The Nernst
Equation
COMPILED BY
Prof. Sudhir Kumar Awasthi
Dept. Of Life Sciences
CSJMU
❖ The Nernst equation is an equation that relates the reduction potential of a reaction (half-cell or full cell reaction) to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the chemical species undergoing reduction and oxidation.
❖ It was named after Walther Nernst, a German physical chemist who formulated the equation.
E°cell and DG (cont.)
• The above relationship states that by measuring
E°cell, we can determine K.
E°cell = (0.0257 V) ln(K) = (0.0591) log(K)
n n
E°cell and DG
E°cell = (0.0591 V) log(K)
n
DG° = -RTln(K)
DG° = -nFE°cell
An Example
• Balance, determine E°cell and K for the following:
S4O62- (aq) + Cr2+(aq) Cr3+(aq) + S2O3
2-(aq)
S4O62- S2O3
2-
Cr2+ Cr3+ + e-
22e- +
x 2
S4O62- + 2Cr2+ 2Cr3+ + 2S2O3
2-
An Example (cont.)
• Determining E°cell
S4O62- S2O3
2-
2Cr2+ 2Cr3+ + 2e-
22e- +
S4O62- + 2Cr2+ 2Cr3+ + 2S2O3
2-
E°1/2 = 0.17 V
E°1/2 = 0.50 V
E°cell = 0.67 V
An Example (cont.)
• Determining K
S4O62- + 2Cr2+ 2Cr3+ + 2S2O3
2-
E°cell = 0.67 V
E°cell = (0.0257 V) ln(K)
n
= (0.059 V) log K
n
n(E°cell)
(0.059 V)
2 (0.67 V)
(0.059 V)= = 22.7 = log K
K = 1022.7 = 5 x 1022
Concentration and Ecell
• Consider the following redox reaction:
Zn(s) + 2H+ (aq) Zn2+(aq) + H2(g) E°cell = 0.76 V
DG°= -nFE°cell < 0 (spontaneous)
• What if [H+] = 2 M?
Expect shift of equilibrium to products.
Therefore DG decreases, and Ecell increases
How does Ecell dependend on concentration?
Concentration and Ecell (cont.)
• Recall, in general:
DG = DG° + RTln(Q)
• However:
DG = -nFEcell
-nFEcell = -nFE°cell + RTln(Q)
Ecell = E°cell - (RT/nF)ln(Q)
Ecell = E°cell - (0.0591/n)log(Q)
The Nernst Equation
Concentration and Ecell (cont.)
• With the Nernst Eq., we can determine the effect of concentration on cell potentials.
Ecell = E°cell - (0.0591/n)log(Q)
• Example. Calculate the cell potential for the following:
Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s)
Where [Cu2+] = 0.3 M and [Fe2+] = 0.1 M
Concentration and Ecell (cont.)
Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s)
• First, need to identify the 1/2 cells
Cu2+(aq) + 2e- Cu(s) E°1/2 = 0.34 V
Fe2+(aq) + e- Fe(s) E°1/2 = -0.44 V
Fe(s) Fe 2+(aq) + 2e- E°1/2 = +0.44 V
Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) E°cell = +0.78 V
Concentration and Ecell (cont.)
• Now, calculate Ecell
Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) E°cell = +0.78 V
Ecell = E°cell - (0.0591/n)log(Q)
Q =Fe2+ Cu2+
=(0.1)
(0.3)= 0.33
Ecell = 0.78 V - (0.0591 /2)log(0.33)
Ecell = 0.78 V - (-0.014 V) = 0.794 V
Concentration and Ecell (cont.)
• If [Cu2+] = 0.3 M, what [Fe2+] is needed so that Ecell
= 0.76 V?
Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) E°cell = +0.78 V
Ecell = E°cell - (0.0591/n)log(Q)
0.76 V = 0.78 V - (0.0591/2)log(Q)
0.02 V = (0.0591/2)log(Q)
0.676 = log(Q)
4.7 = Q
Concentration and Ecell (cont.)
Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s)
4.7 = Q
Q =Fe2+ Cu2+
= 4.7
Q =Fe2+ 0.3
= 4.7
[Fe2+] = 1.4 M
Concentration Cells
• Consider the cell presented on the left.
• The 1/2 cell reactions are the same, it is just the concentrations that differ.
• Will there be electron
flow?
Concentration Cells (cont.)
Ag+ + e- Ag E°1/2 = 0.80 V
• What if both sides had 1 M
concentrations of Ag+?
• E°1/2 would be the same;
therefore, E°cell = 0.
Concentration Cells (cont.)
Ag Ag+ + e- E1/2 = ? VAnode:
Ag+ + e- Ag E1/2 = 0.80 VCathode:
Q =Ag+
anode
Ag+ cathode
=0.1
1= 0.1
Ecell = E°cell - (0.0591/n)log(Q)
0 V
Ecell = - (0.0591)log(0.1) = 0.0591 V
1
Concentration Cells (cont.)
Another Example:
What is Ecell?
Concentration Cells (cont.)
Ecell = E°cell - (0.0591/n)log(Q)
Fe2+ + 2e- Fe
2 e- transferred…n = 2
2
Q =Fe2+
anode
Fe2+ cathode
=0.01
.1= 0.1
Ecell = -(0.0296)log(.1) = 0.0296 V
anode cathode
e-
Measurement of pH
• pH meters use electrochemical reactions.
• Ion selective probes: respond to the presence of a
specific ion. pH probes are sensitive to H3O+.
• Specific reactions:
Hg2Cl2(s) + 2e- 2Hg(l) + 2Cl-(aq) E°1/2 = 0.27 V
Hg2Cl2(s) + H2(g) 2Hg(l) + 2H+(aq) + 2Cl-(aq)
H2(g) 2H+(aq) + 2e- E°1/2 = 0.0 V
Measurement of pH (cont.)
Hg2Cl2(s) + H2(g) 2Hg(l) + 2H+(aq) + 2Cl-(aq)
• What if we let [H+] vary?
Q = H + 2
Cl− 2
Ecell = E°cell - (0.0591/2)log(Q)
Ecell = E°cell - (0.0591/2)(2log[H+] + 2log[Cl-])
Ecell = E°cell - (0.0591)(log[H+] + log[Cl-])
saturate
constant
Measurement of pH (cont.)
Ecell = E°cell - (0.0591)log[H+] + constant
• Ecell is directly proportional to log [H+]
electrode
REFERENCES
• Atkins’Physical Chemistry by James Keeler
& Peter Atkins’(2002)
• Modern Physical Organic Chemistry by
Dannis A. Dougherty& Eric V. Anslyn
(2005)
• Physical chemistry by I.N. Levin (1990)