ELECTRO CHEMISTRY-1
(Fourth semester)
Part-2
Topics covered




Debye-Huckel-Onsager Theory
Kohlrausch’s law and its applications
Migration of ions
Transport number and determination of transport number by Hittorf’s
method
 Applications of conductivity measurements
T.BALAJI
LECTURER IN CHEMISTRY
Department of Chemistry
SVCR Govt. Degree College, Palamaner
Email:balu2185@gmail.com
Debye-Huckel -Onsager Theory
According to Debye - Huckel –Onsager theory of strong electrolyte,
1. All strong electrolytes completely ionize even in solid state
2. In solid state, the ions are not free to move. The ions become mobile either in molten state or in the
state of solution.
3. The mobility of the ions depends up on viscosity of medium and number of solvent molecules
attached to each ion (salvation).
4. The increase in equivalent conductance of strong electrolytes on dilution is due to increase in the
mobility of ions.
5. A strong electrolyte completely dissociates even at a lower dilution, but equivalent conductivity is
low because of the low mobility of ions at lower dilution.
6. The inter-ions attractions which reduce the mobility of the ions are due to
a. Relaxation Effect
b. Electrophoretic effect
Relaxation Effect :( Asymmetry effect)
Each ion in an electrolyte solution is surrounded by an
atmosphere of oppositely charged ions. When electric
field is not applied, the ionic atmosphere is
symmetrical. On application of the electric field the
central positive ion will move towards cathode, while
its negatively charged ions move towards anode. As a
result, the symmetry of the ionic atmosphere is
destroyed and becomes asymmetrical ionic
atmosphere. In the rear (back) of the moving ion, there will be an excess of negatively charged ions.
Therefore, the central positive ion which is moving experiences a backward pull. The effect thus
decreases the mobility of ion and this effect is known as “Asymmetric effect”. It is also called
relaxation effect because it takes some time to form a new ionic atmosphere.
Electrophoretic effect:
The ionic atmosphere of a central ion always remains associated with solvent molecules. The ionic
atmosphere is oppositely charged with respect to the central ion. When electric field is applied, a
cation migrates towards cathode through medium, while the negatively charged ionic atmosphere
along with solvent molecules moves towards anode. These counter movements causes a retarding
influence on the movement of the central ion. This effect is known as “Electrophoretic effect”.
Debye-Huckel-Onsager equation:
Debye-Huckel mathematically worked on the magnitude of asymmetry effect and Electrophoretic
effect and derived the equation.
=
Where, ε= dielectric constant of the medium
T=temperature of the medium
This in its simplest form can be written as
=
Where, A is a constant which is a measure of Electrophoretic effect
B is a constant which is a measure of the relaxation effect.
C is concentration in gm.eq/lit
Kohlrausch’s law
Kohlrausch’s law:
 According to Kohlrausch’s law, at infinite dilution, when dissociation is complete, each ion makes
a definite contribution towards equivalent conductance of an electrolyte irrespective of the nature of
the other ion with which it is associated.
 According to Kohlrausch’s law, at infinite dilution, the equivalent conductance at infinite dilution
(λ∞) for any electrolyte is the sum of equivalent conductance for the cation (λc) and anion (λa).
This is Kohlrausch’s law.
Applications of Kohlrausch’s law:
1) Determination of equivalent conductance at infinite dilution for weak electrolytes: λ∞ for weak
electrolytes can be determined from known λ∞ values of strong electrolytes. λ∞ for acetic acid can
be obtained from the λ∞ values of HCl ,NaCl and CH3COONa.
= λ∞ (HCl) ̶ λ∞ (NaCl) + λ∞ (CH3COONa)
=λ∞(H+) + λ∞(Cl͞ ̶ ) ̶ λ∞(Na+) ̶ λ∞(Cl͞ ̶ ) + λ∞( CH3COO ̶ ) +λ∞(Na+)
= λ∞ (H+) + λ∞ (CH3COO ̶)
= λ∞ (CH3COOH)
2) Determination of degree of dissociation (α) of weak electrolyte:
Degree of dissociation,
As per Kohlrausch’s law, λ∞= λc + λa. From the known values of λ∞ and λv, degree of dissociation
of weak electrolytes can be calculated.
3) Determination of dissociation constant (K) of weak electrolyte:
According to Ostwald’s dilution law, dissociation constant is given by,
where,
The value of λ∞ for a weak electrolyte can be calculated from Kohlrausch’s law and thus
dissociation constant (K) of weak electrolyte can be determined.
Migration of ions



All electrolytes are fully dissociated at infinite dilution, but their equivalent conductance is
different. This is due to the differences in the speed of ions.
Ex: Equivalent conductance of HCl is three times more than NaCl at infinite dilution, because
the speed of H+ ion is three times more than that of Na+ ion.
The speed of ion changes with the applied electric potential. The term “Ionic mobility” is used
instead of the speed of ion.
Ionic mobility: The distance travelled by an ion per second when a potential gradient
of 1volt per cm is applied is called “Ionic mobility”
Transport number or Transference number
 Transport number of an ion is defined as the fraction of total current carried by that ion.
 Transport number of cation,
 The current carried by an ion is proportional to speed of ion (u)
Transport number of cation,
Transport number of anion,
Where,
and
= speed of cation and anion.

The sum of transport number of cation and anion of an electrolyte is always unity. So if the
transport number of cation is known, then transport number of anion can be calculated.
 Fall in concentration around any electrode is proportional to the speed of that ion which moves
away from it.
Transport number of cation,
Transport number of cation,
Determination of Transport number by Hittorf’s Method
 Hittorf’s apparatus consists of two vertical glass
tubes connected through a U-tube in the middle.
 The left hand glass tube contains anode and is
thus called anodic compartment. The right hand
glass tube contains cathode and thus called
cathodic compartment.
 Each compartment is provided with a stopcock at
the bottom to withdraw the solution.
 U-tube is provided with stop cock at the bottom
and stop cocks at the top of the two limbs to
prevent the intermixing of the solutions in anodic
and cathodic compartment.
 For determining the transport number of Ag+ ion,
the apparatus is filled with a standard solution of AgNO3 and Pt electrodes are used.
 The cell is connected in series with a source of direct current, a variable resistance, copper
voltmeter (coulometer).For electrolysis 10-20 mA of current is passed for 2-3 hours, During the
passage of current, the two stop cocks at the top of the U- tube are kept open and then closed when
current has been passed for 2-3 hours.
 The whole liquid in the anode compartment is drained into a weighed flask and its weight is
determined. The content of silver in the anode liquid is determined by titration.( change in
concentration is determined)
 The weight of Ag deposited in voltmeter is also noted, as it gives the measure of the total fall in
concentration around anode and cathode.
Calculation:Before the Experiment
after the Experiment
 Weight of anode solution= a g
Weight of anode solution = c g
 Weight of AgNO3 in solution=b g
Weight of AgNO3 in solution = d g
 Weight of water = (a-b) g
Weight of water = (c-d) g
 (a-b)g of water is associated with b g of AgNO3 (c-d) g of water is associated with d g of AgNO3
1g of water is associated with
(a-b) g of water is associated with
g of AgNO3
g of AgNO3
= x g of AgNO3
 Weight of Ag deposited in voltmeter = W g
 Fall in concentration of AgNO3 in anode compartment = (b-x) g
We know that, 170 g of AgNO3 is associated with 108 g of Ag
1 g of AgNO3 is associated with
g of Ag
(b-x) g of AgNO3 is associated with
g of Ag = w g
Fall in concentration of Ag+ around anode = w g



Applications of conductivity measurements
1. Determination of degree of dissociation: The degree of dissociation of a weak electrolyte can be
determined by using the equation,
Where,
and
= Equivalent conductance at given dilution and infinite dilution.
2. Determination of dissociation constant: The conductivity measurements help in the
determination of dissociation constant (K) of weak acids. From Ostwald’s dilution law, dissociation
constant is given by,
Where,
3. Conductometric titrations:
 Titrations in which end-point is determined by means of conductance measurements are called
Conductometric titrations.
 In Conductometric titrations, the titrant is added from the burette and the conductance is recorded
during the course of titration and plotted against the volume of the titrant added. Two straight lines
will be obtained which will intersect at a point called “end point”.
Advantages of Conductometric titrations:
 These titrations are very convenient for colored solution where the use of indicator is not possible.
 No observation is required near the end point as it is detected graphically.
D. Titration of weak acid with a weak base
CH3COOH + NH4OH
CH3COO¯ NH4+ + H2O
 Initial conductance of CH3COOH solution is low because it is
Weak acid. Addition of NH4OH, increases the conductance upto
End point due to increase in concentration of (CH3COO¯ NH4+).
 Beyond end point, further addition of poorly ionized NH4OH
Solution does not cause any appreciable change in conductance.
Volume of NH4OH
Conductance
C. Titration of weak acid with a strong base
CH3COOH + Na+OHCH3COO¯ Na+ + H2O
 Initial conductance of CH3COOH solution is low because it is
Weak acid. Addition of NaOH, increases the conductance up to
End point due to increase in concentration of CH3 COO¯ Na+
 Beyond end point, further addition of NaOH results in the
Increase of conductance due to increase in number of Na+ ions
And fast moving OH¯ ions than CH3COO¯.
End point(Vb)
End point(Vb)
Volume of NaOH
Conductance
B. Titration of strong acid with a weak base
H+Cl- + NH4OH
NH4+ Cl- + H2O
 The initial conductance of HCl solution is high due to highly
Mobile H+ ions. On addition of NH4OH solution, the conductivity
Of solution decreases up to end point, because H+ ions are replaced
By slow moving NH4+ ions
 Beyond end point, further addition of poorly ionized NH4OH
Solution does not cause any appreciable change in conductance.
Conductance
Conductance
Examples:
A. Titration of a strong acid with a strong base
 A measured volume of strong acid (HCl) is taken in the
Conductivity beaker and a strong base solution (NaOH) is
Added from a burette.
H+Cl- + Na+OHNa+Cl- +H2O
 The initial conductance of HCl solution is high due to highly
Mobile H+ ions. On addition of NaOH solution, the conductivity
Of solution decreases up to end point, because H+ ions are replaced
End point(Vb)
+
+
By slow moving Na ions and H ions are removed by added OH
Volume of NaOH
To form non-conductivity H2O molecule.
 Beyond end point, further addition of NaOH results in the increase
Of conductance due to increase in number of Na+ ions and fast moving OH- ions.
 The plot of conductance of solution versus volume of base added gives two lines which intersect
at end-point( Vb).By using the principle, NaVa=NbVb one can calculate the unknown
concentration of HCl solution (Na).
End point(Vb)
ALL THE BEST
Volume of NH4OH