Transcript Electroanalytical Chemistry

Electroanalytical
Chemistry
Lecture #4
Why Electrons Transfer?
The Metal Electrode
EF
E
Ef = Fermi level;
highest occupied
electronic energy
level in a metal
Why Electrons Transfer
Reduction
Oxidation
EF
Eredox
E
E
Eredox
E
F
•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
The Kinetics of Electron
Transfer
Consider:
O+
ne-
kR
=R
ko
Assume:
O and R are stable, soluble
Electrode of 3rd kind (i.e., inert)
no competing chemical reactions occur
Equilibrium for this Reaction
is Characterised by...
The Nernst equation:
Ecell = 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]
Equilibrium (cont’d)
At equilibrium,
no net current flows, i.e.,
E = 0  i = 0
However, there will be a dynamic
equilibrium at electrode surface:
O + ne- = R
R - ne- = O
both processes will occur at equal rates
so no net change in solution composition
Current Density, I
Since i is dependent on area of electrode,
we “normalize currents and examine
I = i/A
we call this current density
So at equilibrium, I = 0 = iA + iC
 ia/A = -ic/A = IA = -Ic = Io
which we call the exchange current
density
Note: by convention iA produces positive
current
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)
Summary: Equilibrium
Position of equilibrium characterized
electrochemically by 2 parameters:
Eeqbm - equilibrium potential, Eo
Io - exchange current density
How Does I vary with E?
Let’s consider:
case 1: at equilibrium
case 2: at E more negative than Eeqbm
case 3: at E more positive than Eeqbm
Case 1: At Equilibrium
E = Eo - (RT/nF)ln(CR*/CO*)
E - E0 = - (RT/nF)ln(CR*/CO*)
E = Eo so, CR* = Co*
I = IA + IC = 0 no net current flows
IA
G
O
R
IC
Reaction Coordinate
Case 2: At E < Eeqbm
E - Eeqbm = negative number
= - (RT/nF)ln(CR*/CO*)
 ln(CR*/CO*) is positive
 CR* > CO*  some O converted to R
 net reduction
 passage of net reduction current
IA
G
O
R
IC
I = IA + IC < 0
Reaction Coordinate
Case 2: At E > Eeqbm
E - Eeqbm = positive number
= - (RT/nF)ln(CR*/CO*)
 ln(CR*/CO*) is negative
 CR* < CO*  some R converted to O
 net oxidation
 passage of net oxidation current
IA
IC
I = IA + IC > 0
G
R
O
Reaction Coordinate
Cathodic
Current, A
Overpotential, 
fast
slow

Eeqbm Edecomp Cathodic Potential, V
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
Can We Eliminate ?
What are the Sources of 
 = A + R + C
A, activation
an inherently slow ET = rate determining step
R, resistance
due to finite conductivity in electrolyte
solution or formation of insulating layer on
electrode surface; use Luggin capillary
C, concentration
polarization of electrode (short times, stirring)
Luggin Capillary
Reference electrode
placed in glass
capillary containing
test solution
Narrow end placed
close to working
electrode
Exact position
determined
experimentally
Reference
Working
Electrode
Luggin
Capillary
The Kinetics of ET
Let’s 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 co*
where kR is electron transfer rate constant
The Kinetics of ET (cont’d)
Then the cathodic current density is:
IC = -nF (kRCO*)
Experimentally, kR is found to have an
exponential (Arrhenius) potential
dependence:
kR = kOC exp (- CnF E/RT)
where C = cathodic transfer coefficient
(symmetry)
kOC = rate constant for ET at E=0 (eqbm)
, Transfer Coefficient
 - measure of symmetry of
activation energy barrier
G
 = 0.5  activated complex
halfway between reagents/
products on reaction coordinate;
typical case for ET at type III
M electrode
O
R
Reaction Coordinate
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*
The Kinetics of ET (cont’d)
kA = kOA exp(+ AnF E/RT)
So, substituting
IA= nF CR* kOA exp(+AnF E/RT)
And, since I = IC + IA then:
I = -nF cO*kOC exp(- CnF E/RT) +
nF cR*kOA exp(+ AnF E/RT)
I = nF (-cO*kOC exp(- CnF E/RT) +
cR*kOA exp(+ AnF E/RT))
The Kinetics of ET (cont’d)
At equilibrium (E=Eeqbm), recall
Io = IA = - IC
So, the exchange current density is given
by:
nF cO*kOC exp(- CnF Eeqbm/RT) =
nF cR*kOA exp(+ AnF Eeqbm/RT) = I0
The Kinetics of ET (cont’d)
We can further simplify this expression by
introducing  (= E + Eeqbm):
I = nF [-cO*kOC exp(- CnF ( +
Eeqbm)/RT) + cR*kOA exp(+ AnF ( +
Eeqbm)/ RT)]
Recall that ea+b = eaeb
So,
I = nF [-cO*kOC exp(- CnF /RT) exp(CnF Eeqbm/RT) + cR*kOA exp(+ AnF /
The Kinetics of ET (cont’d)
So,
I = nF [-cO*kOC exp(- CnF /RT) exp(CnF Eeqbm/RT) + cR*kOA exp(+ AnF /
RT) exp(+ AnF Eeqbm/ RT)]
And recall that IA = -IC = I0
So,
I = Io [-exp(- CnF /RT) +
exp(+ AnF / RT)]
This is the Butler-Volmer equation
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
The Butler-Volmer
Equation (cont’d)
For simple ET,
C + A = 1 ie., C =1 - A
Substituting:
I = Io [-exp((A - 1)nF /RT) + exp(AnF
/ RT)]
Let’s Consider 2 Limiting
Cases of B-V Equation
1. low overpotentials, < 10 mV
2. high overpotentials,  > 52 mV
Case 1: Low Overpotential
Here we can use a Taylor expansion to
represent ex:
ex = 1 + x + ...
Ignoring higher order terms:
I = 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
Case 1: Low Overpotential
(cont’d)
I = (Io nF/RT) 
intercept = 0
slope = Io nF/RT
Note: F/RT = 38.92 V-1 at 25oC
Case 2: High
Overpotential
Let’s look at what happens as  becomes
more negative then if IC >> IA
We can neglect IA term as rate of
oxidation becomes negligible then
I = -IC = Io exp (-CnF /RT)
So, current density varies exponentially
with 
Case 2: High
Overpotential (cont’d)
I = Io exp (-CnF /RT)
Taking ln of both sides:
ln 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 then
ln I = ln Io + A nF/RT 
we call this the anodic Tafel equation
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 yintercept
Tafel Equations (cont’d)
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
Tafel Plots
ln |i|
Anodic
Cathodic
Mass transport
limited current
_
ln Io
Eeqbm
+
High overpotential:
ln I = lnIo + (AnF/RT) 
Low overpotential:
I = (Io nF/RT) 
, V
In real systems often see large negative deviations
from linearity at high  due to mass transfer
limitations
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 mV
viewed as n = 1 + 0.5 = 1.5
Interpreted as pre-equilibrium for 1st ET
followed by 2nd ET
Effect of  on Current
Density
A = 0.75 oxidation is favored
C = 0.75 reduction is favored
Homework:
Consider what how a Tafel plot changes
as the value of the transfer coefficient
changes.