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EA-AC
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Lecture 3
1-22-2003
First, they require that a current be developed in a cell containing the analyte, whereas in
potentiometry currents, must be kept at a vanishingly small level. Otherwise the cell will
do work which will change the measured voltage.
Second, in these procedures, the analyte is quantitatively converted to a new oxidation
state, whereas in potentiometry the effect of the measurement on the analyte concentration
is vanishingly small.
Third, in most cases, the cells in these methods are operated as electrolytic cells, whereas
the cells in potentiometry are galvanic.
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Remember
Electrolytic cell – requires an external source of electrical energy for operation.
Drives system away from equilibrium.
Galvanic cell – reactions at the two electrodes proceed spontaneously.
System moves toward equilibrium.
Fourth, the final measurement in these procedures is either the mass of product formed
electrolytically from the analyte or the quantity of charge required to convert the analyte
to a new oxidation state, whereas, the final measurement in potentiometry is that of cell
potential.
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There are three methods described
Electrogravimetry – where we deposit material on an electrode and weigh it.
Coulometry – convert a substance from one redox state to another at constant potential
and count the number of moles of electrons required.
Coulometric titration – have an end point indicator that signals the end of the redox
conversion produced by a constant current. Time is measured and I*t gives Q in C.
Electrogravimetry and the two coulometric methods are moderately sensitive and among,
the most accurate and precise techniques available.
Unlike most of the methods we have examined so far, these methods require no
preliminary calibration against standards because the functional relationship between the
quantity measured and the analyte concentration can be derived from theory and
atomic-mass data.
4 to 6 figure precision possible.
First some background.
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When a current develops in an electrochemical cell, the measured potential across the two
electrodes is no longer simply the difference between the electrode potentials of the
cathode and the anode (the thermodynamic cell potential).
Three additional phenomena come into play as described in the chapter - IR drop,
polarization and overpotential.
These require application of potentials greater than the thermodynamic potential to
operate an electrolytic cell and result in the development of potentials smaller than the
theoretical values of a galvanic cell.
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Here is a typical cell for the determination of cadmium ion:
The cell nomenclature would be
AgAgCl(s), Cl-(0.200 M), Cd2+(0.00500 M)Cd
Here, the working electrode is a metal electrode that has been coated with a layer of
cadmium.
The auxiliary electrode is a silver/silver chloride electrode whose electrode potential
remains more or less constant during the analysis.
Note that this is an example of a cell without liquid junction or salt bridge. As shown in the
transparency, this cell, as written, has a thermodynamic potential of - 0.734 V.
Here the negative sign implies that the cell shown in the diagram is electrolytic and would
require the application of a potential somewhat larger than - 0.734 V to behave in the way
indicated by this equation. I.e. the spontaneous direction is from right to left.
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Cd2+ + 2 Ag(s) + 2 Cl- < == > Cd(s) + AgCl(s)
Note that the cell being considered is reversible, so in the absence of the external potential
shown in the figure, the cell reaction would be the reverse of the equation, and the cell
would behave as a galvanic cell with an output potential of + 0.734 V.
Electrochemical cells, like metallic conductors, resist the flow of charge. Ohm's law
describes the effect of this resistance on the magnitude of the current in the cell. E = IR
The product of the resistance R of a cell in ohms () and the current I in amperes (A) is
called the ohmic potential or the IR drop of the cell.
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In part b of the transparency we have used a resistor R to represent the cell resistance of the
cell in part a. In order to generate a current of I amperes in this cell, we must apply a
potential Eapplied that is - IR volts more negative than the thermodynamic potential.
That is,
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Eapplied = Ecathode – Eanode - IR
where Ecathode and Eanode are electrode potentials computed with the Nernst equation.
We can use this equation to calculate the required driving potential for the determination of
cadmium in the presence of chloride ions under the above concentration conditions.
From the Nernst equation we can calculate the electrode potential of the cadmium cathode
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Ecathode = -0.403 - 0.0592/2 log 1/0.00500 = -0.471 v
and of the silver anode (chloride is a product during the reduction of AgCl to Ag(s)).
Eanode = 0.222 - 0.0592/1 log (0.200) = -0.263 v
So Ecell = Eapplied = Ecathode – Eanode = -0.471 – 0.263 = -0.734 v
Thus, to prevent this cell from behaving as a galvanic cell with a cadmium anode and a
silver cathode we would need to apply a potential of -0.734 V from an external source as
shown in the transparency.
If we take into consideration the cell resistance of 15 ohms, and we want to develop a
current of 2.00 mA, we get
Eapplied = Ecathode – Eanode - IR = -0.734 V - .00200 A x 15  = -0.764 V
Thus, to obtain a 2.00 mA current as shown in the transparency, an applied potential of
0.764 V would be required.
So if we run reactions which produce a measurable current, there is a resistance in the cell
that must be overcome.
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According to our equation, a plot of current in an electrolytic cell as a function of negative
applied potential should be a straight line with a slope equal to the resistance.
As shown in this transparency, the plot is indeed linear with small currents. As the applied
voltage increases, the current ultimately begins to deviate from linearity.
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Cells that exhibit nonlinear behavior at higher currents are said to be polarized, and the
degree of polarization is given by an overvoltage, which is symbolized by capital pi in the
figure.
Note that polarization requires the application of a potential greater than the theoretical
value to give a current of the expected magnitude. Thus, the overvoltage required to
achieve a current of 7.00 mA in the electrolytic cell in the transparency is about - 0.23 V.
For an electrolytic cell affected by overvoltage, our equation then becomes
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Eapplied = Ecathode – Eanode - IR - 
Polarization is an electrode phenomenon that may affect either or both of the electrodes in
a cell. The degree of polarization of an electrode varies widely.
In some instances it approaches zero, but in others it can be so large that the current in the
cell becomes independent of potential. Under this circumstance, polarization is said to be
complete.
Polarization phenomena can be divided into two categories:
Concentration polarization and kinetic polarization – called overpotential by our book.
Concentration polarization plays an important part in the use of the polarograph. We
operate the polarograph so that diffusion is limiting and we had polarization at the
working electrode as we will discuss next week.
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Concentration polarization occurs when reactant species do not arrive at the surface of the
electrode or product species do not leave the surface of the electrode fast enough to
maintain the desired current.
When this happens the current is limited to values less than that predicted by our equation.
Reactants are transported to and from the surface of an electrode by three mechanisms:
(1) diffusion, (2) migration, and (3) convection. Products are removed from electrode in the
same ways.
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This Figure illustrates the thin film of solution called the diffusion layer that surrounds an
electrode. Diffusion involves the movement of ions or molecules from a more concentrated
part of a solution to a more dilute.
Migration involves the movement of ions through a solution as a result of the electrostatic
attraction between ions and the electrodes.
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Convention is the mechanical transport of ions or molecules through a solution as a result of
stirring, vibration, or temperature gradients.
These are not processes that are easy to control.
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So concentration polarization sets in when the effects of diffusion, migration, and
convection are insufficient to transport a reactant to or from an electrode surface at a rate
that produces a current of the magnitude given by the equation.
Concentration polarization requires applied potentials that are more negative than the
theoretical value to maintain a given current in an electrolytic cell.
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Kinetic polarization is when the magnitude of the current is limited by the rate of one or
both of the electrode reactions- that is, the rate of electron transfer between the reactants and
the electrodes.
Harris presents Overpotential as the voltage needed to sustain a particular rate of electron
transfer.
As the text suggests, the best way to think about overpotential is the presence of an
activation energy barrier that limits the rates at which reactions can take place.
In order to offset kinetic polarization, an additional potential, or overvoltage, is required to
overcome the activation energy barrier to the half reaction.
Kinetic polarization is most pronounced for electrode processes that yield gaseous products
and is often negligible for reactions that involve the deposition or solution of a metal.
Kinetic effects usually decrease with increasing temperature and decreasing current density.
These effects are most pronounced when the electrode is a soft metal, particularly mercury.
Again overpotential requires potentials greater than theoretical to operate an electrolytic cell
at a desired current.
The overpotential associated with the formation of hydrogen and oxygen from water are of
great importance, because it is often 1 V or more. This permits many reactions to occur in
aqueous solutions that are theoretically impossible.
For example in an acid solution we have,
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2 H+ + 2 e- < == > H2(g)
Zn2+ + 2 e- < == > Zn(s)
What is Eo?
0.0000 V
Eo = -0.762 V
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As we lower the driving potential from +0.4 V to –1.0 V, which reaction will proceed first?
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The lead storage battery involves the following reactions.
cathode
PbO2(s) + 4 H+ + SO42- + 2 e- === > PbSO4 + 2 H2O
Eo = + 1.69 v
anode
PbSO4 + 2 e- < === Pb(s) + SO42Eo = - 0.35 v
Eocell = Ec – Ea = +1.69 – (-0.35) = + 2.04 v
A 12-volt battery has 6 cells in series.
If it were not for the high overvoltage of hydrogen on lead and lead oxide electrodes, the
lead/acid storage batteries found in automobiles would not operate because of hydrogen
formation at the cathode particularly during charging.
Certain trace metals in the system lower this overvoltage and eventually lead to gassing, or
hydrogen formation, which limits the life-time of the battery.
The basic difference between a battery with a 48-month warranty and a 72-month warranty
is the concentration of these trace metals in the system.
This emphasizes the importance of using deionized or distilled water in wet cell batteries.
In principle, electrolytic methods offer a reasonably selective means for separating and
determining a number of ions.
The feasibility of and theoretical conditions for accomplishing a given separation can be
readily derived from the standard electrode potentials of the species of interest.
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EXAMPLE Is a quantitative separation of Cu2+ and Pb2+ by electrolytic deposition feasible in principle? If so, what range of cathode potentials (vs. SCE) can be used? Assume that
the sample solution is initially 0.1000 M in each ion and that quantitative removal of an ion
is realized when only 1 part in 10,000 remains undeposited.
Cu2+ + 2e- < == >
Cu(s)
Eo = 0.337 V
Pb2+ + 2e- < == >
Pb(s)
Eo = - 0.126 V
It is apparent that copper will begin to deposit before lead because the electrode potential
for Cu2+ is larger than that for Pb2+.
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First we calculate the cathode potential required to reduce the Cu2+ concentration to 10-4 of
its original concentration (that is, to 1.00 x 10-5 M). Substituting into the Nernst equation,
E = 0.337 - 0.0592/2 log 1/(1.00 x 10-5) = 0.189 V
Similarly, we can derive the cathode potential at which lead begins to deposit:
E = - 0.126 - 0.0592/2 log 1/0.100
= - 0.156 V
Therefore, if the cathode potential is maintained between 0.189 V and - 0. 156 V (vs.
SHE), a quantitative separation should in theory occur.
To convert these potentials to potentials relative to a saturated calomel electrode, we treat
the reference electrode as the anode and write
Ecell = Ecathode - ESCE =
0. 189 - 0.244 = - 0.055 V
and
Ecell =
- 0.156 - 0.244 = - 0. 400 V
Therefore, the cathode potential should be kept between -0.055 V and -0.400 V versus the
SCE.
Calculations such as these make it possible to compute the differences in standard electrode
potentials theoretically needed to determine one ion without interference from another;
these differences range from about 0.04 V for triply charged ions to approximately 0.24 V
for singly charged species.
These theoretical separation limits can be approached only by maintaining the potential of
the working electrode (usually the cathode, at which a metal deposits) at a level required
by theory.
The potential of this electrode can be controlled only by varying the potential applied to the
cell.
But we have seen that variations in Eapplied affect not only the cathode potential but also the
anode potential, the IR drop, and the overpotential.
As a consequence, the practical way of achieving separation of species whose electrode
potentials differ by a few tenths of a volt is to measure the cathode potential continuously
against a reference electrode whose potential is known; the applied cell potential can then
be adjusted to maintain the cathode potential at the desired level.
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Thus the book makes a case for three electrode systems instead of two electrode systems.
The working electrode is where the analyte reaction takes place.
The counter (auxiliary) electrode carries the current of the reaction
While the reference electrode monitors the potential of the working electrode.
In this way the current is carried by the working/counter electrode circuit while the
reference electrode has negligible current and so the reference voltage stays constant and is
minimally affected by the polarization and ohmic potential (IR drop).
Now lets look at actual analyses.
Electrolytic precipitation usually involves a metal being deposited on a preweighed
platinum cathode, and the increase in mass is determined. Important exceptions to this
procedure include the anodic deposition of lead as lead dioxide on platinum and of chloride
as silver chloride on silver.
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This figure shows an electrolysis cell for deposition of a metal on a solid electrode without
cathode-potential control, i.e. it is a 2 electrode system which is simpler and cheaper.
In these cases, the potential is maintained at about the initial level until deposition is
complete.
Ideally, we would like a deposited metal to be strongly adherent, dense and smooth so that it
can be washed, dried, and weighed without mechanical loss or reaction with the
atmosphere.
This depends on current density (less than 0.1 A/cm2 is best), temperature, stirring and the
presence of complexing agents.
Many metals form smoother and more adherent films when deposited from solutions in
which their ions exist primarily as complexes of cyanide or ammonia. The reasons for this
effect are not well understood.
In general, constant-potential electrolysis is limited to solutions of one metal or special
cases where there are no interferents.
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This figures shows what happens when copper is deposited from solution containing excess
acid. The potential applied is about –2.5 V.
The current drops, the IR drops, and the cathode-potential changes with time. Notice that as
the cathode potential becomes more negative, other ions could start codepositing.
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At B the H+ starts forming hydrogen gas. At least the acid prevents an interferent at C
from also codepositing.
Although H2 does not codeposit, the bubbles often lead to the formation of nonadherent
deposits.
One way around this is to add a cathode depolarizer such as the nitrate ion. It is reduced at
a less negative potential than hydrogen ion and does not adversely affect the physical
properties of the deposit.
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NO3- + 10H+ + 8 e- < == > NH4+ + 3 H2O
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Here is a list of substances than are commonly determined without potential control.
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Here is the apparatus for controlled-potential electrolysis. You will see next week that it is
nearly identical to the polarograph circuitry.
The system maintains a constant potential between the working electrode and the reference
electrode – usually a SCE.
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As a function of time, the cell potential drops as Ecathode remains constant. This prevents the
deposition of other ions that occurs when the cathode potential becomes more negative in
the two electrode system.
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Here is a list of elements that can be analyzed and the other ions that can be present.
Remember one of the advantages of this technique is that it can be very accurate and
precise. Weights can have 4 to 6 sig figs. Also you do not have to run controls because the
proportionality constants involved are atomic masses which are accurately known.
Note that this method is not good for trace analysis, but for accurate determination of
medium to high concentrations.
The other topic in the chapter involves coulometric methods where we measure the quantity
of electrical charge (electrons) required to convert a sample of an analyte quantitatively to a
different oxidation state.
Remember that a Coulomb is an Ampere x sec, that the Faraday is a mole of electrons and
that there are 96,485 C/F.
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Generally we measure the amount of current (in Coulombs) as a function of time. This
involves integrating the area under the curve. Then we convert coulombs to faradays and
then moles of analyte.
EXAMPLE A constant Current of 0.800 A is used to deposit copper at the cathode and
oxygen at the anode of an electrolytic cell. Calculate the number of grams of each product
formed in 15.2 min, assuming no other redox reaction.
The two half-reactions are
Cu2+ + 2e- == >
Cu(s)
2 H2O == > 4e- + O2(g) + 4H+
Thus the stoichiometric factors are: 1 mol of copper is equivalent to 2 mol of electrons and I
mol of oxygen corresponds to 4 mol of electrons.
Q = 0.800 A x 15.2 min x 60 s/min x 1 C/1 A sec = 729.6 C
no. F =
729.6 C = 7.56 x 10-3 F = 7.56 X 10-3 mol of electrons
96,485 C/F
The masses of Copper and oxygen are
mass Cu = 7.56 x 10-3 mol e- x 1 mol Cu
2 mol e-
x 63.55 g Cu = 0.240 g Cu
1 mol Cu
mass O2 = 7.56 x 10-3 mol e- x 1 mol O2 x 32.00 g O2 = 0.0605 g O2
4 mol e1 mol O2
Two methods have been developed that are based on measuring the quantity of' charge:
potentiostatic coulometry and amperostatic coulometry.
Potentiostatic methods are performed in much the same way as controlled-potential
gravimetric methods, with the potential of the working electrode being maintained at a
constant level relative to a reference electrode throughout the electrolysis.
Here, however, the electrolysis current is recorded as a function of time. The reaction is
over when all or nearly all of the analyte has reacted and the current has gone to near zero.
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Controlled-potential coulometric methods have been applied to the determination of some
55 elements in inorganic compounds.
Coulometric measurements permit the determination of these compounds with a relative
error of a few tenths of a percent.
Amperostatic coulometry is also known as coulometric titrimetry.
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Coulometric titrations are similar to other titrimetric methods in that analyses are based on
measuring the combining capacity of the analyte with a standard reagent. In the
coulometric procedure, the reagent is electrons and the standard solution is a constant
current of known magnitude.
Electrons are added to the analyte (via the direct current) or to some species that
immediately reacts with the analyte until an end point is reached. At that point, the
electrolysis is discontinued.
The amount of analyte is determined from the magnitude of the current and the time
required to complete the titration. The magnitude of the current in amperes is analogous to
the molarity of a standard solution, and the time measurement is analogous to the volume
measurement in conventional titrimetry.
A fundamental requirement for all coulometric methods is 100% current efficiency; that is,
each faraday of electricity must bring about one equivalent of chemical change in the
analyte.
Note that 100% current efficiency can be achieved without direct participation of the
analyte in electron transfer at an electrode.
For example, chloride ions are readily determined by coulometric titration by generating
silver ions at a silver anode.
These ions then react with the analyte to form a precipitate or deposit of silver chloride.
The quantity of electricity required to complete the silver chloride formation serves as the
analytical parameter.
Coulometric titrations, like their volumetric counterparts, require a means for determining
when the reaction between analyte and reagent is complete. Generally, the end points
described in the chapters of volumetric methods are applicable to coulometric titrations as
well.
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There is a discussion of indicators used to detect the end-point of chloride being titrated by
silver ions in Chapter 7 on pages 142-143.