Coulometric titration by means of a controlled-potential-pulsed-current potentiometric technique—I

0039-9140/84 $3.00 + 0.00 Copyright 0 1984 Pergamon Press Ltd

Talonra, Vol. 31,No. 2,pp. 123-129,1984 Printed in Great Britain. All rights reserved

COULOMETRIC TITRATION BY MEANS OF A CONTROLLED-POTENTIAL-PULSED-CURRENT POTENTIOMETRIC TECHNIQUE-I METAL

IONS BY ELECTRO-DEPOSITION

THEOLOG~S

and ANNA

ANDRONIDIS

MARIA GHE

Istituto Chimico G. Ciamician dell’Universita, Scuola di Specializzazione in Chimica Analitica, via Selmi 2, 40126 Bologna, Italy CE~ARE PACURA and SERCIO VALCHER* Istituto di Polarografia ed Elettrochimica Preparativa de1 C.N.R., Corso Stati Uniti 4,351OO Padova, Italy (Received 23 March 1983. Accepied 16 August 1983)

Summary-A new method for electrochemical titrations is proposed, based on the redox transformation of the test species by means of a controlled-potential pulsed current, followed by measurement of the potential in the intervals between the current pulses: the end-point is found by means of Sorensen’s linearization technique. Investigations on various metal ions (Ag +, CU’+, Cd*+, Pb*+) have shown that the accuracy and sensitivity, which depend on the nature of the species titrated, are comparable with those of other titration techniques. The method permits analytical separations and determinations of metal ions in mixtures. No particularly elaborate instrumentation is required and the apparatus described is simple to use, reliable and inexpensive.

coulometry is usually used for analytical separations of metal ions and other electroactive species when the more popular constantcurrent and pulsed-current coulometry’~2 cannot be applied because of their lack of selectivity. For the controlled-potential technique, the electrolysis current is the parameter generally used to determine the end-point, but this approach may sometimes not be accurate enough, particularly at low concentrations, where the background current becomes significant. A means of direct monitoring of the transformed species may then improve the performance. Potentiometry is one such means and gives sensitive end-point detection provided equilibrium is obtained rapidly at the indicator electrode. Since this is usually not the case under constant-current electrolysis conditions, potentiometric end-point detection is more effective if the current is switched off while the potential is being measured. A controlled-potential pulsed-current technique has therefore been devised, which is based on repetitive cycles of the following stages. Controlled-potential

(1) Passage of a current pulse at a workingelectrode potential controlled at a value suitable for redox transformation, of the single species to be determined. The electrolysis current is integrated

*Author for correspondence. 123

until a preset charge has been passed and is then instantaneously reduced to zero. (2) Measurement of the indicator-electrode potential (at zero current) once its value is steady. The set of potentials is then processed in order to get a linear function with respect to the charge passed, and from this the titration end-point can be extrapolated. Besides accuracy, the main advantage of the method is the possibility of evaluating the equivalence point without completing the electrolysis. EXPERIMENTAL Apparatus

The apparatus outlined in Fig. 1 has been used for the separation and determination of metal ions according to the principle described above. The printer and potentiometer are commercial units (Laben 6061 and Orion 701 A, respectively), and the potentiostatic-coulometry unit is specially designed and constructed for use in the method, The potentiostat (a) provides current at controlled potential. The charge passed in a single pulse is controlled by means of the current-to-voltage converter (b) and the integrator (c), the pulse being terminated by a suitable logical network as soon as the charge passed reaches the value preset on the comparator (d). The potentiostat-galvanostat (a) and current-to-voltage converter (b) are operationally closely linked. In the potentiostatic configuration [(i) in Fig. 21 the use of the high-current operational amplifier (No. 1) is quite conventiona13q4whereas in the current-to-voltage converter the high-current operational amplifier (No. 2) is used as a

124

THE~L~G~SANDRONIDIS et al.

feedback

Fig. 1

voltage follower, in conjunction with a second operational amplifier. Diagram (ii) in Fig. 2 clarifies the reasons for this doubling, by showing the logic diagram for current interruption under potentiostatic conditions: instead of the current being switched off, it is instantaneously reduced to zero by activation of a negative feedback loop from the currentto-voltage converter to the potentiostat. This is done to avoid the disadvantages associated with the switching of relatively high currents. To prevent an unsuitable choice of current range from invalidating the coulometric data, a current limiter has been incorporated which operates by taking control of the working-electrode potential when the output of the currentto-voltage converter reaches the highest allowed value (about 11 V). The high-current operational amplifiers HCA.1 and HCA.2 are made by coupling current boosters (limited at lOOmA) to LHO042 and LM308 operational amplifiers respectively. The integrator (c), comparator (d) and stop-reset/start logic network, which is suitable for manual operation, is shown in Fig. 3. A flip-flop (l/2 SN7401) is used to switch the system between the potentiostatic and zero-current configurations and to reset the integrator. Tiirations As can be seen in Fig. 1, the electrolysis and the potential measurements can, if desired, be performed at different electrodes. Nevertheless this configuration has been employed only for special cases, it being generally sttthcient to use a single electrode as both working and indicator electrode. The electrode potential is transmitted from the digital

output of the potentiometer to a printer (at lo-set intervals) and is ,taken as constant if it does not vary by more than 0.1 mV during a time-period chosen in accordance with the behaviour of the electrochemical system.5 The charge to be passed in the pulse is preset by means of the current-range and time-constant selectors (according to the concentrations used and the area of the working electrode) so that about 20-30 data points are obtained for titration of a single species. Cell and electrodes The cell is equipped with a magnetic stirrer, and a nitrogen inlet for deaeration of the test solution. The counter-electrode (generally made of platinum) is separated from the titration cell by a porous glass disk and is housed in a compartment containing the same background electrolyte as the test solution. The saturated calomel reference electrode is similarly connected. The working electrode has a surface area of about 1 cm’ and is made of various materials, as indicated below. Solutions Titrations were done (at 25”) on 20-ml samples, containing the species to be tested, and a background electrolyte chosen to give the best current yield and speed of response of the indicator electrode. The solutions employed are listed in Table 1; they were generally acidic to prevent hydrolysis but care was taken to avoid concentrations at which hydrogen discharge would occur.

Table 1. Composition of the supporting electrolytes for the determination single ions or ion mixtures Type

A B C D E F

Reagents and concentrations

PH

CH,COONa lo-‘M + CH,COOH N 5 x lo-‘M H,SO, 2.5 x 10-3M KC1 lo-‘M + HNO, 2.5 x lo-‘M KC1 lo-‘M + CH,COOH _ 5 x lo-‘M CH,COONa IO-‘M + CH,COOH 7.5 x 10m2M H,SO, 2.5 x 10-3M +(NHJ,SO, 2.5 x 10-“&I

5.8 2.4 3.5 5 5 2.8

of

Pulsed-current potentiometric

(b) i-V

technique---I

125

converter

* to

r

inteqrator

q (a) potent&tat 82OnF

limiter

Q

H.C.A.2

&%pA~~ Fig. 2 End-point determination A linearization technique is used so that the end-point can be deduced from the potentiometric data without completion of the electrolysis reaction. Sorensen’@ method was used instead of Gran’s,’ as the latter makes corrections for dilution, which does not occur in our method. Since deviations from linearity may be encountered both for the initial points (because of the state of the indicator electrode surface) and for those near to the end-point (at low concentrations), the straight lines for extrapolation to the equivalence-point are obtained by using only the most linear subset of the experimental data. This subset is extracted by numerical analysis as described elsewhere* and is referred to here as the highest linearity segment. For a complete set of c data points, it contains (c + 8)/4 consecutive points. This segment, comprising the

points P(n). . . P(n + m), is selected on the basis of the variance minimum given by the three intercepts (on the charge axis) of the segments: (a) P(n - 1). .P(n - 1 + m); (b) P(n). . .P(n +m) and (c) P(N + 1). . .P(n + 1 +m). The selected subset is then used for linear regression analysis, which leads to the best straight line, the correlation coefficient, and the 900/, confidence limits.

RESULTS AND DISCUSSION The proposed technique was developed for the determination of ions by electro-deposition, both in systems containing a single species, and in mixture of several metal ion; in other words, for an electrolytic

precipitation

titration.

126

THEOLCCXX

+15

ANDRONIDIS

et al.

+5

+5

(dlcomparator

l/2

b

SN 7401

LL

-15 I zero current 8 intearator

W integrator

Fig. 3

Fig. 4

? I

+15

Pulsed-current potentiometric

An example of the diagrams used for the determination of the equivalence point is shown in Fig. 4, where a titration of 5 x 10e4M silver is shown. In the plot, the Sorensen function S (defined as S = 10nE’o.05g, n being the number of electrons involved in the reaction, and E the measured electrode potential) is plotted as a function of charge consumed (expressed as C = Q/nFm, where m is the number of moles of silver deposited. The points denoted by 0 pertain to the highest linearity segment, selected as indicated. In the same figure the linear-regression straight line is shown together with the corresponding 90% confidence hyperbolas, the intercepts of which with the charge axis are the confidence limits for location of the end-point. Typical results of determinations of single ionic species at various concentrations are shown in Table 2. It is apparent that with all the species tested a comparison between the present technique and conventional controlled-potential coulometry is in favour of the former since lower concentrations of the ions can be determined.2 This is especially true for silver and cadmium, which can be determined with acceptable error levels down to concentrations of 5 x 10m5M and 2.5 x 10m5M respectively. Of course the accuracy decreases with decreasing concentration, so the uncertainty range, as given by the confidence limits, broadens. To improve this situation, titrations were done with a four-electrode configuration (see for instance experiment 5) and gave much better results for silver, both in terms of relative error and of confidence limits. Another possible source of deviation is manifested in titration 8 (of lead) which gave the highest relative errors for high concentrations. This can be related to the fact that lead, at high current densities, produces dendritic deposits, which make it difficult for the potential of the working-indicator electrode to equilibrate rapidly. The formation of dendritic lead is enhanced if silver electrodes are used, because their smoothness is initially poorer than that of platinum. However, the accuracy obtained is similar to that of other potentiometric titrations based on the Gran linearization method.g The technique proposed is particularly interesting for separate determination of ions in mixtures. Various concentration ratios have been explored in this connection. Table 3 shows typical results obtained for a number of determinations of silver and copper present in the same solution. The relative error in the determination of silver, the first ion titrated, is very similar, in most instances, to that obtained when silver is the only ion present. The second species to be determined deserves more attention. The overall error for a pair of ions is less than or equal to the sum of the relative errors for the various ions. When the amount of copper is calculated from the difference between the total charge passed and the theoretically “known” amount of

,

technique-I

127

128

THEOLOGOS ANDRONIDIS et al.

Table 3. Titrations of mixtures of Ag+ and Cu2+ (silver electrode) Electrolysis potential, mvvs. Molarity Run 13 14 15 16 17 18 19 20 21 22 23 24

Ag+ 5x 5x 5x 5x 5x 2.5 x 1x 5x 5x 5x 5x 5x

10-x IO-3 10-3 10-Z 10-1 lo-’ 10-l 10-d 10-S 10-s 10-3 10-Z

Respective counterions

cuz+ 2.5 x 2.5 x 2.5 x 2.5 x 2.5 x 1.25 x 5x 2.5 x 2.5 x 2.5 x 2.5 x 2.5 x

10-j 10-l lO-3 lo-* IO-’ lo-) 1o-4 lO-4 lO-5 1O-3 lO-4 1O-4

NO, NO; NO; NO; NO, NO; NO, NO, NO, NO, NO, NO,

Coulombs for Ag+

SCE

Solution composition

Ag +

C$+

B B E F F F F F F F F F

+150 +150 +150 +150 +150 +150 +150 +150 fl50 1-150 +150 +150

-250 -220 -220 - 220 -220 - 220 -220 -220 -220 -220 -220 -220

SOiSO:CH,COOso:so:so:so:so: so:so:so:so:-

Expected

Found

9.65 9.65 9.65 9.5 9.65 9.5 96.5 99 9.65 9.5 4.825 4.65 1.93 1.88 0.965 0.92 9.65 x lO-2 9.65 x lo-’ 9.65x 10m2 9.6x lO-2 9.65 9.65 96.5 94.7

Error, % Ag+ 0.0 -1.5 -1.5 f2.5 -1.5 -3.5 -2.6 -4.2 0.0 -0.5 0.0 -1.9

Coulombs for Cu2+ Found Error,

Run

Expected

13 14 15 16 17 18 19 20 21 22 23 24

9.65 9.65 9.65 96.5 9.65 4.825 1.93 0.965 9.65 x lo-* 9.65 0.965 0.965

I (from Ag found) 9.9 9.8 9.8 93.5 9.7 5 1.98 0.97 9.50 0.91 1.01

II (from Ag taken) 9.9 9.65 9.65 96 9.55 4.825 1.93 0.925 -

silver, the error is less than when it is calculated on the basis of the charge passed between the two end-points. This points to the absence of a specific interference between the two ions and indicates that the only additional source of error is the uncertainty affecting the determination of the first ion to be titrated.

Coulombs for Ag+ + Cu’+

$+ I

II

i-2.6 +1.5 +1.5 -3.1 +0.5 +3.6 +2.6 +0.5 -1.5 -5.2 +5.2

+2.6 0.0 0.0 -0.51 -1 0.0 0.0 -4 -

Error, % Ag+ + Cu’+

Expected

Found

19.3 19.3 19.3 193 19.3 9.65 3.86 1.93 9.75 10.61 97.46

19.55 19.3 19.3 192.5 19.2 9.65 3.86 1.81

+1.3 0.0 0.0 -0.2 -0.5 0.0 0.0 -2

9.60 10.56 95.71

-1.5 -0.5 -1.8

Similar considerations can be applied to determinations of ions in other binary mixtures, such as silver and lead (Table 4), for which the figures

obtained are quite satisfactory. The relative proportions of the two components do not greatly affect the results (Tables 3 and 4). Figure 5 shows that successive determination of more than two metals is a possibility; in particular the system Ag+-Cu*+-Pb2+ has been tested (experimental conditions: three-electrode system; Ag working electrode; solution E; electrolysis potentials respectively + 150, -200, - 800 mV us. WE). The relative errors in the various determinations were of the same order of magnitude as those found when the same ions were determined separately. CONCLUSIONS During the present investigation a controlledpotential pulsed-current coulometric method has been developed. The technique, based on the potentiometric determination of the equivalence point by

Pulsed-current potentiometric technique-1

129

means of Sorensen’s linearization procedure permits reasonably short run times as it does not require the titration to be taken to completion. The use of a linearization function permits easy statistical analysis and therefore provides a test of the accuracy of the determination. The procedure offers the advantage over constant-current coulometric titrations that it can be used for analytical separations of mixtures of metal ions which can be electrodeposited. The sensitivity and the accuracy compare favourably with those of other titration techniques. It should be noted that the end-point can also be predetermined in conventional controlled-potential electrolysis (by using plots of log i us. time), but there are instrumental complications regarding the stirring conditions, which must be rigorously controlled; furthermore this variation of the method does not have general applicability. In contrast, the proposed technique calls for less sophisticated instrumentation and, because of the short integration times for each current pulse, makes less severe demands on the integrator performance. REFERENCES 1.

J. J. Lingane, Electroanalytical 484.

Chemistry,

2nd Ed., p.