Coulometry and Electrogravimetry

Chapter-Eight
Coulometry and Electro-
Gravimetric Analysis
Prepared by:-Melaku M.(MSc)
1/3/2020 1

Coulometry and Electro gravimetric Analysis
Electrogravimetry and coulometry are related methods in which
electrolysis is carried out for a sufficient length of time to ensure
complete oxidn or redn of the analyte to a product of known
composition.
 In electrogravimetry, the goal is to determine the amount of analyte
present by converting it electolytically to a product that is weighed as
a deposit on one of the electrodes.
 In coulometric procedures, we determine the amount of analyte by
measuring the quantity of electrical charge needed to completely
convert it to a product.
 Electrogravimetry and coulometry are moderately sensitive and
among the most accurate and precise techniques available to the
chemist.
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Cont…
 Electrogravimetry require no preliminary calibration against
chemical standards because the functional relationship b/n the quantity
measured and the analyte conc can be derived from theory and atomic
mass data.
When there is a net current in an electrochemical cell. The measured
potential across the 2 electrodes is no longer simply the d/ce b/n the 2
electrode potentials as calculated from the Nernst equation.
 2 additional phenomena, IR drop & polarization must be considered
when current is present.
 Because of these phenomena, potentials larger than the
thermodynamic potential are needed to operate an electrolytic cell.
When present in a galvanic cell, IR drop & polarization result in the
development of potentials smaller than predicted.
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Cont…
Coulometric methods of analysis are based on an
exhaustive electrolysis of the analyte.
 By exhaustive we mean that the analyte is quantitatively
oxidized or reduced at the WE or reacts quantitatively with a
reagent generated at the WE.
There are 2 forms of coulometry: controlled-potential
coulometry, in which a constant potential is applied to the
electrochemical cell, and controlled-current coulometry, in
which a constant current is passed through the
electrochemical cell.
The total charge, Q, in coulombs, passed during electrolysis
is related to the absolute amount of analyte by Faraday’s law
Q = nFN ----------------------------8.1
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Cont…
 Where n is the # of es transferred per mole of analyte, F is Faraday’s
constant (96487 C mol–1), and N is the moles of analyte.
A coulomb is also equivalent to an A.s; thus, for a constant current, i,
the charge is given as
Q = ite -----------------------------8.2
Where te is the electrolysis time.
 If current varies with time, as it does in controlled potential
coulometry, then the total charge is given by
---------------8.3
 In coulometry, current and time are measured, and equation 8.2 or
equation 8.3 is used to calculate Q.
 Equation 8.1 is then used to determine the moles of analyte.
 To obtain an accurate value for N, therefore, all the current must
result in the analyte’s oxidation or reduction.1/3/2020 5

Cont…
o In other words, coulometry requires 100% current efficiency (or an
accurately measured current efficiency established using a standard), a
factor that must be considered in designing a coulometric method of
analysis. 8.1. Controlled-Potential Coulometry
oThe easiest method for ensuring 100% current efficiency is to
maintain the WE at a constant potential that allows for the analyte’s
quantitative oxidn or redn, without simultaneously oxidizing or reducing
an interfering species.
o The current flowing through an electrochemical cell under a constant
potential is proportional to the analyte’s conc.
o As electrolysis progresses the analyte’s conc decreases as does the
current.
oThe resulting current vs time profile for controlled-potential
coulometry which also known as potentiostatic coulometry, shown in
Fig.8.1.1/3/2020 6

Cont…
o Integrating the area under the curve (equation 8.3), from t = 0 until t
= te, gives the total charge.
Fig.8.1.current-time curve for controlled potential coulometry.
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Selecting a Constant Potential
 In controlled-potential coulometry, the potential is selected so that
the desired oxidn or redn rxn goes to completion without interference
from redox rxns involving other components of the sample matrix.
 To see how an appropriate potential for the WE is selected, let’s
develop a constant-potential coulometric method for Cu2+ based on its
redn to Cu metal at a Pt cathode WE.
---------------- 8.4
•The potential needed for a quantitative redn of Cu2+ can be calculated
using the Nernst equation
-----------------8.5
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Minimizing Electrolysis Time
 The current-time curve for controlled-potential coulometry in Fig.8.1
shows that the current decreases continuously throughout electrolysis.
 An exhaustive electrolysis, therefore, may require a long time.
 Since time is an important consideration in choosing and designing
analytical methods, the factors that determine the analysis time need to
be considered.
 The change in current as a function of time in controlled-potential
coulometry is approximated by an exponential decay; thus, the current at
time t is i = i0e–kte----------------------8.6
Where i0 is the initial current and k is a constant that is directly
proportional to the area of the WE & the rate of stirring and inversely
proportional to the volume of the solution.
 For an exhaustive electrolysis in which 99.99% of the analyte is
oxidized or reduced, the current at the end of the analysis, te, may be
approximated as i =(10–4)i0----------------------------------8.7
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Cont…
Substituting equation 8.7 into equation 8.6 and solving for te gives
the minimum time for an exhaustive electrolysis as
te= -k-1ln(10-4) = 9.21xk-1
From this equation increasing k leads to a shorter analysis time.
For this reason controlled-potential coulometry is carried out in
small-volume electrochemical cells, using electrodes with large
surface areas and with high stirring rates.
 A quantitative electrolysis typically requires approximately 30–60
min, although shorter or longer times are possible.
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Instrumentation
The potential in controlled-potential coulometry is set using a 3-
electrode potentiostat.
 Two types of WE are commonly used: a Pt electrode manufactured
from Pt-gauze & fashioned into a cylindrical tube & an Hg pool
electrode.
The large over potential for reducing H3O+ at mercury makes it the
electrode of choice for analytes requiring negative potentials.
 For example, potentials more -ve than –1 V vs the SCE are feasible
at an Hg electrode but not at a Pt electrode, even in very acidic so/ns.
The ease, with which mercury is oxidized, however, prevents its use
at potentials that are +ve with respect to the SHE.
Platinum WEs are used when +ve potentials are required.
The auxiliary electrode, which is often a Pt wire, is separated by a
salt bridge from the solution containing the analyte.
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11

Cont…
This is necessary to prevent electrolysis products generated at the
auxiliary electrode from reacting with the analyte and interfering in
the analysis.
A saturated calomel or Ag/AgCl electrode serves as the RE.
 The other essential feature of instrumentation for controlled-
potential coulometry is a means of determining the total charge
passed during electrolysis.
 One method is to monitor the current as a function of time and
determine the area under the curve (see Fig.8.1).
 Modern instruments, however, 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
(Fig.8.3).
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Cont…
Fig.8.3.charge-time curve obtained by integrating the current-time
curve in fig.8.1.
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8.2 Controlled-Current Coulometry
A second approach to coulometry is to use a constant current in
place of a constant potential (Fig.8.4).
 Controlled-current coulometry also known as amperostatic
coulometry or coulometric titrimetry, 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, as opposed to approximately 30–60 min for
controlled-potential coulometry.
 Second, with a constant current the total charge is simply the
product of current and time (equation 8.2).
A method for integrating the current–time curve, therefore, is not
necessary.
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14

Cont…
o Using a constant current does present two important experimental
problems that must be solved if accurate results are to be obtained.
o1st, as electrolysis occurs the analyte’s conc &, therefore, the current
due to its oxidation or reduction steadily decreases.
o To maintain a constant current the cell potential must change until
another oxidation or reduction rxn can occur at the WE.
o Unless the system is carefully designed, these secondary reactions
will produce a current efficiency of less than 100%.
o The second problem is the need for a method of determining when
the analyte has been exhaustively electrolyzed.
oIn controlled-potential coulometry this is signaled by a decrease in
the current to a constant background or residual current (see Fig.8.1).
oIn controlled-current coulometry, however, a constant current
continues to flow even when the analyte has been completely oxidized
or reduced.
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Cont…
A suitable means of determining the end-point of the rxn, te, is
needed.
Fig.8.4.current-time curve for controlled-current coulometry.
Maintaining Current Efficiency
 To illustrate why changing the WE’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 WE in 1 M H2SO4.
 Initially the potential of the WE remains nearly constant at a level
near the standard-state potential for the Fe3+/Fe2+ redox couple.
1/3/2020 16

Cont…
As the conc of Fe2+ decreases, however, the potential of the WE
shifts toward more +ve values until another oxidation rxn can provide
the necessary current.
Thus, in this case the potential eventually increases to a level at
which the oxidn of H2O occurs.
Since the current due to the oxidation of H3O+ 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 rxns 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 (Fig.8.5b).
When the potential of the WE shifts to a more +ve potential, the first
species to be oxidized is Ce3+.
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Cont…
The Ce4+ produced at the WE rapidly mixes with the so/n, where it
reacts with any available Fe2+.
---------------8.8
Combining these rxns gives the desired overall rxn of
 In this manner, a current efficiency of 100% is maintained.
 Furthermore, since the conc of Ce3+ remains at its initial level, the
potential of the WE remains constant as long as any Fe2+ is present.
This prevents other oxidation rxns, 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.
1/3/2020 18

Cont…
Instrumentation
Controlled-current coulometry normally is carried out using a
galvanostat and an electrochemical cell consisting of a WE and a
counter electrode.
The WE, 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, & the appropriate products flushed into the analytical so/n.
A so/n containing the mediator flows under the influence of gravity
into a small-volume electrochemical cell.
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Cont…
The products generated at the anode & cathode pass through separate
tubes, and the appropriate oxidizing or reducing reagent can be
selectively delivered to the analytical solution.
 The other necessary instrumental component for controlled-current
coulometry is an accurate clock for measuring the electrolysis time, te,
and a switch for starting and stopping the electrolysis.
 Analog clocks can read time to the nearest ±0.01 s, but the need to
frequently stop and start the electrolysis near the end point leads to a net
uncertainty of ±0.1 s.
Digital clocks provide a more accurate measurement of time, with
errors of ±1 ms being possible.
The switch must control the flow of current and the clock, so that an
accurate determination of the electrolysis time is possible
1/3/2020 20

Coulometric Titrations
Controlled-current coulometric methods commonly are called
coulometric titrations because of their similarity to conventional
titrations.
 We already have noted, in discussing the controlled-current
coulometric determination of Fe2+, that the oxidation of Fe2+ by Ce4+ is
identical to the reaction used in a redox titration.
Combining equations 8.1 and 8.2 and solving for the moles of
analyte gives
------------------8.9
Compare this equation with the relationship b/n the moles of strong
acid, N, titrated with a strong base of known concentration.
N = (M base) (V base)
The titrant in a conventional titration is replaced in a coulometric
titration by a constant-current source whose current is analogous to the
titrant’s molarity.
1/3/2020 21

Cont…
oThe time needed for an exhaustive electrolysis takes the place of the
volume of titrant, and the switch for starting and stopping the
electrolysis serves the same function as a burette’s stopcock.
Quantitative Applications
o Coulometry may be used for the quantitative analysis of both
inorganic and organic compounds.
Controlled-Potential Coulometry
o The majority of controlled-potential coulometric analyses involve
the determination of inorganic cations and anions, including trace
metals and halides.
oThe ability to control selectivity by carefully selecting the WE’s
potential, makes controlled-potential coulometry particularly useful
for the analysis of alloys.
o 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. 1/3/2020
22

Cont…
A platinum WE 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 Pt electrode is then shifted to –0.08 V vs the
SCE, depositing Bi on the WE.
When the coulometric analysis for bismuth is complete, antimony is
determined by shifting the WE’s potential to –0.33 V vs the SCE,
depositing Sb.
Finally, Cd is determined following its electrodeposition on the Pt
electrode at a potential of –0.80 V vs the SCE.
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. 1/3/2020
23

Cont…
o For example, microgram quantities of uranium in a medium of
H2SO4 can be determined by reducing U (VI) to U (IV) at a Hg WE.
o Controlled-potential coulometry also can be applied to the
quantitative analysis of organic cpds, although the number of
applications is significantly less than that for inorganic analytes.
o One example is the six-electron reduction of a nitro group, –NO2, to
a primary amine, –NH2, at a mercury electrode.
Solutions of picric acid, for instance, can be analyzed by reducing to
triaminophenol.
o Another example is the successive reduction of trichloroacetate to
dichloroacetate, and of dichloroacetate to monochloroacetate
Cl3CCOO–(aq) + H3O+(aq) + 2e– ↔Cl2HCCOO–(aq) + Cl–(aq) +
H2O(l)
1/3/2020 24

Application Cont…
Cl2HCCOO–(aq) + H3O+(aq) + 2e– ↔ClH2CCOO–(aq) + Cl–(aq) +
H2O(l)
Mixtures of trichloroacetate and dichloroacetate are analyzed by
selecting an initial potential at which only the more easily reduced
trichloroacetate is reduced.
When its electrolysis is complete, the potential is switched to a more
negative potential at which dichloroacetate is reduced.
 The total charge for the first electrolysis is used to determine the
amount of trichloroacetate, and the difference in total charge between
the first and second electrolyses gives the amount of dichloroacetate.
1/3/2020 25

Controlled-Current Coulometry
The use of a mediator makes controlled-current coulometry a more
versatile analytical method than controlled-potential coulometry.
 For example, the direct oxidn or redn of a protein at the WE in
controlled-potential coulometry is difficult if the protein’s active
redox site lies deep within its structure.
 The controlled-current coulometric analysis of the protein is made
possible, however, by coupling its oxidn or redn to a mediator that is
reduced or oxidized at the WE.
 Controlled-current coulometric methods have been developed for
many of the same analytes that may be determined by conventional
redox titrimetry.1/3/2020 26
Application Cont…

Application Cont…
 Coupling the mediator’s oxidn or redn to an acid–base,
precipitation, or complexation rxn involving the analyte allows for the
coulometric titration of analytes that are not easily oxidized or
reduced.
For example, when using H2O.
If the oxidn or redn of H2O is carried out externally using the
generator cell then H3O+ or OH– can be dispensed selectively into a
solution containing a basic or acidic analyte.
 The resulting rxn is identical to that in an acid–base titration.
 Coulometric acid–base titrations have been used for the analysis of
strong & weak acids and bases, in both aqueous & non-aqueous
matrices.
 In comparison with conventional titrimetry, there are several
advantages to the coulometric titration.
1/3/2020 27

Cont…
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 & storage as a standard
so/n.
Thus, highly reactive reagents such as Ag2+ and Mn3+ can be used in
coulometric titrations.
 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.
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Cont…
Example1. The purity of a sample of Na2S2O3 was determined by a
coulometric redox titration using I– as a mediator & I3
– as the “titrant.”
A sample weighing 0.1342 g is transferred to a 100-mL volumetric
flask & diluted to volume with distilled water. A 10.00-mL portion is
transferred to an electrochemical cell along with 25 mL of 1 M KI, 75
mL of a pH 7.0 phosphate buffer & several drops of a starch indicator
so/n. Electrolysis at a constant current of 36.45 mA required 221.8 s to
reach the starch indicator end point. Determine the purity of the
sample.
SOLUTION The coulometric titration of S2O3
2– with I3
– is Oxidizing
S2O3
2– to S4O6
2 –requires 1e per S2O3
2– (n = 1). Combining equations
8.1 & 8.2, and making an appropriate substitution for moles of
Na2S2O3 gives
1/3/2020 29

Cont…
represents the amount of Na2S2O3 in a 10.00-mL portion of a 100-mL
sample, thus 0.1325 g of Na2S2O3 is present in the original sample.
The purity of the sample, therefore, is
Note that the calculation is worked as if S2O3
2– is oxidized directly at
the WE instead of in so/n.
1/3/2020 30

Coulometry and Electrogravimetry

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