ELECTROCHEMISTRY
MESRRANAESOSE
Electrochemistry encompasses the study of:
(i) Electrical transport or electrolyte conductance
i) Conversion of electrical energy into chemical energy and vice
versa.
The electrical transport takes place by mean of:
1. Electronic conductors
2. Electrolyte conductors
The behaviour and
properties of the two conductors are as follows:
1. Electronic conductors
)
Conduction of current is carried
(i) The flow of current is
by movement of electrons.
unidirectional.
(i) No chemical changes take
place, only physical changes occur
It
(iv) does not involve transfer of
matter.
(v) Conductivity decreases with
increase in
temperature.
(vi) Conductivity is
generally high.
(vii) Metals in solid state and
2. Electrolyte Conductors
molten state conduct
current.
(i) Current is due to flow
of ions.
(i) Flow of ions takes
place in both the direction.
(ii) Chemical
changes take
(iv) It involves transfer of place, e.g.. electrolysis.
(v) The
matter in the form
conductivity increases with increase inof ions.
temperature.
Electrochemistry
27
(vi) The conductivity is generally low (as compared to electronic
conductor).
(vii) Molten electrolytes and their aqueous solutions conduct
In this chapter we shall
conductance.
1.
current.
study the various aspects of electrolyte
Conductivity of Electrolytes
Ohms law is obeyed by both the types of conductors. The resistance
ofa conductor is directly proportional to its length and inversely proportional
to its cross-sectional area.
R
a
or R=p
where,
a
R = resistance in ohms
P
I
specific resistance or resistivity/proportionality constant
= length in cm
a
area of cross-section in cm2
The specific resistance or resistivity is given by the expression
p R
Now, if a = 1 cm
and l = 1 cm, then
P R.
This ieads to the definition of resistivity as the resistance offered
by the conductor of1 cm length with area of cross-section equal to
I cm*. It may also be defined as resistance offered by a centimeter
cube of a conductor. The unit of resistivity is ohm cm.
The SI unit for resistivity is ohm m
I ohm m =
or
100 ohm cm
1 ohm cm = 0.01 ohm m
For electrolytic conductors, the appropriate property is conductance
instead of resistance and it is defined as reciprocal of resistance.
The conductance is denoted by 'L'. The unit for conductance is
ohm
or mho or Siemens denoted
Conductance R
by S. (1 S
=
ohm', 1 S
=
mho)
The conductivity of electrolytes
is better underst0od by defining
the following terms.
() Specific
(K) is the reciprocal
solution. that is
resistivity) of an electrolytic
Conductance o r Conductivity
of specitic resistance (or
(K)
denoted by Greek letter kappa
P
aR
The unit for specific
conductance
S cm', or mho cm' (ohm
I f = 1 cm, a
=
=
or conductivity ohm cmor
mho)
I cm*, then
K
= R = conductance
is conductance of
Hence, specific conductance or conductivity
1 cm' of electrolytic solution.
in m* and length is
In SI units, area of cross-section is expressed
will be Sm
expressed in m. Then the unit of conductivity
1 S cm= 100 S m
Table 1.2.1: Conductivities of some electrolyte
solutions at 298 K.
Conductivity
Electrolyte solution
(Specific conductance)
ohm'cm
Sm'
or S cm
Pure water
3.5 x 10
3.5 x 10
0.1 M HCi
3.91x 10-2
3.91
0.1 M NaCl
9.2 x 102
1.2 x 103
9.2
1.2x 10
1.29x 10-2
1.29
1.4 x 10-3
4.7 x 104
1.4x 104.7 x10-2
1.6x 10
1.6 x 102
0.01 MNaCI
0.1 M KCI
0.01 M KCI
0.I M CH,COOH
0.01 M CH,COOH
The specific conductance of a solution is determined by measuring
the resistance of a solution using wheatstone bridge in which the use
of direct current give rise to electrolysis and therefore change in
concentration of electrolyte. Now a modified wheatstone's bridge with
alternating current is used. The electrolyte solution is taken in conductivity
cell which measures the conductance or conductivity of the solution.
(ii) Cell Constant: The conductivity cell is a cell which encloses
volume of I cm*'. The conductance of a solution depends upon the
area of each electrode (a) and the distance between them. Thus, every
Electrochemistry
29
conductivity cell has a cell constant defined by the ratio of distance ()
between the two electrodes to the area of cross-section (a).1e
Cm
Cell constant
Cm
a
cm
m
,
m*
m
In laboratory the cell constant is determined by using KCl solution
of known concentration and specific conductance, determ ing its
conductance,
Cell constant
Specific conductance of 0.1 NKCI
Conductance of 0.1 NKCI
S cmem
S
Thus once the cell constant of a conductivity cell is known, by
measuring the conductance of experimental electrolytic solution, the
specific conductance can be determined using the expression.
Specific conductance
= Cell constant x Conductance
(ii) Equivalent and Molar Conductance: The conductance of
an electrolyte solution depends on its concentration. The conductance
data is of not much relevance until the amount of electrolyte in a definite
volume is specified. Keeping this in mind it becomes necessary to
introduce two kind of conductances- equivalent conductance and
molar conductance.
Equivalent Conductances (Aeq) defined as the conductance of all
the ions produced by one g equivalent of an electrolyte in the solution
which is placed between two parallel electrodes one cm apart.
If one gram equivalent of electrolyte is dissolved in
V cm' of
solution, then
AagkV
where, k =specific conductance
1000 cm3 of
In general ifa solution contains N gram equivalent in
will be
solution, the volume of solution containing l gram equivalent
1000
N
1000k
Thus, Aq
N
32
(a)
(or molar) conductance
equivalent
When
Strong electrolyte:
conductance values
observed that the
is plotted against C.it
is
The increase conductane
on dilution.
increase
slightly
are high and
or limiting valu
reaches a maximum
and
dilution
is linear with
at infinite
known as
equivalent (or molar)
denoted by
molar)
in
A
or
dilution
tion
conductance
Ao (or Am or A).
The equivalent (or
be obtained by extrapolation of the
concentration or dilution approaches infinity
conductance can
curve to zero
a mathematical expression
Debye Hucked Onsager developed
conductance Aeq (A) and equivalent
molar)
(or
relate
equivalent
to
at
(or molar) conductance
A
or
infinite dilution
Ac) for strong electrolytes
Aeq or A (or
as:
AAbNC
where,
Aeqequivalent conductance at a given
dilation
Aequivalentconductance at infinite dilution
b
a constant which
depends on nature of solvent and dielectric
constant of the solvent.
C
concentration of the solution
The simplified form of Debye Hucked Onsager expression shows
that as C approaches zero Aeq approaches Aq
For molar conductance
A =A -byC
The plot A
against C
shows that the equivalent (or molar)
conductance is higher for dilute solutions and lower for concentraed
solutions. This is because for strong electrolytes, the number
of ions in the solution do not increase, because they are almost
completely ionised in the solution at all concentrations. Howeve
in concentrated solutions of the
density of ions is, relative
high hence due to inter-ionic attractions the speed of the io1
is reduced lowering the value of
equivalent (or molar) conductan
On increasing the dilution, the ions move
apart and inter-10
attractions are decreased. As a result value of equivalent
(o
molar) conductance increases.
Electroche mustry
33
400
or A)
300 -
A(or A,)
200100-
0.1 0.1 02
Fig. 1.2.1: Variation of Ag or Am
agains
(b) Weak electrolytes: A plot of
c
0.3
for strong clectrolytes
equivalent (or molar) conductance
against C shows that in concentrated solution, the equivalent
(or molar) conductance values are low and it increases steadily
with dilution. A, (or
A) cannot be obtained by extra polation
method because, when concentration
approaches zero, the graph
becomes almost parallel to Y-axis.
400
300-
or200
200
100
0.1 C
Fig. 1.2.2: Variation of Acq or Am agains c
0.2
0.3
for weak electrolytes
However, it may be obtained using Kohlrauseh's Law. For weak
electrolytes, degree of dissociation is inversely proportional to concentration.
Hence at higher concentration, the degree of dissociation is less therefore
equivalent (or molar) conductance is less and vice-versa.
Table 1.2.3: Molar conductivity, A,, in S cmmot of electrolytes at 298K
Concentration
HCI
CHCOOH
0.1
391.32
5.2
0.05
399.09
7.4
0.025
407.24
1.6
0.01
412.00
16.2
0.005
415.8
22.8
0.001
421.3
48.6
0.0005
422.7
34
1.2.2 KOHLRAUSCH LAW
learnt
conductivity
that molar
We have already
value
a limiting
with dilution till
A
is obtained at
increases
Kohlrausch studied A
Table 1.2.4 gives
values of various pairs
molar
the values of
Am of electrolytes
ofstrong electrolytes
conductance at
common
infinite dilution
infinite dilution
ions. Studying
the difference
electrolytes having
give rise to
for some pairsof
dilution for each pairs
infinite
conductance at
in molar
some interesting facts.
Molar
infinite dilution for pairs
conductance of
Smmo
Table 1.2.4:
Evidence for
Kohlrausch's Law
Setll
Set
Electrolyte
0.0150
KCI
NaCl
KNO
NaNO3
KOH
0.0271
0.0248
NaOH
Difference
Electrolyte
0.0023
KCI
0.0023
0.0122
0.0023
Difference
0.0150
0.0005
0.0145
KNO
0.0127
0.0145
of electrolytes in
0.0127
NaCl
NaNO
0.0122
HCI
0.0426
HNO3
0.0421
0.0005
0.0005
difference between A
The interesting fact observed is that the
is
in set I and II are constant. The observation
values for the
pairs
justified only when we assume that A^
is sum of two terms, one
arising due to cation and other due to anion.
Set I has common anions so that the difference can only be
due
in contribution to
by Kt and Na* ions. In the
same way in set II, the constant difference may be attributed to difference
to the difference
A
in contribution to A made by the Cl and NOj ions.
Based on these experimental studies Kohlrausch in 1875 gave a
generlisation that at infinite dilution, when all forces of interaction
between ions disappear, each ion migrates independently of its co-ion
and makes a definite contribution to the total molar conductance of
the electrolyte, and this conribution is independent of the nature of
the other ion with which it is associated in the electrolyte. On the basis
of this conclusion, Kohlrausch put forward the law of independent
Electrochemistry
35
migration of ions in mathematical form. It states that the value of the
molar conductance of an electrolyte at infinite dilution is equal to the
sum of the conductances of the constituent ions at infinite dilution.
This implies that molar conductivity of an electrolyte at infinite
dilution can be expressed as sum of the contributions of the cations
and anions, if .
and
are the molar conductivities of the cation
and anion respectively at infinite dilution, then molar conductivity of
an
electrolyte at infinite dilution A is given by
Where v, and v_ are the numbers of cations and anions
by each formula unit of the electrolyte. For example,
() A (NaC1) =t a
V=1
(i) A
v. = 1 v 2
(BaC1,) = p
+2cr
(ii) ANasso,= 2Na+*so
produced
VI
v, = 2
Table 1.2.5: Molar lonic Conductances at Infinite Dilution
Cation
1° (Sm mol')
Anion
(Sm mol ')
H
0.03498
OH
0.01980
0.00735
SO
Br
0.01600
NH
0.00734
Na
Ag
0.00501
0.00619
C
0.00763
Ba2
0.01273
NO
0.00714
Ca2
0.01190
CH,CO0
0.00409
Sr2
0.01189
0.00784
0.00768
1.2.3 APPLICATIONS OF CONDUCTANCE
MEASUREMENT
(1) Determination of Degree of lonisation
Degree of ionisation (o) is the fraction oftotal number ofmolecules
dissociated into ions, i.e.,
No. of molecules dissociated into ions
Total no. of molecules taken
College Physical Chemistry
36
We also know that the conductivity ofa solution is due to presence
of ions in the solution. Greater the number of ions, greater is the
conductivity
Athe molarconductivity at a particulardilution is proportional
to the number of molecules dissociated into ions at this dilution.
At infinite dilution all the molecules taken are in ionic form
ie., A is proportional to the total number of molecules taken
No. of molecules dissociated into ions
Total no. of molecules taken
A
Thus degree of ionisation at any dilution is the ratio of
molar
conductivity at that dilution to molar conductivity at infinite dilution.
The value of Am can be obtained by direct measurement
conducto meter and AG can be obtained with the
law, i.e.
using
help of Kohlrausch's
A =v.A, +vA
Hence value of degree of dissociation «
can be
calculated.
(2) Determination of Ionisation Constant
Weak electrolytes in aqueous solutions ionise to a
very small extent.
The extent of ionisation is described in
terms of
of
degree
.
In the solution, the ions are in
dynamic
ionisation
equilibrium
molecules. Such equilibrium can be described
ionisation constant.
For example for a weak
AB
A +B
with unionised
by a constant called
electrolyte, AB, the ionisation equilibrium is
If C is the initial
concentration of electrolyte AB in the solution,
then the equilibrjum
concentration of various species in the solution
are;
A B C ( - «)
A] = Co
[B] = Co
(o« is the degree of ionisation)
Then the ionisation constant
of AB is
given by
37
Electrochemistrv
K
B].CcCo
Co
[AB]
(1-)
C(1-)
At any concentration C', the degree of ionisation ( ) is given by
oc=
Then K CAIA
C(G
[1-(A/A)] AAm-A)
Thus knowing A and measuring A, concentration C, the ionisation
constant of the weak electrolyte can be determined.
(3) Determination of Solubility and Solubility Product ofSparingly
Soluble Salt
The solubility of a sparingly soluble salt in solvent is very low.
Even the saturated solution of such salts is so dilute that it can be
assumed to be at infinite dilution.
sal soln
.e., A*m
.
salt
(1)
salt
the molar conductivity ofa sparingly soluble salt at infinite dilution
(A) can be obtained from the Kohlrausch's Law.
sall
A =v.a +v_
(2)
salt
The conductivity of saturated solution of the sparingly soluble
salt is measured (Ksoln). Measuring conductivity of water (Kwater) used
in preparation of the saturated solution of the salt, the conductivity of
the salt (Kal) can be obtained
(3)
KsaltKsoln-Kwater
The molar conductivity of the salt from equation (1)
A
=
Salt
1000 Ksat
C
C000K.sal
A
1000 Ksal
v,A +v_A
sull
or
C 1000(KalnKwater from equation (2) and (3)
v..v
College Physical Chemistry
38
soluble salt in its
of the sparingly
of the sparinglu
molar
the solubility
Cm is the
to
Thus C, is equal
can be obtainedby
saturated solution.
salt in g dm
the
Solubility
of
moles dm".
salt.
soluble salt in
mass of the
molar
the
with
multiplying C,
moles dm
in
solubility
S
C=
i.e.,
concentration
Cm
molar m a s s
Ks, =ry
Since
For univalent
Ksp
S in g dm
S*y
electrolyte,
For bi-univalent
by
=
solubility product K,p
solubility
electrolyte like BaCl2,
2C
x =1 y =2
122sl+2 4 S3
Bas"
BaClh
is given by S2
=
product is given
+
=
K=
For
by
like AICl3 solubility
tri-univalent electrolyte
product is given
A1* +3CI
AICl
gp 1' 3's!3
27 S*
When
concentration
Cm is expressed
in mol m
KsolnH
Solubility S is
expressed as:
3. Ionic Product of
v.A+v.2
Water
the purest
show that water even in
temperatures.
definite conductance at all
but
small
exhibits
though
and
form
weak electrolyte
water behaves as
if
and
only
This is possible if
measurements
The conductance
ionizes according to the equation
HO
H'+OH
The equilibrium constant
for the above ionization js
K-[H]1OH
H,0
of water in any
concentration
Since ionization is very slight the
be included in K.
solution will be constant and can
aqueous
Electrochemistry
39
K K[H,0] =[H'] [OH"]
K, is called the ionic product of water. It is obvious that in any
aqueous solution both hydrogen and hydroxyl ions must be present
and product of thier concentrations must be constant. The value of Ay
can be calculated from Kohlrausch and Heydweiller data on conductance
of pure water.
The steps involved are as follows:
(a) Determination of degree of ionization (o)
Problem: Determine ionic product of
1g equivalent of water,
specific conductance of water which is equal to 0.58 x 10
S cm
at
25°C obtained from conductance data.
1g equivalent of water = 1 mole = 18.016 g
density of water = 0.9971 g cm
=
0.58 x 1o-7
at 25°C
18.016
0.9971
=
1.05 x 10
=
349.8 + 198.0
=
547.8
= 1.9x10
eg1.05x10=1.9x10
547.8
eq
(b) lonic product of water
Since one liter of water weight 997.07 g at 25°C, the molar
concentration C of water is 997.07/18.016
[H]
=
[OH]
=
55.34 molar
Ca
= 55.34 x 1.9 x 10
= 1.05x 107
Ky at 25°C is
K,
= [H*] [OH]
=
K
(1.05 x
107)2
=1.10 x1014
1.2.4 TRANSFERENCE OR TRANSPORT NUMBER
to conduct
it is now known that the capacity of a given electrolyte
electricity depends, among other
factors, also on the velocity of ions