FACULTY OF SCIENCE EDUCATION
DEPARTMENT OF CHEMISTRY EDUCATION
CHE361:ELECTROCHEMISTRY
LECTURER: TWUMASI A. KWARTENG
MIGRATION OF IONS IN SOLUTION
conduction and under what conditions?
Electronic conduction is in metals under any condition of state.
Electrolytic conduction on the other hand is carried out by compounds, called electrolytes
either in solution or molten state. All electrolytes are ionic compouConduction of electric
current takes two main forms.
Activity: What are these forms? Name and define each of them.
If you are correct, the answer to the first part of the question should be;
 Electronic conduction and Electrolytic conduction
In terms of definitions you are correct if you say;
 Electronic conduction is the ‘flow’/passage of electric current by stream of
electrons
 Electrolytic conduction is the ‘flow’/passage of electric current by the movement of
ions.
Activity: What types of substances undergo these types of nds.
MIGRATION OF IONS IN SOLUTION
What is electrolyte?
An electrolyte is a substance that produces an electrically conducting solution
when dissolved in a polar solvent, such as water. The dissolved electrolyte
separates into cations and anions, which disperse uniformly through the solvent.
Types of electrolyte
 Strong electrolyte : They completely dissociate to their ions when dissolved in
solution.
Weak electrolyte :A weak electrolyte only partially dissociates in solution and
produces relatively few ions (exist in water as a mixture of individual ions and in
contact molecules).
 Non-electrolyte: A non-electrolyte does not dissociate at all (present entirely as
intact molecules) in solution and therefore does not produce any ions.
MIGRATION OF IONS IN SOLUTION
Activity: What are the sources of ions in a solution or molten state of an electrolyte?
Usually, most beginners think that the ions in solution or molten state came about as a result of the
passage of the current, but RPK tells us that, ions are present in ionic compounds even in the solid
state except that they are not mobile.
Activity
How many types of ions are in an electrolytic cell and how do they bring
about electrical conduction?
There are two types of ions in an electrolytic cell. These are
(a) cations and
(b) anions.
They bring about conduction by flowing or migrating towards their respective
electrodes in the cell. The cations being positively charged, move towards the
cathode while the anions, being negatively charged, move towards the anode.
Thus electrolytic conduction is by way of the movement of ions towards the
electrodes. This conduction of current through an electrolytic cell obeys Ohms law,
which states that; (students to state the law)
MIGRATION OF IONS IN SOLUTION
The current (I) passing through the cell is directly proportional to the potential
difference between the electrodes(V)’.
Mathematically, this can be represented as: (let students try it out)
IαV
It follows that V⁄ I = q (a constant) (what is the name given to this q?)
Again from RPK, you would recall that this q is called the resistance (R), thus;
R=V⁄I
We also know that R = pl ⁄A, where p (rho) = resistivity, l = length and A = cross
sectional area of conductor. l ⁄A = cell constant
Conductivity, molar conductivity and concentration
The current (I) passing through the cell is directly proportional to the potential
difference between the electrodes(V)’.
Mathematically, this can be represented as: (let students try it out)
IαV
It follows that V⁄ I = q (a constant) (what is the name given to this q?) ,
Again from RPK, you would recall that this q is called the resistance (R), thus;
R=V⁄I
We also know that R = pl ⁄A,
Where: p (rho) = resistivity, l = length and A = cross sectional area of conductor.
l ⁄A = cell constant=G*
Conductivity, molar conductivity and concentration
Activity:
What is (i) conductance and (ii) conductivity?
Conductance is the reciprocal of resistance while conductivity ĸ (kappa) is
the reciprocal of resistivity. Thus;
ĸ = 1 ⁄p
from previous relationship, we know that;
ĸ = l ⁄AR, and
Molar conductivity Ʌ (lambda) is defined by the equation;
Ʌ = ĸ ⁄c where ĸ = conductivity in Ω-I m-I and c = concentration in mol m-3
From the above molar conductivity becomes numerically equal to the
conductivity if concentration is 1 mol m-3.
Example 1
Molar conductivity of 0.005 M KCl is 144 Scm2
mol-1. Calculate its electrolytic conductivity in SI
units (Sm-1).
*(Hint: 1m2 = 104 cm2; mol/L or mol/dm3 convert to
mol m-3).
Conductivity, molar conductivity and concentration
Activity: What is the unit of the molar conductivity? Students to provide answer.
Bear in mind that, if you know the cell constant of a given cell and can measured its resistance,
then you must be able to calculate the conductivity (k) and hence the molar conductivity. Once
measured, the cell constant of a cell is fixed as long as the physical dimensions of the cell are not
changed in any way. This is done by fixing the electrodes in the cell rigidly in their respective
positions. Though the cell constant can be obtained from the cell dimensions, it is usually
measured using a solution such as 0.1M KCl, whose conductivity is known.
The conductivity of a solution is measured in a cell called conductance cell or conductivity
cell.
  1  l 
R  A 
Since l and A are difficult to measure, the usual procedure is to treat
constant, G*.
l
A
as a cell
Example 2
In a certain conductivity cell, the resistance of a 0.01 M
KCl solution is 150 . The known molar conductivity of the
solution is 141.27 -1 cm2 mol-1. Calculate the cell constant
(G*cell unit iscm-1).
• Exercise 3
Using the same conductance cell as in example 2, a
student measured the resistance of a 0.10 M NaCl solution
to be 19.9 .
• Calculate the experimental value of the molar conductivity
of this solution.
Conductivity, molar conductivity and concentration
Activity: What is the unit of the molar conductivity? Students to provide answer.
Bear in mind that, if you know the cell constant of a given cell and can measured its resistance,
then you must be able to calculate the conductivity (k) and hence the molar conductivity. Once
measured, the cell constant of a cell is fixed as long as the physical dimensions of the cell are not
changed in any way. This is done by fixing the electrodes in the cell rigidly in their respective
positions. Though the cell constant can be obtained from the cell dimensions, it is usually
measured using a solution such as 0.1M KCl, whose conductivity is known.
Activity: (a) What is meant by the term ‘cell constant’ and for what purpose is it used?
(b) If the resistivity of 0.1M KCl solution is 361 ohms cm, and the conductivity cell
containing the solution has a resistance of 550 ohms, calculate the cell constant.
(c)
Assuming that the same cell when filled with 0.1M ZnSO4 solution, had a
resistance of 72 ohms, determine the conductivity of this solution.
Activity: What is the relationship between the molar conductivity of a solute and its
concentration?
ASSIGNMENT
In order to determine the molar conductivity ofa
0.05 M solution of AgNO3, you need to measure the
solution resistance in aconductivity cell and
found that R = 75.8 .Then, in the same cell,a
0.02 M KCl solution had aresistance of 157.9 .
Given that the accepted molar conductivity of the KCl
solution is 0.013834 -1 m2mol-1, calculate the molar
conductivity of the AgNO3 solution.
Conductivity, molar conductivity and concentration
Electrical conductance through metals is called metallic or electronic
conductance and is due to the movement of electrons. The electronic
conductance depends on:
(i) the nature and structure of the metal
(ii) the number of valence electrons per atom
(iii) temperature (it decreases with increase of temperature).
Conductivity, molar conductivity and concentration
The conductance of electricity by ions present in the solutions is called
electrolytic or ionic conductance. The conductivity of electrolytic (ionic)
solutions depends on:
(i) the nature of the electrolyte added
(ii) size of the ions produced and their solvation
(iii) the nature of the solvent and its viscosity
(iv) concentration of the electrolyte
(v) temperature (it increases with the increase of temperature).
Conductivity, molar conductivity and concentration
• The molar conductivity of a solute depends on its concentration.
From the equation that links then, molar conductivity is expected to
increase as concentration decreases (with dilution).
But is this
always true?
• In reality, when values of lambda are plotted against the volume of
solution containing 1 mole of solute (dilution), the graphs obtained
for different electrolytes fall into two categories.
Conductivity of electrolytes
MOLAR CONDUCTIVITY AND CONCENTRATION
The two categories of electrolytes identified by the graphs were;
(a) strong electrolytes
and
(b) weak electrolytes. (let students define them)
Strong electrolytes which are those completely ionised in solution, gave the graph
with the shape which swiftly rises to a maximum. This maximum value is called the
molar conductivity at infinite dilution (Ʌ∞ or Ʌo), as further dilution has no effect on
its value.
Weak electrolytes which are incompletely ionised in solution, gave the graph with the
shape that increases gradually without any apparent levelling off. Thus their Ʌ value
increases as the solution becomes more and more dilute. Despite this increase in the
Ʌ value with dilution, there is a limit to the range of concentration within which
measurements can be made. This is because, in very dilute solutions, the conductivity
of the solution gradual tend to approach the conductivity of water, making it difficult
to obtain worthwhile values.
MOLAR CONDUCTIVITY AND CONCENTRATION
Activity What reasons can we give for the presence of this behaviour
of the molar conductivities of the electrolyte solutions?
To explain this behaviour, Arrhenius put forward the IONIC
theory.
THE IONIC THEORY
Arrhenius stated his ionic theory as ‘when an electrolyte dissolves, a certain fraction of
it dissociates (ionizes) into positively and negatively charged particles called ions’.
Based on this theory, he explained the shape of the graph shown by weak electrolytes
as arising from an increase in the ionisation of the solute with dilution.
In line with this, Arrhenius suggested that the fraction, α of the solute that is ionised
gradually increases with dilution. He went on to postulate that if measurements could
be extended to even more dilute solutions, α would approach a value of 1, and Ʌ
would level off at a maximum value, Ʌo. This value of degree of ionisation at any
concentration, known as the conductivity ratio, is expressed mathematically as;
α = Ʌ / Ʌo
With regard to the shape shown by strong electrolytes, he suggested that strong
electrolytes are completely ionised in solution, except at very high concentrations.
(Is this true?)
Thus, though this theory at the time helped to explain a lot about electrolysis and
electrolytic conduction, it was found wanting in other aspects.
Conductivity of electrolytes
Activity:
Is it true that ions exist? What evidence(s) can you put forward to
support your answer? (students should do this for a change, especially the
‘spectators’)
Many evidences can be deduced to support the existence of ions. Some of these
are from;
 Electrolysis
 Ohm’s law
 Faraday’s laws
 ΔH0 of neutralization (strong acids and bases)
 The increase in Ʌ with dilution.
 Chemical properties
 X- ray crystallography
THE DEBYE – HÜCKLE (ONSAGER) THEORY
The last of the evidences for the existence of ions put Arrhenius ionic theory at a
disadvantage with regard to the explanation for the levelling of the conductivity of strong
electrolyte solutions with dilution. This is because x-ray crystallography which was not
available at the time Arrhenius was putting forward his theory, reveals the existence of ions
in salts even in the solid state.
Activity
What then is responsible for the shape of the conductivity curve of solutions
of strong electrolytes?
In order to explain the shape of conductivity curve of solutions of strong electrolytes on
dilution, Debye and Huckle (1923) as well as Onsager (1927), modified the ionic theory as
presented by Arrhenius. According to them, ‘strong electrolytes are always completely
ionised in solution’. In line with this modification, the low conductivity of concentrated
solutions of strong electrolytes was explained in terms of the electrical forces (ionic
interference) between ions.
THE DEBYE – HÜCKLE (ONSAGER) THEORY
Their suggestion was that, the low value for the molar conductivity of strong
electrolytes at high concentrations is not as a result of low number of ions in the
solution as suggested by Arrhenius, but was due to the fact that ions move more
slowly in concentrated solutions.
Activity : What makes ions to move more slowly in concentrated solutions of strong
electrolytes?
In concentrated solutions, ions are closer together than in dilute solutions. Because of
this, the electrical forces between ions are greater. Since unlike charges attract and like
charges repel, cations would have more anions than cations and vice versa in their
immediate environment. It is this attractive force between ions of opposite charges
that reduces their velocity, thereby resulting in the low value for molar conductivity.
MINI QUIZ ( 20 Minutes)
1.
2.
3.
Explain the following terms;
(a) electrolytic conductivity
(b) molar conductivity of an electrolyte
Do ions exist? Explain your answer based on just five
evidences.
(a) Give a diagrammatic sketch of the plot of molar
conductivity
dilution verses for 1 mole each of aqueous
solutions of
ammonium nitrate and ammonia.
(b) Which of them have a constant value for lambda over a
wide
range of dilution? Explain.
(c) Explain what gave rise to the low values of lambda at high
concentration
MOBILITY, TRANSPORT NUMBERS AND ITS MEASUREMENT
Kohlrausch, in his study of conductivity, observed certain interesting relations between the
values of Ʌo for different electrolytes; the difference in Ʌo for pairs of salts having a common
ion was always almost approximately constant. For example, at 25 oC;
Ʌo
NaAOc
HCl
91.0
425.0
From the above, it is clear that, no matter what the ion may be, there is almost an
approximate constant difference between the conductivities of sodium and potassium salts.
This behaviour is easily explained if Ʌo is taken to be the sum of two independent entities, one
characteristic of the cation and the other of the anion. Thus;
Ʌo = λo+ + λowhere λo+ and λo- are the molar ionic (equivalent) conductivities at infinite dilution.
MOBILITY, TRANSPORT NUMBERS AND ITS MEASUREMENT
This relationship is known as Kohlrausch’s law of the independent migration of ions. It
states that, ‘the molar conductivity at zero concentration of an electrolyte, is equal to
the sum of the molar ionic conductivities at zero concentration of the ions produced
by the electrolyte.
This makes it possible to calculate the Ʌo values for weak electrolytes such as organic
acids from values for their salts which are strong electrolytes. As an example, at 25 oC ;
Ʌo(HAc) is given by;
Activity:
What would be the molar conductivity of acetic acid from available
data above?
Ʌo(HAc) = Ʌo(NaAc) + Ʌo(HCl) - Ʌo(NaCl)
= 91.0 + 425.0 – 128.1
= 387.9