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Electroanalytical Chemistry

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concentration. polarization of electrode (short times, ... High overpotential: ln I = lnIo ( AnF/RT) Mass transport. limited current. Low overpotential: ... – PowerPoint PPT presentation

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Title: Electroanalytical Chemistry


1
Electroanalytical Chemistry
  • Lecture 4
  • Why Electrons Transfer?

2
The Metal Electrode
  • Ef Fermi level highest occupied electronic
    energy level in a metal

EF
E
3
Why Electrons Transfer
Reduction
Oxidation
Eredox
E
E
EF
  • Net flow of electrons from M to solute
  • Ef more negative than Eredox
  • more cathodic
  • more reducing
  • Net flow of electrons from solute to M
  • Ef more positive than Eredox
  • more anodic
  • more oxidizing

4
The Kinetics of Electron Transfer
  • ConsiderO ne- R
  • Assume
  • O and R are stable, soluble
  • Electrode of 3rd kind (i.e., inert)
  • no competing chemical reactions occur

kR
ko
5
Equilibrium for this Reaction is Characterised
by...
  • The Nernst equationEcell E0 - (RT/nF) ln
    (cR/co)
  • where cR R in bulk solution co O in
    bulk solution
  • So, Ecell is related directly to O and R

6
Equilibrium (contd)
  • At equilibrium,no net current flows, i.e.,?E
    0 ? i 0
  • However, there will be a dynamic equilibrium at
    electrode surfaceO ne- RR - ne- Oboth
    processes will occur at equal ratesso no net
    change in solution composition

7
Current Density, I
  • Since i is dependent on area of electrode, we
    normalize currents and examineI i/A we call
    this current density
  • So at equilibrium, I 0 iA iC? ia/A -ic/A
    IA -Ic Iowhich we call the exchange
    current density
  • Note by convention iA produces positive current

8
Exchange Current Density
  • Significance?
  • Quantitative measure of amount of electron
    transfer activity at equilibrium
  • Io large ? much simultaneous ox/red
    electron transfer (ET) ? inherently fast
    ET (kinetics)
  • Io small ? little simultaneous ox/red
    electron transfer (ET) ? sluggish ET
    reaction (kinetics)

9
Summary Equilibrium
  • Position of equilibrium characterized
    electrochemically by 2 parameters
  • Eeqbm - equilibrium potential, Eo
  • Io - exchange current density

10
How Does I vary with E?
  • Lets consider
  • case 1 at equilibrium
  • case 2 at E more negative than Eeqbm
  • case 3 at E more positive than Eeqbm

11
Case 1 At Equilibrium
  • E Eo - (RT/nF)ln(CR/CO)E - E0 -
    (RT/nF)ln(CR/CO) E Eo so, CR CoI IA
    IC 0 no net current flows

IA
O
R
?G
IC
Reaction Coordinate
12
Case 2 At E lt Eeqbm
  • E - Eeqbm negative number -
    (RT/nF)ln(CR/CO) ? ln(CR/CO) is positive?
    CR gt CO ? some O converted to R? net
    reduction? passage of net reduction current

IA
O
R
?G
IC
I IA IC lt 0
Reaction Coordinate
13
Case 2 At E gt Eeqbm
  • E - Eeqbm positive number -
    (RT/nF)ln(CR/CO) ? ln(CR/CO) is negative?
    CR lt CO ? some R converted to O? net
    oxidation? passage of net oxidation current

IA
R
?G
IC
O
I IA IC gt 0
Reaction Coordinate
14
Overpotential, ?
fast
slow
Cathodic Current, A
?
Eeqbm
Cathodic Potential, V
Edecomp
  • Fast ET current rises almost vertically
  • Slow ET need to go to very positive/negative
    potentials to produce significant current
  • Cost is measured in overpotential, ? E - Eeqbm

15
Can We Eliminate ?? What are the Sources of ?
  • ? ?A ?R ?C
  • ?A, activationan inherently slow ET rate
    determining step
  • ?R, resistancedue to finite conductivity in
    electrolyte solution or formation of insulating
    layer on electrode surface use Luggin capillary
  • ?C, concentrationpolarization of electrode
    (short times, stirring)

16
Luggin Capillary
  • Reference electrode placed in glass capillary
    containing test solution
  • Narrow end placed close to working electrode
  • Exact position determined experimentally

17
The Kinetics of ET
  • Lets make 2 assumptions
  • both ox/red reactions are first order
  • well-stirred solution (mass transport plays no
    role)
  • Then rate of reduction of O is
  • - kR cowhere kR is electron transfer rate
    constant

18
The Kinetics of ET (contd)
  • Then the cathodic current density is
  • IC -nF (kRCO)
  • Experimentally, kR is found to have an
    exponential (Arrhenius) potential dependencekR
    kOC exp (- ?CnF E/RT)
  • where ?C cathodic transfer coefficient
    (symmetry)
  • kOC rate constant for ET at E0 (eqbm)

19
?, Transfer Coefficient
? - measure of symmetry of activation energy
barrier ? 0.5 ? activated complex halfway
between reagents/ products on reaction
coordinate typical case for ET at type III M
electrode
20
The Kinetics of ET (cont/d)
  • Substituting
  • IC - nF (kR co) - nF c0 kOC exp(-
    ?CnF E/RT)
  • Since oxidation also occurring simultaneously
  • rate of oxidation kA cR
  • IA (nF)kACR

21
The Kinetics of ET (contd)
  • kA kOA exp( ?AnF E/RT)
  • So, substitutingIA nF CR kOA exp(?AnF E/RT)
  • And, since I IC IA then
  • I -nF cOkOC exp(- ?CnF E/RT) nF cRkOA exp(
    ?AnF E/RT)I nF (-cOkOC exp(- ?CnF E/RT)
    cRkOA exp( ?AnF E/RT))

22
The Kinetics of ET (contd)
  • At equilibrium (EEeqbm), recallIo IA - IC
  • So, the exchange current density is given bynF
    cOkOC exp(- ?CnF Eeqbm/RT) nF cRkOA exp(
    ?AnF Eeqbm/RT) I0

23
The Kinetics of ET (contd)
  • We can further simplify this expression by
    introducing ? ( E Eeqbm)
  • I nF -cOkOC exp(- ?CnF (? Eeqbm)/RT)
    cRkOA exp( ?AnF (? Eeqbm)/ RT)
  • Recall that eab eaeb
  • So,I nF -cOkOC exp(- ?CnF ?/RT) exp(- ?CnF
    Eeqbm/RT) cRkOA exp( ?AnF ?/ RT) exp( ?AnF
    Eeqbm/ RT)

24
The Kinetics of ET (contd)
  • So,I nF -cOkOC exp(- ?CnF ?/RT) exp(- ?CnF
    Eeqbm/RT) cRkOA exp( ?AnF ?/ RT) exp( ?AnF
    Eeqbm/ RT)
  • And recall that IA -IC I0So,I Io -exp(-
    ?CnF ?/RT) exp( ?AnF ?/ RT)This is the
    Butler-Volmer equation

25
The Butler-Volmer Equation
  • I Io - exp(- ?CnF ?/RT) exp( ?AnF ?/ RT)
  • This equation says that I is a function of
  • ?
  • I0
  • ?C and ?A

26
The Butler-Volmer Equation (contd)
  • For simple ET, ?C ?A 1 ie., ?C 1 - ?A
  • SubstitutingI Io exp((?A - 1)nF ?/RT)
    exp(?AnF ?/ RT)

27
Lets Consider 2 Limiting Cases of B-V Equation
  • 1. low overpotentials, ?lt 10 mV
  • 2. high overpotentials, ? gt 52 mV

28
Case 1 Low Overpotential
  • Here we can use a Taylor expansion to represent
    exex 1 x ...
  • Ignoring higher order termsI Io 1 (?A nF
    ?/RT) - 1 - (?A- 1)nF ?/ RT) Io nF?/RT
  • I Io nF?/RT so total current density varies
    linearly with ? near Eeqbm

29
Case 1 Low Overpotential (contd)
  • I (Io nF/RT) ? intercept 0slope Io nF/RT
  • Note F/RT 38.92 V-1 at 25oC

30
Case 2 High Overpotential
  • Lets look at what happens as ? becomes more
    negative then if IC gtgt IA
  • We can neglect IA term as rate of oxidation
    becomes negligible thenI -IC Io exp (-?CnF
    ?/RT)
  • So, current density varies exponentially with ?

31
Case 2 High Overpotential (contd)
  • I Io exp (-?CnF ?/RT)
  • Taking ln of both sidesln I ln (-IC) lnIo
    (-?CnF/RT) ?which has the form of equation of a
    line
  • We call this the cathodic Tafel equation
  • Note same if ? more positive thenln I ln Io
    ?A nF/RT ? we call this the anodic Tafel
    equation

32
Tafel Equations
  • Taken together the equations form the basis for
    experimental determination of
  • Io
  • ?c
  • ?A
  • We call plots of ln i vs. ? are called Tafel
    plots
  • can calculate ? from slope and Io from y-intercept

33
Tafel Equations (contd)
  • Cathodic ln I lnIo (-?CnF/RT) ? y
    b m x
  • If ?C ?A 0.5 (normal), for n 1 at RT slope
    (120 mV)-1

34
Tafel Plots
ln i
High overpotentialln I lnIo (?AnF/RT) ?
Anodic
Cathodic
Low overpotentialI (Io nF/RT) ?
ln Io
Mass transport limited current
_
Eeqbm

?, V
In real systems often see large negative
deviations from linearity at high ? due to mass
transfer limitations
35
EXAMPLE
  • Can distinguish simultaneous vs. sequential ET
    using Tafel Plots
  • EX Cu(II)/Cu in Na2SO4
  • If Cu2 2e- Cu0 then slope 1/60 mV
  • If Cu2 e- Cu slow ?Cu e- Cu0 then
    slope 1/120 mV
  • Reality slope 1/40 mVviewed as ?n 1 0.5
    1.5
  • Interpreted as pre-equilibrium for 1st
    ETfollowed by 2nd ET

36
Effect of ? on Current Density
  • ?A 0.75 oxidation is favored
  • ?C 0.75 reduction is favored

37
Homework
  • Consider what how a Tafel plot changes as the
    value of the transfer coefficient changes.
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