ch4005 2013 lectures i given.pdf

8/14/2019 CH4005 2013 Lectures I given.pdf

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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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ch4005 2013 lectures i given.pdf

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