Nernst Equation, Equlibrium and Potential
By S.E. Van Bramer, 2/22/98
Starting with the Nernst Equation for the equlibrium; Ox + n e- <--> Red :
E cell E std_cell
R .T . C ox
ln
n. F
C red
E cell
n .F
E std_cell .
R .T
C ox
E cell
e
ln
Typical form of Nernst Equation
C ox
Rearange
C red
.
E std_cell . n F
R .T
Gives the ratio of oxidized to
reduced form of redox pair.
C red
C ox
e
.
( ∆E ) . n F
R .T
Reduced variables to ∆E, the
difference between the equlibrium
potential and the applied potential.
C red
This function describes how the equlibrium ration of oxidized and reduced form depend upon the applied potential.
Notice that
if ∆E = 0 Where the applied potential is the same as the standard cell potential. Then the exponent is
0, so the ratio of Cox/Cred = 1. This is the conditions for the standard state.
If ∆E > 0 Where the applied potential is positive of Eo. Now the exponent is greater than 0 so the ratio of
C ox/Cred >1. The concentration of the oxidized form is greater than the concentration of the reduced form. This is
consistent with the half reaction because an applied potential positive of Eo pulls e-'s off and causes oxidation.
If ∆E < 0. Where the applied potential is negative of Eo. Now the exponent is less than 0 so the ratio of
C ox/Cred < 1. The concentration of the oxidized form is less than the concentration of the reduced form. This is
consistent with the half reaction because an applied potential negative of Eo pushes e-'s on and causes reduction.
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1
S.E. Van Bramer
svanbram@science.widener.edu
Now let's take a graphical look at this function.
Look at a range of applied potentials for a reaction with 1 electron exchanged:
0.4 .volt , 0.39 . volt .. 0.4 .volt
∆E
n
1
F
96484.6 .coul .mole
Some Constants for electrochemistry:
1
8.31441 .joule .K .mole
R
1
T
298 .K
1
The functions to describe α (the ratio of oxidzied over reduced) and the concentration of
each species (assuming a total concentration of 1.
α ( ∆E , n )
e
.
∆E . n F
R .T
C red( ∆E , n )
C ox( ∆E , n)
α ( ∆E , n )
1
1
C red( ∆E , n)
Nernst Relationships
1
Concentration
1
C red ( ∆E , n )
C ox ( ∆E , n )
0.5
0
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
∆E
Cell Potential
a
Nernst Relationships
0
Concentration
5
ln C red ( ∆E , n )
ln C ox ( ∆E , n )
10
15
20
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
∆E
Cell Potential
nernst.mcd
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2
S.E. Van Bramer
svanbram@science.widener.edu
Now, let's see what happens if the number of electrons changes:
2
Nernst Relationships
1
Concentration
n
C red ( ∆E , n )
C ox( ∆E , n )
0.5
0
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
∆E
Cell Potential
a
Nernst Relationships
0
Concentration
10
ln C red ( ∆E , n )
ln C ox ( ∆E , n )
20
30
40
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
∆E
Cell Potential
n
3
nernst.mcd
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3
S.E. Van Bramer
svanbram@science.widener.edu
Now, let's see what happens if the number of electrons changes:
3
Nernst Relationships
1
Concentration
n
C red( ∆E , n )
C ox( ∆E , n )
0.5
0
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
∆E
Cell Potential
a
Nernst Relationships
Concentration
0
ln C red ( ∆E , n )
20
ln C ox ( ∆E , n )
40
60
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
∆E
Cell Potential
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S.E. Van Bramer
svanbram@science.widener.edu