Physical Chemistry
ELECTROCHEMISTRY
PRINCIPLES, MEASUREMENTS, &
APPLICATIONS
PART 3
ELECTROLYSIS
Ohm’s Law Revisited
I=
ξ
R
where
I = strength of a current [ampere, A]
R = resistance [ohm]
ξ = applied potential [Volt]
Ohm’s Law Revisited
Charge carried by a current
Q = It
where
I = strength of a current
t = time
Unit of Q is Coulomb, C.
1 C = 1 A.s
1 Faraday = 96,490 absolute Coulombs
Ohm’s Law Revisited
The electrical work performed
w = ξIt = ξQ
The rate of electrical work
p = ξI =
ξQ
t
1 J = 1 C.V
1 C = 1 A.s
1 Watt = 1 J/s
Electronic Conduction
• Conduction takes place by direct migration of
electrons through the conductor under the
influence of an applied potential.
“Atoms or ions composing the conductor
are not involved in the process, and except
for a vibration about their mean positions
of equilibrium.”
Electrolytic Conduction
• Electron transfer takes place via migration of
ions, both positive and negative, toward the
electrodes.
“Migration involves a transfer of electricity
from one electrode to another as well as a
transport of matter from one part of the
conductor to another.”
Resistance of electronic conductors increases with temperature, while that of electrolytic conductors always
decreases with increasing temperature.
Electrolytic Conduction
-
Na+
H
ClH+
OHCathode
B
+
Na+
Cl- Cl
Na+
Cl-
H+
OHAnode
Electrolysis – the process of current passage through an electrolytic conductor with all the
accompanying chemical and migratory changes
Mechanism of electrolysis:
(a) Electrons enter and leave the solution through chemical changes at the electrodes
(b) Electrons pass through the solution by migration of ions
Faraday’s Laws of Electrolysis
The mass of a substance involved in
reaction at the electrodes is directly
proportional to the quantity of
electricity
passed
through
the
solution.
The masses of different substances
produced during the electrolysis are
directly
proportional
to
their
equivalent weights.
Transference &
Transference Number
• The fraction of the total current carried by the ions
Current carried by the cations
n+ v+ z + e
I+ =
d
Where
n+ = number of cations
v+ = velocity of the cation in the solution [cm/s]
z+ = charge of the cation
e = quantity of electricity associated with a unit charge [Volts]
d = separation distance of the two plates
Current carried by the anions
n− v− z − e
I− =
d
Where
n- = number of anions
v- = velocity of the anion in the solution [cm/s]
z- = charge of the anion
Transference &
Transference Number
Total current carried by both ions, I
n+ v+ z + e + n− v− z − e
I = I− + I+ =
d
But the condition for electroneutrality of the solution demands that
n+ z + = n− z −
Thus,
n+ v+ z+ e + n+ v− z+ e n+ z+ e ( v+ + v − )
I = I− + I+ =
=
d
d
Transference &
Transference Number
The fraction of the total current carried by cations, t+
I+
n+ v+ z + e
v+
t+ =
=
=
I n+ z + e(v+ + v− ) (v+ + v− )
The fraction of the total current carried by anions, t-
I−
n− v− z − e
v−
t− = =
=
I n+ z + e(v+ + v− ) (v+ + v− )
t + v+
=
t − v−
The fraction of the total current carried by
the ions are directly proportional to their
velocities.
Transference &
Transference Number
t + v+
=
t − v−
Hittorf’s Rule
The fraction of the total current carried by the ions are
directly proportional to their velocities.
t+ + t− = 1
Hittorf’s Rule
loss in cation equivalents at anode due to migration t + v+
= =
loss in anion equivalents at cathode due to migration t − v−
Direct consequences of Hitoff’s rule are:
loss in cation equivalents at anode due to migration t +
= = t+
equivalents of current passed
1
loss in cation equivalents at cathode due to migration t −
= = t−
equivalents of current passed
1
Determination of Transference Numbers
a) Hittorf method
b) Moving boundary method
c) Electromotive force method
Typical Transference Setup
Interionic Attraction Theory of Conductance
Debye-Huckel-Onsager Theory of
Conductance
ion in solution is surrounded by an
Each
atmosphere of other ions whose net charge is on the
average opposite to that of the central ion. When the
ions have no external force applied upon them, this
atmosphere is spherically and symmetrically
distributed about the ion. But when an external
force is imposed, as when a potential is applied
across two electrodes immersed in the solution
during conductance, the ions are set in motion, and
as a consequence certain effects and changes in the
ionic atmosphere arise which result in decrease in
the speeds of the ions.
Debye‐Huckel‐Onsager Theory
• The effects are two-fold:
1. The relaxation of the ionic atmosphere due to an applied
potential: due to the difference in the sign of the central ion
and the ionic atmosphere, a potential applied across the
combination will tend to move the central ion in one direction,
the atmosphere in the other
2. The electrophoretic effect: the countercurrent motion of the
positive and negative ions enhances the difficulty of the ions to
move through the solution
Exercises
1.
2.
3.
A direct current of 0.5 ampere flows through a circuit for 10 min,
under an applied potential of 30 V. Find the quantity of electricity
transported by the current. What is the energy dissipation in
watts? Ans. 300 C
When a potential of 110 V DC is applied to the terminals of an
electric lamp, a current of 12 Amp is found to flow. (a) What is
the resistance of the lamp, and (b) how many calories of heat are
dissipated per hour? Ans. (a) 55 ohms and (b) 189,300 cal
A AgNO3 solution containing 0.00739 g of AgNO3 per gram of
H2O is electrolyzed between silver electrodes. During the
experiment 0.078 g of Ag plate out at the cathode. At the end of
the experiment the anode portion contains 23.14 g of H2O and
0.236 g of AgNO3. What are the transport numbers of Ag+ and
NO3- ions? Ans. t+ = 0.47