1. Coulometry
장 승철
부산대학교 바이오피지오센서연구소

2. Electrochemistry: electron transfer
Electron transfer plays a fundamental role in governing the pathway of chemical reactions.
Electrochemical methods offer the potential to investigate the chemical reaction processes directly by the detection of the electrons involved.
Electrode Reactions: A typical electrode reaction involves the transfer of charge between an electrode and a species in solution. The electrode reaction usually referred to as electrolysis, typically involves a series of steps:

3. Reactant (O) moves to the interface: this is termed mass transport
Electron transfer can then occur via quantum mechanical tunnelling between the electrode and reactant close to the electrode (typical tunnelling distances are less than 2 nm)
The product (R) moves away from the electrode to allow fresh reactant to the surface

4. The above electrode steps can also be complicated by:
The applied voltage on the electrode
The reactivity of the species
The nature of the electrode surface
The structure of the interfacial region over which the electron transfer occurs

5. Electrode Reactions

6. Equilibrium Electrochemistry
The voltage measured can predicts which way electrons would like to flow, this is purely thermodynamic measurement. Like data from chemical equilibrium measurements the infomation tells us whether it is thermodynamically favourable or not for a reaction to proceed. Such experiments allow the measurement of the following quantities:
Enthalpies of reaction
Entropies of reaction
Free energies of reaction
Equilibrium constants
Solution pH

7. However these measurements reveal nothing regarding the kinetics of the process.
To gain kinetic information we must watch the establishment of the equilibrium - this is essentially the area of electrode dynamics.
To examine the kinetics, we need to gain a microscopic view of why electrode reactions occurr, and what this odd term voltage has to do with 'chemistry'.

8. Electron Transfer and Energy Levels
The key to driving an electrode reaction is the application of a voltage (V). If we consider the units of volts: V = Joule/Coulomb
we can see that a volt is simply the energy (J) required to move charge (c). Application of a voltage to an electrode therefore supplies electrical energy.
Since electrons possess charge an applied voltage can alter the 'energy' of the electrons within a metal electrode. The behaviour of electrons in a metal can be partly understood by considering the Fermi-level (EF).

9. Metals are comprised of closely packed atoms which have strong overlap between one another.
A piece of metal therefore does not possess individual well defined electron energy levels that would be found in a single atom of the same material.
Instead a continuum of levels are created with the available electrons filling the states from the bottom upwards. The Fermi-level corresponds to the energy at which the 'top' electrons sit.

10. This level is not fixed and can be moved by supplying electrical energy. Electrochemists are therefore able to alter the energy of the Fermi-level by applying a voltage to an electrode.

11. The Fermi-level within a metal along with the orbital energies (HOMO and LUMO) of a molecule (O) in solution.
(Left) The Fermi-level has a lower value than the LUMO of (O). It is therefore thermodynamically unfavourable for an electron to jump from the electrode to the molecule.
(Right) the Fermi-level is above the LUMO of (O), now it is thermodynamically favourable for the electron transfer to occur, ie the reduction of O.

12. Whether the process occurs depends upon the rate (kinetics) of the electron transfer reaction.

13. Electrogravimetric and coulometric methods
With potentiometric methods, we simply measured Ecell and used the Nernst equation to quantify a substance.
With electrogravimetry and coulometry, a potential is applied, forcing a reaction to go.
polarize the cell
causes unexpected things to happen
work is done on the system
Ecell can change during an analysis

14. Applying a voltage
When we apply a voltage, it can be expressed as the following:
Eapplied = Eback + iR
Where
Eback = voltage required to ‘cancel out’ the normal forward or galvanic reaction.
iR = iR drop. The work applied to force the
reaction to go. This is a function of cell
resistance.

15. Applying a voltage Eback Increases as the reaction proceeds
Actually consist of:
Eback = Erev(galvanic) + overvoltage
Overvoltage
An extra potential that must be applied beyond what we predict from the Nernst equation.

16. Overvoltage or overpotential
A cell is polarized, if its potential is made different than it normal reversible potential – as defined by the Nernst equation.
The amount of polarization is called the overpotential or overvoltage
ƞ = E - Erev

17. Concentration overpotential
There are two types of ƞ.
Concentration overpotential
This occur when there is a difference in concentration at the electrode compared to the bulk of the solution.
This can be observed when the rate of reaction is fast compared to the diffusion rate for the species to reach the electrode.

18. Concentration overpotential
Lets assume that we are conducting a copper electroplating.
As the plating occurs,
copper is leaving the
solution at the electrode.
This results in the [Cu2+]
being lower near
the electrode.
[Cu2+]electrode
[Cu2+]bulk

20. Use efficient stirring Use a low current density
Concentration overpotential can never be eliminated. However, it can be reduced.
Use efficient stirring
Use a low current density
Low current - slower reaction
Large electrode - more area for reaction

21. Activation overpotential
Results from the shift in potential at the electrode simply to reserve the reaction
This effect is at its worst when a reaction becomes non-reversible
Effect is slight for deposition of metals
Can be over 0.5 V if a gas is produced
Occurs at both electrodes making oxidations more ‘+’ and reductions more ‘-’.

22. So the E for electrolysis is actually:
Eapp = (Eanode + ƞac + ƞaa) - (Ecathode + ƞcc + ƞca)
ƞac = concentration overpotential at anode
ƞaa = activation overpotential at anode
ƞcc = concentration overpotential at cathode
ƞca = activation overpotential at cathode
This explains why many reactions do not proceed as expected or will not occur at all.

23. Electrolytic cells In electrolytic cells
The reaction requiring the smallest applied voltage will occur first.
As the reaction proceeds, the applied E increases and other reaction may start.
Lets look at an example to determine if a quantitative separation is possible.

24. Electrolytic example
Can Pb2+ be quantitatively be separated from Cu2+ by electro-deposition?
Assume that our solution starts with 0.1 M of each metal ion.
We’ll define quantitative as only 1 part in 10,000 cross contamination (99.99%)
Cu2+ + 2e = Cu E = V
Pb2+ + 2e = Pb E = V

25. Electrolytic example

26. Electrolytic example

27. Electrogravimetry
A quantitative method based on weight gain. It is also referred to as electro-deposition.
A very old method.
When it works, it works well.
Unfortunately, it only works for a limited number of materials.

28. Electrogravimetry R - Potentiometer A - Ammeter V - Voltmeter Anode
Pt cathode
Stir bar

29. Electrogravimetry Steps in the analysis
The Pt electrode is cleaned, dried and its weight determined.
The electrode is then placed in the system and a potential is applied.
The analyte deposit on the electrode.
The electrode is removed and brought to constant weight.

30. Electrogravimetry
The method can be conducted either with or without a controlled potential.
No control
Simply set a fixed potential and run.
This is simple and inexpensive option.
Unfortunately, it causes problems.

31. Electrogravimetry
The starting potential must initially be high to insure a complete deposition.
Overpotential can cause gas generation.
Our species may not be able to diffuse rapidly enough.
The deposition will slow down as the reaction proceeds.

32. Electrogravimetry
As the reaction proceeds, the current decreases, resulting in the deposition becoming much slower

33. Electrogravimetry Controlled potential
A reference electrode is used in the system.
The potential difference between the working and reference electrode is monitored and held constant.
This helps to reduce overpotential and the time for an analysisOnly a limited number of species work well with electro-deposition.
Only a few metals deposit from an acid solution quantitatively without hydrogen formation.

34. Cathode electrodepositions
Electrogravimetry
Cathode electrodepositions
Copper – Commonly done in an acid solution using a Pt cathode
Nickel – Conducted in a basic solution
Zinc – Requires an acidic citrate solution
Some metal can be determined by deposition of metal complexes (cyanides).
Ag, Cd, Au.

35. Anodic electrodeposition
Electrogravimetry
Anodic electrodeposition
Some metals can be assayed by deposition on the anode.
This requires that we go to a higher oxidation – deposited as metal oxides.
Pb2+ PbO2
Mn2+ MnO2

36. Time – Current requirements for electrodeposition
A coulomb (coul) is a quantity of electricity.
Current is the rate of electrical flow.
96500 coulombs of electricity are required to reduce 1 gram equivalent weight of a metal to a lower oxidation state (1 e- change).
96500 coulombs = 1 Faraday ( F )
Current = Amps = i = coul/ sec

37. Time – Current requirements for electrodeposition
equivalent
weight

38. Example

39. Efficiency

40. Coulometry
Rater than relying on electrode weight gain, an analysis can be conducted based on electrical usage.
Resistance, voltage, current and time can all be measured with great accuracy.
A precipitate is not required so a larger number of reactions can be used.
Smaller quantity can be measured.

41. Coulometry is the general name for methods that measure the amount of electricity required to react exactly with an analyte. It is generally is a redox reaction.
The number of coulombs of electric charge
Q = it
where i is the current in amperes (Coulombs/sec) and t time in seconds.

42. If i varies during the electrolysis,
Q = ∫ i tdt.
A charge of 96,485 Coulombs (1 Faraday) is equal to one mole of electrons. Thus a measurement of Q allows us to calculate the number of moles of electrons involved in that specific half cell reaction.
The most common way to use coulometry is by electrically generating a chemically reactive species within an electrolysis cell.

43. For example, at an anode,
Ce+3 = Ce+4 + e.
The Ce+4 generated may then be used as an oxidant titrant.
In order for the electrically generated titrant to be useful analytically it should have
a rapid reaction between the titrant and the analyte and
a known quantitative reaction with the analyte

44. The use of coulometric generated species allow the use of several unusual reagents that would not be possible with conventional titrants such as
Cr+2, Ag+2, Cu+, Cl2, Ti+3, U+5, Br2, I2
Additional reactants and the electrochemical half-cell for their generation are shown on the next slide.

45. Coulometry Direct coulometry
Methods in which substance is qualified by either oxidation or reduction directly at an electrode.
Two approaches
Constant potential
Constant current

46. Direct coulometry Constant potential
As the reactants are consumed, the current decreased. When the reaction is complete, the current is negligible.
The area under the curve equals the number of coulombs used.

47. Direct coulometry Constant potential
The current is held constant by ‘floating’ the potential. The reaction is complete when the potential no longer changes.
Either type of curve is possible based on the reaction involved.

48. Direct methods are of limited interest
Direct coulometry
Direct methods are of limited interest
Approach is hard to control
Suffers from the same problems with overpotential as electrodeposition.
Unexpected reactions can be a major problem.
Indirect coulometric methods are more useful.

49. Indirect coulometry or coulometric titrations
Basis
A low concentration of a ‘titrant’ is generated electrochemically at a constant rate from a high concentration of the oxidized or reduced form of the titrant.
As it is generated, it reacts stoichiometrically with the substance being determined.

50. Indirect coulometry or coulometric titrations
The method overcomes
Difficulties associate with direct methods because of the concentration of the titrant source
Prevents side reactions
Increases reaction efficiency
The titrant need not be stable

51. Determination of Fe(II)
Example
Determination of Fe(II)
Reaction used: Ce4+ + Fe2+ Ce3+ + Fe3+
Ce4+ solutions are not stable so:
Add a large excess of Ce3+ to the sample.
Convert Ce3+ to Ce4+ which in turn react with our Fe2+.
While direct oxidation of Fe2+ to Fe3+ may occur, it results in no error.

52. Example
The endpoint can easily be determined by monitoring the potential of the system.
During the titration, the Ce4+/Ce3+ is relative constant as long as Fe2+ is present.
Since the amount of Ce is much larger than Fe, it determines the overall Ecell.
Once all Fe2+ is reacted, Ce4+ begins to build up in the system and there is a large change in the potential of the system.

53. Example Endpoint detection Easily determined. The amount of Fe2+
can then be found
based on the time
and applied current.

54. Indirect coulometry

55. Indirect coulometry (coulometric titration)
Advantages
Can detect µg amounts because i and t can be accurately measured.
No standards are required if current efficiency is known.
Can use unstable reagents.
Can easily be automated.
Relatively inexpensive method of analysis.

56. Coulometric titration: examples
The coulometric generation of OH- has the following advantages over conventional titrations with hydroxide:
by being produced in situ very small amounts may be generated.
Eliminates problems with carbonate formation
Apparatus for Electrically generating OH

58. CHLORIDE COULOMETRIC TITRATIONS
Titrant Generator Reaction
Analytical Reaction
The Corning 920M direct-reading digital micro-macro chloride meter provides accurate and rapid determination of chloride in biological samples using a coulometric technique.

59. KARL FISHER TITRATION

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