electrode).
E E
C D
A B
h h
o
c d
a b
= −
0 591
2
.
log
...
...
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 4
Example 1:
Generate Nernst expression for the half-reaction Zn2+
+ 2e ↔ Zn(s)
The Nernst expression is:
The activity of elemental Zn(s) is unity. The electrode potential varies with the logarithm of
reciprocal of molar Zn2+
concentration, assuming that the activity = molar concentration.
2.3 Cell potential
The potential of an elctrochemical cell is obtained by combining the electrode potentials of
the two half cell processes.
Ecell = Ecathode - Eanode (10)
Example 2:
Calculate the cell potential for the cell shown in Figure 1. Assume that the reactants are at
standard condition.
The standard electrode potentials for the Cu and Zn half-cells from Table 1 are +0.337 and -
0.763V, respectively. Since Eo
h value for Cu is higher it will act as cathode.
Therefore, Ecell = +0.337 - (-0.763) = 1.100V
In Example 2, Ecell may be written as Eo
cell, the standard cell potential, since Eo
h values were
used in determining the cell potential. In case the reactants are not at standard condition,
the Eh values can be calculated using the Nernst expression.
Example 3:
Calculate cell potential for the cell shown in Figure 1 when the activities of Zn2+
and Cu2+
are
0.1 and 0.01 mol/L.
The potential for Zn electrode is given by
The potential for Cu electrode will be
E E
Zn
h h
o
= − +
0 591
2
1
2
.
log
E VZn = − − = −−
0 763
0 0591
2
1
10
0 7931
.
.
log .
E VCu = − − = +−
0 337
0 0591
2
1
10
0 2782
.
.
log .
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 5
Therefore, the cell potential will be
Ecell = +0.278 - (-0.793) = 1.071V
3. Equilibrium state
3.1 Equilibrium constant
As a redox reaction proceeds, the concentration of the reactants decrease. Simultaneously
the concentrations of products increase. In a galvanic cell, the potential decreases and
ultimately at equilibrium it becomes zero. Thus,
Ecell = 0 = Ecathode = Eanode (11)
Taking the example of Zn - Cu cell, therefore at equilibrium:
ECu - EZn = 0
or
or (12)
where Keq is the equilibrium constant for the overall reaction, Equation 3.
Note that the concentrations Equation (12) would be the equilibrium concentrations. The
value of Keq can be calculated by substituting the values of standard potentials in the
equation.
3.2 Redox potential
In an aqueous chemical system there may be a number of chemical species giving rise to
corresponding half-reactions. Each half-reaction would develop a half-cell potential whose
magnitude would depend on the standard electrode potential for the half-reaction and the
activities of relevant species and temperature. If the chemical system is at equilibrium
(analogue to zero potential of a galvanic cell), these potentials are equal.
As an example, a natural water may be at equilibrium with respect to the following half-
reactions:
Fe3+
+ e ↔ Fe++
and SO4
2-
+ 10H+
+ 8e ↔ H2S + 4H2O
Therefore, EFe = ES = Esystem
The potential of the system is called the redox potential. It is determined by immersing an
inert electrode, usually platinum, in the chemical system in question and determining the
potential difference with respect to hydrogen or other reference electrode of known potential.
E
Cu
E
Zn
Cu Zn
0
2
0
2
0 0591
2
1 0 0591
2
1
0− − + =+ +
.
log
.
log
2
0 0591
0 0 2
2
E E Zn
Cu
K
Cu Zn
eq
−
= =
+
+
d i
.
log log
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 6
E E pH
H S
SO
h h= − − −
0 2
4
2
0 074
0 0591
8
.
.
log
Example 4:
The redox potential of a sample of water containing Fe2+
and Fe3+
ions is 0.5volt. Which is
the predominant specie of iron?
Write the Nernst expression for Fe3+
+ e ↔ Fe2+
or
or
Therefore, Fe2+
dominates
3.3 Stability field diagrams
Many of the redox reactions include H+
or OH-
ions. Stability diagrams can be drawn to
describe the relationship between Eh(cell potential with respect to hydrogen electrode), pH
and stable chemical species for a particular chemical system.
For example, the ability of a natural environment to oxidise sulphur will vary with its redox
potential. Sea water at the surface, where it is undergoing aeration, may have a potential of
+0.3 volt contains sulphates, while near the bottom sediments in presence of organic
sediments, the potential may be -0.5volt and sulphides may be present. The relevant half-
reaction relating the oxidised specie of sulphur, SO4
2-
, to the reduced specie, H2S, is:
SO2-
4 + 10H+
+ 8e ↔ H2S + 4H2O (13)
Writing the Nernst expression for the above equation relation between Eh and pH is
obtained:
or (14)
Assuming that the ratio of [H2S] and [SO4
2-
] is one and substituting the value of E0
h from
Table 1
Eh = 0.3 - 0.074pH (15)
E
Fe
Fe
h = = −
+
+
0 5 0 77
0 0591
1
2
3
. .
.
log
log
.
.
.
Fe
Fe
2
3
0 27
0 0591
4 58
+
+
= =
log .
Fe
Fe
2
3
4 58
10
+
+
=
E E
H S
SO H
h h= −
R
S|
T|
U
V|
W|− +
0 2
4
2 10
0 0591
8
1.
log .
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 7
A plot of Equation (15) is shown in Figure 3. If the Eh and pH value of a chemical system
plot on this line both the species (H2S and SO4
2-
) have the same concentration. However, if
for example the Eh value is 0.1 and the pH is 7, which is a point on the right side of the plot,
substitution of these values in Equation (14) gives the value of ration [H2S] / [SO4
2-
] = 10-43
.
Therefore, the plotting positions on the right side of the line show a predominance of SO4
2-
species in the water.
The first step in constructing a stability field diagram is to identify the pertinent reactions.
The reactions may not be limited to only redox reactions. The plotting equations are then
developed. Unit activities may be assumed for all soluble species.
Figure 4 shows a stability field diagram for iron. Iron species form various hydroxides and
also react with carbonate. These reactions are therefore included. The concentration of
total carbonic species is assumed as 10-5
M.
Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 8
The diagram also shows the theroretical limits for Eh and pH in nature. The strongest
oxidising agent commonly found in nature is the oxygen of the atmosphere. The upper limit
is given by the half-reaction:
O2 + 4H+
+ 4e ↔ 2H2O (16)
and its plotting equation is:
Eh = 12.2. - 0.59 pH (17)
The lower limit is given by the Nernst expression for Equation (6).
Eh = -0.059 pH (18)
The diagram shows that the change from Fe(II) to Fe(III) falls approximately in the middle of
the field representing conditions in nature, Eh - 0.2 to + 0.8 volt and pH 2 to 10. Shifts in pH
or Eh of the environment changes one form to the other. Reduced iron compounds occur in
sediment layers where Eh may be low. The diagram also indicates that oxidation of iron
takes place more completely under alkaline conditions.

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Download-manuals-water quality-wq-training-30advancedaquaticchemistry

  • 1. World Bank & Government of The Netherlands funded Training module # WQ - 30 Advanced aquatic chemistry: Redox equilibria New Delhi, January 2000 CSMRS Building, 4th Floor, Olof Palme Marg, Hauz Khas, New Delhi – 11 00 16 India Tel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685 E-Mail: dhvdelft@del2.vsnl.net.in DHV Consultants BV & DELFT HYDRAULICS with HALCROW, TAHAL, CES, ORG & JPS
  • 2. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 1 Table of contents Page 1 Module context 2 2 Module profile 3 3 Session plan 4 4 Overhead/flipchart master 5 5 Evaluation sheets 23 6 Handout 25 7 Additional handout 30 8 Main text 33
  • 3. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 2 1. Module context This module discusses redox equilibria relationships significant to characterisation of natural waters. Modules in which prior training is required to complete this module successfully and other, available related modules are listed in the table below. While designing a training course, the relationship between this module and the others, would be maintained by keeping them close together in the syllabus and place them in a logical sequence. The actual selection of the topics and the depth of training would, of course, depend on the training needs of the participants, i.e. their knowledge level and skills performance upon the start of the course. No. Module title Code Objectives 1. Basic chemistry concepts WQ - 02 • Convert units from one to another • Discuss the basic concepts of quantitative chemistry • Report analytical results with the correct number of significant digits. 2. Understanding the hydrogen ion concentration (pH) WQ - 06 • Discuss about the concept of pH • Calculate pH 3. The chemistry of dissolved oxygen measurement WQ - 11 • Appreciate significance of DO measurement. • Understand the chemistry of DO measurement by Winkler method. 4. Understanding chemical oxygen demand test WQ - 18 • Appreciate significance of COD measurement • Understand the chemistry of COD measurement 5. Basic aquatic chemistry concepts WQ - 24 • Understand equilibrium chemistry and ionisation constants. • Understand basis of pH and buffers • Calculate different types of alkalinity. 6. Advanced aquatic chemistry: solubility equilibria WQ - 29 • Explain the principles of chemical equilibrium • Define solubility product and explain how this relates to water quality assessment • Define the octanol-water partition coefficient and explain how this relates to water quality assessment.
  • 4. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 3 2. Module profile Title : Advanced aquatic chemistry: Redox equilibria Target group : HIS function(s): Q2, Q3, Q5, Q6 Duration : One session of 75 min Objectives : After the training the participants will be able to: • Understand the principles of redox reactions • Understand the significance of redox potential measurement Key concepts : • Galvanic cells • Electrode potentials • Stability field diagrams Training methods : Lecture, exercises Training tools required : Board, flipchart, OHS Handouts : As provided in this module Further reading and references : • Chemistry for environmental engineers, C. N. Sawyer, P. L. McCarty & G. F. Parkin, Mc Graw Hill, Inc., 1994 • Process chemistry for water and wastewater treatment, L. D. Benefield, J. P. Judkins & B. L. Weand, Prentice-Hall, Inc., 1982
  • 5. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 4 3. Session plan No Activities Time Tools 1 Preparations: 2 Introduction: • Ask participants to differentiate between different types of chemical reactions • Recapitulate reduction and oxidation reactions in the previous modules 10 min OHS 3. Galvanic Cell: • Describe component of a galvanic cell • Explain the arrangement for study of a galvanic cell • Explain standard hydrogen electrode and standard electrode potential. 15 min OHS 4. Nernst equation and cell potential • Explain how to write Nernst equation • Define cell potential • Explain how to calculate eqilibrium constant 10 min OHS 5. Stability field diagrams • Define redox potential • Discuss relation between Eh and pH • Explain construction and use of stability field diagrams 15 min OHS 6. Exercise 15 min Additional handout 7. Wrap out and evaluation 10 min
  • 6. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 5 4. Overhead/flipchart master OHS format guidelines Type of text Style Setting Headings: OHS-Title Arial 30-36, with bottom border line (not: underline) Text: OHS-lev1 OHS-lev2 Arial 24-26, maximum two levels Case: Sentence case. Avoid full text in UPPERCASE. Italics: Use occasionally and in a consistent way Listings: OHS-lev1 OHS-lev1-Numbered Big bullets. Numbers for definite series of steps. Avoid roman numbers and letters. Colours: None, as these get lost in photocopying and some colours do not reproduce at all. Formulas/Equat ions OHS-Equation Use of a table will ease horizontal alignment over more lines (columns) Use equation editor for advanced formatting only
  • 7. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 6 Reduction - Oxidation Equilibria • Theory of redox reaction • Equilibrium state • Stability field diagram
  • 8. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 7 Recapitulate • DO & COD determination • Reduction and oxidation proceed simultaneously • Gain and loss of electrons • Change in oxidation state or oxidation number
  • 9. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 8 Galvanic Cell (1) • Half-reaction - oxidation Zn(s) ↔ Zn2+ + 2e - reduction Cu2+ + 2e ↔ Cu(s) - overall Zn(s) + Cu2 + ↔ Zn2+ + Cu(s) • Flow of electrons can be monitored - reactions should be separated
  • 10. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 9 Galvanic Cell (2)
  • 11. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 10 Galvanic Cell (3) • Electrodes, anode and cathode - two half-cells • Arrangement for migration of ions • External conductor for flow of electrons
  • 12. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 11 Electrode potential • Potential developed at an electrode can be measured against reference electrode • Reference hydrogen electrode - 2H+ + 2e ↔ H2(g) - Acts as cathode or anode - Potential 0.0v
  • 13. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 12 Standard Electrode Potential (1)
  • 14. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 13 Standard Electrode Potential (2) • All species in the two half-cells are at standard state - P = 1atm, activities = 1 - Flow of electrons from H2 to Cu - E0 h = +0.334V • For Zn /H2 cell - Flow of electrons from Zn to H2 - H2 electrode becomes cathode - E0 h = -0.763V
  • 15. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 14 Standard Electrode Potential (3) O2(g) + 4H+ +4e ↔ 2H2O + 1.229 V Cu2 + 2e ↔ Cu(s) + 0.337 V 2H+ + 2e ↔ H2(g) 0.000 V Zn2+ + 2e ↔ Zn(s) - 0.763 V • Half-reaction always written as reduction • Oxygen most effective electron acceptor in natural enviroment
  • 16. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 15 Nernst Equation aA + bB + … + ne ↔ cC + dD + … • Gives potential when activities are not 1 • For standard conditions Eh = E0 h E E n C D A B at Ch h c d a b = −0 00 0591 25 . log ... ... ,
  • 17. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 16 Nernst Equation: Example Zn2+ + 2e ↔ Zn(s) E0 h = -0.763, n = 2, [Zn(s)] = 1 E E n Zn s Zn h h= − + 0 2 0 0591. log bg E Zn h = − − + 0 763 0 0285 1 2 . . log
  • 18. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 17 Cell Potential • Ordinarily hydrogen reference cell is not used. • Any two half-reactions can be combined • Ecell = Ecathode - Eanode • Recognise cathode (+) and anode (-) on the basis of E0 h values or E values when standard conditions do not prevail.
  • 19. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 18 Equilibrium Constant • Zn - Cu Cell - Cu electrode acts as cathode, E0 Cu > E0 Zn • At equilibrium, Ecell = 0 E E Cu E Zn cell Cu Zn= − R S| T| U V| W| − − R S| T| U V| W|+ + 0 2 0 2 0 059 2 1 0 059 2 1. log . log log . log Zn Cu E E K Cu zn eq 2 2 0 0 2 0 0591 + + = − = d i
  • 20. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 19 Redox Potential • At equilibrium all half-cell potentials are equal. • EZn = Ecu = Esystem (redox potential) • Potential of an inert electrode against a reference electrode • Eh (system) - Oxidising environment ~ +0.3V - Reducing environment ~ -0.5V
  • 21. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 20 Stability Field Diagram (1) • Often redox reactions include H+ or OH- SO4 2- + 10H+ +8e ↔ H2S + 4H2O • Eh, pH and predominant chemical species can be related • When [H2S] = [SO4 2- ] Eh = 0.3 - 0.074pH E E pH H S SO h h= − − − 0 2 4 2 0 074 0 0591 8 . . log
  • 22. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 21 Stability Field Diagram (2)
  • 23. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 22 Stability Field Diagram (3)
  • 24. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 23 5. Evaluation sheets
  • 25. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 24
  • 26. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 25 6. Handout
  • 27. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 26 Reduction - Oxidation Equilibria • Theory of redox reaction • Equilibrium state • Stability field diagram Recapitulate • DO & COD determination • Reduction and oxidation proceed simultaneously • Gain and loss of electrons • Change in oxidation state or oxidation number Galvanic Cell (1) • Half-reaction - oxidation Zn(s) ↔ Zn2+ + 2e - reduction Cu2+ + 2e ↔ Cu(s) - overall Zn(s) + Cu2 + ↔ Zn2+ + Cu(s) • Flow of electrons can be monitored - reactions should be separated Galvanic Cell (3) • Electrodes, anode and cathode - two half-cells • Arrangement for migration of ions • External conductor for flow of electrons Electrode potential • Potential developed at an electrode can be measure against reference electrode • Reference hydrogen electrode - 2H+ + 2e ↔ H2(g) - Acts as cathode or anode - Potential 0.0v Standard Electrode Potential (2) • All species in the two half-cell are at standard state - P = 1atm, activities = 1 - Flow of electrons from H2 to Cu - E0 h = +0.334V • For Zn /H2 cell - Flow of electrons from Zn to H2 - H2 electrode becomes cathode - E0 h = -0.763V
  • 28. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 27 Standard Electrode Potential (3) O2(g) + 4H+ +4e ↔ 2H2O + 1.229V Cu2 + 2e ↔ Cu(s) + 0.337V 2H+ + 2e ↔ H2(g) 0.000V Zn2+ + 2e ↔ Zn(s) - 0.763V • Half-reaction always written as reduction • Oxygen most effective electron acceptor in natural environment Nernst Equation aA + bB + … + ne ↔ cC + dD + … • Gives potential when activities are not 1 • For standard conditions Eh = E0 h Nernst Equation: Example Zn2+ + 2e ↔ Zn(s) E0 h = -0.763, n = 2, [Zn(s)] = 1 Cell Potential • Ordinarily hydrogen reference cell is not used. • Any two half-reactions can be combined • Ecell = Ecathode - Eanode • Recognise cathode (+) and anode (-) on the basis of E0 h values or E values when standard conditions do not prevail. Equilibrium Constant • Zn - Cu Cell - Cu electrode acts as cathode, E0 Cu > E0 Zn • At equilibrium, Ecell = 0 E E n Zn s Zn h h= − + 0 2 0 0591. log bg E E n C D A B at Ch h c d a b = −0 00 0591 25 . log ... ... , E Zn h = − − + 0 763 0 0285 1 2 . . log E E Cu E Zn cell Cu Zn= − R S| T| U V| W| − − R S| T| U V| W|+ + 0 2 0 2 0 059 2 1 0 059 2 1. log . log log . log Zn Cu E E K Cu zn eq 2 2 0 0 2 0 0591 + + = − = d i
  • 29. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 28 Redox Potential • At equilibrium all half-cell potentials are equal. • EZn = Ecu = Esystem (redox potential) • Potential of an inert electrode against a reference electrode • Eh (system) - Oxidising environment ~ +0.3V - Reducing environment ~ -0.5V Stability Field Diagram (1) • Often redox reactions include H+ or OH- SO4 2- + 10H+ +8e ↔ H2S + 4H2O • Eh, pH and predominant chemical species can be related • When [H2S] = [SO4 2- ] Eh = 0.3 - 0.074pH E E pH H S SO h h= − − − 0 2 4 2 0 074 0 0591 8 . . log
  • 30. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 29 Add copy of Main text in chapter 8, for all participants.
  • 31. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 30 7. Additional handout These handouts are distributed during delivery and contain test questions, answers to questions, special worksheets, optional information, and other matters you would not like to be seen in the regular handouts. It is a good practice to pre-punch these additional handouts, so the participants can easily insert them in the main handout folder.
  • 32. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 31 Questions 1. For each cell and given electrode reactions and standard potential, complete the following table. Cell Electrode reacions Eo h, V Cathode Cell potential, V A. Cd2+ + 2e ↔ Cd(s) Ag+ + e ↔ Ag(s) -0.403 +0.799 B. H2 + 2e ↔ 2H+ Cd + 2e ↔ Cd(s) 0.000 -0.403 C. H2 + 2e ↔ 2H+ Ag+ + e ↔ Ag(s) 0.000 0.799 2. A water sample contains both Fe2+ and Fe3+ . If the pH = 7.5 and Eh = +0.25V. Using Figure 3, indicate which species will predominate.
  • 33. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 32 Questions and Answers 1. For each cell and given electrode reactions and standard potential, complete the following table. Cell Electrode reacions Eo h, V Cathode Cell potential, V A. Cd2+ + 2e ↔ Cd(s) Ag+ + e ↔ Ag(s) -0.403 +0.799 Ag 1.202 B. H2 + 2e ↔ 2H+ Cd + 2e ↔ Cd(s) 0.000 -0.403 H2 0.403 C. H2 + 2e ↔ 2H+ Ag+ + e ↔ Ag(s) 0.000 0.799 Ag 0.7999 2. A water sample contains both Fe2+ and Fe3+ . If the pH = 7.5 and Eh = +0.25V. Using Figure 3, indicate which species will predominate. Fe3+
  • 34. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 33 8. Main text Contents 1. Introduction 1 2. Galvanic Cells 1 3. Equilibrium state 5
  • 35. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 1 Advanced aquatic chemistry: Redox equilibria 1. Introduction Chemical reactions can be divided into two groups: (a) reactions in which no change of oxidation state occurs, such as precipitation of calcium carbonate when sodium carbonate is added to water containing calcium ions, neutralisation of carbonate with acid or ionisation of acetic acid in water and (b) reactions in which changes in oxidation state of the reactants occurs. Reduction-oxidation (redox) reactions are involved in the measurement of oxygen and chemical oxygen demand (see module # 11 and 18). Rules for balancing of redox reactions were also given in module # 18. This module discusses the basic theory of redox reactions and its applications in aqueous chemical systems. 2. Galvanic Cells Redox reactions may be the result of direct transfer of electrons from donor to the acceptor. Recall that the loss of electrons from the donor results in its oxidation and the gain of electrons by the acceptor results in its reduction. Thus, if metallic zinc is immersed in a copper sulphate solution the following reactions occur: Oxidation : Zn(s) ↔ Zn2+ + 2e (1) Reduction: Cu2+ + 2e ↔ Cu(s) (2) ------------------------------------------ Overall Zn(s) + Cu2+ ↔ Zn2+ + Cu(s) (3) The individual oxidation and reduction reactions are called half-reactions, copper is deposited directly on solid zinc surface in the overall reaction. The flow of electrons from Zn(s) to Cu2+ can be monitored if the two half-reactions are physically isolated from each other. Such an arrangement is shown in Figure 1 and is called galvanic or electrochemical cell. The anode of the cell is the electrode at which oxidation occurs (Zn), while cathode is the electrode at which reduction takes place. The cell can be considered to comprise two half-cells.
  • 36. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 2 2.1 Standard electrode potentials It is obvious from Figure 1, that the potential of an electrode can be measured only against another half cell. An electrode potential is defined as the potential of a cell consisting of the electrode in question acting as cathode and a standard hydrogen electrode acting as anode. Figure 2 illustrates a reference hydrogen electrode and a copper electrode for measurement of the electrode potential for the half-reaction given in Equation (2). Here instead of a porous disc, as in Figure 1, a salt bridge (a tube containing gelatin and saturated KCl) is provided to allow migration of negatively charged SO= 4 from copper half cell and positively charged H+ from hydrogen half cell to maintain electrical neutrality. The half reaction at the referene electrode is : H2(g) ↔ 2H+ + 2e (4) Note that: • All species in the standard half-cells are at standard state (P = 1 atm, activities = 1). • The reference hydrogen half-cell is assigned a potential of 0.0V. • Copper electrode bears a positive charge and it functions as cathode while the hydrogen electrode functions as anode. • The cell develops a potential of 0.334V and by definition is assigned a positive sign. The standard electrode potential is, therefore, +0.334V. Replacement of Cu-Cu2+ half-cell with Zn electrode immersed in a solution with a Zn2+ activity of one results in a potential of 0.763V. However, in this case the Zn electrode acts as anode. The half-reactions become: Zn(s) ↔ Zn2+ + 2e (5) 2H+ + 2e ↔ H2(g) (6) Since the hydrogen electrode acts as cathode, the electrode potential is assigned a negative sign and is equal to -0.763V. Table 1 lists a few standard electrode potentials for the purpose of illustration. A more complete list may be obtained from chemistry handbooks.
  • 37. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 3 E E RT nF C D A B h h o c d a b = − ln ... ... Half-reactions for standard electrode potential are always written as reductions. A negative sign of the numerical value of the potential signifies that the half-reaction when coupled with the hydrogen reference electrode would be an oxidation reaction. Table 1 Standard electrode potentials, Eo h at 250 C Half-reactions V O2(g) +4H+ + 4e ↔ 2H2O + 1.229 Fe3+ + e ↔ Fe2+ + 0.771 Cu2+ + 2e ↔ Cu(s) + 0.337 SO4 2- + 10H+ + 8e ↔ H2S + 4H2O + 0.3 2H+ + 2e ↔ H2(g) 0.000 Cd2+ + 2e ↔ Cd(s) - 0.403 Zn2+ + 2e ↔ Zn(s) - 0.763 Entries in the table are according to the numerical values of the E0 h. Among the listed reactions oxygen is the most effective electron acceptor. 2.2 The Nernst equation For the generalised raversible half-reaction aA + bB + … + ne ↔ cC + dD + … (7) where capital letters represents formulas for species, e is electron and a,b,c,d and n are number of moles, the potential Eh is given by (8) where Eo h = standard electrode potential, V R = gas constant, 8.316 J.K-1 .mol-1 T = temperature, 298K (25o C) F = the faraday, 96487 coulombs ln = the base for natural logarithms = 2.303 log10 Substitution of numerical values gives: (9) (The subscripts h indicate that the potential measurements are against hydrogen reference electrode). E E C D A B h h o c d a b = − 0 591 2 . log ... ...
  • 38. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 4 Example 1: Generate Nernst expression for the half-reaction Zn2+ + 2e ↔ Zn(s) The Nernst expression is: The activity of elemental Zn(s) is unity. The electrode potential varies with the logarithm of reciprocal of molar Zn2+ concentration, assuming that the activity = molar concentration. 2.3 Cell potential The potential of an elctrochemical cell is obtained by combining the electrode potentials of the two half cell processes. Ecell = Ecathode - Eanode (10) Example 2: Calculate the cell potential for the cell shown in Figure 1. Assume that the reactants are at standard condition. The standard electrode potentials for the Cu and Zn half-cells from Table 1 are +0.337 and - 0.763V, respectively. Since Eo h value for Cu is higher it will act as cathode. Therefore, Ecell = +0.337 - (-0.763) = 1.100V In Example 2, Ecell may be written as Eo cell, the standard cell potential, since Eo h values were used in determining the cell potential. In case the reactants are not at standard condition, the Eh values can be calculated using the Nernst expression. Example 3: Calculate cell potential for the cell shown in Figure 1 when the activities of Zn2+ and Cu2+ are 0.1 and 0.01 mol/L. The potential for Zn electrode is given by The potential for Cu electrode will be E E Zn h h o = − + 0 591 2 1 2 . log E VZn = − − = −− 0 763 0 0591 2 1 10 0 7931 . . log . E VCu = − − = +− 0 337 0 0591 2 1 10 0 2782 . . log .
  • 39. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 5 Therefore, the cell potential will be Ecell = +0.278 - (-0.793) = 1.071V 3. Equilibrium state 3.1 Equilibrium constant As a redox reaction proceeds, the concentration of the reactants decrease. Simultaneously the concentrations of products increase. In a galvanic cell, the potential decreases and ultimately at equilibrium it becomes zero. Thus, Ecell = 0 = Ecathode = Eanode (11) Taking the example of Zn - Cu cell, therefore at equilibrium: ECu - EZn = 0 or or (12) where Keq is the equilibrium constant for the overall reaction, Equation 3. Note that the concentrations Equation (12) would be the equilibrium concentrations. The value of Keq can be calculated by substituting the values of standard potentials in the equation. 3.2 Redox potential In an aqueous chemical system there may be a number of chemical species giving rise to corresponding half-reactions. Each half-reaction would develop a half-cell potential whose magnitude would depend on the standard electrode potential for the half-reaction and the activities of relevant species and temperature. If the chemical system is at equilibrium (analogue to zero potential of a galvanic cell), these potentials are equal. As an example, a natural water may be at equilibrium with respect to the following half- reactions: Fe3+ + e ↔ Fe++ and SO4 2- + 10H+ + 8e ↔ H2S + 4H2O Therefore, EFe = ES = Esystem The potential of the system is called the redox potential. It is determined by immersing an inert electrode, usually platinum, in the chemical system in question and determining the potential difference with respect to hydrogen or other reference electrode of known potential. E Cu E Zn Cu Zn 0 2 0 2 0 0591 2 1 0 0591 2 1 0− − + =+ + . log . log 2 0 0591 0 0 2 2 E E Zn Cu K Cu Zn eq − = = + + d i . log log
  • 40. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 6 E E pH H S SO h h= − − − 0 2 4 2 0 074 0 0591 8 . . log Example 4: The redox potential of a sample of water containing Fe2+ and Fe3+ ions is 0.5volt. Which is the predominant specie of iron? Write the Nernst expression for Fe3+ + e ↔ Fe2+ or or Therefore, Fe2+ dominates 3.3 Stability field diagrams Many of the redox reactions include H+ or OH- ions. Stability diagrams can be drawn to describe the relationship between Eh(cell potential with respect to hydrogen electrode), pH and stable chemical species for a particular chemical system. For example, the ability of a natural environment to oxidise sulphur will vary with its redox potential. Sea water at the surface, where it is undergoing aeration, may have a potential of +0.3 volt contains sulphates, while near the bottom sediments in presence of organic sediments, the potential may be -0.5volt and sulphides may be present. The relevant half- reaction relating the oxidised specie of sulphur, SO4 2- , to the reduced specie, H2S, is: SO2- 4 + 10H+ + 8e ↔ H2S + 4H2O (13) Writing the Nernst expression for the above equation relation between Eh and pH is obtained: or (14) Assuming that the ratio of [H2S] and [SO4 2- ] is one and substituting the value of E0 h from Table 1 Eh = 0.3 - 0.074pH (15) E Fe Fe h = = − + + 0 5 0 77 0 0591 1 2 3 . . . log log . . . Fe Fe 2 3 0 27 0 0591 4 58 + + = = log . Fe Fe 2 3 4 58 10 + + = E E H S SO H h h= − R S| T| U V| W|− + 0 2 4 2 10 0 0591 8 1. log .
  • 41. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 7 A plot of Equation (15) is shown in Figure 3. If the Eh and pH value of a chemical system plot on this line both the species (H2S and SO4 2- ) have the same concentration. However, if for example the Eh value is 0.1 and the pH is 7, which is a point on the right side of the plot, substitution of these values in Equation (14) gives the value of ration [H2S] / [SO4 2- ] = 10-43 . Therefore, the plotting positions on the right side of the line show a predominance of SO4 2- species in the water. The first step in constructing a stability field diagram is to identify the pertinent reactions. The reactions may not be limited to only redox reactions. The plotting equations are then developed. Unit activities may be assumed for all soluble species. Figure 4 shows a stability field diagram for iron. Iron species form various hydroxides and also react with carbonate. These reactions are therefore included. The concentration of total carbonic species is assumed as 10-5 M.
  • 42. Hydrology Project Training Module File: “ 30 Advanced aquatic chemistry.doc” Version 06/11/02 Page 8 The diagram also shows the theroretical limits for Eh and pH in nature. The strongest oxidising agent commonly found in nature is the oxygen of the atmosphere. The upper limit is given by the half-reaction: O2 + 4H+ + 4e ↔ 2H2O (16) and its plotting equation is: Eh = 12.2. - 0.59 pH (17) The lower limit is given by the Nernst expression for Equation (6). Eh = -0.059 pH (18) The diagram shows that the change from Fe(II) to Fe(III) falls approximately in the middle of the field representing conditions in nature, Eh - 0.2 to + 0.8 volt and pH 2 to 10. Shifts in pH or Eh of the environment changes one form to the other. Reduced iron compounds occur in sediment layers where Eh may be low. The diagram also indicates that oxidation of iron takes place more completely under alkaline conditions.