Table Of ContentINTERNATIONAL SERIES OF MONOGRAPHS ON
ANAL YTICAL CHEMISTR Y
Vol. 1. WEISZ—Microanalysis by the Ring 0\en Technique
Vol. 2. CROUTHAMEL (Ed.)—Applied Gamma-Ray Spectrometry
Vol. 3. VICKERY—The Analytical Chemistry of the Rare Earths
Vol. 4. HEADRIDGE—Photometric Titrations
Vol. 5. BUSEV—The Analytical Chemistry of Indium
Vol. 6. ELWELL AND GIDLEY—Atomic Absorption Spectrophotometry
Vol. 7. ERDEY—Gravimetric Analysis
Vol. 8. CRITCHFIELD—Organic Functional Group Analysis
Vol. 9. MOSES—Analytical Chemistry of the Actiniae Elements
Vol. 10. RYABCHIKOV AND GOL'BRAIKH—The Analytical Chemistry of Thorium
Vol. 11. CALI—Trace Analysis of Semiconductor Materials
Vol. 12. ZUMAN—Organic Polarographic Analysis
C ontrolled - Potential
Analysis
by
GARRY A. RECHNITZ
Department of Chemistry
University of Pennsylvania
PERGAMON PRESS
OXFORD · LONDON · NEW YORK · PARIS
1963
PERGAMON PRESS LTD.
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Copyright © 1963
PERGAMON PRESS INC.
Library of Congress Catalog Card Number 63-19612
Set in Monotype Times 10 on 12 pt. and printed in Great Britain by
C. Tinling & Co. Ltd., Liverpool, London and Prescot
The author wishes to thank the Department of
Chemistry and the Laboratory for Research on the
Structure of Matter, University of Pennsylvania,
for providing much of the facilities and equipment
used in the experimental work quoted here. The
valuable help of Miss Judy Leon in the preparation
of the manuscript is gratefully acknowledged.
CHAPTER I
INTRODUCTION
IT IS commonly believed that polarography antedates controlled-
potential coulometry, because polarographic information is so often
used in the selection of optimum conditions for coulometry at
mercury cathodes. In fact, however, as early as the turn of this century
Sand (1) and his contemporaries laid down many of the principles and
techniques basic to this electro-analytic method. Owing to the lack of
experimental convenience, the method received relatively little
attention until 1942 when Hickling (2) published the design of his
device for automatic potential control, the potentiostat. Since then,
largely because of the efforts of Lingane, Furman, MacNevin,
Meites and many others, the technique of controlled-potential
coulometry has found increasingly broad application to problems of
analysis, synthesis, and reaction kinetics.
Controlled-potential analysis involves the measurement of the
quantity of electricity passed in the course of an electrolysis during
which the potential of the working electrode is held constant and at a
value which permits the desired oxidation or reduction to proceed
with 100 per cent current efficiency. The practical problems to
be considered in controlled-potential methods are the accurate
maintenance of the desired potential despite changing electrical
characteristics of the sample, the precise measurement of the number
of coulombs passed while current levels are rapidly decreasing, and
the suppression of electrical and chemical side effects which could
lead to erroneous interpretation of the data obtained.
Controlled-potential electrolysis techniques are particularly useful
to problems of chemical analysis because they provide not only a
measure of concentration or amount of electro-active material
through Faraday's laws but also, in favourable cases, a qualitative
identification from the value and magnitude of the potential. Further-
more, controlled-potential coulometry often is capable of giving
1
2 CONTROLLED-POTENTIAL ANALYSIS
information concerning an oxidation-reduction process in terms of
reaction rates, products, and intermediate species.
Like most electro-analytical methods controlled-potential coul-
ometry appears deceptively simple in principle, but requires some
understanding of possible experimental complications and skill
in the interpretation of data in order to be used effectively and with
confidence. Fortunately, this technique does not stand by itself but
is closely related to, and can draw heavily on, the more familiar
electro-analytical fields of potentiometry and amperometry.
The main advantages of controlled-potential coulometry over
other electro-analytical methods are its specificity and promise of
accuracy combined with great sensitivity. Furthermore, it is an
absolute method in the sense that it can yield a measure of total
amounts of material through basic laws rather than a measured
value related only to some function of the concentration of electro-
active substance present.
Because of its apparent simplicity controlled-potential coulometry
is often passed over entirely or appended as an afterthought to
discussions of polarography in undergraduate and even graduate
courses dealing with instrumental methods of analysis. Yet this
technique deserves wider attention not only because it may be a
powerful tool in the arsenal of the analytical chemist but because many
fascinating questions remain to be answered within its own bounds.
In this monograph, an effort has been made to provide sufficient
information about the theoretical background, instrumental con-
siderations, and experimental techniques of controlled-potential
coulometry so as to enable the practicing analytical chemist to make
use of this method for his own particular requirements. Detailed
procedures for specific analyses will not be given here, but a consider-
able number of typical applications to inorganic analysis have been
critically treated in the final chapter. While this modest monograph
is not intended in any way as a textbook it is hoped that it may serve
to stimulate some interest in this interesting and useful technique.
BASIC BIBLIOGRAPHY
KOLTHOFF, I. M., and LINGANE, J. J., Polarography. 2nd Ed., Interscience,
New York, (1952).
INTRODUCTION 3
LINGANE, J. J., Electroanalytical Chemistry. 2nd Ed., Interscience, New York,
(1958).
MEITES, L., Polarographic Techniques, Interscience, New York, (1955).
CHARLOT, G., BADOZ-LAMBLING, J., and TREMILLON, B., Electrochemical Re-
actions, Elsevier, Amsterdam, (1962).
MEITES, L., "Controlled-Potential Electrolysis", in Physical Methods of Organic
Chemistry. 3rd Ed., Interscience, New York, 1960, pp. 3,281-3,333.
REFERENCES
1. SAND, H. J. S., /. Chem. Soc, 91-92, 373^10 (1907).
2. HICKLING, A., Trans. Faraday Soc, 38, 27-33 (1942).
CHAPTER II
THEORY
LINGANE (1) has classified coulometric methods according to whether
the current, total applied voltage, or potential of the working
electrode is being controlled during the course of electrolysis. Under
controlled-current conditions the potential of the working electrode
will be limited by the electrode process of interest only as long as
sufficient electro-active material is present to carry the applied
current. As the concentration of the electro-active material decreases
the potential of the working electrode will change to a value which
permits the occurrence of some other electrolysis process to support
the total current applied.
Electrolysis at constant applied voltage (2) can provide more
selectivity than constant current electrolysis because the total applied
voltage can be kept small enough so that the back e.m.f. will eventu-
ally become large enough to stop the electrolysis before the potential
of the working electrode can shift to a value which permits some
undesirable reaction to occur. The electrolysis current, however, will
be limited to relatively small values by the applied voltage and the
resistance of the system so that the time required for completion of
electrolysis will be unnecessarily long.
Electrolysis with controlled working electrode potential, on the
other hand, provides not only selectivity but also the largest possible
electrolysis current obtainable under a given set of experimental
conditions. The potential of the working electrode refers to the e.m.f.
between some reproducible and constant reference electrode and the
working electrode. This potential difference is maintained constant by
varying the total voltage applied between the working electrode and
some appropriate counter electrode to compensate for changes in the
electrode potentials, overvoltages, and iR drop during the course of
the electrolysis.
It has been shown (3) that the current resulting from a simple
4
THEORY 5
electrolysis process proceeding with 100 per cent current efficiency
under controlled-potential conditions decreases in a manner which
may be approximately described by a first-order decay expression,
that is
ι'* = ι· 10-» (2.1)
ίβ0
where i is the current at any time t, i is the initial current, and Kis
t t=0
a constant which depends on the cell geometry, the mass transfer
conditions, and the nature of the electrode reaction.
The electrolysis current at any particular time, t, can also be
approximated by
*—'(^) <H>
where n is the number of electrons involved in the oxidation or
reduction of one molecule of the electro-active species, F is the
faraday, and -r- is the number of moles of electro-active material
consumed per unit time. In the case of diffusion control, the instan-
taneous current is given by
U = nFDA ( C~ Ce) (2.3)
b
where D is the diffusion coefficient, A the electrode area, C the bulk
concentration, C the concentration at the electrode surface, and δ the
e
diffusion layer thickness which depends on stirring, temperature, and
composition of the medium. Under controlled-potential conditions
with efficient stirring, the electro-active material will usually be
reduced or oxidized as rapidly as it can diffuse to the electrode so
that its surface concentration approaches zero and
i = nFDA — (2.4)
t
or, since M = CV equation (2.2) may be written as
9
U = *FV(«L} (2.5)
6 CONTROLLED-POTENTIAL ANALYSIS
where V is the solution volume. Equating expressions (2.4) and (2.5)
for the disappearance of electro-active material yields
dC DAC ,.
Λ
d ï=- - F S- (2·6)
which may be integrated and rearranged to
C=C= 10-°^DAlV3 (2.7)
t t 0
Equations (2.1) and (2.7) are of the same form and because the
electrolysis current is proportional to the concentration of electro-
active material it becomes apparent that the constant, K, in equation
(2.1) can be equated to the quantity 0.43 DA/VS for controlled-
potential electrolysis under diffusion controlled conditions.
A plot log i vs. t should therefore yield a straight line for data
t
obtained under the idealized conditions assumed above. The intercept
and slope of such a plot will yield i and K, respectively. The
t β 0
proportionality constant, K in turn, is a measure of the time required
9
to carry out the electrolysis to any desired degree of completion.
Because
#=0.43 DA/V8
the rate of electrolysis will be accelerated by increasing the diffusion
coefficient and electrode area to volume ratio or by decreasing the
diffusion layer thickness.
Recently, Fahland and Herrmann (4) have studied the electrolytic
deposition of metals from dilute solutions using radioactive tracers to
follow concentration changes with the objective of checking the
validity of equation (2.7). The concentration of metal ions in solution
was found to decrease exponentially with time even for 10-8 M
solutions of bismuth. As predicted, the electrolysis was accelerated
by high temperatures, large cathode areas and small electrolyte
volumes.
From the form of equation (2.1) it can be seen that controlled-
potential electrolysis would require infinite time to remove 100 per
cent of the electro-active material. For practical purposes, however,
the fraction of electro-active material remaining may be calculated
from the ratio of the instantaneous electrolysis current to the initial
current. Rearranging equation (2.1) to
8
logf-A-V -*' (2· )
