1. Electrochemistry for Engineers
Electrochemistry for Engineers
LECTURE 2
Lecturer: Dr. Brian Rosen
Office: 128 Wolfson
Office Hours: Sun 16:00

2. The Electrochemical Cell Part II

3. Lower Stability of Water
Starting with
H+(aq) + e-  ½H2(g)
we write the Nernst equation
We set pH2 = 1 atm. Also, Gr° = 0, so E0 = 0. Thus, we have
Again, the lower limit of water solubility in Eh-pH space is governed by the same reaction as in pe-pH space. We repeat the same steps as before, except that for this reaction, E0 = 0, because all the reactants and products have free energies of formation that are zero by convention.

4. Upper Stability of Water
½O2(g) + 2e- + 2H+  H2O
but now we employ the Nernst eq.
In the next three slides, we repeat the calculation of the stability limits for water, but this time in Eh-pH coordinates. There are two reasons for repeating the calculation in this way. The first is to show how pe-pH diagrams and Eh-pH diagrams relate to each other, and to show the slight differences in how they are calculated. The second reason is so that we can use a published Eh-pH diagram to show where different geological environments sit with respect to pH.
The reaction governing the upper stability limit for water on an Eh-pH diagram is exactly the same reaction that we used for the pe-pH diagram. The difference is that, instead of using the mass-action (equilibrium constant) expression, we use the Nernst equation. To employ the Nernst equation given the convention Kehew (2001) has adopted, we must right the reaction as a reduction reaction.
Once the appropriate Nernst equation is written, we can proceed to the next step. Note that, in employing the Nernst equation, the convention employed is that ae- = 1. This is a major difference compared to the pe-pH diagram, where ae- is not necessarily equal to 1. The pe = -log ae-, so if we set ae- = 1 we could not plot a pe-pH diagram, because all pe values would be zero. However, such a situation would make many students happy!

5. Upper Stability of Water
Recall pH = -log (aH+)
We assume that pO2 = 1 atm. This results in
This yields a line with slope of
We need to calculate E0 from the value of Gr° as shown above, and then rearrange the Nernst equation so that we have an equation of a straight line with Eh on the Y-axis and pH on the X-axis. We find that we still have to fix the value of the partial pressure of oxygen to plot the boundary, and so we choose 1 atm as for the pe-pH diagram.

6. The Electrochemical Series

7. Pourbaix Diagram

8. Pourbaix Diagram of Water Stability vs. Ag/AgCl?

9. Recall: A Good Reference is Non-Pol.
+0.00 vs. Ag/AgCl
+0.197V vs. SHE
0.00V vs. SHE

10. Pourbaix Diagram vs Ag/AgCl
E = 1.03 V vs. Ag/AgCl
E = V vs. Ag/AgCl

11. Reconsider : Galvanic vs. Electrolytic

12. Equilibrium (Non-polarized)
Cu+2 + 2e Cu
+ i
- E
+ E
When the electrode is held
at its equilibrium potential,
the forward and reverse current
cancel and the NET current
is zero
- i
E° Cu/Cu+
=0.340 V vs. SHE

13. Cathodic Polarization
Cu+2 + 2e Cu
+ i ΔE
- E
+ E
When the electrode is negative of
its equilibrium potential, reduction
is favored and there is a net flow of
electrons consumed by the electrode
for the reduction reaction.
- i
E° Cu/Cu+
=0.340 V vs. SHE

14. Anodic Polarization Cu+2 + 2e- Cu E° Cu/Cu+ =0.340 V vs. SHE
When the electrode is positive of
its equilibrium potential, oxidation
is favored and there is a net flow of
electrons produced for the
oxidation reaction.
- E
+ E ΔE
- i
E° Cu/Cu+
=0.340 V vs. SHE

15. Real Polarization of Electrodes
In reality, I-V curves for electrodes
take on a variety of shapes and
forms dependent on the kinetic
and mass-transport parameters

16. OPEN CIRCUIT POTENTIAL (OCP)
E Cell (OCP) = 0.74 V i
+ E
- E i
E° Cd/Cd+2
-0.40 vs. SHE
+ E
- E
E° Cu/Cu+2
+0.34 vs. SHE
1M Cd+2
1M Cu+2 Cu Cd
Cd+2 +2e Cd
Cu+2 +2e Cu

17. GALVANIC CELL (SPONTANEOUS)
E° Cd/Cd+2
-0.40 vs. SHE
+ E
- E
E° Cu/Cu+2
+0.34 vs. SHE
E Cell = 0.64 V
-0.35V
+0.29V i i e-
1M Cd+2
1M Cu+2 Cu Cd e- - +
ANODE
CATHODE
Cd+2 +2e Cd
Cu+2 +2e Cu

18. + - ELECTROLYTIC CELL E Applied = 1.5 V -∆E +∆E + E - E E° Cd/Cd+2
-0.4 vs. SHE
+ E
- E
E° Cu/Cu+2
+0.34 vs. SHE
+0.75V
E Applied = 1.5 V
-0.75V i i
+0.29V
1.5V e-
1M Cd+2
1M Cu+2 Cu Cd e- + -
CATHODE
ANODE
Cd+2 +2e Cd
Cu+2 +2e Cu

19. Summary η = (E - E°) = “overpotential”
Galvanic (spontaneous cells) operate below their maximum potential (OCP) due to the electrode polarization required to produce current (anode E is less negative than E°, and cathode E is less positive than E°)
Electrolytic cells require an external voltage more than the minimum required OCP predicted by thermodynamics (anode E is more positive than E°, cathode E is more negative than E°)
η = (E - E°) = “overpotential”

20. Electrode Processes MASS-TRANSFER diffusion convection migration
KINETICS

21. Electrochemical Kinetics

22. Electrode Processes MASS-TRANSFER diffusion convection migration
KINETICS
(FAST)
(SLOW)
In our modeling of kinetics, we will assume
that mass transfer to the electrode is fast
compared to the reaction rate

23. Our Goal
i = f(E) How can we model the current at an electrode as a function of its potential assuming the reaction is the rate limiting step? (i.e. mass transfer to the electrode is FAST)

24. Surface vs. Bulk Concentration
Surface concentration of A
CA f(x,t)
..at surface x=0, therefore surface concentration is CA (0,t) or (CA for short here)
CA* is the symbol we will use for “bulk” concentration

25. Basic Rate Laws (1st order rxn)kf
Ox + ne Red kb
NOTE Cox is really Cox(0,t), the
surface concentration of “Ox”!
Likewise Nox is the number of mols
Of “Ox” on the surface
Therefore v is in units of mols/(time*area)

26. Measured Current #mols Ox on surface i [=] Coulombs / s
v [=] mol/(sec*cm2)
F is the “molecular weight equivalent
of electrons in Coulombs / mol

27. Mercury Drop Electrode
Na+ + 2e-  Na(Hg) E° = V vs. SHE
Dangerous!
Solid Na is NOT stable, hence the VERY negative E°
Reacts exothermically with moisture
Na+ + 2e-  Na E° = V vs. SHE
Na+ Hg

28. The Energy Barrier Gibbs Free Energy AB + C
Reasons for Energy Barriers
Reconfiguration of atomic position
Repulsion forces
Desolvation of ions in solution
Even though the reaction is favorable according to THERMODYNAMICS, it must overcome an
energy barrier.
LARGER BARRIER = SLOWER REACTION

29. - + Energy increases as we bring the sodium ion
closer to the Na(Hg) surface
due to repulsion forces.
Vice-versa also true for energy
of amalgamated sodium atom +
Changing the potential
changes the energy of the
participating electron

30. - + Na+ +e- Na+ +e- Na (Hg) Na (Hg)
The Hg drop electrode is ANODICALLY polarized by ΔE = E - E°
The energy of the electrode changes by F ΔE -
Charge x Voltage = Energy
Na+ +e-
Na (Hg) +

31. - + How do the anodic and cathodic activation barriers
Na+ +e-
Na (Hg)
How do the anodic and cathodic activation barriers
change with overpotential (η = E-E°)?

32. Symmetry Factor, α
The symmetry factor, α, describes what fraction of the overpotential goes towards changing the CATHODIC barrier.
(1-α) , same for ANODIC barrier
For multistep/multi-electron reactions, the symmetry factor is called the transfer coefficient

33. -
Na+ +e-
Na (Hg) +

34. R -
(1-α)F Δ E
αFΔE +

35. Cathodic barrier goes up by the
same amount that the anodic barrier goes down
Cathodic barrier goes up by less than the anodic barrier goes down
Cathodic barrier goes up by more than the anodic barrier goes down

36. Defining the Rate Constant
Substituting our expression for how ΔG changes with η we get
We assume Af = Ab
Where f = F/RT
defining a standard rate constant

37. Butler-Volmer Equation
Inserting our expression for the rate constants into our expression for total current
We get:
We now have our relationship for how the current at an
electrode varies with overpotential!

38. At Equilibrium Ox + ne- Red Recall that at equilibrium, the kinetickf
Ox + ne Red kb
Recall that at equilibrium, the kinetic
model and the thermodynamic model
must match!!!

39. At Equilibrium Ox + ne- Redkf
Ox + ne Red kb
but….. νf and νr are NOT ZERO, rather, they cancel!

40. Equilibrium
At equilibrium, the surface concentration C(0,t) equals the bulk concentration
in solution C*
Which is just an exponential form of the Nernst equation
Kinetic model breaks down into thermodynamic model at equilibrium

41. Exchange Current Density
Although the NET current is zero, the anodic and cathodic currents still have equal but opposite values known as the exchange current density
Raise both sides to -α
Substitute into
to get
Note i0 is dependent
only on kinetic parameters!

42. Current-Overpotential Equation
Divide the Butler-Volmer Equation by i0 to get:
Simplifies to :
..where f = F/RT

43. i0 Visualized

44. Effect of i0 on Polarization

45. Effect of Symmetry Factor on Polarization

46. Tafel Plot
..where f = F/RT
at large η either the left or the right side becomes negligible.

47. What happens when we account for mass transport?