ELECTROCHEMISTRY - Wits Structural Chemistry

Exchange Current Density
Under zero current conditions:
Dynamic Equilibrium
Ox + ne - Red
o RT a
Eeq
= E − ln
nF a
Re d
Ox
EQUILIBRIUM!
Overpotential (η):
the difference between the applied potential and the
equilibrium potential.
η = E – E eq
Equilibrium potential: potential where i = 0
By definition, no net chemical change occurs i = 0
However, this is a dynamic equilibrium! i = ia + ic
= 0
Increasing rate of reduction
η = E – E eq
E eq
Increasing rate of oxidation
η = E – E eq
i.e. there is still current flowing:
i a = −ic
= io
E eq
exchange current
η > 0
Recall: current is the variation of charge with time:
current ∝ rate of electron transfer
dq
i =
dt
η < 0
i o is a measure of the electron transfer activity in both cathodic and anodic directions
at equilibrium.
It is a very useful kinetic parameter in dynamic electrochemistry.
Rate of e - transfer depends on the electrode potential which drives the
transfer of e - ’s.
Current is defined as:
i = nFAν
A = surface area of electrode
ν = reaction rate
Forward reaction:
Reverse reaction:
k k ox
Ox + ne - red
Red
Red Ox + ne-
ν
red
= k
red
C
i
ν c
red
=
nFA
Butler-Volmer
Equation
ox
1 st order
Current at electrode:
ν = k C
ox
ox
i
ν a
ox
=
nFA
Overall rate:
1
ν = νox
− νred
= koxCred
− kredCox
= (ia
− ic
)
nFA
i = ia
− ic
= nFA(k oxCred
− kredCox
)
red
Note: c red or c ox refers to the
conc’s near the electrode surface
Forward reaction:
Reverse reaction:
k
Ox + ne - red
k ox
Red
Red Ox + ne-
Current at electrode:
The rate constant varies with applied potential (in an exponential way):
(1−α
)nF
−αnF
η
η
o
o
RT
RT
k = kred
= k e
ox
k e
k o = standard rate constant (k when potential applied is E eq )
α = transfer coefficient (0 < α < 1) → symmetry factor
(1− α)nF
o
i = nFAk C RT
rede
i = ia
− ic
= nFA(k oxCred
− kredCox
)
η
− Coxe
− αnF
η
RT
(1− α)nF
− αnF
η
η
i = i RT − RT
o e e
Butler-Volmer equation
and
o
io = nFAk C
Current (rate of reaction) depends on:
• Electrode area, A
• Concentration of reactant, C
• Temperature
• The kinetic parameters i o and α
• Overpotential, η
Current density, j:
i
j =
A
(1− α)nF
− αnF
η
η
j = j RT − RT
o e e
(1−α)nF
− αnF
η
η
i = i RT − RT
o e e
i = nFAν
j is independent of electrode area
Butler-Volmer equation in
terms of current density
For small overpotentials (η < ~10 mV):
nF
j = joη
RT
In most practical situations, only the forward or the reverse reaction is significant and
a simplified equation is sufficient.
Large, positive overpotential predominantly oxidation:
In practise, η ≥ ~ +0.12/n V
j
(1−α
)nF
η
RT
= j e o
(1− α)nF
ln j = ln jo
+ η
RT
Large, negative overpotential predominantly reduction:
In practise, η ≤ ~ -0.12/n V
j
−αnF
η
RT
= j e o
αnF
ln j = ln jo
− η
RT
(1− α)nF
j = j RT
o e
η
− e
Anodic current
− αnF
η
RT
Cathodic current
i.e. η nF < 1
RT
Low field region
High field region
Tafel equations
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