Coulometry and Electrogravimetric Analysis

1. 1
Chapter 8
Coulometry and Electrogravimetric Analysis
 Coulometry is an electrochemical technique used to determine the
amount of a substance by measuring the total electric charge (Q)
required for its complete redox conversion (electrolysis).
 It is an accurate, absolute (bulk) method based on Faraday's laws of
electrolysis where the charge is directly proportional to the amount of
chemical change.
 The total charge, Q, in coulombs, passed during an electrolysis is
related to the absolute amount of analyte by Faraday’s law
Q = nFN
 where n is the number of electrons transferred per mole of analyte, F
is Faraday’s constant (96487 C mol–1
), and N is the moles of analyte.

2. 2
 There are two main types of coulometry
 1. Constant-current coulometry (coulometric titration): A
constant current is applied, and the time it takes for the reaction to
complete is measured, which is then used to calculate the total
charge (Q = I t
⋅ e).
 where te is the electrolysis time.
 2. Controlled-potential coulometry: A constant potential is
applied, and the resulting current is measured over time as it
decreases, providing a measure of the total charge passed.
 In this case, then the total charge is given by

3. 3
 To obtain an accurate value for N, therefore, all the current must result in the
analyte’s oxidation or reduction.
 In other words, coulometry requires 100% current efficiency i.e the
reaction consumes all the current.
Controlled-Potential Coulometry
 The easiest method for ensuring 100% current efficiency is to maintain the
working electrode at a constant potential that allows for the analyte’s
quantitative oxidation or reduction, without simultaneously oxidizing or
reducing an interfering species.
 The current flowing through an electrochemical cell under a constant
potential is proportional to the analyte’s concentration.
 As electrolysis progresses the analyte’s concentration decreases, as does the
current.

4. 4
 The resulting current-versus-time profile for controlled-potential
coulometry, which also is known as potentiostatic coulometry,
looks like;
 Integrating the area under the curve, from t = 0 until t = te,
gives the total charge.

5. 5
Selecting a Constant Potential
 In controlled-potential coulometry, the potential is selected so that
the desired oxidation or reduction reaction goes to completion
without interference from redox reactions involving other
components of the sample matrix.
 For example, a constant-potential coulometric method for Cu2+
based on its reduction to copper metal at a Pt cathode working
electrode.
 This reaction is favored when the working electrode’s potential is
more negative than +0.342 V versus the SHE or +0.093 V versus
the SCE.

6. 6
 To maintain a 100% current efficiency, however, the potential must be
selected so that the reduction of H3O+
to H2 does not contribute
significantly to the total charge passed at the electrode.
 The potential needed for a quantitative reduction of Cu2+
can be
calculated using the Nernst equation.
Minimizing Electrolysis Time
 Since time is an important consideration in choosing and designing
analytical methods, the factors that determine the analysis time need to
be considered.

7. 7
 For this reason controlled-potential coulometry is carried out in
small-volume electrochemical cells, using electrodes with large
surface areas and high stirring rates.
 A quantitative electrolysis typically requires approximately 30–60
min, although shorter or longer times are possible.
Instrumentation
 Controlled-potential coulometry uses three-electrode potentiostat
(the device that used to control voltage and measure current).
 Pt and Hg are commonly used as working electrodes.
 However, the large overpotential for reducing H3O+
at mercury
makes it the electrode of choice for analytes requiring negative

8. 8
 But it can’t be used at potentials that are positive with respect to the SHE, Pt
is used when positive potentials are required.
 A saturated calomel or Ag/AgCl electrode serves as the reference electrode.
 The auxiliary electrode, which is often a Pt wire, is separated by a salt bridge
from the solution containing the analyte.
 This is necessary to prevent electrolysis products generated at the auxiliary
electrode from reacting with the analyte and interfering in the analysis.
 The other essential feature of instrumentation for controlled-potential
coulometry is a means of determining the total charge passed during
electrolysis.

9. Analytical Chemistry and Instrumentation 9
 One method is to monitor the current as a function of time and
determine the area under the curve.
 However, modern instruments use electronic integration to
monitor charge as a function of time.
 The total charge at the end of the electrolysis then can be read
directly from a digital readout or from a plot of charge versus
time.

10. Controlled-Current Coulometry
 A second approach to coulometry is to use a constant current in place
of a constant potential.
 It is also known as amperostatic coulometry or coulometric titrimetry.
 Even if it is not applicable for the analysis of mixture of ions (not
selective), it has two advantages over controlled-potential coulometry,
 First, using a constant current makes for a more rapid analysis since the
current does not decrease over time.
 Thus, a typical analysis time for controlled-current coulometry is less
than 10 min.
 Second, the total charge is simply the product of current and time, i.e a
method for integrating the current–time curve is not necessary.
10

11. 11
• However, it has two important problems that must be solved.
• First, as electrolysis occurs the analyte’s concentration and, the
current due to its oxidation or reduction steadily decreases.
• Thus, to maintain a constant current the cell potential must
change until another oxidation or reduction reaction can
occur at the WE.

12. 12
 Unless the system is carefully designed, these secondary reactions will
produce a current efficiency of less than 100%.
 The second problem is the need for a method of determining when the
analyte has been exhaustively electrolyzed (end point).
 In controlled-potential coulometry this is signaled by a decrease in the
current to a constant background or residual current.
 In controlled-current coulometry, however, a constant current continues
to flow even when the analyte has been completely oxidized or reduced.
 A suitable means of determining the end-point of the reaction, te, is
needed.

13. 13
Maintaining Current Efficiency
 To illustrate why changing the working electrode’s potential can lead to less
than 100% current efficiency, let’s consider the coulometric analysis for
Fe2+
based on its oxidation to Fe3+
at a Pt working electrode in 1 M H2SO4.
 Initially the potential of the working electrode remains nearly constant at a
level near the standard-state potential for the Fe3+
/Fe2+
redox couple.
 As the concentration of Fe2+
decreases, however, the potential of the
working electrode shifts toward more positive values until another
oxidation reaction can provide the necessary current.
 Thus, in this case the potential eventually increases to a level at which the
oxidation of H2O occurs.

14. 14
• Since the current due to the oxidation of H2O does not contribute
to the oxidation of Fe2+
, the current efficiency of the analysis is
less than 100%.
• To maintain a 100% current efficiency the products of any
competing oxidation reactions must react both rapidly and
quantitatively with the remaining Fe2+
.
• This may be accomplished, for example, by adding an excess of
Ce3+
to the analytical solution .
• When the potential of the working electrode shifts to a more
positive potential, the first species to be oxidized is Ce3+
.

15. 15
 The Ce4+
produced at the working electrode rapidly mixes with the solution, where it
reacts with any available Fe2+
.
 Combining these reactions gives the desired overall reaction of
 In this manner, a current efficiency of 100% is maintained.
 Furthermore, since the concentration of Ce3+
remains at its initial level, the potential
of the working electrode remains constant as long as any Fe2+
is present.
 This prevents other oxidation reactions, such as that for H2O, from interfering with
the analysis.
 A species, such as Ce3+
, which is used to maintain 100% current efficiency, is called
a mediator.

16. End Point Determination
 Using the same example, once all the Fe2+
has been oxidized current continues
to flow as a result of the oxidation of Ce3+
and, eventually, the oxidation of H2O.
 What is needed is a means of indicating when the oxidation of Fe2+
is complete.
 In this respect it is convenient to treat a controlled-current coulometric analysis
as if electrolysis of the analyte occurs only as a result of its reaction with the
mediator.
 A reaction between an analyte and a mediator is identical to that encountered in
a redox titration.
 Thus, the same end points that are used in redox titrimetry such as visual
indicators, potentiometric and conductometric measurements, may be used.
16

17. 17
Instrumentation
 Controlled-current coulometry normally is carried out using a galvanostat
(the divice that controls current and measure the time) and an
electrochemical cell consisting of a working electrode and a counter-
electrode.
 The working electrode, which often is constructed from Pt, is also
called the generator electrode since it is where the mediator reacts to
generate the species reacting with the analyte.
 The counter-electrode is isolated from the analytical solution by a salt
bridge or porous frit to prevent its electrolysis products from reacting with
the analyte.
 Alternatively, oxidizing or reducing the mediator can be carried out
externally, and the appropriate products flushed into the analytical solution.

18. 18
• A solution containing the mediator flows under the influence of
gravity into a small-volume electrochemical cell.
• The products generated at the anode and cathode pass through
separate tubes, and the appropriate oxidizing or reducing reagent
can be selectively delivered to the analytical solution.
• For example, external generation of Ce4+
can be obtained using an
aqueous solution of Ce3+
and the products generated at the anode.

19. 19
Applications Coulometry
 Coulometry may be used for the quantitative analysis of both inorganic
and organic compounds.
 The majority of controlled-potential coulometric analyses involve the
determination of inorganic cations and anions, including trace metals
and halides.
 The ability to control selectivity by carefully selecting the working
electrode’s potential, makes controlled-potential coulometry
particularly useful for the analysis of alloys.
 For example, the composition of an alloy containing Ag, Bi, Cd, and Sb
can be determined by dissolving the sample and placing it in a matrix of
0.2 M H2SO4.

20. 20
 A platinum working electrode is immersed in the solution and held at a constant
potential of +0.40 V versus the SCE.
 At this potential Ag(I) deposits on the Pt electrode as Ag, and the other metal ions
remain in solution.
 When electrolysis is complete, the total charge is used to determine the amount of
silver in the alloy.
 The potential of the platinum electrode is then shifted to –0.08 V versus the SCE,
depositing Bi on the working electrode.
 When the coulometric analysis for bismuth is complete, antimony is determined by
shifting the working electrode’s potential to –0.33 V versus the SCE, depositing Sb.
 Finally, cadmium is determined following its electrodeposition on the Pt electrode
at a potential of –0.80 V versus the SCE.

21. 21
 Another area where controlled-potential coulometry has found
application is in nuclear chemistry, in which elements such as
uranium and polonium can be determined at trace levels.
 For example, microgram quantities of uranium in a medium of
H2SO4 can be determined by reducing U(VI) to U(IV) at a
mercury working electrode.
 Controlled-potential coulometry also can be applied to the
quantitative analysis of organic compounds, although the
number of applications is significantly less than that for
inorganic analytes.
 One example is the six-electron reduction of a nitro group,
–NO2, to a primary amine, –NH2, at a mercury electrode.

22. 22
 Solutions of picric acid, for instance, can be analyzed by reducing
to triaminophenol.
• In comparison with conventional titrimetry, there are several
advantages to the coulometric titrations.
• One advantage is that the electrochemical generation of a “titrant”
that reacts immediately with the analyte allows the use of reagents
whose instability prevents their preparation and storage as a
standard solution.
• Thus, highly reactive reagents such as Ag2+
and Mn3+
can be used in
coulometric titrations.

23. 23
 Because it is relatively easy to measure small quantities of charge, coulometric
titrations can be used to determine small quantities of analyte that cannot be
measured accurately by a conventional titration.
 Example 1, the concentration of H2S in a wastewater sample can be determined
by a coulometric titration using KI as a mediator and I3
–
as the “titrant.”
H2S(aq) + I3
–
(aq) ↔ 2H+
+ 3I–
(aq) + S(s) or
H2S(aq) + I3
–
(aq) + 2H2O(l) ↔ 2H3O+
(aq) + 3I–
(aq) + S(s)
 A 50.00-mL sample of wastewater is placed in a coulometric cell, along with an
excess of KI and a small amount of starch as an indicator.

24. 24
 Electrolysis is carried out at a constant current of 84.6 mA,
requiring 386 s to reach the starch end point.
 Calculate the concentration of H2S in the sample in parts per
million.
Solution, MW = 34.08 g/mol.
Then calculate the total charge (Q) passed:
Q = I × t = (84.6 × 10 ³ A) × (386 s)
⁻ = 32.6556 C
Calculate the number of mole (N) = Q / nF = 32.6556 C / 96485
C/mol e⁻x2 =1.69225 × 10 mol H S
⁻⁴ ₂

25. 25
 Calculate the mass of H S
₂
 Mass of H S = (1.69225 × 10 mol) × (34.0
₂ ⁴
⁻ 8 g/mol)
 Mass of H S = 0.005766 g
₂ = 5.766 mg
 Calculate the concentration of H S in mg/L:
₂
 The sample volume is 50.00 mL = 0.05000 L.
 Convert the concentration to parts per million (ppm):
 For dilute aqueous solutions, 1 mg/L is approximately equal to 1
ppm.
 Concentration (ppm) = 115.32 ppm

26. 26
 Example 2, a 0.3619-g sample of pure tetrachloropicolinic acid,
C6HNO2Cl4, is dissolved in distilled water, transferred to a 1000-
mL volumetric flask, and diluted to volume. An exhaustive
controlled-potential electrolysis of a 10.00-mL portion of this
homogenous solution requires 5.374 C of charge.
 What is the value of n for this reduction reaction?
 Solution, MW = 260.88 g/mol. the 10.00-mL portion of sample
contains 3.619 mg, or 1.39×10–5
mol of tetrachloropicolinic acid.
 Solving for n and making appropriate substitutions gives


27. 27
 Thus, reducing a molecule of tetrachloropicolinic acid requires
four electrons.
 The overall reaction, which results in the selective formation of
3,6-dichloropicolinic acid,

28. 28
Electrogravimetry
 If acceptable current efficiency is not feasible during coulometric
analysis, it is possible to determine the mass of the analyte
deposited at the working electrode.
 The analyte’s oxidation or reduction leads to its deposition on the
working electrode.
 In this case the working electrode is weighed before beginning
the electrolysis and reweighed when electrolysis of the analyte is
complete.
 The difference in the electrode’s weight gives the analyte’s mass.
 This technique is known as electrogravimetry.
 Mostly used for metal ions analysis.

29. 29
 The oxidation of Pb2+
, and its deposition as PbO2 on a Pt anode is one
example of electrogravimetry.
 Reduction also may be used in electrogravimetry.
 The electrodeposition of Cu on a Pt cathode, for example, provides a
direct analysis for Cu2+
.
 But this method has its own disadvantage;
 1. Other metal ions reduced at similar potentials or interfering species
present, leading to impure deposits (e.g., chromium with copper).
 2. Incomplete drying, contamination, or residual solution on the
electrode produce error.