Download Lecture W1 1-06-03 - Evergreen State College Archives

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EA-AC
Lecture W1
{overhead images in the Cave}
At the end of last quarter, we started a revie
1-06-2003
w of parts of first-year redox chemistry. We covered oxidation, reduction, oxidation
numbers, balancing redox equations, half reactions, electrical potential, and connections with
thermodynamics such as how to calculate Ecell and ∆G, standard potentials and the Nernst
Equation.
This week we continue our review by looking at redox cells and talk about potentiometry –
the use of electrodes to make voltage measurements that provide chemical information.
Problem assignment due next Wednesday is Chapter 14: Problems 8,9,10,35
Chapter 15:2a-c,3,33a,b
Read Chapter 16 for next week about redox titrations.
The week after deals with coulometry, where we count the number of electrons in a reaction
and electrogravimetry, where we measure the mass of material reacting with a known
number with electrons.
The final chapter in this section, Chapter 17, contains several topics. I have divided it into
two sections. The first deals with processes where current is propotional to concentration.
The second is on voltammetry, where the relationship between current and voltage is
examined. This section gives the background to polarography.
I am not going to cover every subject in Chapter 15, so you should know what topics are
present in the chapter for future reference.
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Last quarter we went over balancing simple redox reactions like this.
Which substance is reduced? Silver ion gains electrons
2 Ag+ + Cu(s) < == > 2 Ag(s) + Cu2+
For copper metal and silver ion we have standard half-cell potentials of
Ag+ + e- < == > Ag(s)
Eo = +0.799 v
Cu2+ + 2 e- < == > Cu(s)
Eo = +0.337 v
Remember these are written as reductions.
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Eocell = Eored - Eoox
Eocell = +0.799 v - 0.337 v = +0.462 v
Ecell is positive so this is a spontaneous reaction from left to right.
Now let’s carry out this reaction in an electrochemical cell in which the oxidizing agent and
the reducing agent are physically separated from one another.
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This transparency shows such an arrangement. Remember that the salt bridge isolates the
reactants but maintains electrical contact between the two halves of the cell.
The bridge is necessary to prevent silver ions from reacting directly with the copper metal.
An external metallic conductor connects the two metals. In this cell, metallic copper is
oxidized, silver ions are reduced, and electrons flow through the external circuit to the silver
electrode.
The voltmeter measures the potential difference between the two metals at any instant and is
a measure of the tendency of the cell reaction to proceed toward equilibrium. I.e. is a
measure of the available Gibbs free energy.
Why doesn’t this cell read Eocell? 0.462 V?
From the Nernst Equation we get
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E = Eocell - 0.05916V/n log [Cu2+]/[Ag+]2
E = 0.462 – 0.05916/2 log (0.0200)/(0.0200)2
E = 0.462 – 0.050 = 0.412 V
With time, the potential of this cell will decreases continuously and approaches zero as the
state of equilibrium for the overall reaction is approached.
When zero voltage is reached, the concentrations of Cu(II) and Ag(I) ions will have values
that satisfy the equilibrium-constant expression for the reaction. At this point, no further net
flow of electrons will occur.
It is important to remember that the overall reaction and its position of equilibrium are
totally independent of the way the reaction is carried out, whether it is by direct reaction in a
solution or by indirect action in an electrochemical cell.
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Which of the two electrodes is the cathode? The silver electrode
The cathode is where reduction takes place. Silver ions are being reduced.
The anode is where oxidation takes place.
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The cell we have been examining is called a galvanic or voltaic cell.
Galvanic cells proceed spontaneously and produce a flow of electrons from the anode to the
cathode via an external conductor.
The cell develops a potential of about 0.412 V as electrons move through the external
circuit from the copper anode to the silver cathode.
The potential difference between the two electrodes of a voltaic cell provides the driving
force that pushes electrons through the external circuit.
Therefore we call the potential difference the electromotive (“causing electron motion”)
force, or emf.
As you have learned, the emf of a cell is denoted Ecell and is called the cell potential or cell
voltage.
For any cell reaction that proceeds spontaneously, such as that in a voltaic cell, the cell
potential will be positive.
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Here is a table of standard reduction potentials. When you look that this table you should
be reminded of several things.
1. The reference electrode is the standard hydrogen electrode (SHE). It simply provides a
standard for reference.
2. The chemistry you learned from the periodic table is reflected in these numbers. For
example, fluorine is the most electronegative element and “loves” to take electrons to
become an anion. Thus the standard reduction potential for this half cell is very positive
which makes G very negative.
On the other hand, lithium and sodium are much “happier” as cations and are very reluctant
to accept electrons and become reduced to metals.
3. Reactions high on the table (positive standard potential) when paired with half cells
below them, will cause the lower reactions to be reversed or oxidized.
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For example, chlorine can not take electrons from fluoride ions, but will taken them from
iodide. The first reaction would have a standard cell potential of –1.51 v (not spontaneous)
while the second reaction would have a spontaneous cell potential of +0.30v.
Lithium ions at the bottom of the table can’t take electrons from any of the others but will
gladly give them up. Note that sodium ion can take electrons from lithium metal.
Eocell = -2.71v - (-3.05 v) = + 0.34 v
Now let’s go back to cells. An electrolytic cell, in contrast to a voltaic cell, requires an
external source of electrical energy for operation.
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Our cell could be operated electrolytically by connecting the positive terminal of a battery
having a potential somewhat greater than 0.412 V to the silver electrode and the negative
terminal to the copper electrode.
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Here, the direction of the current is reversed, and the reactions at the electrodes are reversed
as well. Oxidation now occurs at the silver anode and reduction takes place at the copper
cathode.
This copper/silver cell is an example of a reversible cell in which the direction of the
electrochemical reaction is reversed when the direction of electron flow is changed.
In an irreversible cell, changing the direction of current causes an entirely different
half-reaction to occur at one or both electrodes.
Chemists frequently use a shorthand notation to describe electrochemical cells. The voltaic
cell we looked at first is denoted
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Cu(s)  Cu2+ (0.0200 M)  Ag+ (0.0200 M)  Ag(s)
By convention, the anode is always displayed on the left in these representations. (So
electrons always loop from left to right.)
A single vertical line indicates a phase boundary, or interface, at which a potential develops.
For example, the first vertical line in this schematic indicates that a potential develops at the
phase boundary between the copper anode and the copper sulfate solution.
The double vertical line represents two phase boundaries, one at each end of the salt bridge.
A bridge is always denoted with a double line.
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A liquid-junction potential develops at each of these interfaces but the two ends tend to
cancel each other out and are usually ignored. As the book points out, junction potentials
put a limit on the accuracy of potentiometric methods.
Commercial units, such as ion-specific electrodes are designed to minimize junction
potentials, but potentiometry is limited to usually 2 significant figure accuracy and physical
damage to an electrode can rapidly reduce that to one sig fig.
So you need to know the limitations of potentiometric methods and perform measurements
carefully.
An alternative way of writing the voltaic cell shown is
Cu(s)  CuSO4 (0.0200 M)  AgNO3 (0.0200 M)  Ag(s)
Here, the compounds used to prepare the cell are indicated rather than the active participants
in the cell half-reactions. It is assumed that you have the first quarter of the program and
that you recognize that the compounds are soluble and are dissociated into cations and
anions.
The electrolytic cell can be formulated as
Ag  Ag+ (0.0200 M)  Cu2+ (0.0200 M)  Cu
Placing the silver half-cell on the left indicates that the silver couple is now acting as the
anode.
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As shown in this transparency, electricity is transported through an electrochemical cell by
three mechanisms:
1. Electrons carry electricity within the electrodes as well as the external conductor.
2. Anions and cations carry electricity within the cell.
Copper cations, silver cations, and other positively charged species move away from the
copper anode and toward the silver cathode, whereas anions, such as sulfate and, hydrogen
sulfate ions, are attracted toward the copper anode.
Within the salt bridge, chloride ions migrate toward and into the copper compartment,
whereas potassium ions move in the opposite direction.
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3. The ionic conduction of the solution is coupled to the electronic conduction in the
electrodes by the reduction reaction at the cathode and the oxidation reaction at the
anode.
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Remember that the potential difference that develops between the cathode and the anode of
the cell is a measure of the tendency for the reaction to proceed from a nonequilibrium state
to the condition of equilibrium.
Thus, as shown in the upper figure, when the copper and silver ion concentrations in the cell
are both 0.0200 M, a potential of 0.412 V develops, which shows that reaction is far from
equilibrium.
As the reaction proceeds, this potential becomes smaller and smaller until at equilibrium the
meter reads 0.000 V.
At this point, the copper ion equilibrium concentration is then just slightly less
than 0.0300 M and the silver ion concentration is 2.7 x 10-9 M.
For relative electrode potential data to be widely applicable and useful, we must have a
generally agreed-upon reference half-cell against which all others are compared.
As you know, the standard hydrogen electrode has been chosen for this purpose and is
often abbreviated SHE in the geochemical literature. It is sometimes called the normal
hydrogen electrode, but no one abbreviates it as NHE.
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This figures shows how a hydrogen electrode is constructed.
The metal conductor is a piece of platinum that has been coated, or platinized, with finely
divided platinum called platinum black to greatly increase its surface area.
This electrode is immersed in an aqueous acid solution of known, constant hydrogen ion
activity.
The solution is kept saturated with hydrogen gas by bubbling the gas at constant pressure
over the surface of the electrode.
The platinum does not take part in the electrochemical reaction and serves only as the site
where electrons are transferred.
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The hydrogen electrode can be represented schematically as
Pt, H2(g) (PH2 = 1.00 atm)  ([H+] = x M) 
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Here, the hydrogen is specified as having a partial pressure of one atmosphere and the
hydrogen ion concentration in the solution is x M.
The hydrogen electrode is reversible and acts either as an anode or as a cathode, depending
upon the half-cell with which it is coupled. Hydrogen is oxidized to hydrogen ion when the
electrode is the anode. Hydrogen ion is reduced to molecular hydrogen when it acts as a
cathode.
The potential of a hydrogen electrode depends upon temperature and the activities of
hydrogen ion and molecular hydrogen in the solution. The SHE has hydrogen ion activity
of 1 and partial pressure of gas of 1 bar.
.
By convention, the potential of the SHE is assigned a value of 0.000 V at all temperatures.
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Here we see the defining standard electrode potential for the silver ion/silver metal half cell.
The silver ion concentration is at unit activity.
In this reaction the SHE acts as the anode and the silver electrode as the cathode.
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SHE  Ag+ (aAg+ = 1.00 )  Ag(s)
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This figure illustrates the definition of the standard electrode potential for the cadmium
ion/cadmium half reaction.
Notice that the SHE is now acting as the cathode, and the cadmium electrode is the anode.
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Cd(s)  Cd2+ (aCd2+ = 1.00 )  SHE
Now let’s return to analytical chemistry. We can use electrochemical cells to measure the
concentration of an analyte by measuring cell potentials and using the Nernst equation.
This is know as potentiometry.
Here is a typical cell for potentiometric analysis.
This cell can be depicted as
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reference electrode  salt bridge analyte solution  indicator electrode
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The reference electrode Eref in this diagram is a half-cell with an accurately known
electrode potential that is independent of the concentration of the analyte or any other ions
in the solution under study.
It can be a SHE, but seldom is because a standard hydrogen electrode is troublesome to
maintain and use and is a fire hazard.
By convention, the reference electrode is always treated as the anode in potentiometric
measurements.
The indicator electrode, which is immersed in a solution of the analyte, develops a potential
that depends upon the activity of the analyte. Most indicator electrodes used in potentiometry are highly selective in their responses.
The third component of a potentiometric cell is a salt bridge that prevents the components of
the analyte solution from mixing with those of the reference electrode.
For most electroanalytical methods there is a small but negligible junction potential as
described in the chapter. It is usually small enough to be neglected.
However, remember that the uncertainty in the junction potential dose place a limit on the
accuracy of potentiometric analyses.
The ideal reference electrode has a potential (versus the SHE) that is accurately known,
constant, and completely insensitive to the composition of the analyte solution. In addition,
this electrode should be rugged and easy to assemble and should maintain a constant
potential while passing small currents.
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There are two commonly used reference electrodes. The first is the silver/silver chloride
electrode.
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The second is the Calomel Reference Electrode. Calomel is Hg2Cl2 which has limited
solubility in water. You should know this compound by now since Harris seems to like
calomel a lot.
A calomel electrode can be represented schematically as
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Hg  Hg2Cl2 (sat'd), KCl (xM) 
where x represents the molar concentration of potassium chloride in the solution. Three
concentrations of potassium chloride are common, 0.1 M, 1.0 M, and saturated (about 4.6
M).
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The saturated calomel electrode (SCE) is the most widely used reference electrode, because
it is easily prepared. Its main disadvantage is that it has a somewhat larger temperature
coefficient than the other two.
This disadvantage is important only in those rare circumstances where substantial
temperature changes occur during a measurement.
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The electrode reaction in calomel half-cells is
Hg2Cl2(s) + 2e- < == > 2 Hg(l) + 2 Cl- (aq)
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This table lists the compositions and electrode potentials for the three most common
calomel electrodes and two most common silver/silver chloride electrodes and their
temperature variation.
The most common indicator electrodes are inert metallic electrodes.
An inert conductor - such as platinum, gold, palladium, or carbon - responds to the potential
of a redox system with which it is in contact. Platinum is used most commonly.
So how does potentiometry work? Let’s look at three examples based on what some people
call the three kinds of metallic indicator electrodes.
An electrode of the first kind is a pure metal electrode that is in direct equilibrium with its
cation in the analyte solution. A single reaction is involved. Zinc is an example.
Zn2+(aq) + 2e- < == > Zn(s)
The potential for the indicator electrode is then
Eind = EoZn2+ - 0.0592/n log (1/αZn2+) = EoZn2+ + 0.0592/n log αZn2+
Or as p function
Eind = EoZn2+ - 0.0592/n pZn
So the indicator electrode voltage is directly proportional to pZn
This works for Ag/Ag+, Hg/Hg22+, Cu/Cu2+, Zn/Zn2+, Cd/Cd2+, Bi/Bi3+, Tl/Tl+, and Pb/Pb2+
In deaerated solutions.
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Electrodes of the second kind respond to the activities of anions that form sparingly soluble
precipitates or stable complexes with some cations.
The example given in the book is that of silver chloride which you know to have low
solubility.
AgCl(s) + e- < == > Ag(s) + ClEind = EoAgCl - 0.0592/1 log αCl- = EoAgCl + 0.0592 pCl
Again Eind gives a straight line with pCl with an intercept of Eo and a slope of 0.0592.
Electrodes of the third kind are inert conductors and respond to the potential of the redox
system with which they are in contact.
A platinum electrode immersed in a solution containing cerium(III) and cerium(IV) gives
Ce4+ + e- < == > Ce3+
Eind = EoCe4+ - 0.0592/1 log (αCe3+/αCe4+)
Potentiometry is a convenient way to follow many redox titrations.
There is a major caution about these methods due to a subject that we have beat into your
heads.
The application of standard electrode potential data to many systems of interest in analytical
chemistry is complicated by association, dissociation, complex formation, and solvolysis
equilibria involving the species that appear in the Nernst equation.
Such phenomena can be taken into account only if their existence is known and appropriate
equilibrium constants are available. More often than not, neither of these requirements is
met and significant discrepancies arise as a consequence.
The standard iron(III)/iron(II) half cell has a potential of +0.771 V.
In 0.1 M HClO4 the value is +0.75 v.
This difference is attributable to the fact that the activity coefficient of iron(III) is
considerably smaller than that of iron(II) (0.18 vs 0.4) at the high ionic strength of the 0.1 M
perchloric acid solution.
Consequently the ratio of activities of the two species in the Nernst equation is greater than
unity, a condition that leads to a decrease in the electrode potential.
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In a different example, substitution of 1.0 M hydrochloric acid in the iron(ll)/iron(III)
mixture we have just discussed leads to a measured potential of + 0.70 V; in 1.0 M sulfuric
acid, a potential of + 0.68 V is observed; and in a 2 M phosphoric acid, the potential is +
0.46 V.
In each of these cases, the iron(II)/ iron(III) activity ratio is larger because the complexes of
iron(III) with chloride, sulfate, and phosphate ions are more stable than those of iron(II);
thus, the ratio of the species concentrations, [Fe2+]/[Fe3+], in the Nernst equation is greater
than unity and the measured potential is less than the standard potential.
Iron(III) forms FeCl2+ and FeCl2+, Fe(SO4)+, Fe(SO4)2-, and FePO4(aq).
Some times we know all the formation constants for these complexes and the important
concentrations and can make appropriate corrections. Enter FREQC. In other cases we
manipulate the system to eliminate as many problems as possible
There are also times when we can use is same phenomena to our benefit.
Suppose we have a redox system with two analytes that have nearly identical half cell
potentials. Trying to analyze them simultaneously will lead to a mess.
One solution is the physical separation of the two systems, but that can be very time
consuming and lead to errors in the analysis due to lost analyte.
If possible a better solution is to add a “buffer” – a substance that reacts with one redox
couple differently that the other which shifts the cell potentials away from each other.
The buffer could involve complex ion formation, acid formation, or activity coefficient
changes.
We will see how this is used when we talk about polarography.