1
Electroanalytical methods
Introduction
Reductions and Oxidations
Electrodes, Cells
Half-reactions
Reduction Potentials
The Electrochemical Series
Cell Potentials and Thermodynamic Functions
Equilibrium electrochemistry
2
Books and Monograph Series
1. A. J. Bard, Electroanalytical Chemistry, Marcel Dekker, N.Y. , 1970
2. J. Dvořák, J. Koryta: Elektrochemie, Academia, Praha, 1975
3. J. Zýka et al.: Analytická příručka, 3rd ed. SNTL, Praha, 1979
4. J. Koryta: Iontově selektivní elektrody, Academia, Praha, 1984
10. J. Wang: Analytical Electrochemistry, VCH Publishers, N.Y., 1st
ed., 1984, 2nd ed. 1994, 3rd ed. 2006
5. Ch.M.A.Brett, A.M.O.Brett: Electrochemistry, Oxford, 1993
6. P. Klouda: Moderní analytické metody, P.K., Ostrava, 1994
8. K. Markušová: Elektrochemické metódy, PF UPJŠ, Košice, 2003
7. J.O´M. Bockris, A.K.M.Reddy: Modern Electrochemistry 1,2A,2B,
Plenum Press, N.Y. 1998
L. Trnková : Moderní elektrochemické metody, v přípravě
9. J. Barek, F. Opekar, K. Štulík: Elektroanalytická chemie, Učební
texty UK v Praze, 2005 (skripta)
11. A. J. Bard, R. L. Faulkner: Electrochemical Methods: Fundamentals
and Applications, 2nd ed., Wiley, 2000.
12. F. Scholz: Electroanalytical Methods: Guide to Experiments and
Applications, 2nd ed., Springer, 2002.
3
Journals
1. Journal of Electrochemical Society (J. Electrochem. Soc.)
5. Journal of Applied Electrochemistry (J. Appl. Electrochem.)
3. Journal of Electroanalytical Chemistry (J. Electroanal. Chem.)
2. Electrochimica Acta (Electrochim. Acta)
4. Bioelectrochemistry (and Bioenergetics) (Bioelectrochem.)
10. Sensors
13. Langmuir
12. Corrosion Science
7. Journal of Colloid and Interface Science (J. Colloid Interface Sci.)
8. Analytical Chemistry (Anal. Chem.)
6. Journal of Solid State Electrochemistry (J. Solid State Electrochem.)
14. Elektrokhimiya
11. Sensors and Actuators
9. Electroanalysis
15. Journal of Physical Chemistry (J. Phys. Chem.)
16. Biophysical Chemistry (Biohys. Chem.)
Conferences ISE - Symposium
4
 Recent Advances in Electrochemical Instrumentation and Electrodes
 Electrochemistry meets Biology: Fundamental Aspects of Electrochemistry
with Biological Systems
 Advanced Materials Design for Bioelectrochemical Applications: from
Biosensors to Biofuel Cells
 Advanced Batteries and Electrochemical Capacitors
 Fuel Cells: Materials, Properties, Performance and Durability
 Physical Modeling and Numerical Simulation of Electrochemical Power
Generators
 Cathodic and Anodic Routes to Electrochemical Fabrication
 Electroactive Polymeric and Inorganic Materials
 Corrosion Science and Engineering
 Electrochemical Process Engineering and Technology
 Intermediates and Mechanisms at a Molecular Level
 Photoelectrochemistry, Electrochromism, Electrochemiluminescence
 Physical Electrochemistry: from Fundamentals to Smart Materials and New
Catalysts
 Electrochemistry at Liquid-Liquid Interfaces
 General Session
5
Equilibrium electrochemistry
 Galvanic cell
 Electrolytic cell
 Reduction
 Oxidation
 Half Reactions
 Redox Couple
 Anode
 Cathode
 Standard Electrode Potential
6
Some Symbols
 Potential ………E,φ [V]
 Potential of Electrolytic cell ……U, E [V]
 Current ………I, i [A]
 Current density…... …j [A/m2]
 Resistance ……… R [Ω] or [S-1]
 Charge ……… Q,q [C]
 Conductivity……… G [S] or [Ω-1]
 Capacity……… C [F]
 Impedance……… Z [Ω]
 Permitivity …... …ε0 [F/m] or εr [-]
7
Introduction
- was born from a union between biochemistry and electricity
Methods of solutions (basic) Electrochemistry (EC)
Luigi Galvani, 1791, Bologna
8
Introduction
The Royal
Society
London
- silver plate and zinc plate, a pasteboard membrane with
salt water , “ artificial electric organ“
Alessandro Volta, 1800
9
Introduction
– the relation between the amount of electricity consumed
and the amount of metal produced in solid form from
Rolls
Royce
cars
Michael Faraday, 1834
10
pedant Julius Tafel, 1905 – electric currents passing across
metal-solution interfaces could be made to increase
exponentially by changing the electric potential
Introduction
Debye and Hückel, 1923 – a credible
theory of the properties of ionically
conducting solutions
vthermal ~ A exp (-Ea/RT)
velchem ~ B exp (-αEF/RT)
– the first moon landing in 1969
– electrochemical fuell cells ( U.S. space vehicles)
– electrochemical sensors (diabetics)
– corrosion inhibition (sea oil platform)
application
11
Polarograph, Model 1924
Introduction
Jaroslav Heyrovský Nobel Prize 1959
Jaroslav Heyrovsky and
Michael Heyrovsky
12
Introduction
ELECTROCHEMICAL METHODS (current = 0)
- Potentiometry
direct (pH)
titration determination of equilibrium
constants,
protonation - pKa
complexation - pKAL
13
Introduction
ELECTROCHEMICAL METHODS (current 0)
- Polarography (d.c., tast, a. c.)
- Pulse Polarography (PP) , voltammetry (PV)
- Differential Pulse Polarography (DPP) , voltammetry (DPV)
- Linear Sweep Voltammetry (LSV)
- Cyclic Voltammetry (CV), Fast CV
- Adsorptive Stripping Voltammetry (AdSV)
- Square Wave Voltammetry (SWV)
- Constant Current Derivative Chronopotentiometric
Stripping Analysis (CPSA)
- Coulometry (Coul)
- Elimination Polarography (EP)
- Elimination Voltammetry with Linear Scan (EVLS)
14
Introduction
Two kinds of EC
EC ELECTRODICSIONIC
the electrode is the stage
the solution is the theater and audience
ion – solvent interactions
ion – ion interactions
ion transport
ionic liquids
interfacial region
mechanism of electrically
controlled surface reactions
e- X-+
15
Introduction
e
e
e
e
e
e
e e e
e
e
e
e
e
e
e
e
e
e
e
e
UNCUT METAL - ELECTRONS RANDOM
e
“ electron gas“ , Pauli princip (fermiony)
Fermi-Dirac statistics
Fermi function
e
quantal
particles
16
Introduction
Enrico Fermi
(Nobel prize 1938)
Paul Adrien Maurice Dirac
(Nobel prize 1933)
electron - fermion
17
Fermi-Dirac statistics is a particular case of particle statistics
developed by Enrico Fermi and Paul Dirac that determines the
statistical distribution of fermions over the energy states for a
system in thermal equilibrium. In other words, it is a probability
of a given energy level to be occupied by a fermion.
Fermions (spin 1/2, 3/2, 5/2 …) are particles which are
indistinguishable and obey the Pauli exclusion principle, i.e., no
more than one particle may occupy the same quantum state at the
same time. Statistical thermodynamics is used to describe the
behaviour of large numbers of particles. A collection of noninteracting
fermions is called a Fermi gas.
  T/kEE
P
BF

exp1
1
Introduction
TkversusE BF
18
F-D statistics:
the expected number of particles in states with energy εi is:
where:
is the number of particles in state i,
is the energy of state i,
is the degeneracy of state i (the number of states with energy ),
is the chemical potential (sometimes the Fermi energy
is used instead, as a low-temperature approximation),
is Boltzmann's constant, and
is absolute temperature.
In the case where μ is the Fermi energy and
the function is called the Fermi function:
Introduction
19
Fermi-Dirac distribution as a
function of E/EF plotted for 4
different temperatures.
Occupancy transitions are
smoother at higher temperatures.
Introduction
TkE BF 
Tk/2E BF 
Tk/10E BF 
Tk/100E BF 
FE/E
  T/kEE
P
BF

exp1
1
P
20
Introduction
The Fermi-Dirac distribution function
21
Schematic representation of the potential distribution in a cell. For
clarity, the potential in the metal M and in the reference electrode is
not shown
Introduction
22
Energy diagram of the metal | electrolyte interface
Introduction
23
Introduction
e
e
ee
e
e
ee
e
e
e
e
e
e
e
e
e
e
S
O
L
U
T
I
O
N
Negative excess charge
Positive excess charge
CUT METAL
e
e
e
e
24
Introduction
eOne phase
contains
electrons
Other
phase
contains
ions
the fundamental act in EC
25
Introduction
power
supply
2e2e
RhPt
2H+
2IH2
I2
HI H++Ielectrochemical
reactor
pumping
electrons
into Pt
plate
electrons
flow back
to the
power
source
oxidationreduction
26
Introduction
HI H+ + I-
2HI 2H+ (aq) + 2I- (aq)
2I- (aq) I2 (g) + 2e
at Pt electrode
in solution
2H+ (aq) + 2e H2 (g)
at Rh electrode
net reaction 2HI H2 (g) + I2 (g)
CHEMICAL REACTION
H I
H I
thermal
collisional activation
H
H
I
I
bond breaking
H2 + I2
H
H
I
I
+
27
Introduction
HI (g) H+ (aq) + I- (aq)
water
H2 (g) I2 (g)
ELECTROCHEMICAL
(ELECTRIC)
REACTION
28
Introduction
Electrochemical cell for measuring the electrode potential on the SHE
scale. A salt bridge is an ionic conductor introduced to physically
separate the two solutions, but keeping at the same time their inner
potentials equal or almost equal
Standard Hydrogen Electrode
SHE
29
Electrochemical dissolution of zinc. The beaker on the left and
the salt bridge are filled with a solution of sodium nitrate, and
the beaker on the right is filled with nitric acid
Introduction
electrones current
30
Diagram of an OTTLE electrode. The working electrode is a fine
metallic grid placed in a UV-VIS cell with a short optical path
Introduction
Optically
Transparent Thin
Layer Electrode
CE
RE
WE
OTTLE
31
Schematic representation of the working principle of a lead acid accumulator
Pb + 2H2SO4 + PbO2 → PbSO4 + 2H2O + PbSO4
Pb + SO4
2− → PbSO4 + 2e− PbO2 + 4H+ + SO4
2− + 2e− → PbSO4 + 2H2O
Pb + HSO4
− → PbSO4 + H+ + 2e− PbO2 + 3H+ + HSO4
− + 2e− → PbSO4 + 2H2O
oxidation reduction
2V
2
- +
charging
sulphation!
secondary galvanic cellLead acid battery
32
Schema of electron transfer at an electrode
33
Lithium metal and ion battery
Schematic diagram of the principle of Li battery and Li ion battery
Li/Si
LiCl/KCl
primary galvanic cell
MnO2
metal oxidLi/C
Li salt in organic solvent
34
Hydrogen and oxygen are introduced via the porous electrodes. The
electrochemical reactions happen at the electrode | membrane interface
(oxidation of hydrogen into protons at the anode, reduction of oxygen
and the production of water at the cathode).
Fuel cell
Schematic diagram of a low-temperature fuel cell
REACTION
Anode : 2H2 + 2O–2 → 2H2O + 4e–
Cathode : O2 + 4e– → 2O–2
Overall Cell : 2H2 + O2 → 2H2O
35
Demonstration model of a directmethanol
fuel cell. The actual fuel
cell stack is the layered cube shape in
the center of the image
Fuel cell
Alcaline fuel cells (AFC)
Phosphoric acid fuel cells (PAFC)
Solid oxide fuel cells (SOFC)
Molten carbonate fuel cells (MCFC)
Polymer electrolyte membrane fuel cells
(PEMFC)
Proton exchange membrane fuel cells
(PEMFC)
NASA
36
Two Practical Cells
 At left is a
primary cell
(used once
only).
 At right is a
secondary
cell (may be
re-charged)
37
Reactions at electrodes
 Left: Galvanic
cell. Electrons
are deposited on
the anode (so it
is neg) and
collected from
the cathode (so it
is positive)
 Right: Electrolytic
cell. Electrons
are forced
out of the anode
(positive) and
into the cathode
(negative)
Galvanic cell Electrolytic cell
as Rh as Pt
H2I2
as Zn as Cu
Zn2+ Cu0
X
38
Two Versions of the Daniell Cell
GC with conversion GC without conversion
39
Constructing a Daniell Cell
KCl
10%KNO3
or
40
Cell Notation
 In the version of the Daniell cell with the porous pot
there is a liquid junction (diffusion or liquid potential).
This is denoted as Zn(s)|ZnSO4(aq):CuSO4(aq)|Cu(s)
 When the liquid junction potential has been essentially
eliminated by use of a salt bridge the Daniell cell is
denoted as Zn(s)|ZnSO4(aq)||CuSO4(aq)|Cu(s)
 Other punctuation in cell notations includes a comma
to separate two species present in the same phase.
Daniell cell
Redox reactions and electrode
processes
https://learnnext.com/CBSE-Class-XI-Chemistry/Lesson-Redox-Reactions-
And-Electrode--Processes.htm
41
42
Types of Electrodes
 (a) metal/metal
ion electrode
 (b) metal/
insoluble salt
electrode
 (c) gas electrode
 (d) redox
electrode
43
Types of Electrode
DesignationElectrode type
Metal/metal ion M(s)/M+ (aq) M+(aq) + e = M (s)
Gas Pt(s)/X2(g)/X+(aq) X+(aq) + e = 1/2 X2(g)
Pt(s)/X2(g)/X-(aq) 1/2X2(g) + e = X-(aq)
Metal/insol. salt M(s)/MX(s)/X- (aq) MX(s)+ e=M(s) +X- (aq)
Redox M2+/M+ M2+(aq) + e = M+(s)
Half reaction
44
Cells with a Common Electrolyte
 a cell in which the
anode is a hydrogen
electrode and the
cathode is a silversilver
chloride
 electrode is denoted
Pt|H2(g)|H+(aq), Cl-(aq) | AgCl(s)|Ag(s)
Pt|H2(g)|HCl(aq)|AgCl (s)|Ag(s)
45
Varieties of Cell
The two basic types:
concentration cells and chemical cells
 Concentration cells are:
 electrolyte concentration cells, where the
electrode compartments are identical except
for the concentrations of the electrolytes,
 electrode concentration cells, in which the
electrodes themselves have different
concentrations, such as amalgams or gas
electrodes at different pressures.
 Most cells are chemical cells.
46
The Cell Potential
 Since w = DG
= - work output, and
since electrical work
output = (charge) x
(voltage) = nFE ,
 DG = - nFE
DG…….Gibbs energy
n……….number of electrons
F ………Faraday constant
E……….potential
 A spontaneous
reaction has a
negative DG and a
positive E
E is intensive
47
The Nernst Equation
 Substituting DG = - nFE into
DG = DGo + RT ln Q gives
- nFE = - nFEo + RT ln Q
or
E = Eo – (RT/nF) ln Q NERNST EQUATION
 At 25oC……… RT/F = 0.02569 V = 25.69 mV
 A practical form of the Nernst equation is
E = Eo - (25.69 mV/n ln Q
 At equilibrium, E = 0 and Q = K, so
ln K = nFEo/RT Eo = RT ln K /nF
 At 25oC……… ln K = nEo/(25.69 mV)
reaction A+B=C+D
Q = aCaD/aAaB
Walther Hermann Nernst (1864-1941)
48
Concentration Cells
 A concentration cell derives its potential from
the difference in concentration between the
right and left sides.
M|M+(aq, L)||M+(aq, R)|M
 The cell reaction is M+(aq, R) - M+(aq, L)
 Using the Nernst equation, E = Eo - (RT/nF) ln Q
 Eo = 0 ! (Do you see why?)
 Q = aL/aR
 So for a conc. cell, E = - (RT/nF) ln (aL/aR)
49
Standard Electrode Potentials
 Eo
cell can be found from DrGo using the
equation DrGo = -nFEo
(or in general, DrG = -nFE)
 But Eo
cell can also be found from values of Eo
for the two electrodes involved.
 Standard electrode potentials are given in
Tables
 Since it is impossible to measure the potential
of one electrode alone, these are all relative to
hydrogen standard electrode
Eo
cell = Eo
R - Eo
L
Eo
cell Eo
cell x Eo
50
E and Spontaneity
 Eo > 0 goes with K > 1, which indicates a
spontaneous reaction
 However, the direction of a reaction can
sometimes be reversed by judicious
manipulation of the concentrations of product
and reactant species. (That is, by altering Q =
aCaD/aAaB from reaction A+B=C+D)
 Any given reaction proceeds left to right when
E 0 (not Eo !)>
51
The Electrochemical Series
 A species with a low standard reduction
potential has a thermodynamic tendency to
reduce a species with a high standard
reduction potential.
- More briefly, low reduces high (LRH).
- Equivalently, high oxidizes low (HOL).
 This is the basis for the activity series of metals.
 Other couples can also be fitted into the activity
series.
52
Activity Series of Metals
potassium
sodium
calcium
magnesium
aluminum
zinc
chromium
iron
nickel
tin
lead
copper
silver
platinum
gold
increasingreactivity
React violently (strongly) with cold water
React slowly with cold water
React very slowly with steam but quite
reactive in acid
React moderately with high levels of acid
< HYDROGEN comes here
Unreactive in acid
Noble metals
53
The Hydrogen Electrode and pH
 The potential of a hydrogen electrode is directly
proportional to the pH of the solution. Consider the
calomel-hydrogen cell
Hg(l)| Hg2Cl2(s)| Cl-(aq)|| H+(aq)|H2(g)|Pt
for which the cell reaction is
Hg2Cl2(s) + H2(g) = 2 Hg(l) + 2 Cl-(aq) + 2 H+(aq)
 If the H2(g) is at standard pressure and the chloride
ion activity is constant and incorporated into Eo´, the
Nernst equation becomes E = Eo´ - (RT/2F) ln a(H+)2
= E = Eo´ - (RT/2F) 2ln a(H+) = Eo´ + (RT ln 10/F) pH
= Eo´ + (59.15 mV) pH
 So the pH can be determined from the cell potential.
pH = -log a(H+)
54
Thermodynamic Functions and E’s
 Because of the relationship
DrG = - nFDE
DrGo = - nFDEo
 It is possible to obtain the thermodynamic
value of the standard reaction Gibbs energy by
measuring cell potentials.
- DrG = nFDE = RT ln K - RT ln Q
DE = (RT/nF) ln K – RT/nF ln Q
DEo
55
Finding Eo via DGo
 Eo’s for two half-reactions can be combined
directly as long as the number of electrons is
the same in each half-reaction and the
electrons cancel out when the half-reactions
are combined.
 Eo’s cannot be directly combined for halfreactions
in which the electrons do not cancel
out.
• For instance, Eo for Cu2+|Cu+ cannot be
found by directly combining Eo’s for Cu2+|Cu
and Cu+|Cu .
 In these cases, Eo’s may be converted to DGo’s
for and the DGo’s for then directly combined.
Gibbs energy
56
Other Thermodynamic Values - DrHo
 The van’t Hoff equation may be modified to
give DrHo if Eo is measured at two different
temperatures.
• Substitute -DrGo/RT for ln K
• Substitute -nFEo for DrGo
–or do it in one step by replacing nFEo /RT
for ln K
van’t Hoff reaction isobar
2
0
RT
H
T
K rD







 ln
Enthalpy
57
Other Thermodynamic Values - DrSo
 With expressions for both DrGo and DrHo
the entropy can also be obtained.
 DrSo is given by the relation
000
STHG rrr DDD
12
1
0
2
0
0 )()(
TT
TETE
nFSr


D
Entropy
Exercise
58
 Is the equilibrium constant for the displacement of
copper by zinc greater or smaller than 1? Calculate the
equilibrium constant for this reaction.
 Solution: For this cell reaction,
R : Cu2+ + 2e = Cu Eo
R = +0.34 V
L : Zn2+ + 2e = Zn Eo
L = - 0.76 V
Eo
cell = Eo
R - Eo
L = +0.34 v – (-0.76 v) = +1.10 V
Since Eo is positive, the reaction is spontaneous, and
K>1.
ln K =n Eo/(25.69 mV) = 2 (1100 mV)/(25.69 mV)
K = 1.554 * 1037