basics
TRANSCRIPT
Basics
Electrode potential and Galvanic cells
Potential
The potential is the basic expression of electrical energy. By potential, what we mean is
potential difference and it is commonly known as electromotive force. Whether the potential is
applied to a voltaic cell to carry out electrolysis or the potential is derived from a Daniel cell or a
battery, it is the expression of electrical energy. The driving force in electrolysis is the electrical
energy, which is converted to chemical energy. Similarly in an electrochemical cell or Daniel
cell the driving force is the chemical reaction and the chemical energy is converted to electrical
energy. But the point to remember is whether it is application of electrical energy into a voltaic
cell or derivation of electrical energy from an electrochemical cell, two terminals are required.
Even in the measurement of potential, two probes are required. By potential, we mean potential
difference. In AC the potential difference is measured between phase and neutral terminals. In
DC, the potential difference is across electron deficient (+) and the electron rich (-) terminals.
The flow of electron is the flow of electricity. The unit for potential or potential difference or
EMF is volt, which is the basic unit.
Basic expression
The current is measured in Ampere and it can be regarded as the electrical equivalent of
quantity of chemical undergoing change in an electrochemical system. When it is combined with
time or duration of the reaction, the quantity of electricity coulomb is obtained.
Coulomb is the quantity of electricity when 1 ampere is passed through a load for one
second q = As. Electrical power is expressed in watt, which is the product of potential difference
in volts and current strength in ampere,
Watt = VA
The consumption of electricity is measured as units of electricity.
One unit of electricity = one Kwh. (when one kilowatt power is consumed for one hour)
Energy term Joule is related to electrical potential by
Joule = Volt coulomb
= Volt Ampere second VAs
= Watt second
1HP = 750 watts
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Electrochemical cell or Daniel cell
A cell in which chemical energy is spontaneously converted to electrical energy is called
electrochemical cell. What is the origin of potential? Why should the reaction occur in the cell?
What is the driving force? The following section brings answer to all these questions.
Origin of potential:
When a metal rod is kept immersed in its salt solution, some metal atoms go into solution
as ions, leaving behind the electrons in the metal lattice. For example when a zinc rod is kept
immersed in zinc sulphate solution, zinc goes into solution as zinc ions. The electrons in the
metal lattice and the positive ions in the solution orient themselves in an array called electrical
double layer, as shown in figure.
Figure 1.1 Formation of Electrical Double Layer
At this stage some of the metal ions return to metal lattice, by combining with electrons.
Soon, an equilibrium is established between the metal atoms and the ions, which is dynamic. At
this stage a potential is generated at the Zn rod.
(1.1)
The zinc rod is now called zinc electrode.
The formation of electrical double layer and the onset of equilibrium are responsible for
the generation of potential. This equilibrium potential is called single electrode potential. A
direct way to establish this fact, is to measure the potential. But as described earlier, the potential
is the potential difference. For this another such system is needed. A copper metal in contact with
its ions may be taken as the other electrode. Formation of double layer and establishment of
equilibrium between copper and its ions occur in the system.
(1.2)
These dynamic equilibria will exist for a long time if undisturbed.
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The two metal rods are externally connected by a conducting wire, which provided a path
for the flow of electrons. The two electrolytes are connected by a salt bridge, which facilitates
ionic charge transfer.
Figure 1.2 Electrochemical cell-Daniel cell
A voltmeter if connected across the two electrodes (zinc and copper) a potential
difference is recorded. This is a direct proof for the generation of potential at the two electrodes.
This system is an electrochemical cell and each electrode is a single electrode or a half cell. The
potential difference arises from chemical reactions that occur at the electrodes. In an
electrochemical system the basic reactions are simultaneous oxidation and reduction.
The next aspect is to find out the sites of oxidation and reduction in the cell. It is well
known that of the two electrodes, zinc is more electropositive or baser than copper and hence has
a higher tendency to undergo oxidation. Copper is nobler or more electronegative than zinc and
hence has a higher tendency to undergo reduction. When the two are combined in the cell, zinc
undergoes oxidation spontaneously. The equilibrium is disturbed and shifted to right.
The electrons travel through zinc lattice, pass through the metallic wire and reach copper
electrode. There they combine with copper ions from the solution to form metallic copper, which
deposits on the copper rod. The equilibrium (4.2) is shifted to the left i.e., copper ions are
reduced.
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The overall cell reaction is oxidation of zinc and reduction of copper ions. Physically the
overall reaction is dissolution of zinc and deposition of copper. This electrochemical system is
called a ‘Redox’ system, since reduction and oxidation occur simultaneously.
Likewise any two metals can be combined and a cell can be constructed. One of them
will undergo oxidation and the other reduction. Hence the driving force for the occurrence of
chemical reaction in an electrochemical cell is the difference in the oxidizing or reducing
tendency of the two electrodes. The oxidizing tendency of a metal electrode is called its
oxidation potential and the reducing tendency, the reduction potential. For assigning numerical
values to the oxidation or reduction potentials, hydrogen electrode is chosen as the base. The
hydrogen electrode is set up as follows:
Figure 1.3 Standard hydrogen electrode
A platinum foil is kept immersed in hydrochloric acid and pure dry hydrogen gas is
bubbled through a fine nozzle kept close to the foil. The gas molecules get adsorbed on the foil
surface. When considerable concentration of absorbed hydrogen molecules is reached, some of
the molecules ionize into the solution as hydrogen ions. Soon, an equilibrium is established
between hydrogen molecules and hydrogen ions in solution.
This equilibrium is similar to any metal/metal ion equilibrium. Hence a potential is
generated and the electrode is called hydrogen electrode (HE). At this point it may be appropriate
to point out that if any substance in its normal state of existence is capable of establishing an
equilibrium with its ion in solution, it forms an electrode and generates a potential. For assigning
a value to HE, the conditions which affect the potential are standardized.
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i. Activity of molar concentration of the hydrogen ions is fixed as unity.
ii. Temperature unless otherwise specified is taken to be 25 oC or 298 K.
iii. Pressure of hydrogen gas is fixed as one atmosphere.
iv. The surface of platinum should be pure and fresh and to ensure this platinized platinum
foil is taken.
Under these standard conditions, the hydrogen electrode, HE becomes standard hydrogen
electrode (SHE) and its potential is arbitrarily fixed to be zero.
The potential of any other electrode can be determined by coupling it with SHE and
forming an electrochemical cell. The cell is connected to a very sensitive potentiometer, which
draws negligible current from the cell. At this zero current condition, the potential difference of
the cell or EMF is determined. The potential of the test electrode is the potential difference
measured, since the potential of SHE is zero. Likewise, the potentials are determined under zero
current condition and arranged in an order. According to IUPAC convention, the potentials of
electrodes under standard condition are expressed as reduction potential and arranged in the
increasing order. This list is called electrochemical series or EMF series or standard electrode
potentials or equilibrium electrode potentials.
It is to be noted that the oxidation potentials of these electrodes will be the same, with sign
reversed.
Table 1.1
Standard reversible potentials (reduction) E0 values
Species in equilibrium E0 Volts Species in equilibrium E0 Volts
Li+/Li –3.01 H+/H 0.0
K+/K –2.92 Cu++/Cu 0.34
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Ba++/Ba –2.90 O2/OH- 0.401
Ca++/Ca –2.87 Cu+/Cu 0.52
Na+/Na –2.713 I2/I- 0.536
Mg++/Mg –2.38 Hg22+/Hg 0.798
Al+++/Al –1.66 Ag+/Ag 0.799
Mn++/Mn –1.18 Hg++/Hg 0.858
Zn++/Zn –0.763 Br2 (l) /Br 1.065
Fe++/Fe –0.44 Pt++/Pt 1.2
Cd++/Cd –0.402 Cl2(g)/Cl– 1.358
Co++/Co –0.28 Au+/Au 1.70
Ni++/Ni –0.25 H2/H– 2.2
Sn++/Sn –0.14 F2(g)/F– 2.87
Pb++/Pb –0.126
Significance of the EMF series:
i. The sign of the potential indicates the spontaneity of the reaction. If it is positive the
reaction occurs from left to right spontaneously i.e., reduction is favoured. If it is
negative, oxidation is spontaneous.
ii. When the potential of Mg electrode is compared with that of SHE, it is less reducing
or more oxidizing to the extent of 2.38 volts. If the two are coupled in a cell, Mg will
undergo oxidation and hydrogen ion reduction.
iii. If SHE is combined with copper electrode which is more reducing, the spontaneous
cell reaction is oxidation in SHE and reduction in copper electrode.
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iv. When any two electrodes are combined in this series, one with a lower reduction
potential (higher oxidation potential) undergoes oxidation and the other with a higher
reduction potential, undergoes reduction.
v. One with a higher oxidation potential displaces the one lower in the series, with less
oxidation potential. Iron dipped in copper sulphate solution, displaces copper from
the solution.
vi. When the potential difference between two electrodes is large, the oxidation and
reduction occur readily.
vii. For metals whose oxidation potentials are very high compared to SHE, such as K, Li,
Ba, Ca and Na an equilibrium in aqueous solution is not attainable. ΔG is highly
negative and the oxidation occurs extremely fast and irreversibly. For these electrodes
Eo values are obtained indirectly from thermodynamic data. (Calculation beyond the
scope of this book)
viii. Due to the above said fact, sodium reacts with water very fast, displacing hydrogen.
As a redox couple,
The amount of hydrogen ion present in water is very low, 10 -7 gm.eqts / L. The
oxidizing power of Na, Li or K is so high to initiate the reduction of this H+ or
reduction of water.
ix. Down the series, Mg, Al, Zn, Fe, do not undergo oxidation so fast in water. But in
dilute acid where H+ concentration is more, redox couples are set up and the metals
dissolve displacing hydrogen.
x. But nickel and lead which are above SHE, do not displace hydrogen even from dilute
acids. The threshold energy requirement is high and the difference in potential with
SHE, is not high enough to initiate the reaction. Metals below SHE, as expected do
not displace hydrogen from acids.
Spontaneity of the cell reaction:
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For any spontaneous reaction, it has already been seen, that the free energy change must
be negative. i.e.,
ΔG = -nEF
ΔG - free energy change.
N - number of electrons involved in the change.
F - Faraday.
E - Potential
For any electrochemical reaction, when E is positive, ΔG becomes negative and the
reaction is favoured from left to right. When E is negative, ΔG is positive and the reaction is
favoured in the other direction.
Cell Notation
According to IUPAC convention, an electrochemical should be represented such that the
spontaneous reaction occurs from left to right and the cell potential should be positive. For
example when zinc and silver electrodes are combined, the cell notation,
Interface
The metals are in the solid state. The concentration of each solution is one molar. Two
single vertical lines represent solid-solution interfaces. One double vertical line denotes salt
bridge or porous diaphragm. As per the convention, the spontaneous reaction occurs from left to
right. That is zinc gets oxidized and silver ions are reduced. If the total cell EMF is positive the
above assumption and notation are correct.
The total cell reaction:
The total cell potential can be determined as
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i. Algebraic difference of the oxidation potentials of the two electrodes so that E is
positive.
Standard oxidation potential for zinc is
EoOP = +0.763 V (R.P is –0.763)
Standard oxidation potential for silver is
EoOP = -0.799 V (R.P is +0.799)
Total cell potential is
Eocell = Eo
OP of Zn – EoOP of Ag
= 0.763 – (-0.799)
= 1.562 V
ii. The algebraic difference of the reduction potential of the two electrodes, such that the
result is positive.
Standard reduction potential of zinc is
EoRP = -0.763 V
Standard reduction potential of silver is
EoRP = +0.799 V
Total cell potential Eocell = Higher RP – Lower RP
= EoAg+/Ag - Eo
Zn++/Zn
= 0.799-(-0.763)
= 1.562 V
iii. The total cell potential may also be determined as the algebraic sum of oxidation
potential of one electrode and the reduction potential of the other so that a positive EMF
value is obtained.
Eocell = Eo
op of Zn + Eoop of Ag
= 0.762 + 0.799
= 1.562 VHE and SHE are represented as
Pt;H2(g) H+ –HE at 25 oC (any pressure) [M]
Pt;H2(g) H+ – at 25 oC (1 atm pr.) [M]
The cell reaction in this notation is oxidation
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If reduction reaction of SHE is to be expressed the notation is
H+ H2(g), Pt SHE at 25 oC[1M] (1atm. Pr.)
Whether oxidation or reduction occurs in hydrogen electrode depends on the other
electrode with which it is combined. When coupled with electrodes placed above SHE, reduction
occurs and with electrodes below, oxidation occurs in SHE spontaneously.
Reversible and Irreversible cells:
Daniel cell discussed earlier is an example of reversible cell. A reversible cell is one in
which the spontaneous cell reaction can exactly be reversed when a higher potential than the cell
potential is applied externally to the cell, opposing the cell EMF. With 1molar concentration
each of zinc and copper ions, the cell voltage at 25 oC is 1.103 volts. During this zinc dissolves
and copper gets deposited.
Cell reaction:
When an external potential is applied to the cell opposing the cell voltage, the rates of zinc
dissolution and copper deposition decrease. When the external potential is increased to exactly
1.103 volts, the cell reaction completely stops. When the applied potential is still increased,
copper gets oxidized i.e., goes into solution as Cu++ and zinc ions are reduced i.e., zinc gets
deposited as zinc metal.
The reactions are exactly reversed and this is a reversible cell.
Irreversible cell:
This is one in which the spontaneous reactions are not exactly reversed, when an external
voltage is applied to the cell. For example, a pair of zinc and copper electrodes are kept
immersed in dilute sulphuric acid and are connected. Immediately hydrogen bubbles appear on
copper. The spontaneous cell reaction is dissolution of zinc and zinc ions (oxidation) and
reduction of hydrogen ions to hydrogen gas which bubbles on copper.
Cell reaction
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When an external potential higher than the cell potential is applied in an opposing way,
the reactions are dissolution of copper and reduction of hydrogen ion to hydrogen, which appears
now on zinc. If the reactions are exactly reversed, then hydrogen should have been oxidized and
zinc ions reduced. This kid of cell is called an irreversible cell.
Cell reaction:
Variation of potential with concentration:
How does the change in concentration of the electrolyte reflect on the potential? The
relationship between electrode potential and the concentration of the solution is given by Nernst
equation. For a general reversible reaction, the free energy change at constant pressure and
temperature and its equilibrium constant are related as shown below.
The free energy change for this reaction is
[C]c[D]d
∆G = -RTlnK + RTln [A]a[B]b
K = equilibrium constant
The terms in square brackets are the activities of the species, which may be assumed to
be their molar concentrations. It is already noted that
∆G = -nEF
Substitution for ∆G,
E = RT lnK + RT ln [A] a [B] b nF nF [C]c[D]d
If the concentration ratio term is unity,
E = RT lnK = E0
nF
Eo is the standard equilibrium potential. Substituting this value in the earlier equation.
E = E0 + RT ln [A] a [B] b nF [C]c[D]d
In general terms,
E = E0 + RT ln [Product of molar concentration of reactants]
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nF [Product of molar concentration of products]
This is called Nernst equation.
Substituting the values of R, T, F
R = 8.314 joule, T = 298 K, F = 96 500 coulombs and converting natural logarithm to log to base
10,
E = E0 + 0.059 log [Reactants] n [Products]
n is the number of electrons taking part in the electrochemical reaction. For a given
electrode/electrolyte system Eo is constant.
When the ratio [Reactants] [Products] becomes one, E = Eo i.e the standard equilibrium potential. E is made up of two terms, of which
one is constant and other varies with concentration. The following examples illustrate the
application of the Nernst equation.
1. Hydrogen electrode (HE)
The electrode reaction (as reduction)
Applying Nernst equation,
E = E0 + 0.059 log [H + ] 2
2 [H2]The activity or molar concentration of any substance in its normal state of existence is unity. On
simplification,
E = E0 + 0.059 log [H+], When [H+] = 1, E = E0 = 0 [SHE =0]
E = 0.059 log [H+]
The potential of hydrogen electrode depends on the concentration of hydrogen ion. The
potential is related to pH as,
E = –0.059pH
2. A cell can be constructed by combing hydrogen electrode (HE) and standard hydrogen
electrode (SHE). Let us see how the potential of hydrogen electrode (as reduction) varies
when the concentration is more than unity and b) less than unity (at unity it is zero).
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a) [H+] = 1.5 M
E = 0.059 log (1.5) = 0.0104 V
At concentration > 1, reduction of [H+] is favoured
[H+] = 0.1 M
E = 0.059 log (0.1) = –0.059 V
Since a negative value is obtained, reduction is not favoured when
[H+] is < unity. Oxidation is favoured. Hence the cell notation will be (SHE and HE)
a) Pt;H2(g) H+ H+ H2 (g); Pt (1 atm) [1 M] 1.5 M 1 atm.
SHE HE Spontaneous reaction.
b) Pt;H2(g) H+ H+ H2 (g); Pt (1 atm) [0.1 M] 1 M 1 atm.
HE SHE Spontaneous reaction.
3. For Daniel cell type.
[Zn2+] = 0.1 M; [Cu2+] = 1.8 M
The cell is,
Zn (s) Zn++ Cu++ Cu (S) [0.1 M] 1.8 M
Spontaneous reaction.
Zn undergoes oxidation and copper ion reduction.
Ecell = EOP + ERP
Applying Nernst equation.
Eop = E0op + 0.059 log [Zn]
2 [Zn2+]
= 0.763 + 0.059 log 1.0 2 0.1
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= 0.7925 V
When the solution becomes more dilute, the oxidation potential is more which indicates
that the dissolution or corrosion is more in dilute solution.
At copper electrode reduction occurs
Applying Nernst equation,
ERP = E0RP + 0.059 log [Cu 2+ ]
2 [Cu] = 0.34 + 0.059 log 1.8 2 1.0 = 0.3475 V
It is seen here that the reduction potential of the electrode increases, when the
concentration of the solution increases. In concentrated solution, the population of ions per unit
volume is more and hence the tendency of the ions to come out of the solution is more.
Ecell = EOP + ERP
= 0.7925 + 0.3475
= 1.14 V
For any electrode, its OP increases with dilution and RP increases with increase in
concentration.
4. The total potential can be found out by the difference between their oxidation potentials.
For this method, the electrode reaction should be written as oxidation, whether it is
spontaneous or not.
For zinc electrode: (as oxidation)
Applying Nernst equation
Eop = E0op + 0.059 log [Zn]
2 [Zn2+]
= 0.763 + 0.059 log 1.0 2 0.1 = 0.7925 V
For copper electrode (as oxidation)
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Applying Nernst equation.
Eop = E0op + 0.059 log [Reactants]
2 [Products] = – 0.34 + 0.059 log Cu 2 Cu2+
[Cu] = unity [Cu2+] = 1.8 M
Eop = -0.34 + 0.059 log [1] 2 [1.8] = –0.3475 V
Ecell = EOP of Zn – EOP of Cu = 0.7925 – (–0.3475) = 1.14 V
The total cell potential can be determined by the algebraic difference of reduction potentials. The
half cell reactions are written as reduction.
For zinc electrode
Applying Nernst equation,
ERP = E0RP + 0.059 log [Reactants]
2 [Products] = – 0.763 + 0.059 log 0.1 2 1.0 = –0.7925 V
For copper electrode, the reduction is
ERP = E0
RP + 0.059 log [Cu 2+ ] 2 [Cu] = 0.34 + 0.059 log 1.8 2 1.0 = 0.3475 V
Ecell = ERP of Cu – ERP of Zn = 0.3475 – (–0.7925) = 1.14 V
Example:
Construct as many cells as possible by combining the following electrodes,
[Zn2+]/[Zn]; [Cu2+]/[Cu]; [Cu+]/[Cu]; and [Ag+]/[Ag];
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Each electrolyte is 0.1M concentrated. Write the cell notation and calculate the EMF of
the cell at 25 oC. Eo values can be taken from the table 1.1.
a) Zn (s) Zn++ Cu++ Cu (S) [0.1 M] 0.1 M
Eop = E0op + 0.059 log [Zn]
2 [Zn2+]
= 0.763 + 0.059 log 1.0 2 0.1 = 0.7925 V
ERP = E0RP + 0.059 log [Cu 2+ ]
2 [Cu] = 0.34 + 0.059 log 0.1 2
Foot Note:
In calculating the potential for half cells and total cells, the students are advised,
i. To follow Nernst equation, in the form given here
E = E0 + 0.059 log [Reactants] n [Products]
ii. To write the cell reaction, split it into 2 half cell reactions.
iii. To find the total cell potential follow one of the three methods given above.
= 0.3105 V
Ecell = 0.7925+0.3105 = 1.103 V
b) Zn (s) Zn++ Cu+ Cu (S) [0.1 M] 0.1 M
Zn electrode potential = 0.7925 V
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ERP = E0RP + 0.059 log [Cu + ]
1 [Cu] = 0.52 + 0.059 log 0.1 1 = 0.461 V
Ecell = 0.7925+0.461 = 1.254 V
c) Zn (s) Zn++ Ag+ Ag (S) [0.1 M] 0.1 M
EZn/Zn++ = 0.7925 V
ERP = E0RP + 0.059 log [Ag + ]
1 [Ag] = 0.8 + 0.059 log 0.1 1 = 0.741 V
Ecell = 0.7925+0.7410 = 1.5335 V
d) Cu (s) Cu++ Cu+ Cu (S) [0.1 M] 0.1 M
Eop = E0op + 0.059 log [Cu]
2 [Cu2+]
= –0.34 + 0.059 log 1.0 2 0.1 = –0.3105 V
The reduction potential of cuprous electrode is 0.461
Ecell = –0.3105 + 0.461 = 0.1505 V
e) Cu (s) Cu++ Ag+ Ag (S) [0.1 M] 0.1 M
The oxidation potential of copper is – 0.3105 V
The reduction potential of Ag is +0.741 V
Ecell = –0.3105 + 0.741 = 0.4305 V
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f) Cu (s) Cu+ Ag+ Ag (S) [0.1 M] 0.1 M
Eop = –0.52 + 0.059 log 1.0 2 0.1
= –0.461 V
Silver reduction potential is found as 0.741 V
Ecell = –0.461 + 0.741 = 0.2800 V
Reference Electrode
There are some basic defects with standard hydrogen electrode.
1) Setting up of SHE is very cumbersome and tedious.
2) Platinum electrode is highly prone to get poisoned by traces of impurities in hydrogen
gas. Hence hydrogen gas passed must be in a high state of purity.
3) Reproducibility is of low order.
Hence other electrodes, whose potential will not vary with use, are developed, which are
called reference electrodes. Very widely used reference electrodes are calomel and silver/silver
chloride electrodes.
Calomel Electrode
Calomel is Hg2Cl2 mercurous chloride. A small quantity of a paste consisting of a few
drops of mercury, a pinch of calomel (mercurous chloride) and a few drops of saturated
potassium chloride solution is prepared and taken in a small hard glass tube. The tube is fitted
with a porous, sintered glass frit. A platinum wire kept immersed in the paste, facilitates external
connection. This glass tube is kept in an outer glass tube, also fitted with a porous frit at the
bottom as shown in the figure. This frit serves as a salt bridge, when the electrode is immersed in
the test solution, during measurement. Potassium chloride solution of a fixed concentration (0.1
N, 1.0 N or saturated) is filled in the outer tube. The electrode can be immersed in the test
solution and the measurement can be made conveniently.
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Figure1.4: Calomel Electrode
Reactions and functioning of calomel electrode:
Mercurous chloride, being a sparingly soluble salt, forms a very dilute but saturated
solution in water. Hence the following equilibria are exhibited.
Hg2Cl2 aq is transitory because it is fully dissociated, being very dilute and the real equilibrium is
Applying Nernst equation,
Ecalomel = E0calomel + 0.059 log [Hg2Cl2(s)]
2 [Hg]2[Cl]2
[Hg2Cl2(s)] = 1; [Hg] = 1
Rearranging
Ecalomel = E0calomel – 0.059 log [Cl-]
EoCalomel is constant and the potential of calomel electrode depends on the concentration of
Cl-. But the amount of chloride ions obtained by dissociation of mercurous chloride is very low;
but chloride ions from KCl is very large and also is constant. Thereby the potential of calomel
electrode is constant. When it is coupled with another electrode of higher oxidation potential,
reduction occurs in calomel electrode. Hg2Cl2 will be converted to mercury and chloride ion. If
calomel electrode is connected to another electrode of higher reduction potential, oxidation will
occur at calomel electrode. Some Cl- will be converted to Hg2Cl2. This addition or removal of Cl–
from the already present very large quantity of chloride ions from potassium chloride, does not
make any significant change in potential. Hence the potential of calomel electrode is constant.
Silver-Silver chloride electrode:
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This is very similar in construction and functioning to calomel electrode. A silver rod,
having a thin surface film of silver chloride is used instead of Hg2Cl2/Hg paste. Other aspects of
construction are the same.
The reaction is,
E = E0 + 0.059 log [AgCl(s)]
1 [Ag][Cl–] = [AgCl(s)] = 1; [Ag] = 1
E = E0– 0.059 log [Cl-]
Indicator Electrodes:
The electrode whose potential changes according to the concentration of some species
present in the solutions is called an indicator electrode. Concentration dependence of the
electrode is selective. For example the electrode which follows change in hydrogen ion
concentration will not respond to change in concentration of metal ions.
Two electrodes, i) quinhydrone electrode and ii) glass electrode are typical examples for
indicator electrodes for hydrogen ion (H+) concentration changes.
Quinhydrone Electrode:
This is constructed by keeping a platinum wire in a solution of H+ (acid), containing a
small quantity of quinhydrone. The potential of this is a function of [H+]. Quinhydrone is an
equimolar mixture of quinone and hydroquinone. The equilibrium between them can be
represented as
EQH = E0QH + 0.059 log [Q][H + ] 2
2 [H2Q] [Q] = 1; [H2Q] = 1
E = E0 + 0.059 log [H+]
E = E0 – 0.059 pH
This is used as an indicator electrode in pHmetric titration.
Glass electrode:
When two solutions of different hydrogen ion concentrations are separated by a thin glass
membrane, a potential difference, depending on (H+) concentration difference is developed. The
electrode consists of a glass bulb containing a solution of constant (H+) and a Ag/AgCl reference
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electrode. When it is dipped in a test solution of [H+], the potential of the electrode responds to
the change in concentration of H+. Its potential is
Eglass = E0glass + 0.059 log [H+]
E = E0 – 0.059 pH
E depends on [H+] change. It is used as an indicator electrode in acid-base titration.
Ion selective electrodes:
a) Solid state electrodes consist of compact disc of active material like silver halides or
silver sulphide and are selective to the respective anions.
b) Fluoride ion selective electrode consists of a single crystal membrane of LaF3 in
contact with a mixture of 0.1M solution of NaCl and NaF. This is used to estimate F –
in water and fluoride-tooth pastes.
c) Heterogeneous membranes or pungor electrodes are prepared from varied active
materials like insoluble salts, metal complexes and ion exchange resins. The active
material is impregnated in silicone rubber and used as a membrane. They respond to
changes in SO42–, NO3
–, PO43–. A graphite matrix is also used instead of silicone rubber.
These ion selective electrodes are called selectrodes.
The electrodes discussed in detail in the above sections can be grouped or classified as:
I. Metal-metal ion electrode (Zn++/Zn, Cu++/Cu)
II. Metal-insoluble salt electrode (Reference electrodes)-(Calomel, AgCl/Ag)
III. Gas electrode-(HE and SHE) SHE is a standard electrode.
IV. Indicator electrodes-(Glass and Quinhydrone)
V. Ion selective electrodes-(Pungor electrodes)
VI. Inert or redox electrodes used in potentiometric titration to follow change in the ratio
of oxidized species to reduced species-Pt and Au electrodes.
VII. Amalgamated electrodes. The potential depends on the concentration of the metal in
the amalgam.
Concentration cells:
Any two electrodes, in the EMF series when combined, give rise to a potential difference
due to their inherent property of oxidizing or reducing power. But a concentration cell is one in
which the same electrodes and same electrolyte of different concentrations are used. The driving
force for the reaction is the difference in concentration of the solution.
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Figure 1.5: Concentration cell
In the previous section it was seen that in concentrated solution reduction is favoured.
This was evident from the increase in reduction potential as the concentration was more than one
molar. From a physical sense, as more number of ions are crowded in unit volume of solution of
higher concentration, the tendency of the ions to come out of the solution is more. Similarly, it
was also seen that the oxidation potential of an electrode increases when the concentration is less
than one molar. Metal dissolution is more in dilute solution.
The following example may be considered. Two silver rods are dipped separately in two
silver nitrate solutions of concentration C1 and C2 molar. The two rods are connected by a metal
wire externally and the two solutions by a salt bridge.
Since C2>C1 oxidation occurs in lower concentration C1 and reduction in solution of
higher concentration C2. The cell is represented as,
Ag (s) Ag+ Ag+ Ag (S) [C1] [C2]
Spontaneous
According to convention, oxidation half cell is placed on the left and reduction half cell
on the right. Cell potential is calculated as the sum of oxidation potential of left half cell and the
reduction potential of right half cell.
Left hand side
Eop = E0op + 0.059 log [Ag]
1 [Ag+] E0
op + 0.059 log 1 1 [C1]
22
Right hand side, ERP = E0
RP + 0.059 log [Ag + ] 1 [Ag] = E0
RP + 0.059 log [C2] 1 Ecell = EOP +ERP = [E0
OP +E0RP] + 0.059 log [C2]
n [C1]
= E0RP = – E0
op
= E0op + E0
RP = 0
Ecell = 0.059 log [C2] 1 [C1]
Generally, the potential of a concentration cell,
E = 0.059 log [C2] n [C1]
Where n is the number of electrons taking part in the reaction.
C2 should be higher C1: only then E will be positive. During working of the cell, the
concentration increases in the anode half cell and decreases in the cathode half cell. Finally the
cell stops functioning when both concentrations become equal.
Measurement of EMF of a Cell
The electrochemical cell is formed by coupling two electrodes as discussed above. The
electrodes can be connected to a voltmeter across (in parallel) and the emf can be directly
measured. But the voltage will be maximum only under ‘zero current withdrawal’ condition. If
the measuring device draws current, erroneous result is produced.
But with the advancement of technology, very sensitive vacuum tube voltmeters
(VTVM), which draw negligible current (<microampere) are available. These can be used to
measure the potential.
The traditional age-old method is the Poggendorf compensation method. A DC source is
connected to a long, uniform potentiometer wire AB. A is connected to a standard Weston
cadmium cell, a galvanometer and a sliding contact in series. The connection should be made in
such a way that the potential of standard cell opposes the applied potential from DC source. The
point of no current (D) flow (Galvanometer is Zero) is determined by sliding the contact over the
wire. Weston cell is replaced by the test cell and the null point (E) is determined as above.
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Figure 1.6: Measurement of emf of a cell
AD = EMF of Weston cell AE EMF of test cell
Values of AD, AE and EMF of Weston cell being known, EMF of test cell is determined E of
western cell = 1.0183 V at 25oC.
Besides the determination of EMF by this method, the polarity of the cell electrodes can
be fixed. As mentioned above the standard cell must be connected so that its potential opposes
the applied potential. If the connection is made otherwise the null point can not be determined.
The electrode of the test cell which is connected to the positive (electron deficient) terminal of
the DC source becomes positive. (null point is determined) and other electrode of the test cell in
negative. In Daniel cell electron flows from Zn to Cu and positive electricity from Cu to Zn.
Weston cadmium cell
One of the widely used standard cells is Weston cadmium cell. It has a constant emf of
1.0183 V at 25 oC and has a low temperature coefficient of –4 10-5 v/deg.
Weston cadmium cell is represented as,
12.5% Cd in Hg 3 CdSO4.8H2O (s) CdSO4 (aq. satd.) Hg2SO4 Hg (l)
It consists of cadmium amalgam (12.5%) in a glass limb. On top of this a layer of solid
crystals of 3CdSO4.8H2O and a saturated solution of the same salt are present. The other limb
contains saturated mercurous sulphate over Hg at the bottom and saturated cadmium sulphate
solution.
24
Figure 1.7: Weston Cadmium cell
Applications of EMF measurements
1) Equilibrium constant for a reversible reaction under standard conditions of temperature
and pressure can be determined from EMF values.
The relation is,
E0 = RT lnK nF
Eo is the standard potential of the cell or electrode.
R = 8.317 J, T = 298 K, F = 96 500
The equation is simplified as,
E0 = 0.059 log K n
For the equilibrium
E0
= 0.763; n = 2,
K = 7.318 × 1025
∆Go
= -nE0
F = -2 × 0.763 × 96 500
= 1,47,259 Joules or 147.3 KJ.
For the reaction,
E0cell = E0
op + E0RP
25
= 0.763 + (–0.44)
= 0.323 V
∆Go
= -nE0
F = -2 × 0.323 × 96 500
= -62.3 KJ/mol
2) Thermodynamic parameters like enthalpy change, entropy change and free energy change
can be calculated from EMF values.
Example:
i. The EMF of the cell
Pt;H2 HCl (aq) AgCl Ag at 25 oC is 0.35 V
The temperature coefficient of the EMF is –0.45 mv/deg. The spontaneous cell reaction is
from left to right. Write the cell reaction and calculate ∆G, ∆H and ∆S for the reaction.
Oxidation reaction at anode is
Reduction or cathodic reaction is,
Cell reaction
Free energy change
∆G = -nEF = –1 × 0.35 × 96 500
= – 33.78 KJ/mol
= – 8.07 Kcal/mol
∆H = nEF + nFT δE
δT P
= –33.78+96500 × 298 × (-0.45 × 10 –3 ) 1000
= –46.72 KJ/mol or –11.17 Kcal/mol
∆G = ∆H –T∆S or ∆S = nF δE
δT P
26
∆S = 1 × 96500 × –0.45 × 10–3
= –43.43 J/per degree
= –10.38 Cal deg–1
3) pH measurements and pH metric estimations can be made using HE, quinhydrone and
glass electrodes.
4) Solubility product of a substance can be determined, eg., AgCl from coupling AgCl/Ag
electrode with SHE or Hg2Cl2 by coupling calomel with SHE.
5) Very important analytical application of EMF measurements is potentiometric titration
a) K2Cr2O7 Vs FeSO4
It is called redox titration because the potential depends on the ratio of the activities of
oxidized and reduced species. When dichromate is added to ferrous solution in acidic medium,
the reactions are,
Applying Nernst equation
EOP = EoOP + 0.059 log [Fe 2+ ]
1 [Fe3+]
Applying Nernst equation
ERP = EoRP + 0.059 log [Cr 6+ ]
3 [Cr3+]
Polarization and overvoltage
The flow of electrons or charge in an electro chemical system at dynamic equilibrium is
known as exchange current. For unit area of the electrode surface it is called exchange current
density and its value is very low, of the order of 10-8 Å. In any industrial electrolysis this value is
very low has no practical significance.
In any electrochemical cell the electrodes are polarized i.e. charged and the potential is
called rest potential. For the reaction to occur at a desired rate of practical importance much
higher potential is required to overcome the polarization, that is, higher than the rest potential.
This excess potential over the equilibrium potential for any electrochemical reaction to occur at a
definite rate is called over potential. Hence
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Applied potential = Equilibrium potential + over potential
Over potential is classified as
1. Activation over potential
2. Concentration over potential
3. IR over potential.
Activation over potential
This activation energy or over potential depends on the system i.e., the following factors.
a) Nature of the reactions:
It varies from one reaction to another. But an approximate generalization is possible. The
activation over potential for a gaseous discharge reaction is considerably higher than a
metal ion discharge reaction. Activation over potential for hydrogen ion discharge
reaction
2H+ + 2e– → H2 or
Chlorine gas evolution
Cl– → 1/2Cl2 + e– or
Hydroxyl ion discharge leading to oxygen evolution
4OH– → 2H2O + O2 + 4e–
is much higher than copper or nickel or silver ion discharge from the corresponding metal
salt solution.
Cu++ + 2e– → Cu
Ag+ + e– → Ag
Ni++ + 2e– → Ni
In fact the activation energy values among the gaseous discharge reactions or among the metal
ion discharge reactions, differ under other conditions being identical but the difference is not
much.
b) Nature of the substrate:
The AOP values for the same reaction differ from one substrate to another. For example
hydrogen ion discharge reaction needs different energy values for different metals.
The AOP for H+ discharge is the lowest on platinum and the highest on mercury. Other
metals like lead, silver, nickel and copper show intermittent values. For this reason, Platinum
electrodes are used in industrial electrolysis of water, so as to minimize the voltage to be applied.
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In lechelanche cell mercuric compounds are used as additives in order that hydrogen should not
be evolved. For the same reason mercury is used as polarographic liquid (dropping mercury
electrode), which facilitates the study of the reduction of most of the metal ions before H+ is
reduced.
Similarly oxygen over voltage on platinum is high and low on lead. Lead-antimony alloy
electrodes are used as anodes in chromium plating, which effects oxygen evolution at lower
applied potential than with other electrodes.
Graphite electrodes are used in electrolytic manufacture of chlorine gas, where the over
voltage is moderate.
c) Texture of the substrate:
The surface texture or finish plays a role in deciding the AOP value. Micro-etched or matt
metal surface has lower AOP than polished surface of the same electrode, for the same reaction.
Similarly a porous surface facilitates more easily gaseous discharge reaction and eventually
gaseous evolution than an ordinary surface of the same metal.
d) Surface area:
As the area increases AOP decreases, all other conditions being the same. Platinizing platinum
is deposition of micro fined platinum on platinum surface. This increases the surface area many
fold and brings down the AOP.
e) Current density:
Activation over potential is directly proportional to the current density. If the reaction rate is
increased, activation energy increases; the limit will be the reach of applied potential for the
reduction of metal species present in the solution. For examples nickel deposition from nickel
sulphate solution can be considered. The rate of deposition can be increased by increasing over
potential or by increasing applied potential (equilibrium potential, for a reaction, at a particular
concentration is constant) till reduction of H+ or H2O occurs, leading to hydrogen evolution.
f) Temperature:
AOP is inversely proportional to temperature. As temperature is increased ionic mobility
increases and thereby ion transport is facilitated. Hence AOP decreases. But in industrial practice
where a rise in temperature is needed to sustain the desired current heating is accomplished.
Other wise the process is conducted at room temperature. For example bright nickel and bright
chromium deposition are carried out at elevated temperature. But copper deposition from acid
29
copper sulphate is carried out at room temperature at lower current densities and 50-60 oC for
higher current densities beyond 5 A/dm2.
Concentration over potential:
This phenomenon is explained by taking the example of nickel deposition from NiSO 4
solution, using nickel soluble anode. The positive terminal of DC supply is connected to nickel
anode through an ammeter in series. The negative terminal of the supply is connected to a copper
cathode (or any substrate) through a variac. A voltmeter is connected across the DC supply. Let
us assume that 4 volt is applied to effect a current of 100 A (at 4 A/dm2). As the deposition
occurs, nickel ions present near the cathode will be discharged.
Ni++ + 2e– → Ni
This leads to a decrease in concentration of nickel ions at the vicinity of the cathode than in
the bulk. Nickel ions from the bulk will migrate to the cathode.
Figure
On the other hand, as the nickel anode dissolves forming nickel ions, which crowd near
the anode. Thereby the concentration of nickel ions is more near the anode than in the bulk.
They migrate slowly towards the bulk.
Hence at any instant of time the concentration of Nickel ions is high near the anode and
gradually decreases to the bulk and finally to the cathode, where it is the least. That is, a
concentration gradient in decreasing order from anode to cathode gets established. This
concentration gradient is equivalent to a potential gradient (evident from Nernst equation). This
potential opposes the external applied voltage. This opposition manifests itself as a reduction in
the rate of deposition; reading in the ammeter falls (probably from 100 to 80). Voltmeter reading
does not change. To bring back the rate of deposition to the original level (80 to 100), an extra
potential (from 4 to 4.5 perhaps) will be required. This extra potential is required to overcome
the resistance offered by concentration gradient or concentration polarization and is known as
concentration overpotential.
30
Application of a higher voltage is not a permanent solution. Again the current will
decrease and potential is to be increased further and this is repetitive. Permanent remedy to
overcome this is to stir or agitate the solution effectively to maintain a uniform concentration
throughout the entire bath. The energy spent in providing air or mechanical agitation is
equivalent to concentration overpotential.
4. IR overpotential:
This extra energy is required to overcome the resistance offered by the system. The electrical
connection from the DC power supply to the bus bar of the reaction tank, the jig carrying the job,
the electrolyte and the electrodes. Proper care must be exercised to minimize internal resistance.
i. Electrical Connections:
The materials used for connecting the DC supply to the tank, the bus bar and the jigs must be
of high conducting ones electrically and thus copper is extensively used for this purpose.
The dimension (size and shape) of the connecting materials, the bus bar and the jigs must
be adequate to carry the desired current. If sufficient cross section is not available, energy
will be dissipated as heat. For example 4” ¼” copper flats can carry current upto 1200 A.
Where higher current is required, copper flats of appropriate size are used for electrical
connection (Remember R 1/a) R-resistance and ‘a’ is area of cross section).
ii. Electrolyte
To reduce the resistance offered by the electrolyte, its concentration must be increased to the
maximum. The limit will be its solubility in water, for aqueous electrolyte. Generally
sulphates, nitrates and chlorides are soluble in water. In plating, sulphate is preferred. The
use of nitrate and chloride salts increases the anodic polarization i.e., anodic dissolution. The
maximum amount than can dissolve at room temperature is generally taken. Wherever
permitted strong acids such as H2SO4 can be added to increase the conductance or reduce the
IR component.
iii. Electrodes:
The electrode at which the desired reaction is carried out is called job and no choice is
available here. For example if plating is to be done on an MS article, a lead or graphite article
cannot be taken even though the AOP may be lesser on Pb or C, than on MS, for that deposition.
Similarly in plating, soluble anode is employed whenever possible. At other proceses SS,
graphite and lead anodes are used for economic considerations.
31
But the positioning of electrodes is done to minimize internal resistance. If they are far
apart, the resistance is more and increases the AP; if they are too close the volume of entrapped
electrolyte will be less and this hastens the onset of concentration polarization. Agitation must be
more efficient to overcome this. Hence the electrodes are positioned at optimum distance.
Thus the applied potential for an electrochemical process is
AP = EP + [AOP + COP + IROP]
EP- is equilibrium potential at the employed concentration and is constant for a particular
reaction.
AOP-Activation over potential – this increases the AP.
COP – controlled by agitation.
IROP- minimized
Tafel equation and Tafel plots
Tafel equation governs the irreversible behaviour of an electrode. To understand this we
can consider the general mechanism of electron transfer to an electrode.
Consider an electrolyte in which an inert or noble electrode is kept immersed. It is called
working electrode, (WE). Also assume that an oxidized and a reduced species are present near
the electrode and exhibit the following electron transfer reaction.
…… (1)
O is oxidized and R is reduced species present at equilibrium and is stable in the solution. Let us
assume that no other electron transfer reaction other than the above occurs. Let the concentration
of O and R be CO and CR respectively and they are very low. An inert electrolyte is also present
to minimize IR drop. Along with WE, a reference electrode (RE) is also kept immersed, to form
the cell. Since the potential of RE is constant, variation in cell emf is the variation in WE, and
vice versa.
At the thermodynamic equilibrium of the system no net current flows across RE and WE,
no chemical reaction takes place and hence the composition of the solution remains unchanged.
The potential of the working electrode will be its equilibrium potential E e, which according to
Nernst equation is
…… (2)
nF
32
Where Eeo is the standard or formal reversible potential and is constant. Ee depends on the ratio
of [CO/CR]. The square bracketed term should be in terms of activity rather than molar
concentration; but at low concentration the replacement is error free.
The equilibrium mentioned above is dynamic. Though no net current flows across the
electrodes, both reduction and oxidation takes place at equal rate, so that the composition of the
electrolyte does not change. The dynamic flow of electrons or charge in both directions can be
written in terms of current densities as follows.
IA = – IC = I0 ---- (3)
Where IA is anodic and Ic is cathodic current densities. By convention anodic current
density is given +ve sign and cathodic –ve sign. Io is known as exchange current density. It may
be defined, as “the flow of charge or electrons across an electrochemical system in equilibrium is
known as exchange current density”. Its value normally is very low, of the order 10 -8 A. It refers
to the extent of both oxidation and reduction that occurs.
The equilibrium situation at an electrode is characterized by equilibrium potential and
exchange current density.
For the reaction to have practical significance, a net current should flow and a net
reaction either oxidation or reduction should occur. For this the kinetic aspect of the system must
be considered. It is to be recalled that thermodynamics fixes the direction and kinetics
determines the rate.
For this let as apply an external potential to WE, more negative than Ee. This cause, an
increase in cathodic current and a net quantity of O will be reduced to R. The value of the ratio
[CO/CR] at the electrode surface will diminish. The magnitude of net cathodic current and the
time for the new value of [CO/CR] takes to achieve depend on the rate or the kinetics of the
electron transfer reaction. The net cathodic current will be due to the increase in partial cathodic
current (-Ic) and a decrease in partial anodic current (IA) at this new potential. Hence reversible
condition changes to irreversible condition. This is achieved by applying a more –ve potential or
excess potential than Ee, which is known as overpotential. Conversely it can be argued that if
WE is made more positive than Ee (by applying external potential more positive than Ee) a net
anodic current will flow through the cell. To summarize the situation.
At the equilibrium potential
33
Ee -IC I = -IC +IA = 0 IA No net current
-IC Negative to Ee I = -IC + IA < 0 IA net cathodic current
-IC
Positive to Ee I = -IC + IA > 0 IA net anodic current
The kinetic equation for this electron transfer reaction can be derived. Generally electron transfer
processes are first order reactions. Hence rate of reduction of [O] is proportional to its
concentration at the electrode surface (Remember that it is assumed that surface concentration is
equal to bulk concentration).
Rate of reduction of [O] = kRCo …… (4)
The partial cathodic current density will be
-Ie = nFKc[CO] …….. (5)
The rate of the electron transfer process depends on the applied potential and the potential
dependence is of the form
Kc = K0 exp [–αcnF E] ……... (6) RT
Where αc is the cathodic transfer coefficient and ko is the rate constant for electron transfer at E =
0 and E is the applied potential.
Substituting for the kc value in 5, we get
-Ie = nFKoCoexp [–αcnF E] ……... (7) RT
The corresponding equation for oxidation of R, occurring simultaneously will be
Rate of oxidation = kACR …….. (8)
IA = nFKACR …….. (9)
KA = K0 exp [αAnF E] ……... (10) RT
IA = nFKoCR exp [αAnF E] ……... (11) RT
The current density at any potential will be the sum of cathodic and anodic current
densities.
34
I = IA + (-IC) ……... (12)
= nF KoCRexp(αAnF E) – KoCoexp(–αCnF E) ….. (13) RT RT
But overpotential
η = E -Ee …… (14)
η is a deviation of experimental potential from equilibrium potential. At E = Ee, IA = -IC = Io.
Hence
Io = nFKoCRexp(αAnF Ee) = – nFKoCoexp(–αCnF Ee) ….. (15) RT RT
Substitution of (14) in (13) and using equation (15), the famous Butler-Volmer equation is
obtained.
I = I0 exp(αAnF η) – exp(–αCnF η) ….. (16) RT RT
From this equation, it can be understand that the measured current density is a function of
i) over potential (η) ii) exchange current density (Io) and iii) anodic and cathodic transfer
coefficients (αA + αC)
Transfer coefficients are not independent variables. In general
αA + αC = 1 …… (17)
For many reaction αA + αC = 0.5
Equation 16 indicates that the current density at any overpotential is the sum of cathodic and
anodic current densities. At the extreme condition of overpotential being highly negative.
Cathodic current density increases while anodic current density becomes negligible. At this
stage, the first term in Butler-volmer equation (16) becomes negligible. The equation can be
written as
-I = -IC = Io exp(-αcnF η) ….. (18) RT
When the overpotential is higher than above 52mV, this equation shows that the increase in
current is exponential with overpotential. The current also depends on Io. Equation 18, may also
be written as
log-IC = log Io – αcnF η ….. (19) 2.303RT
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Equation 19 is called cathodic tafel equation. Similarly at positive overpotentials higher
than 52 mV anodic current density is much higher than cathodic and the second term in equation
16 can be neglected. Hence
I = IA = Io exp(αAnF η) ….. (20) RT
Log IA = log Io + (αAnF η) ….. (21) 2.303RT
Equation 21 is called anodic Tafel equation.
When log I values are plotted against overpotential we get Tafel plots. These offer simple
method for experimentally determining Io, transfer coefficients.
The intercept is log Io from which Io can be calculated.
From the anodic slope, A and from cathodic slope C can be determined.
At very low values say < 10 mV, Butler-Volmer equation has another form when A =
c = 0.5,
I = Io (nF/RT) η ….. (22)
Since exchange current density depends on both the concentration of O and R, it can be replaced
by standard rate constant. Then
Io = nFKoCoαA CR
αC ….. (23)
Or Io = nFKoCoα CR
1-α …… (24)
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The effect of C on current density is shown in the following plot.
a) αC = 0.25 oxidation is favoured
b) αC = 0.50 symmetrical
c) αC = 0.75 reduction is favoured
As cathodic transfer coefficient value increases reduction is favoured and oxidation is not
favoured and vice versa for anodic transfer coefficient.
Note: The above simple treatment assumes that the concentration of (O) + ( R ) are uniform in
the electrolyte as well as near the electrodes. Modes of mass transport like migration, convection
and diffusion are not treated.
37