Analyst, October, 1980, Vol. 105, $$. 939-943 939 A New Approach to the Quantitative Analysis of Overlapping Anodic-stripping Voltammograms Juei H. Liu Department of Criminal Justice, University of Illinois at Chicago Circle, Chicago, Ill. 60680, USA A method, analogous to that used for studying overlapping bands in absorption spectroscopy, has been developed for the quantitative analysis of overlapping anodic-stripping voltammograms. Six simultaneous equations were formulated to resolve general overlapping voltammograms. When the second species is not oxidised at the peak potential of the first species these six equations are reduced to four. Provided that the oxidation currents are additive, this approach is not limited by the degree of overlap. The method has been shown to be satisfactory by studying the cadmium - lead pair as an example.Keywords : A nodic-stripping voltawametvy ; overlapping voltawanvnograms; quantitative analysis Anodic-stripping analysis of mixtures often involves dealing with overlapping voltammograms. For quantitative determination of individual species the contribution of each species to the overlapped signal has to be resolved. The standard pr~cedurel-~ involves extrapolation of the preceding peak and determination of the peak height from this extrapolated base line. Sophisticated measurements4 have also been made using an on-line computer. An empirical equation was first developed that described the general voltammograms for a wide variety of electroactive species, then this function was fitted to a number of standard voltammograms and the constants in the function, specifically determined for each species, were stored in a library.When analysing an unknown mixture these constants were used to regenerate the standard graph, a composite of which was then fitted to the unknown signal. In this work an alternative approach, analogous to those usedin handling overlapping bands in absorption spectroscopy, was developed for solving the problem of overlapping voltammo- grams. Resolution of overlapping voltammograms is achieved by solving four or six simul- taneous equations, depending upon the severity of the overlap. This approach eliminates the uncertainty of the traditional extrapolation pr~cedurel-~ which cannot be used for severely overlapped voltammograms. In contrast to the numerical deconvolution method, it does not require any additional instrumentation. Essentially this approach involves the measurement of two current values a t the peak potentials of the two species involved and the solution of equations derived from the following assumptions: (i) the current values measured are the sum of the oxidation currents of each species; (ii) the ratio of the currents contributed by the species in a peak potential is determined by their concentration ratio and their specific current height ratio; and (iii) peak current is proportional to concentration with a proportionality constant that can be obtained by plotting the current height newus concentration results obtained for each individual species in isolation.Information required for the interpretation of overlapping voltammograms can therefore readily be derived from the voltammograms of individual species in isolation.Two individual voltammograms are therefore obtained using known concentrations of the species under study. The information obtained is then used to solve the simultaneous equations derived, to obtain the concentration of each species in the mixture. Experimental Apparatus All experiments were performed on a polarograph constructed in our laboratory (Fig. 1). A saturated calomel electrode (S.C.E.), a platinum electrode and a hanging mercury drop electrode were used as the reference, counter and working electrodes, respectively. A two- channel Hewlett Packard, Model 7100-15, recorder was used for recording the voltammograms and the anodic-voltage scans.940 LIU: NEW APPROACH TO QUANTITATIVE ANALYSIS OF Analyst, Vd.105 0 t15 V I I Fig. 1. Simplified schematic diagram of the polarograph. Solution Preparation A 1 M buffer solution of pH 5.9 & 0.1 was prepared by dissolving 2.4 ml of 99.77; acetic acid and 129.2 g of sodium acetate trihydrate in de-ionised distilled water and diluting to 1 1. A 0.1 M acetate buffer, prepared from the 1 M stock solution, was used as the supporting electrolyte. The buffer solution was passed through a Chelex 100 (Bio-Rad Laboratories, Richmond, Calif.) column to remove trace amounts of copper. M) of cadmium and lead were prepared by dissolving appropriate amounts of analytical-reagent grade cadmium nitrate and lead nitrate in the 0.1 M acetate buffer.Stock solutions Procedure In a typical experiment the following conditions were used: (i) a mercury drop with radius and surface area of 0.0490 cm and 0.0302 cm2, respectively; (ii) a 5-min de-aereation of 50 ml of 0.1 M acetate buffer solution in the electrolysis cell, before the addition of thesolution containing the species to be determined; (iii) pre-electrolysis a t .- 0.85 V (zleysus S.C.E.) for 3 min with stirring and then I min without stirring; and ( ~ z J ) an anodic scan rate of 1.22 V min-I. Concentrations of working solutions were changed as necessary by the addition of 2.5 x M standard solutions. Results and Discussions In most instances the second species is not oxidised a t the peak potential of the first species (Type I). The overlapping therefore involves only the addition of the tailing oxidation current of the first species to the oxidation current of the second species.Severely overlapped voltammograms (Type 11) also include the oxidation current of the second species at the peak potential of the first species. The cadmium -lead voltammogram (Fig. 2 B) obtained under the experimental conditions described represents Type I overlapping. Type I1 overlapping would be shown on the same voltammogram by imagining that the peak potential of the cadmium voltammogram was - 0.42 V ( v c y s m S.C.E.). Current measured at this potential is then considered to be the peak current of the hypothetical cadmium species. Two types of overlapped anodic-stripping voltammograms are commonly observed.Voltammograms preceding this potential are ignored.October, 1980 OVERLAPPING ANODIC-STRIPPING VOLTAMMOGRAMS 94 1 I -0.55 -0.42 -0.38 VoltagelV, versus S.C.E. Fig. 2. Voltammoerams of A. 0.1 ;acetate buffer (PH = 5.9); B, 12.38 x lO-'nr Cd and Pb mixture; C, 7.48 x IO-'M Cd; and D, 9.96 x lo-' M Pb. In the simultaneous determinations of several species by electrochemical methods, it is commonly assumed that the electrochemical behaviour of a species is not affected by the presence of the other species in the mixture by, for example, the formation of an inter-metallic compound. IVith this assumption six equations can be presented for the examples used in this work: Hsurn,Cd = HCd,Cd + HPbrCd * * . . . . . . (la) H8um9Pb = HCd,Pb + HPb,Pb * a . . * . . . (lb) HCd,Cd = BCdCCd * * .. . . . . . . (2a) HPb,Pb = BPbCPb * . . .. .. . . (2b) . . * . . . (3a) HCd,Cd hCd,Cd cCd HPbvCd hPb,Cd cPb x - . . __=__ . . .. . . . . (3b) where C, is the concentration of species w in the mixture, B, is the slope of the peak current versus concentration graph for species x , H,,, is the current of species y measured a t the peak potential of species z and h,,, is the same as H V , , but measured with the species in isolation. The values of h,,, in Equations (3a) and (3b) are obtained a t the same concentrations and represent the currents produced by unit concentration of species y. For the best statistical results5 the h,,, ratios are replaced by the corresponding slope ratios from the current versus concentration graphs. Equations (3a) and (3b) can therefore be rewritten as HCd,Pb = hCd,Pb CCd HPb,Pb hPb,Pb cPb ... . . . . . (4a) HCd,Cd - bCd,Cd cCd HPb,Cd bPb,Cd cPb X- . . . . . . . . . . (4b) H x b - bCd,Pb HPb,Pb bPb,Pb942 LIU: NEW APPROACH TO QUANTITATIVE ANALYSIS OF Analyst, Vol. 105 where by,z is the slope of the current versus concentration graph of species y measured at the peak potential of species z measured with species y in isolation. It should be noted that all currents are measured from the base line rather than from the extrapolated voltammogram of any species. The cadmium - lead pair is an example of Type I overlapping. As lead is not oxidised at the cadmium peak potential, Hpb,Cd = bpb,Cd = 0 (entries 11 B and 11 c in Table I) and equations (la) and (4a) may be eliminated, leaving four simultaneous equations.Before the quantitative analysis of the overlapped unknown mixture data (entries I11 A and I11 F in Table I), BCd (= bCd,Cd), B,, (= and bCd,,, are derived from the current uerszhs concentration graph for the species in isolation. Under the experimental conditions used, these values are 0.248, 0.174 and 0.0607, respectively (entries I C, I1 G and I G in Table I). Equations (lb), (2a), (2b) and (4b) are solved. The calculated values of CCd and Cp, are 12.18 x and 12.10 x 1 0 - 7 ~ , respectively, which are in excellent agreement with the expected value of 12.38 x lo-' M. TABLE I ANODIC-STRIPPING VOLTAMMETRY DATA FOR CADMIUM, LEAD AND A CADMIUM - LEAD MIXTURE IN 0.1 M ACETATE BUFFER (pH = 6.9)#6 Column A B C D E F c' L---------' L-- -Y--- L-- ---d At Cd peak At hypothetical A t Pb peak potentials potential? Cd peak potential: 7 Concen- ?-----h--- - r----_A ~ r---L--- tration Slope of current Slope of current Slope of current Row Species x lo-' M IT versus concentration IT versus concentration 18 versus concentration graph graph I Cd 0.00 0.00 BCd= bcdtcd 0.00 Bed= bcd,cd 2.50 0.595 =0.248 0.165 = 0.0815 4.99 1.18 0.335 7.48 1.80 0.603 9.96 2.44 0.802 12.4 3.08 0.980 I1 Pb 0.00 0.00 BPb,Cd= bpb,cd 0.00 BPbrCd= bPb,cd 2.50 0.00 = O .O O 0.150 = 0.0632 4.99 0.00 0.262 7.48 0.00 0.374 9.96 0.00 0.531 12.4 0.00 0.673 I11 Cd - Pb 12.38 Hsum,Cd mixture each 3.01 2.99 Hsum,Cd 1.62 1.64 graph 0.00 bcd,pb= 0.0607 0.165 0.290 0.395 0.630 0.755 0.00 &b= bpb,pb= 0.174 0.344 0.770 1.24 1.67 2.13 2.88 * Symbols used in the table are defined in the test.t -0.55 V (ocvsus S.C.E.). -0.42 V (vevws S.C.E.). 5 -0.38 V (oevsus S.C.E.). 7 In units of 0.1 FA. Assuming that currents measured at -0.42 V (versus S.C.E.) (Fig. 2) are peak currents of cadmium and, ignoring voltammograms preceding this potential, a Type I1 overlap is pro- respectively (entries I E and 11 E, respectively, in Table I). CCd and c,, are then calculated from equations (la), (Ib), (2a), (2b), (4a) and (4b); the values obtained are 12.27 x and 12.11 x These results are in excellent agreement with those expected. Compared with the peak lead current the hypothetical cadmium, peak currents measured at -0.42 V (versus S.C.E.) (entry I D in Table I) are considerably lower. This indicates that this approach can be used even when the preceding species is in much lower concentration. The consistently low concentrations calculated for both cadmium and lead with both types of overlap are probably caused by the reduction in the mercury surface available to each species in the mixture.This error should be reduced by working at lower concentration levels. duced. The Values Of B C d (= bCd,Cd) and B p b , c d ( = bpb,,,) aIe niDw 0.081 5 and 0.053 2, M, respectively.October, 1980 OVERLAPPING ANODIC-STRIPPING VOLTAMMOGRAMS 943 If the solution in the electrolysis cell is changed reproducible results may not be obtained. The approach described here requires three separate solutions, one for the unknown mixture, one for cadmium and one for lead. A constant concentration of bismuth was added to each solution before the solution was changed. The peak current of the constant concentration of bismuth in each solution was used to check the reproducibility and to make corrections if necessary. A definite advantage of this approach compared with the traditional extrapolation method, is that all currents are measured from the supporting electrolyte solution base line. These measurements should eliminate the uncertainty caused by extrapolation. This procedure allows severely overlapped voltammograms to be resolved. References 1 . 2. 3. 4. 6. Delahay, P., “Sew Instrumental Methods in Electrochemistry,” Interscience, New York, 1954, p. 129. Ben-Bassar, A. M, I., Blinderman, J.-M., Salomon, A,, and Wakshal, E., Anal. Chem., 1975, 50, 534. Vydra, F., Stulik, K., and Julakora, E . , “Electrochemical Stripping Analysis,” Halsted Press, New Gutknecht, W. F., and Perone, S. P., Anal. Chem., 1970, 42, 906. Bauer, E. L., “A Statistical Manual for Chemists,” Second Edition, Academic Press, New York, Received March 13th. 1980 Accepted May 15th, 1980 York, 1976. 1971, p. 140.