Simple Approach to the Problem of Overlapping Waves Using a Microprocessor Controlled Polarograph A. M. Bond' and B. S. Grabaric' Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia
The use of a microprocessor controlled polarograph has enabled the development of an exceedingly simple experimentally based method for determining two species giving rise to overlapping polarographic waves. Based solely on storage of data followed by subtraction of one component and requiring no curve fitting procedures or complex algorithm, the method is completely general and can be applied to all classes of electrode processes and voltammetric technlques Including anodic stripping voltammetry! In the present work the techniques of differential pulse polarography and differential pulse anodic stripping voltammetry have been considered and the practically important problem of determining lead and thallium in zinc sulfate electrolyte by anodic stripplng voltammetry has been examined In detail. Two orders of magnitude improvement are gained over the conventional situation and the Iimitation of the method is basically governed by the reproducibility of recording I-€ curves.
The problem of determining two species with similar halfwave potentials has been a problem of substantial interest in polarography since the inception of the technique as an analytical method ( I ) . With DC polarography the sigmoidal shaped curves provide a particularly disadvantageous situation and the usual approach to provide the required resolution ( 1 ) has been to preferentially complex one of the species or mask one of the electrode processes. Thus in reality it has generally been considered essential to avoid the problem of overlapping waves by varying the medium and, if this could not be done, then the determination is described as being interfered with by the species giving rise to the overlapping wave. While derivative, alternating current, differential pulse, square wave, and many other polarographic techniques are considerably superior with respect to resolution ( 2 ) ,practical analysis in the presence of overlapping waves is still not particularly convenient with these methods when using conventional analog instrumentation. Even though appropriate curve fitting procedures ( 3 )may be developed and applied to the readout of such instrumentation the procedures involved are necessarily both tedious and time consuming and unlikely to be generally useful in routine analytical work. The widespread advent of minicomputers and on line polarographic techniques (4-7)has opened up new dimensions in the application of analytical polarography. Despite the availability of the technology it is doubtful even at this point in time if many laboratories performing routine analytical work have departed from the analog based instrumentation and taken advantage of the many possibilities (8, 9). If polarographic data can be stored directly, and in digital format, complex calculations or other data manipulation are readily performed in real time, and prospects for undertaking routine determination of two species giving rise to overlapping polarographic waves become a reality as has been admirably On leave from the Department of Inorganic Chemistry, Faculty of Technology, University of Zagreb, Zagreb, Yugoslavia. 1624
.
demonstrated by Perone and co-workers ( 1 0 , l l )with respect to linear sweep voltammetry at a dropping mercury electrode. Recently, a relatively inexpensive commercially available multifunctional polarograph contro!!ed by a microprocessor has been developed (see Experimental). This microprocessor controlled system provides all the features associated with digital instrumentation and includes the facility for storage of polarographic data and the mathematical manipulation of subtraction. In the present communication we wish to demonstrate that these features are all that are required to undertake the routine determination of two species giving rise to overlapping polarographic waves. The method is extremely simple and reliable, and is completely experimentally based. Since the method does not depend on utilizing any complicated algorithm or curve fitting procedures, mathematical expressions describing the wave shapes are not required and the method is completely general for all classes of electrode process, assuming, of course, that no cross redox reactions or other phenomena ( 1 2 ) leading to nonadditivity of current occur. The problem we chose to investigate via the reported method concerns the problem of determining lead and thallium simultaneously. This is a well-known example of two species giving rise to overlapping polarographic waves in many media (13).In particular, we also chose to investigate the feasibility of applying our method to an immediate problem confronting these laboratories ( 1 4 ) .The efficiency and purity of the product in the electrolytic reduction of zinc from zinc sulfate electrolyte is critically determined by trace amounts of many metals (14,15). Batley and Florence have already shown that in this medium anodic stripping voltammetry for the determination of lead and thallium a t a hanging drop mercury electrode is complicated by the similarity of their E112 values (16). We are now able to report that via our method using differential pulse anodic stripping voltammetry with a microprocessor controlled polarographic system that thallium can be determined directly in zinc sulfate electrolyte in the presence of a 50-fold excess of lead and lead in the presence of a 100-fold excess of thallium. This represents about two orders of magnitude improvement over the conventional situation.
EXPERIMENTAL All chemicals used were of reagent grade purity. Solutions were degassed with Argon for 5 min prior to recording a polarogram. No thermostating of solutions was used and ambient temperatures of (22 f 1)OC were considered acceptable for temperature control. The instrumentation consisted of a Princeton Applied Research Corporation (Princeton, N.J.) Model 374 Microprocessor Controlled Polarograph and a Model 302 Universal Mercury Electrode with Model 301 Cell Compartment. A three-electrode system was used with the working electrode being either in the pressure controlled dropping mercury electrode format (differential pulse polarography) or the hanging mercury drop mode (differential pulse anodic stripping voltammetry). The reference electrode was Ad AgCl (saturated KCl) and the auxiliary electrode was platinum wire. Further experimental details for operation of the polarograph are given in the Results and Discussion section. Theoretical simulations of differential pulse polarograms were performed on a PDP-11 minicomputer. The program for successive
ANALYTICAL CHEMISTRY, VOL. 48, NO. 11, SEPTEMBER 1976
containing A plus B and
Prepare blank plus A
Prepare blank plus B
polarogram
t’ Subtract result from sample
Examine result visually
I ’:.’.;::‘ ! r e s u l t fror”
~
~
1-1
visual1
r Amount o f
Amount o f A :
(1) too l i t t l e ( 2 ) correct ( 3 ) t o o much
I
Figure 2. Simulated differential pulse polarographic curves showing the determination of two reversibly reduced species, A and 6,of equal concentration
B:
(2) correct ( 3 ) t o o much
nA = nB = 1; A € = -25 mV; Drop time = 0.5 s; 6 = 40 ms; separation in €112 = 75 mV. (A) Polarograms of individual components, A and B. (B) Polarogram actually recorded(A plus B). (C and D)Addition of A and B to blank, respectively. (E)Determination of B (Ai-@ curves observed after subtraction of increasing concentrations of A. (F) Determination of A (Ai-@ curves observed after subtraction of increasing concentrations of B
P-l
r-5
Determine A
Determine B
Flgure 1. Flow diagram of the method for determining two species giving rise to overlapping waves
subtraction o f curves w i t h increasing amounts of individual component f r o m the curve of “sample” and procedures for recording the simulated polarograms directly onto a n XY recorder were written in Basic language.
THEORY The theory for determining two species giving rise to overlapping waves is exceedingly simple as are the experiments involved in the determination. Figure 1 is a flow diagram of the operations involved and Figures 2 and 3 demonstrate simulated results with differential pulse polarography. The theory used for the simulation of the differential pulse polarograms is for reversible reduction ( I 7) and includes terms for faradaic distortion. Figure 3. Simulated differential pulse polarographic curves for deter-
+
where Ai = differential pulse current, Ai = i 2 ( 7 6) - il(7); 7 = time a t which current, i 1 ( ~ )is , measured prior to pulse application at potential E l ; 6 = time at which current, i 2 ( 7 6), is measured after pulse application; €1 = exp[(nF/RT)(El - E1/2)]; u2 = exp[(nF/RT) AE];AI3 = pulse amplitude; K is a constant; C = concentration. All other symbols have their usual meaning. For differential pulse stripping voltammetry, similar equations apply but terms for faradaic distortion (area growth of dropping mercury electrode) can be ignored. The same calculation procedures also of course would apply in ac, square wave, and other polarographic waves. It should be immediately recognized, however, that the method utilized does not require a mathematical description of the wave shape and is generally applicable to reversible, irreversible, and kinetically controlled processes (see flow diagram, Figure 1).
+
mining two species. Same as Figure 2 except nB= 2 and separation in Ella = 50 mV
Experimentally, the following sequence of procedures is undertaken. In the first instance the differential pulse polarogram of the solution to be determined is recorded and stored in memory. Consider, for example, the situation when two species, A and B, give rise to the overlapping waves, with A being reduced at more positive potentials than B. The shape of the observed polarogram will depend on the separation in Elj2, the concentration ratios, and of course the nature of the electrode process. Figures 2 and 3 demonstrate some of the possibilities as simulated on a PDP-11 minicomputer. After recording the sample solution, a blank solution containing neither A nor B is placed in the polarographic cell. If A is to be determined then increasing concentrations of B are titrated into the cell and polarograms of the blank plus B recorded.
ANALYTICAL CHEMISTRY, VOL. 48, NO. 11, SEPTEMBER 1976
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Ai
-06 - 0 5 -04 - 0 3 -02 Volt vs A g l A g C l
B
-06 - 0 5 -04 -03 -02
Volt vs A g I A g C l
0 -06 - 0 5
-04 -03
-06 - 0 5 -04 -03
Volt vs Ag /Ag CI
Figure 5. Determination of thallium in zinc sulfate electrolyte by differential pulse anodic stripping voltammetry at a hanging drop mercury electrode Volt
Flgure 4. Determination of
lom7 M thallium and
VE
AglAqCl
M lead in 1 M zinc
sulfate by differential pulse anodic stripping voltammetry at a hanging drop mercury electrode Electrolysis time = 2 min. Equilibration time = 15 s. (A) Curve for mixture of M lead and M thallium. (E) Curve for M lead. (C) Curve for M thallium. (D) Curves for determination of lead. 1, 2,3, and 4 designate the subtraction of increasing amounts of thallium. (E) Curves for determination of thallium. 1, 2, 3, and 4 designate the subtraction of increasing amounts of lead
After each addition of B the Ai-E curve for this solution is automatically subtracted from that for the polarogram of the mixture already stored in memory. The resultant Ai-E curve is then examined. After addition to the blank of close to the amount of B present in the sample solution to be determined, the resultant polarogram obtained by the subtraction procedures will contain the peak height of A void of interference from electrode process B and A can then be determined in the normal way by reference to a standard calibration curve. If too much B has been added to the blank, then after subtraction, Ai values on the more negative potential side of peak A will lie below zero. This point is readily recognized as seen from Figures 2 and 3. The subtraction operation, as well as eliminating B, also nulls the charging current contribution to the polarogram so the use of an absolute zero as a guideline or reference point is readily implemented. Having determined A, then the determination of B is easily undertaken by commencing with a new blank, titrating A into the cell, and repeating the calculation procedure. However, on this occasion the point where excess A has been added will be revealed by a resultant negative Ai value on the more positive rather than negative potential side of the B peak (Figures 2 and 3). Table I provides quantitative data obtained from the simulated curves to show how the peak height and position of the species being determined varies during the course of an experiment. Provided that the currents for the two electrode processes are additive, then the above procedure is completely general and does not depend on knowing the mathematical formulation of either electrode process. The method also has the added advantage that visual observations provide a clear guideline that the method has been successfully implemented, Le., peak potentials and wave shapes should be the same as 1626
Electrolysis time = 2 min. Equilibration time = 15 s. (A) Curve normally recorded shows no thallium. (E) Curves for determination of thallium. 1, 2, 3 designate the subtraction of increasing amounts of lead. Concentration excess of lead is approximately 40-fold
standards and addition of too much of one species in the titration procedure leads to negative Ai values. To use the commercially available PAR 374 microprocessor controlled polarograph in the above format, simple alterations to the standard operating procedure need to be made. The polarogram usually recorded first and stored for subsequent calculations in this instrumentation is the “blank”, not the solution to be determined. However, in our proposed method we reverse all operations and record the solution to be determined in the “blank mode” as the first stage of the experiment. The sign of the Ai data is then changed and the result with inverted sign is stored in memory. The blank plus deliberately added A or B is then recorded in the “sample” mode with the inverse sign for Ai compared with the “usual” format and stored in memory. The instrumental subtraction of “sample” mode minus “blank” mode is then undertaken with the sign of the result being again inverted, if required, to give the display direction considered simplest to examine visually.
RESULTS AND DISCUSSION Experimental results exactly follow the pattern predicted by theory. With the universal mercury electrode, changing from differential pulse polarography to anodic stripping voltammetry at a hanging drop mercury electrode is extremely simple because the same electrode assembly is used in both instances. Since the stripping mode is usually considered the far more difficult procedure, experimental data are presented with this technique to demonstrate how simply the proposed method works in the practical situation. The example chosen as mentioned in the introduction is a practically important one, the determination of thallium and lead in zinc sulfate electrolyte. Figure 4A shows the differential pulse anodic stripping M lead and low7 voltammogram of a synthetic solution of M thallium in 1 M ZnSO4 acidified to pH 2 with HzS04.Figures 4B and 4C show the curves individually obtained for each of the species at the M level in 1 M ZnSOr. The peak potentials are -0.37 and -0.43 V vs. Ad AgCl for the electrode
ANALYTICAL CHEMISTRY, VOL. 48, NO. 11, SEPTEMBER 1976
Table I. Variation of Peak Position and Peak Current During the Course of an Experiment Determination of A AE1/2
% species A or
B added
= 75 mV
-(Ep)AppA
50 mV
(Aip)AppA
-(Ep)~pp~
(Aip)AppA
115" 115" 114" 114" 114" 113 113 1126
23sc 236c 235 233c 228C 195 188 184 182 17gb 176b 174 172b
473c 392c 308' 224' 143'
191a 190" 190" 190" 189a 189 188 187 187 185 185 184 183
0 20 40 60 80 90 100e 110 120 140 160 180 200
AE1/2 =
l l l b llOb
1096 108b 107
118 113 109 106 lOlb
97b 93b 91b
AEt/z
= 25 mV
-(Ep)AppA
212c 211' 210c 209' 206 200c 188 177 171 164 159 156 152
(Ai p)AppA 513c 43OC 347c 263 180C 142 113 97 87 756 66 60 556
Determination of B AE1/2
% species A
or B added
0 20 40 60 80 90 100e 110 120 140 160 180 200
= 15 mV
- (E,)A,,~
(Aip)AppB
262d 262d 262d 262d 262 263 263 263 263 263 263 263 263
448d 443d 438d 433d 428 425 422 420 417 413b 408 403 3986
AEtiz = 50 mV
, ( E ~ ) A , , ~ (Aip)AppB 236d 236d 237d 237 237 237 238 238 238 238 238 239 239
475d 46fid 455d 444 433 428 423 417b 412 402 391 381 371
AEl/z = 25 mV
-(Ep!~ppB 211 211 212 212 212 212 213 213 213 213b 214b 214b 214
(Aip)AppB
513 496 478 459 44 1 432 423 414 404 386 368 350 332
a Apparent peak of species A is actually a shoulder. Part of curve on side of species being added falls below zero current. c Apparent peak of species A is not observed because of severity of overlap. Peak tabulated is the one observed for overlapping system. Species A is observed as a shoulder. e True values appear in 100%row. f Simulated differential pulse polarograms for the determination of two reversibly reduced species A and B of equal concentration. E 1 1 2 ~= -200 mV vs. reference electrode; n A = 1; r7.B = 2; drop time = 0.5 s; pulse amplitude = -25 mV; 6 = 40 ms; temp = 25 "C; (E,)A,,* = apparent peak potential of A in mV; = apparent peak potential of B in mV; (Aip)~ppA= apparent peak height of A in arbitrary units; (Aip)AppB = apparent peak height of B in arbitrary units.
+
+
processes Pb(Hg) e Pb2+ 2e and Tl(Hg) e T1+ e, respectively. Figure 4D shows the determination of thallium via the method described in the theoretical section, when lead is added to the blank 1 M ZnSO4. Figure 4E shows the determination of lead by addition of increasing amounts of thallium to the blank ZnS04 and the subtraction from the curve for the sample solution. The peak height obtained for each of lead and thallium on the sample solution via the subtraction procedure is identical with that for the M solutions recorded separately within the limit of experimental error (&l%). Further recognition that the correct waves have been obtained should be made on the basis of comparing peak potentials and wave shape (half-width) with calibration curves. Error in the subtraction procedure would obviously arise if reference electrode or instrumental potential drift were to occur. However, potential drift over a period of 10 days was
