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CH4005 Physical Chemistry IV
Lectures 1-2 Mon, 3-4 Wed, Th 2-3
Labs commence week 2 Mon 9.00-12.00
Wed 10.00-13.00
Examinations End of term 65%
Mid term 10% date tbc (Week 7/8)
Labs 25% (including lab exam
based on lab and lecturematerial)
Labs are compulsory as is submission of reports, failure
to attend labs/submit reports will entail repeating themodule next year as labs can not be repeated
Office hours Mon 9.0010.00 Tues 10.0011.00
MS1018 [email protected]
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CH4005 Physical Chemistry IV
MODULE AIMS/OBJECTIVES
To familiarise the student with electrochemical methods of
chemical analysis.
To introduce the area of large scale electrochemical technology.
To provide an understanding of electrochemical corrosion
problems.
SHORT SYLLABUS
Analytical techniques of electrochemistry; corrosion; protection of
metals; electrodeposition; surface treatment; chlor-alkali cells;
electrosynthesis.
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LONG SYLLABUS
Mass Transport in Solution. Ficks Laws of Diffusion. Electron
transfer reactions. Overpotential/Polarization Effects. Electrode
reactions, oxidation/reduction. Electrode kinetics, Butler-Volmer
equation, limiting forms. I/E curves, interplay of mass transport
and electron transport. Electrical double layer. Ideally polarizable
electrode, capacitance, interfacial effects, models of the double
layer. Analytical techniques of electrochemistry. Polarography,
steady-state, sweep, convective/diffusion and A.C. techniques.Electrodeposition: Electrocrystallisation, bath design, additives
(brighteners, throwing and levelling power). Surface Treatment:
Anodizing, electroforming, electrochemical (E.C.) machining, E.C.
etching, electropolishing. Industrial Production: Electrocatalysis,chlor-alkali cells, electrosynthesis, metal extraction/refining
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Learning Outcomes Describe the basic principles of corrosion in metals and alloys.
Assess and use basic electroanalytical methods including
potentiometry, conductimetry, voltammetry in chemical analysis.
Demonstrate competent laboratory skills in experimental
physical chemistry
Use mathematical equations to manipulate data to calculateunknowns and to plot data for visual representation and
verification.
Select suitable conditions for potentiostatic and
potentodynamic experiments.
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Learning Outcomes Appreciate electrochemical kinetics and the factors
influencing the kinetics of reaction at an electrode.
Demonstrate knowledge of techniques used to elucidate reactionmechanisms at electrodes.
Demonstrate knowledge of the chemical and electrochemical
technology involved in industrial eletrosynthesis of organic and
inorganic compounds.
Differentiate between chemical and electrochemical corrosion and
explain the mechanisms and kinetics of corrosion processes
Detect the manifestations of corrosion and the basics of corrosion
prevention
Assess critically various electrochemical surface treatment
techniques.
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Text books
Physical Chemistry, Atkins and de Paula, 9thed, OUP.
Electrode Kinetics, W.J. Albery, OUP
Electrochemical Methods2nded. A.J. Bard and L.R.
Faulkner, Wiley
Instrumental Methods in Electrochemistry, Southampton
Electrochemistry Group, Ellis Horwood.
Lecture NotesWill be on sharepoint folder but will not be complete, need to
attend lectures
Problem sets to be completed for tutorials
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Laboratory experimentsExperiment 1 Investigation of Electropolishing
Experiment 2 Electroplating
Experiment 3 Anodising of Aluminium and Dyeing the Surface
Experiment 4 Aqueous Corrosion
Experiment 5 Electrode Reactions Involving Adsorbed Intermediates
Experiment 6: Cyclic Voltammetry of the Ferro/Ferricyanide System
Reports to be typed and submitted one week after the lab
Attendance at labs and submission of reports is compulsory.
Labs can not be repeated and failure of lab component will entail
repeating the module in the following year.
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What can electrochemistry do?
Metal plating &
recovery
Organic
synthesis
Recycle
reagents
Effluent treatment
organic wastes
Nickel
Copper
Tin
Zinc
Cadmium
Gold
Silver
Adiponitrile Cr6+/Cr3+ NaClO2
Oxidation of
organic species
Electrodestruction
of organic
materials
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Cheapest
Electricity
Iron powder
Zinc Dust
NaBH4KMnO4
Na2Cr2O7
LiAlH4
Most expensive
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What can electrochemistry do?
1. Preparation of inorganic species, e.g. Cl2, NaOH, MnO2,
KMnO4, K2Cr2O7.
107 t of Cl2produced per annum in US
2. Metal extraction and refining, e.g. Al, Cu, Zn
3. Corrosion control, e.g. cathodic protection of ships hulls
4. Batteries
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5. Plating/deposition
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6. Fuel Cells
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7. Solar Cells
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Voltaic cells
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Strengths of Oxidising and Reducing Agents
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Standard Reduction (Half-Cell) Potentials
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Cell Potentials
For the oxidation in this cell: Eored= 0.76 V
For the reduction: Eored= +0.34 V
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Strengths of Oxidising and Reducing Agents
The strongest oxidisers
have the most positive
reduction potentials.
The strongest reducers
have the most negative
reduction potentials.
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Cell emf and G
G for a redox reaction defined by:
G = nFE A positive value of Eand a negative value of Gboth
indicate that a reaction is spontaneous.
Consequently, under standard conditions:
G= nFEn is the number of moles of electrons transferred.
F is Faradays constant: 1 F = 96,485 C/mol = 96,485 J/Vmol
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Electrochemical Cells
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(a) Zn/Zn2+, Cl-/AgCl/Ag (b) Pt/H2
/H+, Cl-/AgCl/Ag
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The presence of a constant quantity of electricity on an e- (1 602 x
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The presence of a constant quantity of electricity on an e (1.602 x
10-19C) provides a simple and ready explanation of Faradays
laws.
Example: In the electrolysis of silver nitrate, the mass of silverdeposited was 0.1392 g. How much electricity was passed
through the solution?
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Electrode reaction
El t d ti
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Electrode reaction
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Electrode reaction
Langmuir Isotherm
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Langmuir Isotherm
ka k
A(g) + M(surf) MA(ads) P
kd
Two cases:
(i) is small (i.e. little surface coverage):
= (ka/ k
d) p
A = Kp
A
d[P]/dt = k = kKpAand reaction is order in A
(ii) is close to unity (surface is almost completely covered):
d[P]/dt = k = k
reaction is order in A
KpA1
KpA
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Assumptions of Langmuir Isotherm
1. Only monolayer is adsorbed. Not generally true.
2. Hadsof each binding site is the same (each adsorption site isequivalent).
Poor assumption, as Hadsdecreases with increasing qas theenergetically most favourable sites are occupied first.
3.
Not generally true.
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BET equation
x = p/po, c = term including Hads
multi-layer adsorption, works best at medium pressures
)cxx1)(x1(
cx
V
V
m
Electron Transfer & Electrochemical Kinetics
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O + ne-R
Reference couple H++ e-H
G =nFE
Go
=nFEo
=RT ln Keq
dG = VdPS dT
PP dT
EnF
dT
G-S
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o
RT ln airG = rGo+ RT ln Q Q = reaction quotient ([O]/[R])
Divide by nF
Eo= - rGo/nF
[R]
[O]
lnnF
RT
EE o
Electron Transfer & Electrochemical Kinetics
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O + ne- R
Nernst equation
Application of a potential more negative than Eowill result in
reduction of O (as long as it is available)
Application of a potential more negative than Eo will result in
reduction of O (as long as it is available)
However considerably higher potentials may be required to makeredox process occur at a reasonable rate as k for a heterogeneous
electron transfer reaction is a function of applied potential, unlike
for a homogeneous reaction, which is a constant at a given T. The
additional potential is the overpotential, h.
[R]
[O]ln
nF
RTEE o
Polarization, Electron Transfer & Electrochemical Kinetics
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,
At equilibrium
i = i
When an electrochemical cell is operating under non-equilibriumconditions
i i
and there is a net current density:
imeas= ii
The electric potential difference between the terminals of the cell departs
from the equilibrium value
je= Eeq= e.m.f.the electromotive force [zero current potential]
If the cell is converting chemical free energy into electrical energy:
j
< je
If the cell is using an external source of electrical energy to carry out a
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g gy y
chemical reaction:
j> je
The value of j depends on the current, i, at the electrodes
The difference jije= h
is called the polarization of the cell or the overvoltage/overpotential
The value of his determined in part by the potential (iR term) necessaryto overcome the resistance R in the electrolyte and leads.
The corresponding electrical energy (i2R, the power) is dissipated as
heat, being analogous to frictional losses in irreversible mechanicalprocesses
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The remaining part is due to rate limiting processes at the electrodes (the
irreversibility of the electrode reaction)
The activation barrier is surmounted from the energy of the electric field
activating charged species.
There is also a thermal contribution to the energy of activation since the
reactions are carried out at temperature > 0 K.
Separating the various contributions leads to the theory of the transitioncoefficient, a.
How does this part of the overpotential, h, arise?
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An electrode reaction can be viewed as a succession of steps similar to
those in heterogeneous catalysis.
1. Diffusion of reactants to the electrode.
2. Reaction in the layer of solution adjacent to the electrode.
3.
4. Transfer of electrons .
5. Desorption of products from electrode.
6. Reaction in layer of solution adjacent to electrode.
7.
The reaction sequence may not necessarily include steps and 6.
A l f h t ld b th d iti f f ti f
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An example of such a step would be the decomposition of formation of a
complex ion before or after an electron-transfer step:
Before: C.E. Mechanism ChemicalElectrochemical.After: E.C. Mechanism ElectrochemicalChemical
An over-potential can arise from each of the processes involved in steps
17.
The overpotentials are generally divided into 3 broad types
1. Activation overpotential
2. Concentration overpotential3. Ohmic overpotential
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1. Activation overpotential (step 4, some 3, 5) This has its origins in the
slowness of some electrode reactions. Here the rate of the chemical
reaction depends on the energy of activation.
The magnitude of the activation overpotential of different electrodes
varies considerably.
Example
The overpotential of the hydrogen/platinum electrode is generally
very small whereas that of the oxygen/platinum electrode is large.
In the cell for the electrolysis of water almost the whole of the cell
over voltage is due to the oxygen overpotential.
2. Concentration overpotential (Steps 1 & 7) This arises whenever the
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reaction causes concentration changes to take place in the vicinity of the
electrodes
Cu2++ 2e-Cu Cu Cu2++ 2e-
(-) (+)
Cu Cu
In the vicinity of the cathode the [Cu2+] decreases whilst in the vicinity
of the anode it increases. This causes a change in the potential of each
electrode.Nernst equation E = Eo+ (RT/nF) ln [O]/[R]
3 Oh i i l i h l d i
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3. Ohmic overpotential arises whenever an electrode reaction causes
changes in the resistance of the cell.
Example
When O2is evolved an oxide/film can form on the surface. This will
(usually) have a high electrical resistance and so to maintain a
constant current the potential must be increased.
Total overpotential h ha hc ho iR
ha = activation overpotential
hc =ho =
iR = solution and leads
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How does this part of the overpotential, h, arise?
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An electrode reaction can be viewed as a succession of steps similar to
those in heterogeneous catalysis.
1. Diffusion of reactants to the electrode.
2. Reaction in the layer of solution adjacent to the electrode.
3.
4. Transfer of electrons to and from adsorbed reactant species.
5. Desorption of products from electrode.
6. Reaction in layer of solution adjacent to electrode.
7.
The reaction sequence may not necessarily include steps 2 and 6.
Electrode reaction
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Electrode reaction
In any cell at least 5 overpotentials (assume no oxidation on surface)
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In any cell at least 5 overpotentials (assume no oxidation on surface)
1. haat working electrode 2. hconcat working electrode
3. iR in cell 4. haat second electrode5. hconcat second electrode
Usually only interested in 1 and 2
If a 2-electrode cell were used, the plot of I versus E would tell
little about the electron transfer processes in the cell, since both the
overpotentials and the iR term vary with the current and in quite
different ways.
The cell is designed so that the I/E response is characteristic of the
processes at only one of the electrodes. This is achieved by
introducing a third electrode, the reference electrode into the cell.
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The potential of the working electrode is controlled versus the
reference electrode using a feedback circuit or potentiostat
based on an operational amplifier.
Thi l t d i l d i id L i b th ti f hi h i
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This electrode is placed inside a Luggin probe, the tip of which is
positioned very close to (but not touching) the working electrode
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The feedback circuit drives the current between the working and
secondary electrodes whilst ensuring that none passes through the
reference electrode circuit.
contribution of iR drop to the measure potential is minimised.
There remains a relatively small iR drop because the tip of the
Luggin cannot be placed right on the electrode surface (usuallynegligible).
The working electrode should be much smaller than the counter
electrode so that no serious polarization of the counter electrode can
occur and therefore the characteristics of the counter electrodereaction do not contribute to the response of the cell.
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Now transport problems No 1 and 7 of the steps of an electrode
reaction concern the diffusion of species to an electrode and hconcarises due to concentration changes in the vicinity of the electrode.
- Both transport problems
R
R In a certain time the amount of R
ne- coming in must equal the amount
O of O coming out
O
(Amount of R arriving) = (Amount of O departing)
Electrode is a surface with no volume space to store species
=
Iratedepartureratearrival 1
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These are the units of flux, J.
arrival departure
Different sign, flux is positive if in the X direction, i.e away
from the electrode x
FnOofRof
12-1
2
scmmolmolA.s.
cmAFI
n1
nAF
iJJ s
o
s
R
[Note: some experiments do not require transport to the electrode]
Mads M+ads+ e-
Nernst-Planck equation
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q
Ji(x) is the flux of speciesi, Dithe diffusion coefficient, Ci/x theconcentration gradient, f(x)/x the potential gradient, zi thecharge and v(x) the velocity
Mass transport is governed by Nernst-Planck equation, when terms
corresponding to and are
negligible, reduces to diffusion terms
Transport Mechanism
1 Mi ti i d di f l i l i l [ li
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1.Migration- arises due to a gradient of electrical potential [applies
only to ions]
2. Diffusion - arises due to a gradient of concentration [down a
concentration gradient]. Diffusion is a slow random process.3. Convection
- natural convection arises due to a gradient of pressure, from high to
low (via density differences leading to a pressure difference).
- forced convection arises through stirring or agitation of theelectrolytewhen used they have a large influence on I.
Convection is fast (e.g. sugar in a tea-cup, stir = pressure difference
Diffusing species moving in the solvent whereas in convection thesolvent is moving as well.
Mass transport in only one direction
, is important.
Linear Diffusion to a Plane Electrode
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Linear Diffusion to a Plane Electrode
In unstirred solution and in the presence of a base electrolyte,
diffusion is theonly form of mass transport for the electroactive
species which need to be considered. The simplest model is that oflinear diffusion to a plane electrode.
It is assumed that the electrode is perfectly flat and of infinite
dimensions, so that concentration variations can only occur
perpendicular to the electrode surface.
The investigation of the mechanism and kinetics of electrode
processes is normally undertaken with solutions containing a large
excess of base electrolyte,
Thereby the migration of the electroactive species of interest is
unimportant and the balancing charge through solution is carried out
predominantly by the base electrolyte.
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Two types of experiment are common
(i) using solutions
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(i) using solutions
(ii) using a form of forced convection which may be described
exactly, by far the most important system is the rotating disc
electrode.
In (i), the experiment is carried out so that we may assume that
diffusion may then be characterised by Ficks Lawsin a one-
dimensional form.
Ficks First Law, states that the flux of any species, i, through a
plane parallel to the electrode surface is given by:
Where D is the diffusion coefficient and typically has a value
of cm2s-1
gradient
conc.
xi
c
iDFlux
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Flat electrode of Plane parallel to and
infinite dimensions distance x from surface
Flux of O and R perpendicular to the surface
Flux = -DiCi/x
Flux of O
Flux of R
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t)dx(xJt)dx(xJt)(xC
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dx
t)dx,(xJt)dx,(xJ
t
t)(x,Ci
This leads to the equation
Integration of Ficks Second Law with initial and boundary
conditions appropriate to the particular experiment is the basis of
the theory of instrumental methods such as chrono-potentiometry,chrono amperometry and cyclic voltammetry.
The First Law applied at the electrode surface x = 0, is used to
relate the current to the chemical change:
or
2i
2
ii
xCD
dtC
0x
o
ox
CDFlux
nF
I
0x
R
Rx
CD
nF
I
The zone close to the electrode surface where the concentrations of O
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The zone close to the electrode surface where the concentrations of O
and R are different from those in the bulk is known as the diffusion
layer.
In most experiments its thickness increases with time until it reaches a
steady state value approx. 102cm thick, when natural convection
stirring the bulk solution becomes important. It takes of the order of
10 seconds for this boundary layer to form this also means that for the
first 10 s of any experiment the concentration changes close to this
electrode are the result of diffusion only. Thereafter the effects of
Consider an experiment carried out with a solution where initially O
is present but not R where:
O + ne-R
is caused by the electrode potential being stepped at t = O so that the
surface concentration of O changes instantaneouslyfrom Coto zero.
At short times the concentration of O will only have changed from its
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At short times the concentration of O will only have changed from its
initial value Co, at points very close to the electrode surface and the
concentration gradient will consequently be steep with increasing time.
Diffusion will cause the concentration profiles to relax towards their
steady state by extending into solution and becoming less steep. Since
the current is a simple function of the flux of O at the electrode surface,
the current time.
Co CR
Co
increasing t increasing t
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To obtain a more detailed knowledge of the above transient we
must solve the equation
with the initial and boundary conditions which describe this
particular potential step experiment.
2
o
2
o
o
x
CD
t
C
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2
1
2
1
2
1
t
CnFDI o
Cottrell equation
It should be noted that the above equation has been derived from amodel which assumes linear diffusion to a planar electrode. In the
lab we cannot use electrodes that are flat on a molecular level or of
infinite dimensions. The most commonly used electrodes are wire or
disc.
Unimportant provided the electrodes are of reasonable size, and for
time scales below 10 s the more complex equations for 3-D geometry
lead to the same equation this is a general observation and the theory
for most electrochemical experiments can be safely developed usinga one dimensional model.
Diffusion
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How long will it take for a species with a diffusion coefficient of 5 x
10-6cm2s-1to diffuse a distance of 100 mm?
s = (Dt)1/2
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Nernst diffusion layer
Estimates flux of material to the
electrode surface
i/FA = jd = DB[[B]bulk[B]o]/d
[B]ois the concentration of B at the
electrode surface
is the Nernst diffusion layerthicknesss and is ca. 0.5 mm for
mm sized electrode
[B]o= 0 at very positive (oxidising)
or negative (reducing) conditions
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Detection
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Fig. 3.Plot of charge passed (0-30 s) for the reduction of 5 mMolal ferricyanide in plasma (A), whole
blood containing 31% Hct (B), and whole blood containing 50% Hct (C). The standard deviations for A, B
and C are 2, 8 and 11%, respectively.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 10 20 30
Time/ s
i/A
A
B
C
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oRED
o
CknFand
CkOofreductionofRate
I
RED
However the rate constant for a heterogeneous electron transfer
process has a particular property, it is dependent on the potential field
close to the surface driving the movement of electrons and therefore
on the applied electrode potential.
Experimentally it has been found that the potential dependence of kox
and kredis of the form
where h= E - Eeq, kois the rate constant for electron transfer at theequilibrium potential and acis the cathodic transfer coefficient.
RT
nFexpkk C
ored
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RT
nFexpCk
nF
IC
oo
The corresponding equations for the oxidation of R, which is
occurring simultaneously with the reduction of O are:
Rate of oxidation =
Since at equilibrium
Rox
Ck
ha
RT
nFexpkk ao
ox
ha
RT
nFexpCknFIandkkk a
R
o
ox
o
redox
Where aais the anodic transfer coefficient
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.
In general aa+ ac = 1 and it is common for aa= ac =
The observed current density at any potential is
Now
negative)isI(whereIII redredox
RT
nFexpCknF
RT
nFexpCknFI C
o
oa
R
o
aC o
R
o
oC.CknFI
For the particular case where
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p
CR
= CO= C
then: I = nFkoC and
This is the Butler-Volmerequation. This is an often used equation in
experimental and applied electrochemistry and shows that themeasured current density is a function of:
(i) over potential
(ii) exchange current density, Io
(iii) the aa and ac
h
ah
a
RT
nFI
RT
nFII C
o
a
oexpexp
haha
RT
nF
RT
nF1II CCo expexp*
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The terms in the square brackets represents the anodic and
cathodic contributions to the net current and Iois a scaling
factor that depends on ko, Co, CR.
The symmetry of the curve depends on the value of the
transfer coefficient ac
ha
ha
RT
nF
RT
nF1II CCo expexp*
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ha
ha nFnF
II CC exp)1(
exp
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hh
RTRTII o expexp
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There are limiting forms of the Butler-Volmer equation
a) when one or other exponential terms in the equation dominates.
Example: when h is negative, Ired increases while Iox decreasesrapidly, Ired>>Iox then the first exponential term in the B-V
becomes negligible compared with the second exponential term
and we have
hahaRT
nFRT
nFII CCo exp)1(exp
ha
RT
nFII Coexp
This applies when the over potential is larger than ~52 mV and in this
potential region the current increases exponentially with h
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potential region the current increases exponentially with h.The above equation can also be written as:
Similarly at when h is made positive (positive over potentials)
h> 52 mV ; Iox>> Ired and
The last two equations are known as the Tafelequations for cathodic
and anodic processes.
A plot of log I vs h can be used to extract a value for Io and awhereaa= ac= 0.5 and n = 1 the slopes are (1/120) mV-1at 25C.
RT2.3
nFIlogI)(log Co
RT2.3
nFIlogIlog ao
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(b) The B-V equation has another limiting form which applies at
very low over potentials h10 mV.
It is obtained by expanding the exponentials as a Taylor series and
then ignoring squared and higher terms: When aa= ac= 0.5 itreduces to
and shows that in this narrow potential range close to h= 0, Idepends linearly on h.
(ex= 1 + x)
RT
nFIIo
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For the evolution of hydrogen at a mercury electrode in a dilute
aqueous solution of H SO at 25C the following data were obtained
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aqueous solution of H2SO4at 25C, the following data were obtained
h/V 0.6 0.65 0.73 0.79 0.84 0.89 0.93 0.96j/ mAm-2 2.9 6.3 28 100 250 630 1650 3300
y = 8.4906x - 11.702, R2= 0.998
-7.0
-6.5
-6.0
-5.5
-5.0
-4.5
-4.0
-3.5
-3.0
0.50 0.60 0.70 0.80 0.90 1.00
n/ V
logj
Example
The transfer coefficient for the couple M3+/2+ in contact with an
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The transfer coefficient for the couple M3+/2+in contact with an
electrode at 25oC is 0.42. The current density is 17 mA cm-2 when
the overpotential is 105 mV. What is the overpotential required for
a current density of 72 mA cm-2?
Example
Estimate the number of protons that are transported per second to
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Estimate the number of protons that are transported per second to
the surface of a 1 cm2platinum electrode Pt | H2 | H+when the
exchange current density is 7.9 x 10-4A cm-2.
The interplay of electron transfer and mass transport control
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p y p
The process
O + ne- R
is at least a 3-step process
mass transport
Obulk Osurface
electron transfer
Osurface Rsurface
mass transport
Rsurface Rbulh
involving both mass transport and electron transfer.
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At the equilibrium potential, no net current flows
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As E becomes less than Eeq, I is observed. Initially it is very small
and Cosremains close to its bulk value.
This potential region will lead to a linear plot of I vs E (low over
potential)
As the potential is made more negative, the rate of reductionincreases rapidlyexponentiallylog I vs E is linear
Eventually Cosbecomes significantly less than Co
, then mass
transport will need to occur and the current comes under mixed
control.
The log I vs. E plot is non-linear and the current density becomes
sensitive to the mass transport conditions.
On making the potential even more negative the Cosdecreases from
C to effectively zero
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Co
to effectively zero.
At this point the current density becomes independent of potential
and the process is said to be Mass Transport Controlled.
Whether an electrode reaction appears reversible or irreversible
depends both on the kinetics of electron transfer and the mass
transport conditions.
For a steady state experiment in unstirred solution:
ko
> 2 x 10-2
cm s-1
- reversible I/Eko< 5 x 10-3 cm s-1- irreversible I/E
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