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.