Automatic Potentiometric Titrations

223 Pages·1978·3.381 MB·English

by  G. Svehla, R. Belcher and H. Freiser (Auth.)

Other Titles in the Series in Analytical Chemistry
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AUTOMATIC
POTENTIOMETRIC TITRATIONS
BY
G. SVEHLA
The Queen's University, Belfast
PERGAMON PRESS
OXFORD NEW YORK TORONTO SYDNEY
PARIS FRANKFURT
U.K. Pergamon Press Ltd., Headington Hill Hall,
Oxford OX3 OBW, England
U.S. A. Pergamon Press Inc., Maxwell House, Fairview Park,
Elmsford, New York 10523, U.S.A.
CANADA Pergamon of Canada Ltd., 75 The East Mall, Toronto,
Ontario, Canada
AUSTRALIA Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street,
Rushcutters Bay, N.S.W. 2011, Australia
FRANCE Pergamon Press SARL, 24 rue des Ecoles,
75240 Paris, Cedex 05, France
FEDERAL REPUBLIC Pergamon Press GmbH, 6242 Kronberg/Taunus,
OF GERMANY Pferdstrasse 1, Federal Republic of Germany
Copyright © 1978 G. Svehla
All Rights Reserved. No part of this publication may he
reproduced, stored in a retrieval system or transmitted in
any form or by any means: electronic, electrostatic,
magnetic tape, mechanical, photocopying, recording or
otherwise, without permission in writing from the
publishers
First edition 1978
Library of Congress Cataloging in Publication Data
Svehla, G.
Automatic potentiometric titrations.
(International series in analytical chemistry; v. 60)
Biobliography: p.
Includes indexes.
1. Electrochemical analysis. I. Title.
QD115.S95 1977 543'.087 77-24989
ISBN 0-08-021590-4
Printed in Great Britain by A. Wheat on & Co. Ltd., Exeter
LIST OF FIGURES
Fig. 2.1. A galvanic cell 9
Fig. 2.2. A membrane electrode 22
Fig. 3.1. Linear titration curves 32
Fig. 3.2. Titration of 10ml 001 M HC1 with 01 M NaOH (explanation in the text) 34
Fig. 3.3. Ascending (a) and descending (b) logarithmic titration curves, their first (c, d) and second
(e, f) derivatives 34
Fig. 3.4. Variation of the absolute titration error (AK) with the steepness of the titration curve
at the equivalence point 36
Fig. 3.5. Titration of strong acids 49
Fig. 3.6. Graphical method for calculating hydronium ion concentrations (explanation in the
text) 52
Fig. 3.7. Feasibility regions of titrations of weak acids 55
Fig. 3.8. Titration of weak acids (10 ml of 01 M weak acid titration with 01 M NaOH) 55
Fig. 3.9. Automatic potentiometric titration curve (continuous line) of 20 ml 005 M boric acid,
titrated with 01 M NaOH, with theoretical pH values calculated for various stages
of the titration 56
Fig. 3.10. Automatic potentiometric titration curve (continuous line) of 20 ml 005 M boric acid
with 01 M NaOH in the presence of 1 g mannitol 57
Fig. 3.11. Titration of polybasic acids (10 ml of 01 M acid titrated with 01 M NaOH) 61
Fig. 3.12. Titration of strong bases 63
Fig. 3.13. Feasibility regions of titrations of weak bases 67
Fig. 3.14. Titration of weak bases (10 ml 01 M weak base titrated with 01 M HC1) 67
Fig. 3.15. Feasibility regions of titrations leading to the formation of a precipitate of the type
BA 80
Fig. 3.16. Titration of silver ions with sodium chloride and ammonium thiocyanate using a silver
indicator electrode 81
Fig. 3.17. Titration of chloride, bromide and iodide ions with silver nitrate, using a silver indicator
electrode 83
Fig. 3.18. Simultaneous titration of chloride, bromide and iodide ions with silver nitrate, using
a silver indicator electrode 85
Fig. 3.19. Mole fractions of various ionic forms of EDTA present in aqueous solutions 89
Fig. 4.1. Various types of glass electrode 112
Fig. 4.2. Various types of mercury electrode 119
Fig. 4.3. Ion-sensitive electrode with solid-state membrane 122
Fig. 4.4. Ion-sensitive electrode with a liquid-state membrane 124
Fig. 4.5. Response of ion-sensitive electrodes to the cation A2+ in the presence of the interfering
cation By+ with the selectivity coefficient K 125
AB
Fig. 4.6. Some forms of the mercury electrode used in potentiometry 127
Fig. 4.7. Calomel electrodes 130
Fig. 4.8. The silver-silver chloride reference electrode 133
Fig. 5.1. Cell resistance and input impedance of pH-meters 136
Fig. 5.2. Simple triode amplifier circuit 139
Fig. 5.3. Dynamic transfer characteristics of a triode amplifier 140
Fig. 5.4. Reproduction of a signal in a triode amplifier 141
Fig. 5.5. Simple (n-channel) f.e.t. amplifier 141
Fig. 5.6. The principle of negative feedback 143
Fig. 5.7. Amplifier stage of a pH-meter with an open-ended input, using field effect transistor 146
Fig. 5.8. pH-meter with balanced input (simplified circuit) 147
Fig. 5.9. (a) pH-meter with signal modulation, (b) Shapes of signals at the various stages of
operation 148
IX
LIST OF FIGURES
X
Fig. 5.10. Signal modulation with a mechanical chopper 149
Fig. 5.11. Signal modulation with a vibrating capacitor 149
Fig. 5.12. Phase-sensitive rectifier and meter 150
Fig. 5.13. Measurement of e.m.f. by Poggendorff's compensation method 151
Fig. 5.14. Zero-detector pH-meter 151
Fig. 6.1. Solenoid valve, devised by Bett, Nock and Morris(135) 156
Fig. 6.2. Electromagnetic valve, devised by McKay and Eades(136) 156
Fig. 6.3. Solenoid valve, devised by Brown and Volume0 3 7) 157
Fig. 6.4. Automatic piston burette 159
Fig. 6.5. Syringe microburette, devised by Allen0 3 8) 159
Fig. 6.6. Structure, symbols and notation of junction transistors 163
Fig. 6.7. A transistor switch 163
Fig. 6.8. Delays in electronic switching 164
Fig. 6.9. A thyristor: (a) semiconductor layers and connections, (b) electronic symbol, (c) the
thyristor as the combination of a diode and a transistor 165
Fig. 6.10. Schmitt-trigger circuit 166
Fig. 6.11. Input voltage and load current in a Schmitt-trigger circuit 166
Fig. 6.12. A recording potentiometer (T-Y recorder) 167
Fig. 6.13. Electronic derivative circuit 170
Fig. 7.1. Curve-recording titrator with constant rate of delivery 173
Fig. 7.2. Curve-recording titrator with end-point anticipation 176
Fig. 7.3. (a) Theoretical titration curve, (b) Recorded titration curve with end-point anticipation,
(c) One step enlarged with explanation 176
Fig. 7.4. Automatic titrator with preset end-point 179
Fig. 7.5. Second-derivative titrator 181
Fig. 7.6. Digital second-derivative titrator, devised by Hieftje and Mandarino(149) 183
Fig. 7.7. Continuous potentiometric titrator, designed by Blaedel and Laessig(150) 184
Fig. 7.8. Recording obtained by the continuous potentiometric titrator designed by Blaedel and
Laessig(150) 185
Fig. 8.1. Simple graphical method for the location of end-points 188
Fig. 8.2. Kolthoffs method 189
Fig. 8.3. Hahn's first method and Fortuin's method 189
Fig. 8.4. Nomogram to Fortuin's method 191
Fig. 8.5. Hahn's second method 192
Fig. 8.6. The application of Gran's method when titrating 100ml of 001 M HC1 with 01 M
NaOH. (a) The titration curve for 0-9 ml titrant consumption, (b) tabulation of data,
(c) the Gran plot 194
Fig. 8.7. The method of circles (a) with its geometrical explanation (b) 195
Fig. 8.8. The method of tangents for symmetrical titration curves (a) with its geometrical explana-
tion (b) 195
Fig. 8.9. The method of tangents for asymmetrical titration curves (a) with its geometrical
explanation (b) 196
Fig. 8.10. Ebel's method (a) and its geometrical explanation (b) 196
Fig. 8.11. Ruler for end-point location by graphical differentiation. A, B: plastic rulers; C, D:
glass rods; E, F: holes to insert rods; G, H: slots for marking the position of the
end-point; J: refracted images of the curve(201) 198
Fig. 8.12. Evaluation by means of linear calibration graphs 203
CHAPTER 1
TITRIMETRIC ANALYSIS AND
ITS AUTOMATION
1.1. Introduction
The history of titrimetric analysis can be traced back as far as 1729, when Geoffroy(1)
measured the strength of vinegars by adding potash to the solution until bubbling
ceased. The weight of potash added was used to characterise the strength of vinegar.
Ever since, titrimetric methods are popular among chemists, and, despite the immense
number of new techniques available, they are extensively used in analytical laboratories
throughout the world.
In classical methods of titrimetric analysis the end-point of the titration is detected
visually from the colour change which occurs in the solution. Although such changes
are easily recognisable by the human eye, titrations with visual end-point detection
have their own limitations. To perform such titrations a certain skill, care and practice
are required as well as favourable working conditions (among which the proper illumina-
tion of the working bench has to be mentioned). These subjective factors, however,
are less important when compared to those objective limitations which originate from
the chemical processes involved in the titration. There are fast and stoichiometric reac-
tions which cannot be used in visual titrations simply because of the lack of a suitable
indicator. Some other reactions are too slow to be applicable for routine titration pro-
cesses. Sometimes the solution of the sample is dark or coloured, making visual indica-
tion impossible.
All these and similar other difficulties can be overcome by the application of instru-
mental methods of end-point detection. These are all based on the monitoring of the
concentration of a species which is involved in a titration reaction. There are many
extensive physical quantities which can be measured, hence the large number of electro-
chemical, optical or radiochemical methods applied for end-point detection in titrimetric
analysis. When using these methods the titrant is added in small portions, and after
the addition of each portion the extensive physical quantity is measured. The titration
is generally carried over the equivalence point, when the build up of the excess of
the titrant can be monitored. From the results a diagram (the titration curve) is con-
structed, and the end-point is determined graphically.
Such a simple manual procedure has several drawbacks, which prevent the large-scale
use of such techniques for routine analyses. One drawback is the slowness of such
a procedure. While a skilled person can easily perform 20-30 visual titrations per hour
(provided that samples and reagents are prepared in advance), this number decreases
to 5-8 if manual instrumental titrations are carried out. Another drawback is the inten-
1
2 AUTOMATIC POTENTIOMETRIC TITRATIONS
sive work required by the analyst during this time. The titrant has to be dispensed,
the volume measured and noted, then the physical quantity measured and noted, to
obtain a single point on the titration curve. This procedure has to be repeated 20-30
times during one titration. When all the measurements are made the titration curve
has still to be constructed. The only way in which these difficulties can be overcome
is to introduce some degree of automation into such techniques. It is relatively simple
to construct automatic burettes which dispense the titrant with a controlled rate. At
the same time the extensive physical quantity which is measured during the course
of the titration can be most easily converted into an electric signal, which can be ampli-
fied and either recorded simultaneously with the volume, obtaining thus the titration
curve, or used to control the operation of the burette, switching off the latter at the
end-point. Even other operations, like taking a sample, filling the burette or rinsing
the vessels, can be automated. With the combination of these facilities various types
of automatic titrator have been constructed, which are widely used nowadays both
in industrial and in research laboratories.
There are numerous advantages connected to the use of automatic titrators. The
most important of these are the savings in labour costs and time. With adequate skill
and training one operator can supervise anything up to half a dozen units simul-
taneously, and might have even the time to prepare samples for the subsequent titra-
tion. The instrument does the monotonous routine work, and the analyst's task is simply
to prepare samples, collect the results, evaluate titrigrams, as well as the general main-
tenance work which such instruments require. The output of a laboratory, equipped
with automatic titrators, might considerably supersede those where the emphasis is laid
on manual work. Another advantage often connected with the use of automatic titrators
is the reduction of scales and increased precision, achieved mainly by the application
of precision microburettes. Finally, some of the titrators produce a recorded titration
curve, a document which can be attended to later and may be filed away for further
reference.
These definite advantages have to be weighed against the costs which have to be
met when installing automatic titrators into a laboratory. The instruments themselves
cost quite a lot. Power lines, earth connections have to be installed. The laboratory
where these instruments are housed must be protected against fumes or gases which
otherwise would not interfere seriously with simple manual work. Although there are
savings in labour costs because of the reduced number of persons doing the analysis,
the average standard of education of the operators of these instruments must be defi-
nitely higher than that of an ordinary laboratory assistant, who might otherwise be
able to perform simple analytical work. The users of such instruments have to be able
not only to operate them, but also to find the optimal experimental conditions required
for a given task, and also to recognise (and possibly to avoid) errors, which is the
more difficult to do the more complex the instrument. The higher wages paid to such
people have to be kept in mind when buying automatic titrators. Laboratories which
are well equipped with instruments often find themselves compelled to set up a small
electronic workshop with a skilled engineer or technician to ensure that the instruments
are kept always in good working condition. This of course means expenses which again
must be kept in mind.
Most instrumental methods of end-point detection can be applied as a basis to operate
automatic titrimeters. Thus, conductometric, radio-frequency, amperometric, spectro-
TITRIMETRIC ANALYSIS AND ITS AUTOMATION 3
photometric, radiometric, etc., titrations can be automated relatively easily. The most
important technique, however, is potentiometry; much work has been done in the past
30 years to develop automatic potentiometric titrators and to apply them both in routine
laboratory work and in research. Commercial automatic titrimeters, with few exceptions,
are based on potentiometric end-point detection. The present book is devoted solely
to the theoretical and practical aspects of automatic potentiometric titrations.
1.2. Titrimetric Analysis
Titrimetric methods are based on chemical reactions in solution between the reactant
(R), that is the substance to be determined, and the titrant (T). These reactions must
be stoichiometric, complete, and they must be fast. (These requirements will be discussed
later in more detail.) The titrant is applied in the form of a solution of known concen-
tration (standard solution) and is added either continuously or in increments to the
reactant, its volume (or sometimes its weight) being measured. When all the reactant
has been reacted, the equivalence point is reached. All titrations need a suitable method
to indicate when this is achieved. As this can be done only with a limited accuracy,
the experimentally determined end-point of the titration will differ from the equivalence
point to some extent. The volume of the titrant corresponding to the end-point must
be determined (vjml). If the titration reaction obeys the stoichiometry of eqn. (1.3)
below, the m amount of the reactant can be calculated with the formula
R
m = vcM^ 10"3 g (1.1)
R e T R v
T
where c is the concentration of the titrant in moll-1 units, M is the relative molecular
T R
mass (formula weight) of the reactant (its unit being gmol-1), v and v are the stoichio-
R x
metric numbers. With the Q equivalent weight [0(g )_1] of the reactant and the N
K eq T
normality of the titrant [(ge)l_1] the expression is somewhat simpler:
q
™ = t;NeRlO-3g. (1.2)
R e T
The factor of 10-3 (lml-1) is needed to obtain the result in grams, with the units
given, in both equations.
The requirements mentioned earlier represent the three basic conditions which have
to be met if a chemical reaction is applied for quantitative analysis. The first of these
requires that the reaction should be stoichiometric, or quantitative. This means that
during the course of the titration only one reaction, the titration reaction itself, should
proceed. The titration reaction between the reactant (R) and titrant (T) leading to the
formation of products (C and D) can be expressed as
vR + vT->vC + vD (1.3)
R T c D
where v, v, v and v are the stoichiometric numbers needed to balance the equation.
R T c D
The condition means that neither R nor T should be involved in any other reaction
than (1.3), neither should C and D be involved in reactions where either R or T or
both are regenerated. Other side reactions may proceed and sometimes might even
be desirable, to ensure that the reaction becomes complete.
4 AUTOMATIC POTENTIOMETRIC TITRATIONS
The requirement that the reaction should be complete is the thermodynamical condi-
tion. Strictly speaking, all chemical reactions lead to an equilibrium reaction (1.3) there-
fore should be written as
vR + vT <± vC + vD. (1.3)
R T c D
The equilibrium can be characterised by the equilibrium constant which can be defined
as
dvcc x qg> [CP- x [D]VD
aR x aV [R]VR x [T]VT 1 ]
R
where a denotes activities and concentrations; the notation over activities and concen-
trations refers to equilibrium values. It is obvious from eqn. (1.4) that the reaction
is the more complete (that is, the equilibrium is the more shifted towards the direction —•)
the higher the value of the K equilibrium constant. In the present book we shall often
often examine the feasibility of a titration through the equilibrium constant of the titra-
tion reaction.
If the equilibrium constant is not favourably high to ensure that the reaction becomes
complete, we might be able to shift the equilibrium towards the formation of the reaction
products by making use of the law of mass action. We can, for example, do so by
removing one of the reaction products from the equilibrium system (e.g. by precipitation,
complexation, etc.).
Whether a particular reaction will proceed or not depends on the initial concentrations
of the reaction partners and on the value of the equilibrium constant. The feasibility
of a reaction can be tested quantitatively by calculating the chemical potential change
which occurs when the reaction proceeds from the initial stage to equilibrium.(2) If
this A/i chemical potential change is negative the reaction will proceed, if it is positive
it will proceed in the opposite direction—if the change is zero, the system is in equilib-
rium, and therefore no (visible) changes will occur when mixing the reaction partners.
For the process, described in eqn. (1.3), the change of chemical potential can be
expressed as
AJH = (vcfic + vDA*D) - (VR^R + VTfiT). (1.5)
The /x chemical potential of each substance depends on its activity (concentration) in
the solution. Denoting the initial activities of these substances by a, a, %, %, we
c D
can express the individual chemical potentials in the following way:
/ic = Mc + RTtlnac, (1.6)
lk> = I& +RT tlnao, (1.7)
l± = I& +RTtlna (1.8)
K9
fi = $ + RTX\na (1.9)
T T
where R is the gas constant and T the temperature. The fi° values are individual con-
stants characteristic for the particular substances. They could be called chemical poten-
tials of the standard statet (and are acquired in solutions with activities of lmoll"1).
fThey should not be called "standard chemical potentials" as such a term is defined in a different way
in chemical thermodynamics.
TITRIMETRIC ANALYSIS AND ITS AUTOMATION 5
Provided that the reaction proceeds under isothermal conditions, we can combine eqns.
(1.5M19) to obtain
A/i = [(v/ic + v/4>) - K/iR 4- v/i?)]
c D T
4- [(v In a 4- v In a) — (v In a 4- v In a)]. (1-10)
c c D D R K T T
The values in the first bracket are all constants. Using the notation
A|i° = (vcM8 4 vD/xg) - (VRMR 4- VTM?) (1.11)
we can rearrange (1.10) as
= V + * T t a ^ * ;. )
( U 2
0R X
Note that the activities in the logarithm are the initial (that is arbitrary) values, and
not the equilibrium ones, used in the expression of the equilibrium constant. In this
expression all values on the right-hand side but that of A/i° are known. This can be
calculated, knowing the fact that at equilibrium the chemical potential change is zero,
A/i = 0, (1.12a)
equ
and therefore for equilibrium conditions eqn. (1.12) can be transformed as
Au° = -/J Tin -RTlnK (1.13)
(where the a values are the equilibrium activities). Thus, if the equilibrium constant K
is known, the chemical potential change can be calculated from the expression obtained
by combining (1.12) and (1.13):
Aji= -RTlnK 4 RTIn (1.14)
As said before, reaction (1.3) will proceed only if A/i < 0.
Such a calculation is especially useful to decide whether a particular titration can
be carried out with a certain accuracy. The equilibrium constant must be known, and
one can easily calculate the concentrations of the reactant, titrant and the reaction
products in a solution in which, say, 99-9% of the reactant has been titrated (and only
01% is left untitrated). Substituting these values as activities into eqn. (1.14), the chemical
potential change can be calculated. If this is negative, the reaction will still go on
under such circumstances, that is the unreacted reactant and titrant will react to form
the product. If, however, the chemical potential change is positive, this means that
the reaction will proceed just in the opposite direction and therefore the titration cannot
be carried out with an error equal to or less than —01%.
A titration reaction might be stoichiometric and thermodynamically feasible, but still
unsuitable for practical applications, because the kinetic condition is not fulfilled, that
is that the reaction is not fast enough. The velocity of a reaction can be judged from
the rate constant. The rate of reaction (1.3), as known from elementary reaction kinetics,
can be expressed as
- =kx [R]VR x [T]VT. (1.15)