Table Of ContentOSCILLOMETRY
and
CONDUCTOMETRY
by
E. PUNGOR D.Sc.
Professor of Analytical Chemistry
Technical University
Veszprém
Translated by
T. DAMOKOS
Translation edited by
A. TOWNSHEND
Department of Chemistry
University of Birmingham
PERGAMON PRESS
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Copyright © 1965
Akadémiai Kiadó, Budapest
First edition 1965
Library of Congress Catalog Card No. 64.—17803
In memory of
Prof. Elemér Schulek, D. Sc,
Member of the Academy of Sciences,
who introduced me to scientific work
PREFACE
MONOGRAPHS serve to facilitate the survey of scientific fields
and to evaluate the newer accomplishments therein. In writing
this book, I have not only taken these objects into considera
tion, but I have also included didactical points of view. For
the sake of lucidity — mostly when giving lists of various in
struments — I have restricted myself to the principal types,
not mentioning the numerous variants described in the literature.
It was not my object to mention in the bibliography all the
papers published on high frequency methods, and, more parti
cularly, on conductometry. I selected only those which may
be of importance for those working in the field of oscillometry
and conductometry.
In compiling the bibliography, I have had the valuable assis
tance of L. Balâzs, a University assistant, and K. Szabó, an
undergraduate.
In solving the technical problems that arose while writing
my book, my wife, and Felix Lang, have both given me valu
able help. I am also greatly indebted to Sândor Farkas for carry
ing out the photographic work, and to Mrs. M. Pal for the typing.
I express my sincere thanks to all others who have helped me
in the course of this work.
This book has been written in the hope that it will promote
the further development and use of oscillometry and conducto
metry.
E. PUNGOR
INTRODUCTION
THE conductometric ti trat ion of solutions was one of the first
instrumental methods of analysis to be developed. According
to Kolrausch's law, the ions present in a solution contribute
independently to the electrical conductivity. It is obvious that
the conductivity of the solution changes if the number and
identity of the ions present in the solution are varied during the
titration. Consequently, the titration can be followed by deter
minations of the conductivity of the solution during the expe
riment.
In conductometric titrations, otherwise called conducto-
metry, the conductivity is measured by using electrodes immer
sed in the solution. The correct choice of electrode material,
polarization phenomena, etc. are typical of problems involving
the theoretical principles of conductivity, and hence conducto
metric measurements. Such difficulties are not encountered in the
high-frequency titration, because it is an "electrodeless" method:
there is no galvanic contact between solution and measuring
system. Such titrations have been recently renamed oscillo-
metric titrations. This technique has a number of advantages
over the conductometric method. For example, with properly
chosen parameters, the titration is sensitive and rapid, and the
electrodes need not be made of a noble metal.
In addition, the field of application of the oscillometric me
thods extends far beyond simple titrations. The oscillometric
technique makes possible the examination of liquids contained
in a closed system; for instance, changes with time in the con
tents of sealed ampoules can be followed if the changes cause a
change in conductivity. The method is also readily applicable
XV
xvi INTRODUCTION
for indication in Chromatographie work. Furthermore, the os-
cillometric unit can be a measuring device in an automated
circuit; in this kind of application, however, it is of paramount
importance that variations in the electrode properties with
time, which would render the measurements unreliable, should
not occur.
Not only the conductivity of the various solutions, but ano
ther important property, the dielectric constant, can also be
followed oscillometrically. Consequently, the analytical applica
tion of this technique is greatly extended by the possibility of
ielectric constant measurements.
CHAPTER 1
FUNDAMENTALS
(A) ELECTRICAL CONDUCTIVITY
MATERIALS can be classified as conductors or insulators accord
ing to their degree of conductivity; however, the conductivity
of the latter group is not necessarily zero. Between these two
groups, there exists a continuous transition that represents
the range of semiconductors, that is, poor conductors of electri
city, which are of great importance in connection with modern
electrical techniques.
In metals, electric current is conducted by electrons. The
conductivity of most of the semiconductors and insulators is
brought about similarly.
In the other type of electrical conductivity, electricity is
conducted by particles other than electrons. This is so with
the so-called second order conductors; such conductors are
generally systems in the liquid phase, that is, solutions.
The solvents used for the preparation of solutions are generally
poor conductors. The specific conductivities of a few pure sol
vents are listed in Table 1. As we can see from the table, the con
ductivity of non-polar solvents, as compared with that of the
polar ones, is vanishingly low, in spite of the fact that even the
conductivity of the polar solvents is very low. The conduction
of electricity by a solvent is the result of a form of reaction
taking place in that solvent. The solvent molecules react with
each other, causing "self-dissociation" of the solvent; according
to this, for example, in water, the reaction
2 H 0 ^=± H 0+ + OH" . . . (1.1)
2 3
takes place with the formation of electrically charged particles,
that is, ions. These ions are capable of migration in the solution
3
4 OSCILLOMETRY AND CONDUCTOMETRY
because of an electric field impressed across it. The conductivity
of the liquid is governed by the number and migration velocity
of the ions.
TABLE 1. SOME SPECIFIC CONDUCTIVITIES
Specific
Substance conductivity
(Û"1 cm"1)
Conductivity water 1 x io-6
Pure water, according to Kohlrausch 4-41 x io-8
Ammonium hydroxide 1 x io-7
Methanol 44 x io-«
Ethanol 6-4 x io-»
Propanol 5 X 10-8
Acetone 2 X 10-8
Pentane <2 X 10-1°
Benzene <1 X IO"18
Any material, when dissolved in a solvent, either remains
in the molecular state, or else it undergoes electrolytic disso
ciation. In the latter case, the number of ions is defined by the
degree of dissociation and the concentration of the solute. The
specific conductivities of a few solutions are given in Table 2.
{Specific conductivity is defined as the reciprocal of the resistance
of a cube-shaped conductor of 1 cm2 cross-section and 1 cm
length. Its unit is the reciprocal ohm, designated as mho, or the
Siemens.) In the fourth column of the table, the equivalent
conductivity is also shown. The latter is the product of the dilu
tion of the solution and its specific conductivity.
(B) THE THEORETICAL INTERPRETATION OF
ELECTRICAL CONDUCTIVITY
For the sake of simplicity while giving a theoretical inter
pretation of electrical conductivity, the behaviour of a selected,
single ion in the solution will be considered.
If a potential difference is impressed across the pair of metal
plates immersed in the solution, i.e. across the electrodes, the
ion will move towards the oppositely charged electrode. If there
FUNDAMENTALS 5
TABLE 2. SPECIFIC AND EQUIVALENT CONDUCTIVITY OF SOLUTIONS AT 18°C
Concentration Specific Equivalent
Substance (g. equiv. 1_1) Conductivity Conductivity
(Ω~ι cm"1) (ß-1 cm2 g. equiv.)
1-405 3-948 X IO"1 281-0
2-877 6-302 X 10-1 2191
HC1 6-034 7-615 X IO"1 126-2
9-482 6-620 X IO"1 69-8
1-053 2-075 X IO"1 198-0
2-176 3-915 X 10-1 179-0
4-655 6-527 X IO"1 140-2
H2S04 10-649 6-800 X IO"1 63-8
18-375 3-726 X IO"1 20-27
28-25 1-105 X IO"1 3-91
0-0100 0-00122269 120-3
o-iooo 0-0111919 111-9
1-0000 0-098201 98-2
KC1 1-427 1-359 X IO"1 95-2
2-208 2-020 X IO"1 91-5
3-039 2-677 X IO"1 88-9
3-213 2-810 X IO"1 87-5
0-307 0-0256 83-4
0-641 0-0476 74-3
AgN0 1-407 0-0872 62-0
3
3-477 0-1565 45-0
6-764 0-2101 311
0-501 0-0389 77-7
BaCl 1-050 0-0733 69-8
2
2-894 0-1534 53-0
0-050 3-18 X IO"4 6-36
0-167 5-84 X IO-4 3-50
1-688 15-26 X IO-4 0-904
CHgCOOH 3-417 16-05 X IO"4 0-470
6-994 10-81 X IO"4 0-1546
13-36 1-46 X IO"4 0-0109
17-41 4 X IO"8 2-3 X 10-6
0-059 2-51 X IO-4 4-25
0-933 8-67 X IO"4 0-929
2-307 10-95 X IO"4 0-475
NH OH* 4-55 10-38 X IO"4 0-228
4
8-87 6-32 X IO-4 0-0713
16-01 1-93 X IO"4 0-0121
* Determined at 15°C.
6 OSCILLOMETRY AND CONDUCTOMETRY
were no "friction" between the ion and the solvent molecules
surrounding it, the force acting upon the ion would result in an
acceleration. However, there is friction, and consequently the
ion achieves a constant velocity.
According to Coulomb's law, the force p acting upon the ion
is
p = Zi · e · P (1.2)
where z,· — the number of unit charges on the ion,
e = the charge on the electron,
P = the electrical field strength.
The movement of the ion towards the electrode is restrained
by the frictional resistance of the medium. The velocity of the
ion in a stationary state is
= lLïJ!L (1.3)
Ot
300 Ti
where K = the frictional resistance and
P' = the field strength, expressed in V · cm" 1 units.
The velocity brought about by a field strength of 1 V · cm -1,
that is, the absolute, ionic mobility, is expressed by
^l_ ^r±_
= (14)
P' 300K
Assuming that in the solution there are N cations and N_
+
anions, the solution as a whole being uncharged, the relation
N z = N_z_ (1.5)
+ +
must hold.
Consider the conductivity of this solution when placed in a
tube of cross-section A and length Z.The intensity of the current
caused by a field strength P' is
i = eAP'(N z u + N_z_u_) (1.6)
+ + +
