1. Electrogravimetry and Coulometry
Lecture 1

2. Electrogravimetry and Coulometry
Three electroanalytical methods are based on electrolytic oxidation or reduction of an analyte for a sufficient period of time, to assure its quantitative conversion to a new oxidation state. These methods are constant-potential coulometry; constant-current coulometry (or coulometric titrations), and electrogravimetry. In electrogravimetric methods, the product of the electrolysis is weighed as a deposit on one of the electrodes. In the two coulometric procedures, on the other hand, the quantity of electricity needed to complete the electrolysis is a measure of the amount of analyte present.

3. These three methods generally have:
moderate selectivity, sensitivity, and speed
In many instances, they are among the most accurate and precise methods available, with uncertainties of a few tenths of a percent RSD being common.
Finally, these three techniques require no calibration standards; that is, the relationship between the quantity measured and the mass of analyte, or electrical charge passed, can be calculated from theory.
Applications of electrogravimetric methods will be discussed only briefly, as the topic is rather familiar and simple. Before starting a detailed discussion, we explore the processes that occur in an electrolytic deposition.

4. Units for Quantity of Electricity
The quantity of electricity, or charge, is measured in units of coulombs (C). A coulomb is the quantity of charge transported in one second by a constant current of one ampere. Thus, for a constant current of I amperes for t seconds, the charge in coulombs Q is given by the expression: Q = It For a variable current i, the charge is given by the Integral:

6. The faraday F is the charge in coulombs of one mole of electrons
The faraday F is the charge in coulombs of one mole of electrons. The charge of the electron is *10-19 C, so we may therefore write:
Faraday's law relates the number of moles of the analyte nA to the charge
where n is the number of moles of electrons in the analyte half-reaction.

7. CURRENT-VOLTAGE RELATIONSHIPS DURING AN ELECTROLYSIS
An electrolysis can be performed in one of three ways:
Using a constant applied cell voltage,
Using a constant working electrode potential, or
Using a constant electrolysis current passing through the cell.
It is useful to consider the consequences of each of these modes of operation. For all three modes, the behavior of the cell is governed by the equation:
Eappl = Ec – Ea – IR + (Pcc + Pck) + (Pac + Pak)

8. where Eappl is the applied voltage from an external source and Ec , and Ea , are the reversible, or thermodynamic, potentials associated with the right- and left-hand electrodes, respectively. The term P represents overvoltages resulting from concentration and kinetic polarization at both electrodes. The values for Ec , and Ea , can be calculated from standard potentials using the Nernst equation. In many cases, only the working electrode is polarizable because the other electrode is a non-polarizable reference electrode. The overvoltage, P, is the extra voltage, above the thermodynamic potential, required to drive the electrode reaction at a certain rate, and thus produce the required current in the cell.

9. Methods Based on Electrogravimetry
We have three modes of electrolysis:
Constant Cell Potential Electrolysis
Constant Working Electrode Potential Electrolysis
Constant Current Electrolysis
We will study all three techniques.

10. 1. Operation of the Cell at a Constant Applied Potential
The simplest way of performing an analytical electrolysis is to maintain the applied cell potential at a constant value. In practice, electrolysis at a constant cell potential is limited to the separation of easily reduced cations from those that are more difficult to reduce than hydrogen ion. In the cell below, the cathode is a platinum electrode, with a surface area of 150 cm2 immersed in 200 mL of a solution that is M in copper(II) Ion and 1.00 M in hydrogen ion. When a suitable potential difference is applied (to be determined later) between the two electrodes, copper is deposited on the cathode, and oxygen is evolved at a partial pressure of 1.00 atm at the anode. Cu2+ + H2O g Cu(s) + ½ O2(g) + 2H+ The analyte here is copper(Il) ions in a solution containing an excess of nitric acid.

12. Calculation of the Required Cell Potential
Standard potential data for the two half-reactions in the cell under consideration are: Cu2+ +2e g Cu(s) EO = V ½ O2(g) + 2H+ + 2e g H20 EO = 1.23 V Cu2+ + H2O → Cu(s) + ½ O2(g) + 2H+ EO = V The thermodynamic potential for this cell can be shown to be V (since Cu2+ needs to be deposited). Ecell = Ec – Ea = 0.34 – 1.23 = V Thus, we expect no current at applied potentials less negative than -0.94V. At just greater negative potentials, a linear increase in current with potential should be observed in absence of kinetic or concentration polarization. However, usually a much larger potential is needed to force high current passage (mainly due to concentration polarization), and thus reduce time required for electrodeposition.

14. assume that we wish to operate the cell initially at a current of 1
assume that we wish to operate the cell initially at a current of 1.5A, which corresponds to a 0.010A/cm2 current density (for a 150 cm2 cathode): → in the literature it is found that the oxygen overvoltage (at the anode), will be about -0.85V → concentration polarization will be negligible at the beginning (at the cathode) → because the concentration of copper ions is initially high (0.022 M, this means an electrode potential of 0.29 V) → assuming a solution resistance of 0.05 Ohms Eappl = Ec – Ea + (Pcc + Pck) + (Pa) – IR Eappl = (-0.85) x 1.5 = -2.54V * thus, a rough estimate of the potential required to produce an initial current of 1.5A is -2.5V

16. Current Changes during an Electrolysis at Constant Applied Potential
It is useful to consider the changes in current in the cell under discussion when the potential is held constant at V throughout the electrolysis. Under these conditions, the current decreases with time as a result of the depletion of copper ions in the solution, as well as the increase in cathodic concentration polarization. In fact, with the onset of concentration polarization, the current decrease becomes exponential in time. That is: It = Io*e-kt and k = 25.8 D*A/Vd where It , is the current at time t in min, after the onset of polarization and Io is the initial current.

17. D: the diffusion coefficient(cm2/s), or the rate at which the reactant diffuses under a unit concentration gradient, A: the electrode surface area(cm2), V: the volume of the solution (cm3), and δ: the thickness of the diffusion layer in which the concentration gradient exists Typical values for D and δ are 10-5 cm2/s and 2 × 10-3 cm The constant 25.8 includes the factor of 60 for converting D to cm2/min, thus making k compatible with the units of t in the equation for It

18. (a) Current; (b) IR drop and cathode potential change during electrolytic deposition of copper at a constant applied cell potential.

19. When the initial applied potential is - 2
When the initial applied potential is V, we find that concentration polarization, and thus an exponential decrease in current occurs essentially immediately after applying the potential. The previous figure depicts this behavior; the data for the curve shown were computed for the cell using the preceding equation. After 30 min, the current decreases from the initial 1.5 A to 0.08 A. By this time, approximately 96% of the copper has been deposited.

20. Potential changes During an Electrolysis at Constant Applied Potential
The thermodynamic anode potential remains substantially unchanged throughout the electrolysis because of the large excess of the reactant (water) and the small change in the concentration of reaction product (H+).
The calculated reversible cathode potential (the dashed line), Ec, becomes smaller (more negative) as the copper concentration decreases.
The IR drop shown in figure parallels the changes in current with time.
The shift in cathode potential that accompanies concentration polarization often leads to codeposition of other species and loss of selectivity

21. IR drop and cathode potential change during electrolytic deposition of copper at a constant applied cell potential.

22. the IR drop decreases continually as the reaction proceeds, since the current continues to decrease, due to decreased mass transport to electrode surface. The reason for this decrease is primarily concentration polarization at the cathode, which limits the rate at which copper ions are brought to the electrode surface and thus the current decreases. As shown in the previous figure, the decrease in IR must be offset by an increase in the cathode potential (more negative) because the applied cell potential is constant.

23. It should be noted that co-deposition of hydrogen during electrolysis often leads to formation of non-adherent deposits, which are unsatisfactory for analytical purposes. This problem can be resolved by introducing another species that is reduced at a less-negative potential than hydrogen ion and does not adversely affect the physical properties of the deposit. One such cathode depolarizer is nitrate ion. Hydrazine and hydroxylamine are also commonly used. Consider a case in which a solution contains Cu2+ and Pb2+ ions. Lead (II) begins to deposit at point A on the cathode potential curve. Hence lead (II) ions would co-deposit well before copper deposition (at point D) was complete and would interfere.

24. The decrease in current and the increase in cathode potential is slowed at point B by the reduction of hydrogen ions. Because the solution contains a large excess of acid, the current is now no longer limited by concentration polarization of copper ions, and co-deposition of copper and hydrogen ions occurs simultaneously until the remainder of the copper ions is deposited. Under these conditions, the cathode is said to be depolarized by hydrogen ions. Note that as the cathode potential becomes more negative, metals that are reduced at potentials less than B will co-deposit with the analyte. However, metals that are reduced at point C will not co-deposit because of the almost constant non-increasing potential (solid line), as a result of reduction of H+, which has a high concentration.

25. The cathodic depolarizer, nitrate ion, gets reduced at a potential less negative than at point B (thus preventing hydrogen evolution):
NO H+ + 8e D NH4+ + 3H2O

26. Co-deposition of hydrogen during electrolysis often leads to spongy and flaky deposits that do not adhere to the electrode. Such a situation is unsatisfactory for analytical purposes. The use of depolarizers often improves the efficiency of the process. A depolarizer is a substance which gets reduced at the cathode without gasification or gets oxidized at the anode before oxygen evolution and stabilizes the potential of the working electrode by minimizing concentration polarization. Thus copper deposited from a nitric acid solution is smoother and more adherent because nitrate ions act as cathodic depolarizers and prevent evolution of hydrogen. Generally reducing agents like hydrazine hydrochloride will act as anodic depolarizers.

27. Consider now the fate of some metal ions, such as lead(Il), that begins to deposit at point A on the cathode potential curve. Lead(II) would co-deposit well before copper deposition was complete and would therefore interfere with the determination of copper. In contrast, a metal ion that reacts at a cathode potential corresponding to point C on the curve would not interfere because depolarization by hydrogen gas formation prevents the cathode from reaching this potential. At best, an electrolysis at constant potential can be used only to separate easily reduced cations, such as Pb(II), Cd(II), Ag(I), TI(I), Cu(II), and Zn(II), from those that are more difficult to reduce than hydrogen ion, such as AI(III). Therefore, hydrogen evolution occurs near the end of the electrolysis and prevents interference by cations that are reduced at more negative potentials.

28. 2. Electrolysis at Constant Working Electrode Potentials
From the Nernst equation, we see that a tenfold decrease in the concentration of an ion being deposited requires a negative shift in potential of only /n V. Electrolytic methods, therefore, are reasonably selective. For example, as the copper concentration of a solution is decreased from 0.10 M to 10-6 M, the thermodynamic cathode potential E, changes from an initial value of to V (values are derived from Nernst equation). In theory, then, it should be feasible to separate copper from any element that does not deposit within this 0.15V potential range.

29. Species that deposit quantitatively at potentials more positive than V could be eliminated with a prereduction step, (by adjusting the potential at less positive potential than V); ions that require potentials more negative potentials than V would not interfere with the copper deposition. Thus, if we are willing to accept a reduction in analyte concentration to 10-6 M as a quantitative separation, it follows that divalent ions differing in standard potentials by about 0.15 V or greater can, theoretically, be separated quantitatively by electrodeposition, provided their initial concentrations are about the same. Correspondingly, about 0.30 and 0.10V differences are required for univalent and trivalent ions, respectively.

30. Separations with Controlled electrode Potential Electrolysis
An approximate value of the limiting potential of the working electrode for a specific electrogravimetric process can be calculated from the Nernst equation, but lack of knowledge concerning the overpotential term(s) for a system severely limits its usefulness. A more reliable method utilizes the overpotential information obtained from current–potential curves at solid electrodes. Example: What range of cathode potentials is needed to deposit silver quantitatively (that is, to lower the silver concentration to at least 10−6 M) from a solution M in silver nitrate? Ag+ + e D Ag(s) Eo = V Deposition of silver will commence when the cathode potential is: E = log 0.01 = V

31. The removal of silver ions would be considered complete at: E = 0
The removal of silver ions would be considered complete at: E = log 10-6 = V Thus, the deposition would begin at V and would be completed at V, a difference of V. When a saturated calomel electrode (0.242 V versus the standard hydrogen electrode) is used as the auxiliary reference electrode, the range would be from to V

32. Would the silver removal be complete before the copper would commence to plate from a solution that is 0.010M in copper(II) ions? Copper(II) ions would commence to deposit at: E = {0.0592/2} log 10-2 = V (0.036 vs SCE) The removal of silver would be complete at V (versus SCE), whereas copper would start to deposit at V versus SCE. Controlling the cathode potential somewhere in the interval between 0.2 and 0.05 V versus SCE should be satisfactory. The current through the system steadily decreases as the deposition proceeds. However, the maximum permissible current is used at all times so the electrolysis proceeds at the maximum rate.

33. Consider the quantitative removal of cadmium from a solution 0
Consider the quantitative removal of cadmium from a solution M in cadmium ions, using a platinum electrode (the hydrogen overpotential over platinum is about 0.09 V) in a 0.1 M nitric acid solution. To what pH must the solution be adjusted in order to prevent interference from the evolution of hydrogen gas? In a 0.1M nitric acid solution, hydrogen would commence to evolve at a platinum electrode when: E = {0.0592/1} log 10-1 = V However, cadmium would not commence plating until: E = {0.0592/2} log 10-2 = V The separation is impossible at pH 1 with use of platinum electrodes since hydrogen will evolve at V, a much lower negative potential than cadmium starting deposition potential, and therefore it interferes.

34. This is not enough to exclude interference of H+
However, two changes in the procedure will enable cadmium to be deposited at this pH.
Using an acetate buffer and adjusting the pH of the solution to pH 5 will shift the electrode potential at which hydrogen evolves to a more negative value.
E = {0.0592/1} log 10-5= V
This is not enough to exclude interference of H+
Second, use an electrode that has been pre-coated with copper because the hydrogen overpotential is about 0.4 V on copper. This means that hydrogen will not evolve at potentials less negative than V on this copper coated electrode. Therefore, hydrogen will not interfere until the cathode potential reaches about −0.7 V. At this potential,
-0.7 = {0.0592/2} log [Cd2+]
[Cd2+] < 1.4*10-10 M

35. Is a quantitative separation of Cu2+ and Pb2+ by electrolytic deposition feasible in principle? If so, what range of cathode potentials versus the saturated calomel electrode (SCE) can be used? Assume that the sample solution is initially M in each ion and that quantitative removal of an ion is realized when only 1 part in 10,000 remains undeposited. Cu2+ +2e D Cu(s) Eo = V Pb2+ +2e D Pb(s) Eo = V Note that based on the standard potentials, copper will begin to deposit at more positive applied voltages than lead. Let us first calculate the potential required to reduce the Cu2+ concentration to 10-4 of its original concentration (that is, from M to 1.00*10-5 M).

37. Large Versus Small Currents
Concentration polarization and overvoltage may prevent application of theoretically deduced potential differences for separations. This is mainly due to the fact that the change in cathode potential is governed by the decrease in IR drop (due to decrease in current with time). Thus, for instances in which relatively large currents are applied initially, the change in cathode potential can ultimately be expected to be large. On the other hand, if the cell is operated at low current levels so that the variation in cathode potential is decreased, the time required for completion of the deposition may become prohibitively long.

38. Apparatus for controlled-potential, or potentiostatic, electrolysis
Apparatus for controlled-potential, or potentiostatic, electrolysis. Contact C is adjusted as necessary to maintain the working electrode (cathode in this example) at a constant
potential. The current in the reference electrode is essentially zero at all times. Modern potentiostats are fully automatic and frequently computer controlled.
The electrode notations in the figure are the currently acceptable notations.