Electrochemistry

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CHEM 12032
Electrochemistry
Part iii
Dr. K.A.S Pathiratne Department of Chemistry
University of Kelaniya, Sri Lanka.
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Resistivity and Conductivity
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? Proportionality constant ?
Resistivity When A 1 l 1
R ? the resistivity
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SI units of Resistivity is ?m e.g. A piece of Cu
wire of length 0.2 m and cross sectional area of
10-2 m has the resistance of 3.4510-5 ?
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Conductivity (k)
Resistance of a Unit cube of 1m each side
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An alternative Interpretation for conductivity, k
k current density per unit field
strength k is the current per unit area when a
unit field strength is applied.
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Measurement of conductance of electrolytes
Using a conductivity meter the resistance of a
solution block is measured. The resistance is
used to calculate conductance.
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Meter consisting of a Wheatstone Bridge is used
to determine the unknown resistance
Wheatstone Bridge Circuit
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Two types of conductance cells are used. (1).
Dip cell (2). Pour cell
For solution with low conductivities
Dip Cell
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Cell constant
For a given cell, l/A is known as the cell
constant. It will be determined by measuring
conductance of a solution with a known
conductivity. e.g. The resistance Ro of a
solution with known conductivity, ko is available.
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• l /A can be calculated.
• l /A cannot be determined accurately
  geometrically,by measuring l and A.

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Molar Conductivity For a given electrolyte at a
given temperature conductivity depends on
concentration of electrolyte. As a result
conductivity cannot be used as a parameter for
determining current carrying capacity of an
electrolyte.
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Molar conductance, ? is defined as
Where, ? molar conductivity C concentration
e.g. The conductivity of KCl solution at a
concentration of 102 mol m-3 is 1.29 O -1m-1 at
25o c. Calculate the molar conductivity of the
solution.
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• Another important property to be considered in
  comparing the conductivities is the number of
  unit charges carried by a particle.
• It is preferable to compare the conductivities of
  substances corresponding to the same number of
  unit charges. It is better to specify
• A mole of NaCl as mole of NaCl.
• A mole of ZnSO4 as ½ ZnSO4
• A mole of AlCl3 as 1/3 AlCl3

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• Now a mole of each provides the same number of
  charges and thus molar conductivities of each is
  comparable.
• What is the physical meaning of molar
  conductivity?
• Variation of molar
• Take the mole as the amount carrying 1 mole of
  unit charge paires.
• Mole ofunit charge paires ½ mol of ZnSO4
• 1/3 mol of AlCl3
• Can molar conductivity be used as a parameter to
  indicate the charge carrying capacity of an
  electrolyte?

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Variation of molar conductivity with
concentration
Molar conductivities of aqueous solutions at
250in units of mhocm2mol-1.
Siemen, is the SI unit for mho
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Conclusion As concentration decreases molar
conductivities of all are increased and reach
towards a limiting value. (see figure) This is
known as limiting molar conductivity Symbol is ?
Variation of molar conductivity with dilution
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Strong and weak electrolyte
Kohlrausch (1900) showed in some cases for
dilute solutions, variation of ? with
concentration can be expressed by the equation.
Where, k is a constant. ? and ? are molar
conductivities at C and at dilution resp.
Applicable for 1. Strong electrolyte 2. ?
Can be determined using ? vs plots.
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There are two extremes.
1. Electrolytes such as KCl, NaCl which exhibit
higher conductivity (strong electrolyte ) 2.
Other shown by HOAC (e.g Organic acids and
bases) Where ? increase of very rapidly at
very high dilutions.
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For these behavior linearly ?8 can be determined
through extra potation.
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Applications of Conductance Measurements
?/ ?8 will be equal to the degree of
ionization,If the speed of the ions do change
with dilution,for potential (week) electrolytes.
For true electrolytes the degree of ionization
at all concentration is complete, even at solid
state are completely ionized.
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Delye-Hickel theory explains why ? increases as
concentration decreases for strong(true)
electrolytes. Consider sodium chloride Sodium
ions and chloride ions are not randomly
distributed in the solution. Each Na ions
attracts towards itself Cl- ions and tends to
repel Na ions. These electrostatic forces will
be affected to a large degree by the thermal
motion of the ions. every Na ion will be
surrounded by a cloud containing more Cl- than
Na,similarly each Cl- ions will have its cloud
containing more Na than Cl-
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Suppose now a current is passed. Lets consider
the behaviour of Na ions will move towards
cathode and it cloud which move along the
opposite direction. This results in breaking of
the original cloud and forming a new one. In
practice a short time is required for the
completion of this operation. This time is known
as time of Relaxation. Before the original ion
cloud is decayed the sodium ion will be off
centre and there will be a back ward attraction.
The speed of the sodium ion will be reduced. This
effect is known as relaxation effect or asymmetry
effect.
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Ion clouds also contains water molecules. Cl-
ions are solvated. This results an increase of
viscose drag due to the water molecules moving
along opposite direction. This shows down the
speed of Na still more. This effect is known as
ELECTROPHORETIC EFFECT.
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As the solution is more diluted ions are far
apart and the density of ions cloud decreases
interaonic attractions are less. Speed of the
ions are increased. This increases current and
the molar conductivity is high. This change will
continue until at 8 dilution ions are at
infinitely far apart and interionic effect is
zero. Under this condition i.e. at 8 dilution,
the molar conductivity will be maximum.
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On the basis of these arrangements, Debye and
Huckel were affected derived an expression
relating observed molar conductor ? at a
particular concentration C to molar conductivity
?8 at initiate dilution. Calculation were later
modified by Onsager and the equation relating the
parameters is called the Debye-Huckel Onsager
equation given below.
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A and B are theoretically determined and depend
on the nature and temperature of the solvent.
The equation is a theoretical verification for
the Kohlrausch empirical law. Equation holds
accurate for concentration up to 10-3 moldm-3
Accurate within few for up to 10-2 moldm-3
for uni-uni valent electrolyte.
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However concentrated solutions and dilute
solutions of multivalent electrolyte the onsuger
equation breaks down. One reason for this is
that at higher concentration ion pairs are
formal, when opposite charged ions approach one
another. This is considered more or less as carry
no charge and no contribution to the conductance.
These ion pairs are not stable and continuously
charge particles. In the case of strong
electrolyte ? is a measure of the speed of the
ions ?8.
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Limiting molar conductivities of ions
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Kohlrausch Low of Independent Ionic Migration
Low.
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Consider the difference of ?8 values given in
columns (1). They are constant. The anions of the
pairs are the same for each pair. The cations are
different. The difference in ?8 should be due to
the difference in cation. Similarly the
difference ?8 in the 4th column in totally due to
the difference in anion. Using these observations
Kohlrausch postulated this LAW OF INDEFENDENT
IONIC MIGRATION.
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i.e. Each ion contributes a definite amount of
the total limiting molar conductivity of the
electrolyte irrespective of the nature of the
other ion. This law can be represented by the
equation. ?8 ?8 ?8-
Where ?8 and ?8 are the limiting molar
conductivities of the cation and anion
respectively.
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Limiting molar conductivities of ions can be
calculated using transport numbers. Molar
conductivities of the ions carrying the same
charge are compared. Molar conductivity is a
measure of the amount of current it can carry.
This is more significant if molar conductivities
of the ion carrying the same charges are
compared.
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Compare ?8(Na) with ?8(1/2 Mg2) and ?8(1/3 M3)
rather than ?8(Mg2) or ?8(Al3) This way ?8 of
ion carrying equivalent amount of charges are
compared. Suppose that a mole, of electrolyte
provide ? of moles of cations and ?- of
moles of anions then ?8 ? ?
8 ?- ?8-
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An application of Kohlroucsh law of independent
ionic migration. ?8 values for weak electrolytes
cannot be determined using ? vs plots.
Inde Kohlrausch
e.g. ?8(CH3COOH) ?8(H) ?8(CH3COO-)
349.8 40.9 O-cm2mol-1 390.7
O-cm2mol-1
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e.g. ?8(CH3COOH) ?8(HCl) ?8(CH3COONa) -
?8(NaCl) ?8(H) ?8(Cl-)
?8(CH3COO-)
?8(Na) -?8(H) - ?8(Cl-) .
?8(H) ?8(CH3COO-)

Since NaCl, HCl and CH3COONa are strong
electrolytes
?8 for CH3CO2Na, NaCl, HCl can be determined by
extrapolation method. They are strong
electrolytes.
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Ionic Mobility and Ionic conductance
The electrical conductance of an electrolyte is a
measure of its current carrying ability. The
current is the rate of transfer of charges.
Charges is carried by ions. Therefore conductance
depends on the rate at which the ions carry
charges.
The rate depends on three factors. 1. The
number of charges each ion carries 2. The
concentration of ions 3. The speed of the
ions.
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The speed of the ion in turn depends on (a).
Strength of the electrical field (b). Viscosity
of the medium (c). Asyymmetric effect (d).
Electrophoretic effect
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Consider an electrolyte with concentration, C.
Assume that the degree of ionization a
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Let, the concentration of the caton
C the concentration of the anion
C- The intensity of the electric fund
E The velocities of the cations and
anions ? and ? - The charge of the cations
the anions Z and Z-
Consider a plane with an area A in between the
two electrodes which is parallel to either of the
electrodes. At time t 0 there will be a certain
number of cations on the plane with the area A.
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After time, t all the cations that were on the
plane with the area A have now traveled a
distance,?xt, towards the cathode. All the
cations that passed through the plane with the
area A now are present in the solution volume
?.t. A.
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• The amount of cations present in
• the volume ?.t.
  A. ?.t. A.C ? (1)
• The number of moles unit charges present in
• the volume ?.t.
  A.C .Z ? (2)
• The amount of charge corresponding to the this
  number of
• unit charges ?.t.
  A.C .Z.F ?( 3)
• Therefore the current carried by
• cations (I) (?.t.
  A.C .Z.F)/t ? (4)
• (I) ?. A.C .Z.F
  ? (5)

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Similarly, the current carried by anions to the
opposite direction (I-) ?-. A.C- .Z- .F ?( 6)
The total current (IT) ( I I- )? (7)
ITFA( ?CZ ?-C-Z- ) ? (8) If the number
of moles of cations and the number of moles of
anions produced per 1 mol of the electrolyte is
? and ?- respectively C C a ? and
C- Ca ?- IT C aFA (?Z?) (?-Z- ?-) ?
(9)
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Also ? a E and ?- a E
? uE and ?- u-E Where
u and u- are the speed of cations and anions at
unit field strength and they are called
mobilities of ions. U
mobility of cations U-
mobility of anions
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Equation (9) can be written as IT C
aFAE (Z ? u) (Z- ?- u-) ?(10) IT/p
current density (i.e. current per unit area
of the electrode represented by)
I C a FE (Z ? u) ( Z- ?- u-) ?(11) I/E
k conductivity k C a F(Z ?
u) ( Z- ?- u-) ? (12) K/C ?
? a F(Z ? u) ( Z- ?- u-) ? (13)
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At infinite dilution a will be unity, for weak
electrolytes. If we denote mobilities of cations
and anions at initiate dilution by U and U ,
the equation (13) can be rewritten as electrlyte
by
? F(Z u ?) ( Z- ?- u- )
? (14)
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? F Z u
and
? - F Z- u- )
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e.g. calculate the ionic mobility at dilution for
a cation with a molor conductance at of 60
molcm2mol-1
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Determination of transport number using moving
boundary method Transport number depends on the
speed of ions. Moving boundary method depends on
this principle. The method can be explained using
the vertical cell. The cell contains a
uni-univelent electrolyte MA (e.g. KCl) at
concentration C together with two other solutions
called indicator solution. One indicator in MA
(e.g.LiCl) deferent cation but same anion
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The other indicator solution MA/ (e.g. CH3CO2K)
same cation but deferent anion. The solution MA
is placed between the two indicator solutions in
such a way that the most dense indicator solution
is at the bottom of the cell. This prevent
mixing, boundaries a and b are formed in
between the three solutions.
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ais solely due to the deference between M M/
and b is to that of A A/. On applying an
electric field the cation will travel towards the
cathode moving the boundary towards that
direction. Anion move towards anode, So does the
boundary. Requirements for the boundary to
remains sharp 1. At boundary a sped of M gt
speed of M/ 2. At boundary b speed of A gt speed
of A/
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Under these condition the distance travel by M,
aa/ is propotional to speed of M Likewise speed
of A is propotional to bb/ i.e. aa/
a ? bb/ a ?-
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• APPLICATIONS OF CONDUCTANCE MEASUREMENTS
• Determination of Solubility Products of Sparingly
  Soluble Salts.
• The molar conductance of a salt at any given
  concentration c, can be related to its
  conductivity ksalt according to the equation.

? (1)
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Since a solution of a sparingly soluble salt is
very dilute, it is possible to assume that the
solution is at 8 dilution and under such
conditions ?8salt can be substituted to equation
(1) in place of ?salt and The concentration C
then should represent the concentration of salt
in the saturated solutions. The
values of ?8salt at that concentration are
available for most salts. C can be determined
if ksalt is available at concentration C.
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The conductivity of a saturated solution of a
sparingly solution kSolution is the sum of the
conductivity of the pure salt, ksalt and the
conductivity of the pure solvent ksolvent as
represented by the equation below.
ksolution ksolvent ksalt
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Therefore, by measuring the conductivities of a
saturated solution of the salt and that of pure
water at a given temperature, it is possible to
obtain the conductively of pure salt and hence
the solubility C of the salt. However, the
results obtained are approximate due to many
reasons. Suggest these reasons.
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e.g. The conductivity of a saturated solution of
AgCl at 250C is 3.14 x 10-6 O-1cm-1 and that of
water at the same temperature is 1.60 x 10-6
O-1cm-1. Given that the limiting molar
conductivities of the Ag ion and Cl- ion are
61.92 and 76.34 O-1cm2mol-1 respectively at 250C,
Calculate the solubility of AgCl at this
temperature.
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• Limitations
• Solubility of the salt should be really very low
  to consider it at infinite dilution.
• No uncharged ion pairs or complexes formed from
  the cation anion of the salt present in the
  solution.
• If uncharged ionpairs occur they do not
  contribute to conductance.

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DETERMINATION OF DISSOCIATION CONSTANTS OF WEAK
ACIDS For strong electrolytes this is
complicated but for weak electrolytes possible.
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• CONDUCTOMETRIC TITRATIONS
• During titrations concentrations of ionic species
  are changed. The conductance which depends on
  concentration of ions should then change. Hence
  conductance measurements can be used to detect
  end points of
• (a) Acid/Base titrations
• Preparation titrations.
• A knowledge of relative magnitudes of
  molar conductance of ions at 8 dilution are
  useful to understand the variation of
  conductances in these titrations.

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Limiting molar conductivities of most ions at 8
dilution are in the range 40 70
O-1cm2mol-1 Exceptions H and OH- ions H
350 and OH- 198O-1cm2mol-1 Although
experiments are not performed at 8 dilutions
these values can be used to predict the changes
of conductance.
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STRONG ACID/ STRONG BASE TITRATIONS Consider the
titration of HCl and NaOH. Originally the
solution contains H, and Cl- ions. When NaOH-is
added H combines with OH- resulting H2O. At the
end of the titration the solution will have Na
and Cl-. The ions arising from very slight
dessociation of H2O is neglected. Their
contribution to the conductance are small.
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Until the end point highly conducting H is
removed by weakly conducting Na ions.
H Cl- Na
Cl- H2O Therefore, Conductance is decreased.
After the end pt. Na OH- ions are added to
the solution. This increases the conductivity as
highly conducting ions are added to the solution.

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For these titrations actual conductance
measurements are not required. Conductance
readings of the conductivity meter are
sufficient. The above arrangement predicted a
linear decrease and a linear increase of
conductance. However, these variations in
experimental results do not fall on straight
lines. As solutions are diluted due to addition
of titre to the titrant.
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To correct this measured conductance G, it is
multiplied by the volumes of the solutions and
plot KVG. (volume of base)
KG
Strong acid
Strong base
End pt.
?
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Where,
V Volume of unknown ? Volume of standard
solution added
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TITRATION OF AWEAK ACID WITH A STRONG BASE
Initial concentration of H is lower as the acid
dissociates partially HA
H A- When NaOH is added H are removed by
Na, this shifts equilibrium to the right.
However due to increase of A- the dessociation
of HA is suppressed.
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At the end pt. the NaOH added remained as Na
OH- ions and this results a rapid increase in
conductance.
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(c) VERY WEAK ACID/STRONG BASE When acid is very
weak the number of ions present in the solution
is very negligible. When alkali is added the salt
is, which is fully ionozed and the titration is
regarded as addition of ions (Na A) in to the
solution. So conduct increases. Beyond the end
pt, the rate of increase is larger as OH- are
added, in place of A-.
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(d) TITRATION OF ACIDS WITH WEAK BASES When
acids are titrated with weak bases the shapes of
the graph obtained before the end pt. is the same
as that obtained for strong base. After the end
pt. the excess base present will be largely
unionized. This makes no contribution to the
conductance of the solution.
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(e) MIXTURES OF ACIDS (WEAK STRONG VS STRONG
BASE) Strong acid is nutralized completely
first. Then the weak acid neutralization start
next.
V1 volume of base required for strong
acid V2-V1 volume of base required for weak acid
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PRECIPITATION TITRATION e.g. KCl with AgNO3
(I) KCl AgNO3 KNO3 AgCl
GK
?
End point
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Until the end point addition of AgNO3 result
replacement Cl- by NO3- ions. The limiting ionic
conductance of Cl- NO3- are nearly the same.
After the end pt addition of AgNO3 results
increasing of ionic conc. hence conductance.
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II. Titration of MgSO4 with Ba(OH)2 MgSO4
Ba(OH)2 BaSO4 Mg(OH)2
GK
MgSO4
Ba(OH)2
?