3. 3. POTENTIAL
AND
ELECTROCHEMICAL
CELLS

4. Two-Electrode Cell : 1
a working electrode, at which the electron transfer process of interest occurs 2
a counter electrode, to maintain the electro-neutrality of the solution through a half-reaction of opposite sign

5. How to measure the potential?
Impossible to measure the absolute potential of each of the two electrodes (i.e. the energy of the electrons inside each electrode)
Experimentally the difference of potential between the two electrodes: cell voltage, V (sum of a series of differences of potential)

6. sharp changes in potential at each of the electrical double layer (controlling the rate of the faradic reactions at the two electrodes)
Each of the two jumps in potential is identified as the electrode potential of the respective electrodes
Cell Voltage
The cell voltage includes a resistance term, Rs. when the current flows through the solution between the two electrodes it gives rise to the so-called ohmic drop(i.R , is defined as the iRs drop)
When iRs = 0 (or negligible) the measured cell voltage reflect the difference between the two electrode potentials (V= ΔE)
impossible to control the potential of the working electrode unless :
the potential of the counter electrode is invariant
the iR drop is made negligible.

7. Example : saturated calomel electrode (SCE)
A counter electrode of constant potential is obtained making use of a half-cell system in which the components are present in concentrations so high as to be unaffected by a flow of current through it
Example : saturated calomel electrode (SCE)
The activity of the solid Hg and Hg2Cl2 (by definition)
and the Hg22+ ions(in high concentration) remains constant. Consequently, the electrode potential also remains constantly fixed at the value determined by the Nernst equation
This type of counter electrode is defined as a reference electrode, at 25°C the saturated calomel electrode (SCE) has a potential of V with respect to the standard hydrogen electrode (NHE)

8. Three-electrode cell
A reference electrode does function as a counter electrode has the disadvantage that the incoming current can cause instantaneous variations in the concentration of its components, leading to a different potential value
Still the problem of ohmic drop that, for example, in experiments performed in non-aqueous solvents
Then a third electrode, auxiliary electrode (AE) is inserted

9. Auxiliary electrode
can be of any material since its electrochemical reactivity does not affect the behavior of the working electrode
must be positioned in such a way (in a separate compartment, by means of sintered glass separators) from the working electrode that its activity does not generate electroactive substances that can reach the working electrode and interfere with the process under study

10. iR drop can be minimized by positioning the reference electrode close to the working electrode through a Luggin capillary
The ideal positioning is at a distance 2d from the surface of the working electrode, where d is the outlet diameter of the capillary
Luggin capillary

11. Rnc : non-compensated solution resistance
since the majority of the current has been conveyed towards the region between the working and the auxiliary electrodes, most of the ohmic drop iR, has no influence on the cell voltage between the working and the reference electrodes, thus allowing the condition:
Rnc : non-compensated solution resistance

12. KINETIC ASPECTS OF THE ELECTRODE REACTIONS

13. 4.1. Electron Transfer Recalling basic aspects:
concentration
concentration
overall rate
At equilibrium(vf = vr):
constant

14. equilibrium conditions
Simple faradic process:
If a potential value corresponding to the equilibrium (zero-current) is applied to the working electrode so that both S and S- are stable at the electrode surface
hOx =hRed
equilibrium conditions

15. If one now sets the potential of the working electrode more positive than that of equilibrium, the oxidation process is facilitated
The energy barrier for the oxidation is lower than that of reduction.

16. If a potential more negative than that of equilibrium is applied to the working electrode, the reduction process is favored

17. Consider the general electron-transfer process:
activity
activity coefficient
concentration of the active species in the bulk of the solution
formal electrode potential of the couple Ox/Red :

18. In the electrode process under consideration there is either the reduction
path or the oxidation path, Expressing the concentration of a species, at a distance x from the electrode surface and at the time t, as C(x,t),that the reaction rate for the reduction reaction is given by:
cathodic current
anodic current
overall reaction rate
current generated at the electrode

19. Butler-Volmer equation
rate constants of the electron transfers
ko = standard rate constant, which expresses the value of kRed or kox when the applied potential E is equal to Eo’
α = transfer coefficient (0 < α < 1);
n = number of electrons (simultaneously) transferred per molecule of ox.
Upon substituting in the preceding relationship:
Butler-Volmer equation