1. The document discusses electrolytes and their conductivity properties. It defines strong and weak electrolytes and gives examples of each. 2. Kohlrausch's law of independent migration of ions states that at infinite dilution, each ion in an electrolyte contributes a characteristic value to the molar conductivity that is independent of the other ions present. 3. The document outlines several applications of Kohlrausch's law, including determining the degree of ionization of weak electrolytes, calculating ionization constants, and determining the ionic product of water and solubility products of sparingly soluble salts.

1. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
• Electrolytes : Definition, Strong and weak electrolytes and their conductance
measurement, Ions and electrical conductivity by ions
• Kohlrausch law of Independent Migration of Ions
• Applications of Kohlrausch law
• Transference No. and its determination using Moving Boundary Method
• Factors affecting transport number
CONDUCTOR : It is a substance which allows an electric current to flow through
it. Conductors are of two types:
NON-ELECTROLYTES :
✓ Aqueous solution does not conduct electricity
Examples are solutions of cane sugar, glucose, urea etc.
ELECTROLYTES : A chemical compound which dissociates into positively charged
cations and negatively charged anions in the solution state or in molten state
which can conduct electricity is called electrolyte.
✓ solution in water conducts electric current
✓ Conduction by the movement of ions
Examples are salts, acids and bases
Strong Electrolyte :
• Highly ionized in the solution
• Only free ions of the compound are present
• Solution is Good conductor of electricity
• Molar conductance increases slightly on dilution
• Ostwald’s dilution law is not applicable
Example - HCl, HBr , H2SO4, NaOH, NaCl , KOH etc
Weak Electrolytes
• Only feebly ionized in the solution
• Free ions as well as molecules of the compound are present
• Solution is poor conductor of electricity
• Molar conductance increases rapidly with dilution
• Ostwald’s dilution law isapplicable
Example - H2CO3, CH3COOH, NH4OH, NH3, Aniline ,HCOOH , HF , C6H5COOH etc
TYPES OF ELECTROLYTES

2. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
VARIATION OF EQUIVALENT AND MOLAR CONDUCTANCE WITH
CONCENTRATION
The variation of equivalent conductance with dilution can be studied by plotting a
graph of 𝜆 against √𝐶 .
✓ The 𝜆 value of strong electrolyte shows a linear variation with concentration
✓ For other electrolyte variation of 𝜆 with concentration is not small
✓ For the experimental observation, Kohlrausch suggested equation
𝝀𝒄 = 𝝀∞ − 𝒃√𝑪
Where 𝝀𝒄 is equivalent conductance at concentration ‘c’
𝝀∞ is equivalent conductance at infinite dilution or zero concentration
Value of ‘b’ and 𝝀∞ constant for a given electrolyte
✓ Incase of weak electrolyte ionisation is incomplete hence value of 𝝀 decreases
with increase in concentration. Thus conductivity is proportional to degree of
dissociation of electrolyte ( 𝜶 )
✓ Degree of dissociation is defined as fraction of total electrolyte that has
dissociated into ions. At infinite dilution electrolyte is completely dissociated,
hence according to Arrhenius, degree of dissociation can be written as
Kohlrausch law of Independent Migration :
Kohlrausch studied molar conductivity at infinite dilution for different electrolytes
having an ion common and concluded that each ion contributes a characteristic
Set 1 Set 2
Electrolyte 𝝀∞ Difference Electrolyte 𝝀∞ Difference
KCl 0.0150 0.0023 KCl 0.0150 0.0005
NaCl 0.0127 KNO3 0.0145
KNO3 0.0145 0.0023 NaCl 0.0127 0.0005
NaNO3 0.0122 NaNO3 0.0122
KOH 0.0271 0.0023 HCl 0.0426 0.0005
NaOH 0.0248 HNO3 0.0421

3. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
value of its own to molar conductivity at infinite dilution irrespective of the nature
of other ion present.
In Set 1 , the common difference between the molar conductance at infinite
dilution is due to difference in 𝝀∞ values of K+ and Na+ .
In Set 2 , the common difference between the molar conductance at infinite
dilution is due to difference in 𝝀∞ values of 𝐶𝑙−
and 𝑁𝑂3
−
.
On the basis of this observation , Kohlrausch stated the law of independent migration of ions
“ At infinite dilution , when all the forces of interaction between ions
disappear, each ion migrates independently of its co-ion and
contributes a definite value to the total conductance of the
electrolyte solution.”
This contribution is independent of nature of other ion with which it is
associated.
In mathematical form Kohlrausch stated the law –
“ 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”.
In other words, a given ion will have same value of limiting equivalent
conductance in all its salt solution.
Mathematically, the law can be given
𝝀𝒎
∞
= 𝝂+ 𝝀+
∞
+ 𝝂− 𝝀−
∞
Where 𝝂+ and 𝝂− are the numbers of cation and anions produced by each
formula unit of the electrolyte.
Example : For different electrolytes the law can be written as
1) 𝝀𝒎
∞(𝑵𝒂𝑪𝒍) = 𝝀𝑵𝒂+
∞
+ 𝝀𝑪𝒍−
∞
; 𝝂+ = 𝟏 , 𝝂− = 𝟏
2) 𝝀𝒎
∞(𝑩𝒂𝑪𝒍𝟐) = 𝝀𝑩𝒂+𝟐
∞
+ 𝟐 𝝀𝑪𝒍−
∞
; 𝝂+ = 𝟏 , 𝝂− = 𝟐
3) 𝝀𝒎
∞(𝑵𝒂𝟐𝑺𝑶𝟒) = 𝟐 𝝀𝑵𝒂+
∞
+ 𝝀𝑺𝑶𝟒
−𝟐
∞
; 𝝂+ = 𝟐 , 𝝂− = 𝟏

4. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
Applications of Kohlrausch law :
1) Determination of degree of ionisation :
Degree of ionisation is the fraction of total electrolyte that has dissociated into ions.
∝=
𝑁𝑜. 𝑜𝑓 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑑𝑖𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑖𝑛𝑡𝑜 𝑖𝑜𝑛𝑠
𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑝𝑟𝑒𝑠𝑒𝑛𝑡
For a weak electrolyte, the molar conductance at a given concentration, is the
measure of extent of dissociation of weak electrolyte. At infinite dilution, the weak
electrolyte will be completely dissociated.
Therefore , 𝜶 =
𝝀𝒄
𝝀∞
---- (1)
𝝀𝒄 can be obtained by direct measurement using a conductometer and 𝝀∞ can be
obtained with the help of Kohlrausch law
𝝀𝒎
∞
= 𝝂+ 𝝀+
∞
+ 𝝂− 𝝀−
∞
Thus 𝜶 can be calculated using equation (1)
2) Determination of ionisation constant of weak electrolyte:
The extent of ionization of a weak electrolyte is expressed in terms of
degree of ionization 𝜶 .
In solution of weak electrolyte, the ions are in dynamic equilibrium
with unionised molecule.
Consider an electrolyte ‘AB’ 𝑨𝑩 ↔ 𝑨+
+ 𝑩−
If ‘c’ is concentration of electrolyte and 𝜶 is degree of dissociation
then
𝑨𝑩 ↔ 𝑨+
+ 𝑩−
(1- 𝜶) 𝜶 𝜶
Concentration, c (1- 𝜶) c . 𝜶 c . 𝜶
The ionisation constant of ‘AB’ is
𝑲 =
[𝑨+] [𝑨−]
[𝑨𝑩]
=
𝜶.𝒄 𝒙 𝜶.𝒄
(𝟏−𝜶)𝒄
=
𝜶𝟐.𝒄
(𝟏−𝜶)
.
But 𝜶 =
𝝀𝒄
𝝀∞
; 𝑲 =
(
𝝀𝒄
𝝀∞
⁄ )
𝟐
𝒙 𝒄
(𝟏−
𝝀𝒄
𝝀∞
)
Therefore , 𝐾 =
𝝀𝒄
2
. 𝐶
𝝀∞ (𝟏−𝝀∞)

5. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
i) Cell constant is determined by measuring conductance of 0.1N KCl
and using value of specific conductance of 0.1N KCl from table.
𝐶𝑒𝑙𝑙 constant =
Specific conductance of 0.1NKCl
Conductance of 0.1NKCl
= _____𝑐𝑚−1
ii) Using cell constant , specific conductance of different concentration
of weak electrolyte is calculated using relation.
Specific conductance = k = Conductance x Cell constant
iii) From the value of specific conductance , molar conductance of
weak electrolyte is calculated using relation
𝝀𝒄 =
𝑺𝒑𝒆𝒄𝒊𝒊𝒇𝒄 𝒄𝒐𝒏𝒅𝒖𝒄𝒕𝒂𝒏𝒄𝒆
𝑪
iv) 𝝀∞ can be calculated using Kohlrausch law .
Using above values , ionisation constant can be calculated from
equation 𝐾 =
𝝀𝒄
2
. 𝐶
𝝀∞ (𝟏−𝝀∞)
3) Determination of Ionic product of water :
Water can be treated as a weak electrolyte and ionizes according to
equation, H2O H+
+ OH-
The equilibrium constant for above ionization is
𝑲 =
[𝑯+] [𝑶𝑯−]
[𝑯𝟐𝑶]
𝒊. 𝒆 𝑲 [𝑯𝟐𝑶] = [𝑯+] [𝑶𝑯−]
Since ionization is weak, concentration of water in aqueous solution
will be constant
𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆 , 𝑲𝒘 = [𝑯+] [𝑶𝑯−]
𝑲𝒘 is called ionic product of water .
The value of 𝑲𝒘 can be calculated using Kohlrausch law and by
measurement of conductance.
i) Cell constant is determined by measuring conductance of 0.1N KCl
and using value of specific conductance of 0.1N KCl from table.

6. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
𝐶𝑒𝑙𝑙 constant =
Specific conductance of 0.1NKCl
Conductance of 0.1NKCl
= _____𝑐𝑚−1
ii) Using cell constant , specific conductance of pure water is
calculated using relation.
Specific conductance = kwater = Conductance of water x Cell constant
iii) Molar conductance of water is calculated using relation
𝝀𝒄 =
𝑺𝒑𝒆𝒄𝒊𝒊𝒇𝒄 𝒄𝒐𝒏𝒅𝒖𝒄𝒕𝒂𝒏𝒄𝒆
𝑪
Where C = Concentration of water = Moles of water per m3
iv) Molar conductance at infinite dilution ( limiting molar conductance)
is determined using Kohlrausch’s law
𝝀𝑯𝟐𝑶
∞
= 𝝀𝑯+
∞
+ 𝝀OH−
∞
v) The degree of dissociation can be calculated using equation ,
𝛼 =
𝜆𝑐
𝜆0
𝐼𝑜𝑛𝑖𝑐 product of water = 𝐷𝑖𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠 𝑡𝑎𝑛 𝑡 𝑜𝑓 𝑤𝑒𝑎𝑘 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑙𝑦𝑡𝑒
𝐼𝑜𝑛𝑖𝑐 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑐𝑎𝑛 𝑏𝑒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑢𝑠𝑖𝑛𝑔 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 , 𝐾𝑤 =
𝛼2
× 𝑐
(1-𝛼)
4) Determination of solubility & solubility product of sparingly
soluble salt :
The solubility of a sparingly soluble salt in solvent is very low. Even saturated
solution of such salt is so dilute that it can be assumed to be at infinite dilution.
𝑖. 𝑒 Λ𝑐
𝑠𝑎𝑡 soln
= Λ∞
𝑠𝑎𝑡 soln
𝑀𝑜𝑙𝑎𝑟 conductivity can be obtained from Kohlrausch's law
Λ𝑐
𝑠𝑎𝑡 soln
= Λ∞
𝑠𝑎𝑡 soln
= Λ0
𝑠𝑎𝑡 soln
= 𝜆0
+
+ 𝜆0
−
𝑀𝑜𝑙𝑎𝑟 conductivity of salt can be determined by 𝜆salt
∞
=
1000𝑘𝑠𝑎𝑙𝑡
𝑐
–(1)
Measurement of ksalt :
i) Cell constant is determined by measuring conductance of 0.1N KCl
and using value of specific conductance of 0.1N KCl from table.

7. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
𝐶𝑒𝑙𝑙 constant =
Specific conductance of 0.1NKCl
Conductance of 0.1NKCl
= _____𝑐𝑚−1
ii) Using cell constant , specific conductance of different concentration
of weak electrolyte is calculated using relation.
Specific conductance = k = Conductance x Cell constant
iii) Specific conductance of pure salt is obtained as the difference
between the specific conductance of saturated solution and that of
distilled water.
𝒌𝒔𝒂𝒍𝒕 = 𝒌𝒔𝒂𝒍𝒕 𝒔𝒐𝒍𝒏 − 𝒌𝒔𝒐𝒍𝒗𝒆𝒏𝒕
𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑜 𝑙𝑢𝑏 𝑖 𝑙𝑖𝑡𝑦:
𝜆𝑠𝑎𝑙𝑡
∞
=
1000𝑘𝑠𝑎𝑙𝑡
𝑐
∴ 𝑐 =
1000𝑘𝑠𝑎𝑙𝑡
𝜆𝑠𝑎𝑙𝑡
∞
The molar concentration ‘c’ of sparingly soluble salt is equal to the
solubility of salt in mol.dm-3
∴ S =
𝟏𝟎𝟎𝟎𝒌𝒔𝒂𝒍𝒕
𝝀𝒔𝒂𝒍𝒕
∞ =
𝟏𝟎𝟎𝟎(𝒌𝒔𝒂𝒍𝒕 𝒔𝒐𝒍𝒏 − 𝒌𝒔𝒐𝒍𝒗𝒆𝒏𝒕)
( 𝝀+
∞
+ 𝝀−
∞ ) mol/dm𝟑
Solubility in g/dm3
= S(mol/dm3
) x Molecular wt.
𝐷𝑒𝑝𝑒𝑛𝑑𝑖𝑛𝑔 𝑜𝑛 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑜𝑓 𝑠𝑎𝑙𝑡, Solubility product (Ksp) can be
calculated using relation
𝐾𝑠𝑝 = 𝑥𝑥
. 𝑦𝑦
. 𝑆(𝑥+𝑦)
𝐸. 𝑔. For BaCl2, x = 1 , y = 2
∴ 𝐾𝑠𝑝 = 4𝑆3
For AlCl3, x = 1 , y = 3
∴ 𝐾𝑠𝑝 = 27𝑆4

8. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
Transport number / Traansference number :
The fraction of total current carried by ion is known as transport no.
It is represented by the symbol t+ for cations and t- for anions.
But current carried by cation is proportional to u+ and
current carried by anion is proportional to u-
t = t+ + t- = 1
Relation between transport no. and eq. conductance :
The current carried by ion is proportional to ionic conductance.
i.e current carried by cation is proportional to λ+ and
current carried by anion is proportional to λ-
Total current carried by ions is proportional to λ+ + λ-
and
Determination of transport number by Moving Boundary method:
Principle :
This method is based on the measurement of movement of a boundary
generated and maintained between two electrolyte solutions, due to
difference in the velocities of the ions of the two electrolyte. From the
distance travelled by the boundary in a given time interval transport
no. of the ion can be calculated.
Let MA ( eg HCl) be the electrolyte whose transport no. is to be
calculated. This electrolyte is known as principal/experimental
electrolyte.
−
+
−
−
+
=
u
u
u
t
1
t
0
and
1
=
t
+
t
thus
;
I
+
I
=
I
I
+
I
I
=
t
;
I
+
I
I
=
t
+
-
+
-
+
-
+
-
-
-
+
+
+

 _
_
−
+
+
+
+
=
u
u
u
t
−
+
+
+
+
=



t
−
+
−
−
+
=



t

9. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
For determination of transport no. of MA another electrolyte (NA) eg.
CdCl2 is required which is known as indicator electrolyte and should
satisfy the following conditions
i) NA should have common anion for determination of transport
no. of cation
ii) Solution of indicator electrolyte NA should be denser than MA.
iii) Mobility or conductance of M+ ion should be greater than N+ ion.
iv) A sharp boundary must be established at the start of the
experiment.
Apparatus:
Apparatus consists of a glass tube fitted with 2 electrodes. The top
platinum electrode is cathode. The lower portion of tube contains
solution of indicator electrolyte in which electrode of the same metal is
dipped.
The electrolyte MA whose transport no. is to be determined is added
slowly over the solution of indicator electrolyte. The boundary aa’
maintained between two solution is marked with some colour.
Working : When a current I is passed the Cd dissolves at anode.
Cd Cd+2
+ 2 e
At cathode reduction of H+ ion will occur.
H+
+ e ½ H2 (g)
As H+ ions migrates towards cathode their place is taken by Cd+2 ion.
A current of ‘I’ ampere is passed for ‘t’ sec. Throughout the experiment

10. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
anion moves towards anode and cations moves upward towards
cathode. Hence the boundary between the two solution moves in
upward direction from ‘aa’ to ‘bb’. Coulometer is used to calculate the
total quantity of current passed.
Calculations :
Let ‘l’ be the distance travelled by the boundary in time interval ‘t’ sec.
If ‘A’ is area of cross section of the tube then the volume swept by the
boundary after passing electric charge ‘Q’ coulombs will be .
V = A x l
Let the concentration of principle electrolyte be ‘c’ moles/dm3
Therefore the amount of H+ ion carried towards cathode will be ,
V x c = A x l x c
The amount of current passed during the electrolysis is given by
Q/F where Q = I x t and F = 96500 C
Therefore transport no. of H+ ion will be
t
I
F
c
l
A
Q
F
c
l
A
F
Q
c
l
A
passed
current
H
of
Amount




=



=


=
=
+
+
Total
cathode
towards
moved
tH
Factors affecting transport no. :
1) Concentration :
Transport no. of an ion increases with decrease in the concentration
of an electrolyte. The variation of transport no. with concentration c ,
is given by the equation.
t = t0 - A√c where t0 = transport no. at infinite dilution,
A = constant
2) Temperature : An increase in temperature brings the transport no.
values of all the ions close to 0.5 . Thus, those transport no. values
which are smaller than 0.5 increases and those which are greater
than 0.5 decreases with increase in temp.

11. SYBSC - SEM III –PAPER I SOLUTIONS OF ELECTROLYTES Dr. Aqeela Sattar
3) Nature of co-ion:
The transport no. of ion depends on the nature of its co-ion.
Eg. Transport no. of Cl-
in NaCl is 0.61 and in HCl is 0.17
𝑁aCl HCl
𝒕Cl− =
𝑢𝐶𝑙−
𝑢𝑁𝑎+ + 𝑢𝐶𝑙−
tCl− =
𝑢𝐶𝑙−
𝑢𝐻+ + 𝑢𝐶𝑙−
tCl− = 0.61 tCl− = 0.17
Though the speed of Cl- ion is same in each case, the speed of H+ ion is
much greater than that of Na+ ion. Therefore transport no. of Cl- in HCl
is much less than that in NaCl.
4) Size of the ion: Transport no. depends on the speed of the ion which
in turn depends on the size of the ion. Smaller the size greater will be
the velocity. In aqueous media the hydration increases the size of the
ion and decreases its speed. Smaller the ionic size, maximum is
hydration and transport no. value is small.
Eg. Transport no. of Li+
, Na+
and K+
ions in aqueous solution are
0.33 , 0.38 and 0.48 respectively. The ionic size of these ions
increases from Li+ to K+, hence it is expected that Li+ should travel
fast and should have highest transport n. But due to hydration Li+
has least transport no.
5) Complex formation : Sometime transport no. of an ion decreases
with increase in concentration and it becomes abnormal . Eg.
Complex formation such as [CdI4]-2 , [FeCl6]-4 shows the cation
migrating towards anode instead of cathode. Hence, such ions shows
–ve transport no. value.
Consider solution of CdI2
CdI2 Cd+2
+ 2 I-
CdI2 + 2 I-
[CdI4]-2
If anion [CdI4]-2 moves faster than cation Cd+2 , then there will be an
increase in concentration of Cd around anode instead of decrease.
Therefore value of transport no. of Cd+2 ion will become abnormal at
high concentration.
************