Title: Electroanalytical Chemistry
1Electroanalytical Chemistry
- Lecture 4
- Why Electrons Transfer?
2The Metal Electrode
- Ef Fermi level highest occupied electronic
energy level in a metal
EF
E
3Why 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
4The 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
5Equilibrium 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
6Equilibrium (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
7Current 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
8Exchange 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)
9Summary Equilibrium
- Position of equilibrium characterized
electrochemically by 2 parameters - Eeqbm - equilibrium potential, Eo
- Io - exchange current density
10How 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
11Case 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
12Case 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
13Case 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
14Overpotential, ?
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
15Can 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)
16Luggin Capillary
- Reference electrode placed in glass capillary
containing test solution - Narrow end placed close to working electrode
- Exact position determined experimentally
17The 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
18The 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
20The 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
21The 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))
22The 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
23The 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)
24The 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
25The Butler-Volmer Equation
- I Io - exp(- ?CnF ?/RT) exp( ?AnF ?/ RT)
- This equation says that I is a function of
- ?
- I0
- ?C and ?A
26The Butler-Volmer Equation (contd)
- For simple ET, ?C ?A 1 ie., ?C 1 - ?A
- SubstitutingI Io exp((?A - 1)nF ?/RT)
exp(?AnF ?/ RT)
27Lets Consider 2 Limiting Cases of B-V Equation
- 1. low overpotentials, ?lt 10 mV
- 2. high overpotentials, ? gt 52 mV
28Case 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
29Case 1 Low Overpotential (contd)
- I (Io nF/RT) ? intercept 0slope Io nF/RT
- Note F/RT 38.92 V-1 at 25oC
30Case 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 ?
31Case 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
32Tafel 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
33Tafel 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
34Tafel 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
35EXAMPLE
- 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
36Effect of ? on Current Density
- ?A 0.75 oxidation is favored
- ?C 0.75 reduction is favored
37Homework
- Consider what how a Tafel plot changes as the
value of the transfer coefficient changes.