1209
Anal. Chem. 1904, 56, 1209-1214
The heavy metals are important interferents in the CSV determination of sulfides in solution (10)as they react with S2-. When H2Sis accumulated directly from the gaseous phase at the AgMPE, minimal complications can be expected in this respect (1) because of the large differences in the solubility product values between Ag2S and the heavy metal sulfides (Pb, Cu, Zn), which are found most frequently as trace interferents in the base electrolyte solution, and (2) because of the small volume of supporting electrolyte existing in the pores of the AgMPE. The noninterference of these anions and heavy metals on the determination of H,S by our method was verified experimentally. Serious interference can be expected from volatile mercaptans.
CONCLUSIONS The AgPME can be used for the constant potential collection and subsequent CSV determination of H2S. A certain minimum amount of H2Smust be collected in order to obtain an analytically useful CSV current peak. This critical amount most probably depends on the porosity and the amount of silver making up the electroactive part of the electrode
membrane and will have to be found experimentally for a given electrode. Registry No. H2S,7783-06-4;Ag, 7440-22-4;A@, 21548-73-2.
LITERATURE CITED Gifford, P. R.; Bruckenstein, S . Anal. Chem. 1980, 5 2 , 1024. Gifford, P. R.; Bruckenstein, S . Anal. Chem. 1980, 52, 1028. Beran, P.; Bruckenstein, S. Anal. Chem. 1980, 5 2 , 2209. Nygard, D. D. Anal. Chlm. Acta 1981, 727, 257. Beran, P.; Bruckenstein, S. Anal. Chim. Acta 1980, 736, 389. Brainina, K. 2 . Talanta 1971, 78, 513. Mlwa, T.; Fujii, Y.; Mizuike, A. Anal. Chlm. Acta 1972, 6 0 , 475. Youssefi, M.; Birke, R. L. Anal. Chem. 1972, 4 9 , 1380. Florence, T. M. Anal. Lett. 1978, 7 1 , 913. Florence, T. M. J. Electroanal. Chem. 1979, 9 7 , 219. Florence, T. M. J. Nectrosnal. Chem. 1979, 9 7 , 237. Shimizu, K.; Osteryoung, R. A. Anal. Chem. 1981, 5 3 , 584. Sherwood, W. G.; Martinchek, G. A.; Gal-Or, L.; Bruckenstein, S. Tech. Prog. R e p . - U S . Bur. Mlnes 1975, Grant No. 155007. Opekar, F.; Bruckenstein, S., unpublished results SUNY at Buffalo, 1981. Shah, I.; Perone, S. P. Anal. Chem. 1961, 33, 325
RECENEDfor review December 19,1983. Accepted March 12, 1984. This work was supported by the Air Force Office of Scientific Research under Grant No. 83-0004.
Precision in Differential Pulse and Alternate Drop Differential Pulse Polarography Per Baecklund, Leif Nyholm, and Gunnar Wikmark*
Department of Analytical Chemistry, Uppsala University, P.O. Box 531, S - 751 21 Uppsala, Sweden
I t is shown that the relative precision Is better In ordinary than alternate drop differential pulse polarography from millimolar to micromolar concentrations of Pb( I I). At the lower concentratlon level, the reproduclbllity of the two techniques is equal. The theory presented for the repeatability, based on proportionality between nolse and Faradaic current, Is in good agreement with the results obtained at the higher concentration level.
Little has been reported on the precision of current responses in concentration determinations in polarography. In the studies made, very few clarify whether the reported precision is obtained from consecutive experiments on the same solution (repeatability) or from experiments on different days (reproducibility). Investigations of direct current polarography (DCP) with two matched dropping electrodes have been made (1,2)with a precision as good as 0.1% reported. Lingane (3) investigated time-integration of the diffusion current in DC polarography and reported a precision of *0.1% in 1-10 mM solutions of cadmium and zinc in 1M potassium chloride. In a study on background correction Bond and Grabaric ( 4 ) reported a standard deviation of 2 % , using differential pulse polarography (DPP) for solutions of about IO4 M and 3% for solutions of lo-' M. By integration of the DPP peak, Stutts et al. (5)obtained a precision of 1-2% for lo+ M anthraquinone. This study was made because, for analytical purposes, a thorough investigation was needed to evaluate the precision of differential pulse polarography. To diminish the possible
influence from instrumental artifacts, two polarographic instruments were used, one analog and one microcomputercontrolled digital polarographic analyzer. The influence on repeatability from choice of electrode assembly, a PARC 303 static electrode or a dropping mercury electrode (DME), from the use of the first drop technique and choice of evaluation procedure are discussed. When Christie et al. introduced the alternate drop differential pulse polarography (ADPP) (6) they reported an improvement in accuracy and precision, defined as an increased signal-to-noiseratio, in favor of the ADPP technique compared to the DPP technique. Their conclusions are based on noise measurements on the supporting electrolyte. In a preliminary work we wanted to exploit the advantages of the ADPP technique, but the expected improvement ih precision was not obtained. As will be shown, the fluctuations in Faradaic current are of considerable importance for the overall precision. Whenever these fluctuations are greater than the background noise, DPP would be expected to have better relative precision than the ADPP technique.
THEORY The Alternate Drop Differential Pulse Polarography. In ordinary DPP the current is measured twice on each drop, once before the pulse is applied and once at the end of the pulse, immediately before the dislodgement of the mercury drop (7). The current response recorded is the difference between the second and the first sampling. The alternate drop technique requires two drops for the two samplings of the current. The potential program applied to the first drop is identical with that in ordinary DPP, but the only current sampling taken is the one corresponding to the second Sam-
0003-2700/84/0356-1209$01.50/00 1984 American Chemical Society
1210
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
pling in ordinary DPP. To the second drop, a DC potential equal to the sum of the ramp and the pulse potential is applied. The current is again sampled immediately before the dislodgement of the drop. The current response recorded is the difference between these two current samplings. In this way the capacitive current charging the mercury drop is compensated. The direct current contribution (DC effect (a)), arising from the increasing area of the drop between the samplings in DPP, is also eliminated. The current samplings during the potential pulse are identical in the two techniques. The current measured in the absence of the pulse will be larger when ADPP is used, due to a more polarizing potential then in DPP, and thus the difference between the two current samplings taken is smaller in ADPP than in DPP. Accordingly, the expressions for the peak currents will be ~ D P P= ipulse - ~ D C
~ A D P P= ipuise
- ~DCM
(1)
= E1/2 - m/2
(3)
At this potential, the factor M is interpreted as
+ exp[nF(-AE/2)/R!Fj 1 + exp[nF(+AE/2)/RT]
(4)
The quotient between the ADPP and DPP peak current responses, called the diminution factor, d , is defined by
d =
iADPP/iDPP
(5)
For a reversible process this equation has been shown (6) to imply that
d = 1-
[7tp/3tdI1l2
Introduction of the expressions for the different current samplings according to eq 8 gives =
g2lADPp Q21p",e[1
(6)
where t, is the duration of the pulse and t d is the drop time. d is always smaller than 1. By insertion of the definition of the diminution factor (eq 5) into eq 1 and 2, expressions for the current responses as functions of ipulse are obtained
where z = ( d - l)/(d - M). Sources of Error. The noise in the polarographic current measurement has many sources. A source of noise can give either a constant contribution (powerline noise pickup, electronic noise, etc.) or a contribution dependent on drop area. The drop-area dependent noise arises from variations in concentration (dilution errors), vibration of the drop, unstable reference electrode, etc. and is proportional to the current response since the polarographic current is proportional to the drop area (7).The constant contribution is equally present in background measurements and actual samples. Only part of the drop-area dependent noise will be present in the current recorded with supporting electrolyte. At sufficiently high
+ (ZW21
(9)
In the DPP mode some covariation of the errors in the samplings is expected because the samplings are taken on the same drop and rather close in time. This covariation will reduce the sum of variances in the DPP mode according to u21Dpp
=
uzlpuhe
+ u2$Dc
-
2c(ulpu~w)(ulD~)
where c is the coefficient of correlation between the sampling before and on the pulse in the DPP mode. c can have a value between 0 and 1 when there is a positive covariation. As in the case of ADPP, the standard deviation of the current noise is assumed to be proportional to the current, hence, implied by eq 7 U2iDPP = u21p",se[l
1
M=
As stated above, the noise and thus the standard deviation, u, of the current measurements is assumed to be proportional to the current response, thus (cf. eq 2)
(2)
where ipulse and iDc are the current samplings at the peak potential during the pulse and in absence of the pulse, respectively. The factor M is the ratio between the current samplings at different potentials on the DC wave in the two modes. This factor is always bigger than one as described above. In eq 1 and 2 and the derivations below, the DC effect has been neglected, since its contribution to the recorded peak current normally is very small. Assuming a reversible process, the peak potential in differential pulse polarography is given by (9) Epeak
sample concentration the background noise can be neglected. Errors in the current response at the different ADPP samplings are assumed to be independent since they are taken on different drops. The total variance, uziADPP, of the current noise is then given by the sum of the variances of the different samplings, uzipdw and u2iocM a2impp - dzipulse+ g 2 i , c ~
+ 22 - 2 x 1
(10)
The ratio between the standard deviations of the two modes is obtained by combination of eq 9 and 10
".=[
UIDPP
+z 2 w 1 + 2 2 - 2zc 1
1
li2
(11)
Since 0 € c € 1, eq 11 indicates that the absolute error is always larger in the alternate drop mode than in the ordinary mode. This is mainly due to the higher current in the ADPP sampling without pulse (M > 1). Assuming no covariation (c = 0), normal polarographic conditions ( t d = 0.5 s, t, = 0.05 s, AI3 = -50 mV and the number of electrons, n = 2) will give d = 0.52 and M = 7 , and the standard deviation ratio is about 1.2. The lower ADPP current read-out (difference between current samplings) causes the relative standard deviation to be l / d times higher than that of DPP. Thus the ratio in relative standard deviation, (uADPP/rrDPP)(l/d), is about 2.3 with the above given conditions. The signal-to-noise ratio is defined by S / N = (average signal)/(RMS noise) The average signals for the DPP and ADPP current responses are given by eq 7 and 8, respectively. By combining these equations with the expressions for the RMS noise (the standard deviation of the current noise, from eq 9 and 101, one obtains
where k is a proportionality constant. As before, proportionality between the noise and the Faradaic current has been assumed. Figure 1 shows the SIN ratios vs. drop time for the
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984 S/N
(normalized)
1211
The double distilled mercury (KEBO AB, Solna, Sweden) was purified through washing with 10% sodium hydroxide for several hours, followed by washing with 10% nitric acid, water, and drying. The deaeration of the samples was performed with nitrogen passed through a BASF BTS catalyzer (BASF AG, Ludwigshafen, West Germany) to remove traces of oxygen, and through 10% sodium hydroxide solution, 10% sulfuric acid, and water. All chemicals were Pro Analysi (Merck AG) and were not further purified. Three solutions were used, one pure background electrolyte of 0.1 M sodium nitrate, one 0.2609 mM Pb2+in 0.1 M sodium nitrate, and one 3.914 pM Pb2+in 0.1 M sodium nitrate. The latter solution was prepared daily. All solutions were 0.01 M in “OB. Each sample consisted of a 10.0 mL solution. The samples were deaerated for 10 min at the higher concentrations and 15 min at the lower. The flow of the nitrogen was constant during the whole work. In the experiments with the PAR instrument the mercury flow rate was 1.11mg/s. When the computerized equipment was used, the mercury column height wa8 lowered and the flow was 0.99 mg/s: In these latter experiments, the samples also had an addition of 20 FL of a 0.1% Triton X-100 solution. These changes were done in order to minimize streaming, which had not been observed with the PAR instrument. Evaluation Procedures. Peak heights obtained in the determinations of lead with the PAR 174 were evaluated by measurement of the peak height relative to the background with a ruler. Three different evaluation procedures to obtain the peak current response were employed with the computerized instrument. The first utilizes a single point, i.e., the point of maximum current. The second procedure involves nonlinear least-squares fitting of the theoretical reversible polarogram (8, 9) to the recorded polarogram. The third uses integration of the peak. Integration of a DPP polarogram will result in a normal pulse polarogram. With a method similar to the area determination described by Stutts et al. (5),the sum of all the 208 current points was multiplied by the potential step and divided by the pulse height. Theoretically, the normal pulse diffusion current is obtained in this way, and with the parameters used in this work the NP current should be 1.33 times bigger than the DP peak current (9). This is in good agreement with our experimental results. In all the above described procedures, a background polarogram recorded the same day as the sample polarogram was subtracted from the latter. Before the subtraction, the polarogram of the background was vertically adjusted to coincide with the base line of the sample polarogram. Background currents were evaluated according to the area determination procedure and also by using the current at the same potential as the point of maximum current in the above determination.
7 1
RDPP
Figure 1. Calculated signal-to-noise ratio vs. drop time for alternate drop (ADPP) and ordinary (DPP) pulse polarography, according to eq 10 and 11: pulse height 50 mV, pulse width 50 ms,n = 2, k = 1, and c = 0. two modes with k = 1 and c = 0. I t is obvious that D P P is superior to ADPP in this respect. When the background noise is bigger or equal to the drop area dependent noise, the discussion above is not valid. Nevertheless, because of the smaller current readout of the ADPP technique, this mode will still have a bigger relative noise level, if the absolute levels are equal. EXPERIMENTAL SECTION Instrumentation. In the first series of experiments a PAR 174 polarographic analyzer (Princeton Applied Research Corp., Princeton, NJ) was used. The polarographic readout was presented on an HP 7044 X/Y recorder (Hewlett-Packard,San Diego, CA). The second series of experiments were performed with a microcomputer-controlled polarographic analyzer described elsewhere (10). The software (11)was slightly modified to produce a 60-ms stripping pulse on each mercury drop before it was dislodged. This stripping pulse regenerated most of the previously reduced metal ions into the solution. Thus, many experiments could be performed on the same sample without significant lowering of the bulk concentration. Noise reduction was accomplished with the microcomputercontrolled instrument by taking the median of three samplings during the first 0.3 ms of each ms. The mean of 20 medians, during 20 ms, was taken as a measure of the current. Noise was further reduced by hardware through optocouplers separating the analog and digital circuitry and by a differential input instrumentation amplifier on the input of a 12 bit A/D converter. The DME capillary had a drownout tip, as described by Meites (12), and all tubing in contact with mercury was made of glass or Teflon. A PAR 174/70 Drop Timer (Princeton Applied Research Corp.) was employed to dislodge the drops. In one experimental series a PARC 303 static mercury drop electrode (Princeton Applied Research Corp., Princeton, NJ), with drop size “small”, was employed. A platinum wire was used as counterelectrode and a Metrohm 437 Ag/AgCl electrode was used as reference electrode. All experiments were performed in a room thermostated to 25 0.2 OC to keep the mercury at constant temperature (3). The polarographic cell was further thermostated to 25 f 0.1 O C by a Haake FJ thermostat (Haake Gebriider, Berlin, West Germany). If not otherwise stated the instrumental parameters used in the polarographic experiment were drop time (td)0.5 s, pulse duration (t,) 60 ms, and pulse height (AE) -50 mV. The potential interval -150 to -550 mV was scanned in each run. With the computerized instrument, this interval was covered by a total of 416 current samplings, i.e., 208 DP current points and consequently a scan rate of -1.92 mV/s in the ADPP mode and -3.85 mV/s in the DPP mode was used. The stripping pulse applied with this equipment had a duration of 60 ms. Chemicals and Solutions. All water used was deionized and distilled and then filtered through a Milli Q filtration system (Millipore Corp., Bedford, MA),
RESULTS Simulation. An evaluation of the described methods of determining the current response was made by simulation of DPP and ADPP polarograms. For evaluation of the peak current, a least-squares refinement of the peak current and half-wave potential of a theoretical polarogram and determination of the area of the peak, as described above, was made. When theoretical DP and ADP polarograms were evaluated, the peak current could be recovered within 0.1 % and the half-wave potential within 0.02 mV, which were the limits set by the convergence criterion in the evaluation programs. Further simulations with noise added to the theoretical polarograms indicated that the use of area evaluation and the least-squares refinement were equally good to recover the peak current. With a rectangular distributed noise of 0-1% of the total cell current added to the polarogram, peak heights were recovered with a relative standard deviation of about 0.1%, with no detectable systematic error. When a single point, Le., the point of maximum current was used in the evaluation, a standard deviation five times higher was noted. Results of the PAR 174 Experiments. Each experiment consisted of ten DP polarograms recorded from the same 10-mL sample. Each day one sample of the higher, one of the
1212
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
to five times on different days during a period of several weeks. Every day, with one exception, a background was recorded and used in the evaluation of that days experiments. Table I1 presents the results obtained from DP and ADP polarographic experiments on the background electrolyte. The results from the solutions of high and low lead concentration are shown in Table 111. First Drop Technique. An experiment to test the influence of the depletion of the solution was made, using the first drop technique. Every “active” drop was preceded by five drops held a t the initial potential. No difference (
