Faraday’s laws and applications of Kohlrausch’s laws
Ramana Murthy. P
Introduction
 Electrochemistry is a branch of chemistry that studies chemical reactions which take place in
a solution at the interface of an electron conductor (a metal or a semiconductors) and an ionic
conductor (the electolyte), and which involve electron transfer between the electrode and the
electrolyte or species in solution.
 Alessandro Volta's discovery, in 1793, that electricity could be produced by placing two
dissimilar metals on opposite sides of a moistened paper.
 In 1800, Nicholson and Carlisle, using Volta’s primitive battery as a source, showed that an
electric current could decompose water into oxygen and hydrogen.
 By 1812, the Swedish chemist Berzelius could propose that all atoms are electrified, hydrogen
and the metals being positive, the nonmetals negative.
 Humphry Davy prepared the first elemental sodium by electrolysis of a sodium hydroxide
melt.
 Michael Faraday, to show that there is a direct relation between the amount of electric charge
passed through the solution and the quantity of electrolysis products
 Chemical reactions where electrons are transferred between molecules are called
oxidation/reduction (redox) reactions. In general, electrochemistry deals with situations where
oxidation and reduction reactions are separated in space or time, connected by an external
electric circuit to understand each process.
Electron Transfer Reactions
 Electron transfer reactions are oxidation-reduction or redox
reactions.
 Results in the generation of an electric current (electricity) or be
caused by imposing an electric current.
 Therefore, this field of chemistry is often called
ELECTROCHEMISTRY.
Terminology for Redox Reactions
 OXIDATION :loss of electron(s) by a species; increase in
oxidation number; increase in oxygen.
 REDUCTION: Gain of electron(s); decrease in oxidation
number; decrease in oxygen; increase in hydrogen.
 OXIDIZING AGENT: Electron acceptor; species is reduced.
 REDUCING AGENT: Eelectron donor; species is oxidized.
OXIDATION-REDUCTION REACTIONS
Direct Redox Reaction
Oxidizing and reducing agents in direct contact.
Cu(s) + 2 Ag+(aq) ---> Cu2+(aq) + 2 Ag(s)
Why Study Electrochemistry?
• Batteries
• Corrosion
• Industrial production of chemicals
such as Cl2, NaOH, F2 and Al
• Biological redox reactions
The heme group
Classification of Conductors
 These may be divided into three main categories; they are:
(I) gaseous (II) metallic or electronic (III) electrolytic.
 Gases conduct electricity with difficulty and only under the influence of high potentials or if
exposed to the action of certain radiations.
 Metallic or electronic conductors : Conductors which transfer electric current by transfer of
electrons, without transfer of any matter, are known as metallic or electronic conductors. Metals
such as copper, silver, aluminum, etc., non-metals like carbon (graphite - an allotropic form of
carbon) and various alloys belong to this class.
 Electrolytic conductors : (a) Conductors like aqueous solutions of acids, bases and salts in which
the flow of electric current is accompanied by chemical decomposition are known as electrolytic
conductors.
b)The substances whose aqueous solutions do not conduct electric current are called nonelectrolytes. Solutions of cane sugar, glycerine, alcohol, etc., are examples of non-electrolytes.
Fig. 1. Illustration of electrochemical terms
Mechanisam of electrolytic conduction and electrolysis
H+ + 2e2Cl- - 2e-
2NaCl(aq) + 2H2O(l)
H2 (hydrogen gas at the (-)cathode).
Cl2 (chlorine gas at the (+)anode).
The overall reaction is
2Na+(aq) + 2OH-(aq) + Cl2(g)+ H2(g)
Electrolysis of sodium chloride solution
NaCl ↔ Na+ + ClH2O ↔ H+ + OHAt cathode
H+ + e- → H
2H → H2
At Anode
Cl- → Cl + e2Cl → Cl2
Electrolysis of copper sulphate solution using platinum electrodes
CuSO4 ↔ Cu2+ + SO42H2O ↔ H+ + OHAt cathode
At Anode
Cu2+ + 2e- → Cu
2OH- → H2O + O + 2eO + O→O2
Some more examples of electrolysis
Electrolyte
Electrode
Cathodic reaction
Anodic reaction
Aqueous acidified CuCl2
Pt
Cu2+ + 2e-→ Cu
2Cl
→
Molten PbBr2
Pt
Pb2+ + 2e- → Pb
2br
→
Br2 + 2e-
Sodium chloride solution
Hg
2Na+ + 2e-→2Na
2Cl-
→
Cl2 +
Silver nitrate solution
Pt
Ag+ + e-→Ag
2OH-
→ 1/2 O2 + H2O + 2e-
Sodium nitrate solution
Pt
2H+ + 2e- → H2
2OH-
→ 1/2 O2 + H2O + 2e-
Cl2
+2e-
2e-
The decreasing order of discharge potential or the increasing order of deposition of some of the
ions is given below:
For cations: K+, Na+, Ca2+, Mg2+, Al3+, Zn2+, H+, Cu2+, Hg2+, Ag+
For anions: SO42-, NO3-, OH-, Cl-, Br-, I-
TABLE OF STANDARD
REDUCTION
POTENTIALS
oxidizing
ability of ion
Eo (V)
Cu2+ + 2e-
Cu
+0.34
2 H+ + 2e-
H2
0.00
Zn2+ + 2e-
Zn
-0.76
To determine an oxidation
from a reduction table, just
take the opposite sign of the
reduction!
reducing ability
of element
Faraday’s laws of electrolysis
 The laws, which govern the deposition of substances (In the form of ions) on
electrodes during the process of electrolysis, is called Faraday's laws of electrolysis.
These laws given by Michael Faraday in 1833.
 Faraday's first law: It states that, the mass of any substance deposited or liberated
at any electrode is directly proportional to the quantity of electricity passed.
WαQ
W = Mass of ions liberated in gm,
Q = Quantity of electricity passed in Coulombs
= Current in Amperes ( i ) × Time in second (t)
Wαit
W=Zit
Where, Z = constant, known as electrochemical equivalent (ECE) of the ion deposited
 Faraday's second law: It states that, when the same quantity of electricity
is passed through different electrolytes, the masses of different ions
liberated at the electrodes are directly proportional to their chemical
equivalents (Equivalent weights).

WαE
W1/W2 = E1/E2 or Z1it / Z2it or Z1/Z2 = E1/E2
(W = Zit)
E α Z or E = FZ or E = 96500 × Z
 Faraday's law for gaseous electrolytic product for the gases, we use V = It
Ve/96500
Where, V = Volume of gas evolved at S.T.P. at an electrode
Ve = Equivalent volume = Volume of gas evolved at an electrode at S.T.P. by
1 Faraday charge
conductance and its measurement
Ohm’s law
 Metallic as well as electrolytic conductors obey Ohm’s law which states the
strength of current (I) flowing through a conductor is directly proportional
difference (V) applied across the conductor and is inversely proportional to
the resistance (R ) of the conductor
I = V/R
R - Resistance in V/A = Ω (Ohm)
V - Voltage or potential difference in Volts, V
I - Current in Amperes, A
If a material has a resistance of 1 Ω, it means that when applying a potential
difference of 1 V, the current in the material is 1 A.
For metals:
Ohm’s Law
R = V/I
R: resistance
Dimension: Ohm, 
Conductance is the ability of a material to pass electrons
C=1/R
Specific conductance or conductivity
 The resistance of any conductor varies directly as its length (l) and
inversely as its cross sectional area (a), i.e.,
R α 1/a or R = ρ 1/a , Here ρ = specific resistance
If l = 1 cm and a = 1 cm2, then
R=ρ
Κ= 1/ρ, Κ = kappa - the specific conductance
ρ = a/l. R or 1/ρ = 1/a.1/R
K = 1/a×C (1/z = cell constant)
Specific conductance = cell constant x Conductance
The unit of specific conductance is ohm-1 cm-1.
Specific conductance or conductivity
-
+
-
anode
Solution
Cathode
+
1c
m
1c
m
Representation of specific conductance
 Specific conductance depend on the nuber of ions present in unit volume
(1 ml ) solution
Equivalent conductance (/\)
 To understand the manning of equivalent conductance, imagine a
rectangular trough with two opposite sides made of metallic conductor
(acting as electrodes) exactly 1 cm apart, If 1 cm3 (1 mL) solution
containing 1 gram equivalent of an electrolyte is places in this container is
measured.
/\ = KV
 In case, if the concentration of the solution is c g equivalent per litre, then
the volume containing 1 g equivalent of the electrolyte will be 1000/C.
So equivalent conductance
/\ k 1000/c
/\ = k × 1000/N
Where N = normality
The unit of equivalent conductance is ohm-1 cm-2 equi-1.
 One of the factors on which the conductance of an electrolytic solution depends
is the concentration of the solution. In order to obtain comparable results for
different electrolytes, it is necessary to take equivalent conductances.
 Equivalent conductance is defined as the conductance of all the ions produced
by one gram equivalent of an electrolyte in a given solution.
1 cc
m
1c
1 cm
Representation of Equivalent conductance
Molar conductance
 The molar conductance is defined as the conductance of all the ions
produced by ionization of 1 g mole of an electrolyte when present in V mL
of solution. It is denoted by.
Molar conductance
Λ m = k ×V
Where V is the volume in mL containing 1 g mole of the electrolyte. If c is
the concentration of the solution in g mole per litre, then
Λ m = k × 1000/c
It units are ohm-1 cm2 mol-1.
 Equivalent conductance = (Molar conductance)/n
Where
n = (Molecular mass) / (Equivalent mass)
Effect of dilution on equivalent conductance
Conductance’s of electrolytes of different type
Kohlrausch’s law of independent ionic mobilities
At time infinite dilution (m) , the molar conductivity of an electrolyte can be
expressed as the sum of the contributions from its individual ions
Λ∞m = v+ λ∞ + + v- λ∞v+ and v- are the number of cations and anions per formula unit of electrolyte
respectively and, λ∞+ and λ∞- are the molar conductivities of the cation and
anion at infinite dilution respectively
Applications of Kohlrausch's law
 Determination of Λ∞m for weak electrolytes
 Determination of the degree of ionization of a weak electrolyte
 Determination of the ionization constant of a weak electrolyte
 Determination of the solubility of a sparingly soluble salt
Determination of Λ∞m for weak electrolytes
 The molar conductivity of a weak electrolyte at infinite
dilution (Λ∞m) cannot be determined by extrapolation
method. However, Λ∞m values for weak electrolytes can be
determined by using the Kohlrausch's equation.
Λ∞CH3 COOH = Λ∞CH3COONa + Λ∞HCI - Λ∞NaCI
Determination of the degree of ionization of a weak electrolyte
 The degree of ionization is given by
ac = Λcm /Λ∞m = Λcm / ( v+ λ∞+ + v- λ∞- )
Thus, knowing the value of Λcm, and Λ∞m (From the Kohlrausch's
equation), the degree of ionization at any concentration (ac) can be
determined.
Determination of the ionization constant of a weak electrolyte
( K ) = C(Λcm / Λ∞m )2 / [ 1 - ( Λcm / Λ∞m )] = C(Λcm)2 / Λ∞m - Λcm ) We
know Λ∞m and Λcm at any concentration, the ionisation constant (K) of the
electrolyte can be determined.
Determination of the solubility of a sparingly soluble salt
 the molar conductivity of a sparingly soluble salt at infinite dilution
Λ∞m = V+λ∞+ + V-λ∞Λ∞salt = 1000 ksalt / Cm
Cm = 1000 ksalt / ( V+λ∞+ + V-λ∞- ),
Cm is the molar concentration of the sparingly soluble salt in its
saturated solution.
Thus,Cm is equal to the solubility of the sparingly soluble salt in the
mole per litre units. The solubility of the salt in gram per litre units can
be obtained by multiplying Cm with the molar mass of the salt.
Zn --> Zn2+ + 2e-
Cu2+ + 2e- --> Cu
Oxidation
Anode
Negative
Reduction
Cathode
Positive
<--Anions
Cations-->
•Electrons travel thru external wire.
•Salt bridge allows anions and cations to
move between electrode compartments.
RED CAT
Charging a Battery
When you charge a battery, you are
forcing the electrons backwards (from
the + to the -). To do this, you will
need a higher voltage backwards than
forwards. This is why the ammeter in
your car often goes slightly higher
while your battery is charging, and
then returns to normal.
In your car, the battery charger is
called an alternator. If you have a
dead battery, it could be the
battery needs to be replaced OR
the alternator is not charging the
battery properly.
H2 as a Fuel
Cars can use electricity generated by H2/O2 fuel cells.
H2 carried in tanks or generated from hydrocarbons