0.061 f 0.001 cm sec-1 with a transfer coefficient of 0.27. Note that the rate constant in this case does not change for a given potential step since the current and therefore the effective potential were almost constant during the time in which currents were measured. Each point on the plot represents one experiment. Attempts were also made to determine kinetic parameters for reduction of Cd(I1) in 1.OM KN03, Cd(I1) in 1.OM KC1, and Co(II1) tris(ethy1enediamine) in 0.1M ethylenediamine/l.OM NaC104. All three systems proved to have rate constants too large to be measured under the conditions of our experiments. As noted above, the shortest time a t which meaningful 'data could be taken was 30 psec. For times of this order, the largest rate constant which could be determined, that is distinguished from diffusion control, is 0.8 cm sec-l. This lower limit of 0.8 cm
sec-1 may be compared to the range of 0.6 to 5.0 cm sec-1 found by ac impedance methods for Cd(I1) in nitrate and chloride media (11). Laitinen and Randles reported a rate constant of 0.13 cm sec-1 for Co(II1) tris(ethy1enediamine) (12); however, Sluyters-Rehback and Sluyters demonstrated that the reduction of the similar system Co(II1) in diethylenetriamine is diffusion controlled though complicated by adsorption of the cobalt complex (13). Received for review August 24, 1972. Accepted May 18, 1973. This work was partially supported by the University of Alabama Research Grants Committee. (11) N. Tanakaand R. Tamamushi, Electrochim. Acta, 9,963 (1964). (12) H . A. Laitinen and J. E. 6 . Randles, Trans. Faraday SOC.. 51, 54 (1955). (13) M. Sluyters-Rehbach and J. H. Sluyters, J. Phys. Chem., 75, 2209 (1971).
Experimental Study of the Phase-Selective Anodic Stripping Analysis of Micromolar Cadmium(l1) at the Micrometer Hanging Mercury Drop Electrode in 0.1M Potassium Chloride E. D. Moorhead and P. H. Davis Departments of Chemical Engineering and Chemistry, University of Kentucky, Lexington, Ky. 40506
Conflicting reports in the literature pertaining to the observed magnitude of the ac phase-selective current obtained in the anodic stripping of Cd from the HMDE prompted an experimental reassessment of the stripping behavior of this metal using a micrometer-type HMDE and 0.1M KCI as base electrolyte. Reproducibility of the stripping analysis was indicated by a 1.20% average deviation in the measured peak height obtained for ten independent runs at the micromolar Cd(ll) level. The functional dependence of peak height on signal frequency, applied ac voltage, and cadmium concentration conformed to theory developed previously for ac polarography. However, observed in-phase peak currents obtained during the stripping step were substantially smaller than those reported by previous authors for the same experiment. The influence of stripping scan rate on the CdCd(Hg) system was examined, and peak heights were found to be strongly dependent on this parameter. The importance of maintaining well-controlled conditions during pre-electrolysis was indicated from brief studies of peak height dependence on solution volume and stirring rate.
Anodic stripping voltammetry (ASV) has been utilized frequently for trace metal analysis a t various electrodes with most of the practical applications to date having been made with the hanging mercury drop electrode [HMDE]. The technique's extraordinary measurement sensitivity hinges on a preconcentration step whereby the trace material in a typical 10-ml to 100-ml sample solution is first electrochemically deposited into a mercury cm3 volume. Applicamicroelectrode of about 5 x 2178
tion of a positive-going voltage sweep to the resulting dilute amalgam then results in re-oxidation or "stripping" of the dissolved metals a t their characteristic potentials. In most of the ASV work reported heretofore, measurement of the collected trace material has involved a rapid, linear reverse scan of electrode potential with simultaneous recording of the direct current peak associated with each of the collected species. As described in several reviews (1-3), such analyses have employed either the Kemula electrode configuration (2), designated here as HMDE(K), where the electrode consists of a stationary drop extruded from a micrometer-driven capillary, or the platinum contact configuration [HMDE(Pt)], in which one or more mercury drops obtained from a dropping mercury electrode are suspended from a Hg-plated Pt contact sealed in glass, the flush Pt ,surface having been etched back ca. 0.1 mm to improve drop stability and shielding of the Pt from the solution ( 4 ) . For either electrode configuration, dc voltammetric stripping results in unsymmetric current peaks which "tail." This theoretically predictable feature of the dc process offers no major disadvantage a t moderate to high trace concentrations, but a t ultra-trace levels with low signal/noise ratios, such drawn-out peaks seriously impair both precision and resolution. To circumvent this prob(1) I . Shain in "Treatise on Analytical Chemistry," Part I , Vol. 4, I . M . Kolthoff and P. J. Elving, Ed., Interscience, New York, N.Y., 1963, Chap. 50. ( 2 ) W. Kernula and Z. Kublik in "Advances in Analytical Chemistry and instrumentation," Vol. 2 , C. N. Reiiley, Ed., interscience, New York. N.Y., 1963, Chap. 3. (3) E. Berendrecht in "Electroanalytical Chemistry-A Series of Advances," Voi. 2, A. J. Bard, Ed., Marcel Dekker, New York, N.Y., 1967, p 53. (4) A. M. Hartley, A. G. Heibert, and J. A. Cox, J . Electroanai Chem., 17, 81 (1968).
A N A L Y T I C A L C H E M I S T R Y , V O L . 45, N O . 13, N O V E M B E R 1973
lem, some authors (5-11) have adopted conventional alternating current (ac) polarographic methods (12). The cardinal advantages of the ac approach include gaussian, or near-gaussian peak readout, plus the additional adjustable experimental parameters of phase angle, $, angular frequency, W , and applied ac voltage amplitude, A E , all of which may be optimized for maximum analytical sensitivity. Detectability limits and precision for both the dc and ac methods are compromised a t low trace metal concentrations due to the fact that the largest fraction of the cell current a t the peak potential, E,,, results from double layer, or interfacial charging current [ic] and not faradaic current [ i f ] , which is the observable of interest. In a paper devoted principally to the development and evaluation of ac theory for direct voltammetry at the HMDE, Underkofler and Shain ( 5 ) extended Erbelding's (13) earlier phase-selective experiments applied to the Hg pool electrode. They exploited the advantage that the phase angle of the background, or quadrature ac charging current [referenced to the superposed ac voltage] differs from the faradaic current flow itself, and by utilizing a phase-selective amplifier they were able to demonstrate a factor of 10 sensitivity increase for the Fe(III)/Fe(II)-oxalate system over the conventional ac polarographic analysis. An abbreviated exploration was also made ( 5 ) of the improved sensitivity which might accrue in applying the phase-selective technique to the ac stripping of cadmium, and current results were reported for the range 10-6M to 10-lOM Cd(I1). With more modern signal handling techniques it is potentially feasible to reduce the quadrature base-line current to zero and to undertake measurements over a wider range of w and AE, The result applied to stripping analysis is a sensitive, relatively inexpensive technique for ultra-trace heavy metals, including toxicologically important species as As, Sb, Pb, Cd, T1, etc. To compare the merits of phase-selective anodic stripping (PSAS) relative to competitive non-electrochemical trace methods, e . g . , atomic absorption, or to intercompare PSAS current data from individual laboratories, accurate current-voltage data for a reference system obtained under controlled conditions using standardized cell equipment would be especially desirable. This need is accentuated by the present unavailability of mathematical expressions to account fully for all the variables which determine the re-oxidation or stripping process. Preconcentration of the trace material itself a t controlled potential is susceptible to individual variations in cell design, stirring rate, solution volumes, etc., which additionally strengthens the argument for standardized information of the kind mentioned. The Cd(1I)-Cd(Hg) process in dilute chloride base electrolyte is a generally well-known reversible couple for which numerous experimental data exist, obtained by techniques other than phase-selective stripping. In fact, with the exception of the 1966 paper by Eisner et al. (6), (5) W . Underkofler and I . Shain, Anal. Chem., 37, 218 (1965). (6) U . Eisner, C. Yarnitsky, Y. Nernirowsky, and M . Ariel, lsrael J . Chem.. 4, 215 (1966). ( 7 ) E. Rosenblatt and Kh. 2. Brainina, Zavod. Lab.. 32, 1450 (1966). (8) L. N . Vasil'eva, N. Lukashenkova, L . Krasnovaeva, and 2. L. Yustus, Zavod. Lab.. 36, 1436 (1970). ( 9 ) A. G . Zemtsovaand B. Ya. Kaplan. Zavod. Lab.. 37, 759 (1971). (10) M . Kodarnaand T. Noda, Bull. Chem. SOC.Jap.. 42, 2699 (1969). ( 1 1 ) N . Velghe and A . Claeys. J. ElectroanalChem., 35, 229 (1972). (12) See, for example, D. E. Smith in "Electroanalytical Chemistry-A Series of Advances," A . J. Bard, E d . , Marcel Dekker, New York. N . Y . , 1966, Chap. I . (13) W. Erbelding, Ph. D. dissertation, Cornell University, Ithaca, N.Y., 1961.
and the recent report by Velghe and Claeys ( I I ) , there have been few papers to appear since the first work of Underkofler and Shain ( 5 ) whose announced aim included an experimental assessment of factors affecting peak response. Accordingly, in this paper we have chosen to report on the phase-selective stripping response of cadmium to such analytically important variables as frequency, applied ac voltage, concentration, solution volume, stirring rate, and the time rate of voltage scan.
EXPERIMENTAL Apparatus. The multipurpose polarograph/potentiostat used for the present work was constructed ( 1 4 ) in this laboratory of linear, solid state devices, and utilized control and measurement circuit configurations, including provision for iR compensation ( I s ) ,of fairly conventional design. To achieve accuracy in measurement of the experimental peak currents, ac calibration signals were impressed on the input circuits. These were processed identically to the voltammetric signals themselves and provided corresponding recorder (Hewlett-Packard, 7000A) calibration markers. Applied ac signals were derived from two sources, either an external signal generator (Hewlett-Packard, 3300/3302), or an internal solid-state 100 Hz & 0.1% sinusoidal source (Connor-Winfield LPOO-BH). An operational amplifier with capacitative input and feedback served to isolate the desired ac current from the conventional current follower output. Output from this capacitatively coupled stage was fed to a n Ithaco System 353 CQ wide-band, lock-in amplifier (LIA) the rms output of which was fed to the recorder and provided both the faradaic in-phase and quadrature current components characteristic of the reaction. Final optimization of the LIA response t o the faradaic component was accomplished with the aid of a Wavetek Model 750 digital phase meter a t the pre-electrolysis potential during the 60-second interim between accumulation and stripping. Except for the scan rate studies, the latter procedure was carried out at 11.1 mV sec-', except as noted. A water-jacketed Metrohm electrolysis cell (EA 876-20) with tungsten or platinum counter electrode (Metrohm EA248) and Ag/AgCl or saturated calomel reference were employed for all measurements; these also utilized a Kemula-type micrometer screw HMDE (Metrohm E-410) for the working electrode. A standard, Metrohm cell cap with tapered joints assured reproducible placement of electrodes within the cell, and thus reproducible mass transport geometry which is of paramount importance if precise replication of the accumulation step is to be achieved. Reagents. Both the KC1 used for the base electrolyte and CdClz were of reagent quality and of sufficient purity for the low stripping sensitivity used. Direct current polarography was applied initially to analyze the cadmium stock solution which was prepared from weighed amounts of CdCl1. Polarographic currents conformed satisfactorily to those predicted by the Lingane-Loveridge modification of the Ilkovic Equation (16). But as a further check, high purity cadmium foil (99.999%) was dissolved in "Ultrex" (J. T . Baker Chemical Co.) grade "03 and polarographed also, with the results compared to a similar measurement on an aliquot of the stock CdC12 solution. A measurement of the difference in diffusion currents established the strength of the stock CdClz as 1.01 x 10-2M. Solvent water of adequate purity for the trace Cd measurements attempted here was of obvious importance. T a p water was first passed a t line pressure through two high-capacity ion-exchange tanks (Culligan, Inc.), then distilled once from a quartzTeflon apparatus (Kontes, W-2) and stored in borosilicate glass under argon. Aliquots of this product were redistilled twice more -the first stage from alkaline permanganate-then stored in polypropylene. The permanganate stage appeared necessary to rid the water of volatile trace organics presumably leached from the upstream ion-exchange stage. Precise conductance measure(14) E. D. Moorhead, unpublished results, University of Kentucky, Lexington, Ky., 1972. (15) E. R. Brown, H. L. H u n g , T. G . McCord, D. E. S m i t h , and G . L. Boornan,Anal. Chem.. 40, 1424 (1968). (16) J. J. Lingane and B. A . Loveridge, J. Amer. Chem. Soc.. 72, 438
(1950).
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO.
13, NOVEMBER 1973
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ments on the final product yielded 0.9 X 10-6 R - l cm-1 comR-1 cm-l for intrinsic water (17). pared to0.05 X Procedure. Since the anodic stripping procedure is a two-step process involving first a collection of the trace metal followed by appropriate electroanalytical determination (dc or ac stripping, chronopotentiometry, etc.), the overall analytical reproducibility is as dependent on the analysis step itself as on the reproducibility characteristic of accumulation. This pre-electrolysis can be stoichiometric or nonstoichiometric (all or part removal of the trace material from the solution), accomplished either by electrolysis a t constant current or controlled potential (2-3, 18). A large fraction, in fact most AS\' analyses, are nonstoichiometric and are carried out at controlled potential (18). This was the procedure adopted in the present study. Of deterministic importance therefore are a reproducible stirring rate and invariant cell geometry, requirements that are very easily satisfied but often overlooked in casual application of the stripping technique. In the procedure adopted here, 20-ml aliquots of the Cd(I1) test solution were degassed with humidified high-purity argon before transfer to the cell where they were dearated for an additional 10 min, then blanketed with a slow stream of argon. Test solutions were maintained a t 30 f 0.1 "C with the cell jacket supplied with thermostated water by a Forma Temp bath. During the pre-electrolysis or plating step, the solution was stirred by a 3-mm X 12-mm Teflon-coated spin bar driven by a second 11-mm X 49-mm Teflon stirring bar mounted on the shaft of an inverted Sargent-Welch Sychronous Rotator (Sargent S76485). The angular rotation of the cell spin bar was 600 rpm confirmed with a "Strobotac" (General Radio, Model 1538-A). A wooden jig carrying the rotator and positioned below the cell guaranteed that the cell spin bar position remained invariant from run-to-run. i.e., just perceptively off center to improve connective transfer to the electrode and just sufficient to avoid vortexing at the electrode surface. For the stirring rate studies ( u i d e infra), the synchronous motor was replaced with a variable speed motor (Cenco, Type NSI-12); otherwise all results refer to 600rpm stirring.
RESULTS AND DISCUSSION A surprisingly small amount of basic experimental information has appeared in the literature since Underkofler and Shain first applied anodic phase-selective stripping to the measurement of cadmium in solution ( 5 ) . Some bits of behavioral insight into the cadmium stripping process have been presented by Eisner et al. ( 6 ) , and Seitz (29), although a large fraction of their effort was devoted to practical applications of PSAS to samples of metallurgical origin (6) or sea water (19) and utilized restricted experimental conditions. The effect of several variables on the cadmium peak current response was recently investigated by Velghe and Claeys (11). but their innovative use of a specialized capillary and 18-min duration DME renders a direct correlation of their results with the more familiar electrode models somewhat difficult. The two-step pre-deposition and measurement procedure which makes up the overall ASV analysis imposes rather stringent requirements not only on the ac analysis step itself but also on the plating mode if acceptable analytical precision is to be attained. At the present time, there is no theoretical framework to describe ac stripping currents obtained from the stationary spherical electrode. Derivation of the manifold equations required for an exact interpretation of factors which influence such processes is beyond the intent of the present paper, although substantial clues to such a derivation are to be found in the recent work of Smith and coworkers (12, 20). In the present authors' view, the ex(17) R . C. Hughes, P. C. Murau. and G . Gundersen, Ana/. Chem.. 43, 691 (1971). (18) J. J. Lingane, "Electroanaiytical Chemistry." 2nd ed., Interscience, New York. N.Y.. 1958. (19) W. R. Seitz, P h . D . dissertation, Massachusetts Institute of Technology, Cambridge. Mass., 1970. (20) J. R. Delmastro and D. E. Smith,Ana/. Chem.. 38, 169 (1966)
2180
penditure of effort required to obtain and analyze such theoretical expressions would be of more fundamental than practical interest. Actual PSAS peak heights are tied to experimental parameters governing the efficiency of the pre-electrolysis step, and would be expected to differ somewhat in individual situations. Some behavioral features of the ac stripping peak are, however, suggested from derivations which apply to the direct voltammetric process. Underkofler and Shain (5) derived Equation 1
for a reversible process using the planar diffusion model employed earlier by Smith ( 2 1 ) . In this expression n/4 is the value of the phase angle 4 (in radians) for a truly reversible process. A designates electrode area, CO bulk concentration of electroactive ion, w angular frequency, and A E peak amplitude of the ac signal; the other terms are those which are used in ordinary electrochemical practice. Although Underkofler and Shain readily confirmed ( 5 ) Equation 1 using the Fe(III)/Fe(II)-oxalate system, Biegler and Laitinen (22) suggested that such an expression is inadequate to account for the direct voltammetric ac behavior of a metal ion-amalgam system, since it neglects geometry or spherical diffusion effects. To remedy this, Delmastro and Smith derived Equation 2.
which applies for a strictly reversible metal ion-amalgam process with a constant applied dc potential (20). In this equation, I,,, is given by Equation 3.
I,,,
=
'
n F 'A(wDJ l i L A E C,, 4RT cosh' ( j / 2 )
(3)
The symbols defined earlier apply as well to Equations 2 and 3; in addition j = (nFIRT)(Ed, - E l , z R e V ) , b = (elDol - DR' 2 ) / ( r o ( l e ) ) ) , and ro is the electrode radius. Computer analysis of Equation 2 (20) indicates that for a kinetically fast cadmium-type process, observed current peaks should exceed those predicted by Equation 1 by as much as 18 to 20%; and the complexity of the deviation increases dramatically for quasi-reversible systems. Consideration of the arguments underlying Equation 2 would suggest the manifestation of similar-type deviations from Equation 1 for the alternative case in which a metal is stripped or re-oxidized from a microspherical amalgam electrode using a linear dc potential sweep. Apart from the spherical diffusion effects on observed current amplitudes (or peak heights) which are likely to characterize the stripping process, the I ( & ) functional dependence on w . A E , $, and CO predicted by Equations l and 2 should be preserved. An experimental study of these relationships is presented here first. followed by an examination of the effects of pre-electrolysis parameters on phase selective stripping currents. Linear Sweep Phase-Selective a c Polarography at the DME. As a confidence check on the apparatus and instrumentation which we planned to use later for the
+
(21) D. E. Smith. Ana/. Chem . 35, 602 (1963). (22) T. Biegler and H . A Laitinen, Anal. Chem.. 37,572 (1965)
A N A L Y T I C A L C H E M I S T R Y . VOL. 45, N O . 13, N O V E M B E R 1973
Table I. Alternating Current Phase-Selective Voltammetry of Cd(ll) in 0.1M KCla,b A. [ C d P f ] = 1 X 1 0 - 5 M i,, FA, r m s c
(1)
(2) B. [Cd2+] = 1 X (1)
(2)
0.22 0.49 10-4M 4.93 4.96
f , Hz
25 100
100
100
A€ MV, rrns 6.00 7.07 7.07 7.07
Data at 100 Hz and 7.07 rnV rrns duplicate conditions reported by Underkofler ( 2 7 ) ; T = 303 O K . /I Diffusion coefficient of C d ( l I ) for A taken ( 2 4 ) . Currents refer to in-phase faradaic comas 7.0 X 10 -6 crnz sec ponent.
~-'
Table II. Reproducibility of In-Phase Stripping Current Obtained with the Micrometer HMDE for 1 0 - 6 M Cd(ll) in O.lMKCla i,. PA rms
Run No.
3
5.17
4 5 6 7
5.20 5.18 5.17 5.17 5.25 5.28 5.34 5.34 5.31
a 9 10 11
12
stripping studies, single sweep phase-selective ac measurements were performed with the DME [m = 1.92 mg sec-1, t = 4.58sec, area = 0.036cm21. The test solution for these experiments consisted of 0.982 x 10-3M CdC12 in 0.1M KC1 with data taken a t f = 100 Hz and AE = 5.0 mV (rrns). Prior to the voltage scan, Einltialwas adjusted to -0.4 V L'S. Ag/AgCl, i.e., in a region where observed current is due only to capacitative charging of the double layer. The LIA system was phaseadjusted to yield a minimum in-phase faradaic current a t the end of drop life (15). Overall instrument sensitivity was then increased 30-fold and enough iR compensation was inserted to reduce the average recorder deflection to zero current. An average of three polarographic scans following this procedure yielded an in-phase faradaic current i l of 28.7 pA (rrns). The total faradaic cell current attributable to Cd(II) is given by i,r = [i~/cos41, where 4 is the true phase angle between i,r and the actual ac voltage across the faradaic impendance. A recent independent study of Cd(I1) in 0.1M KC1 which was undertaken a t 160 Hz by McAllister and Dryhurst (23) lists $ = 25" for 1 x lO-3M Cd(I1) in O.1M KC1. The use of this @ corrected to 100 Hz and our i l value yielded 33.1 pA (rms) for the experimentally measured i ~ . In order to obtain a theoretical comparison, the quasireversible form (12, 20) of Equation 2 was evaluated using cm2 sec-1 ( 2 4 ) ; D R = 1.93 X 10-5 cm2 D O = 7.7 X sec-1 (25); A = 0.0362 cm2; t = 4.58 sec; and CY = 0.405. The latter was obtained from measurement of [EpeakE1'2reV] ( 1 2 ) .The functions F ( t ) and G ( w ) were calculated to be 1.123 and 0.598, respectively 1F(t) exceeds unity in this case, since erf ( - x ) = -erf(x), i.e., erf(x) is "odd" (26)1. The theoretical I ( o t ) thus calculated was 29.5 pA. The resulting 12% relative experimental error was considered fairly good in view of the numerous parameters involved, and it was therefore concluded that satisfactory reliance could be placed on the control and measurement procedures. Linear Sweep Phase-Selective a c Voltammetry at the HMDE(K). Currents obtained a t the micrometer HMDE for Cd(II) in 0.1M KC1 are shown in Table I. These data were obtained for f = 100 Hz, A E = 7.07 mV (rms). and an electrode area of 0.041 cm2, conditions which with the exception of area duplicate those employed by Underkofler who used 0.060 cm2 electrode area (27).
+
D. L. McAllister and G. Dryhurst. Anal. Chim. Acta. 58, 273 (1972) D. J . Macero and C. L. Rulfs, J. Amer. Chem. SOC.. 81, 2942 (1959). D. F. Nazarov, and A. G. Stromberg, Eiectrokhimiya. 1, 851 (1965). "Handbook of Mathematical Functions," M. Abrarnowitzand I . Stegun, Ed., U.S. Dept. Commerce, Washington. D.C., 1964. W. Underkofler, Ph.D. dissertation. University of Wisconsin, 1964.
Mean % Avdev
5.24 1.20
aData refer to 600 rpm stirring rate, 20-ml solution volume, and a scan rate of 11.1 mV sec-'. Frequency 50 Hz: LE = 19.3 mV (rms); T = 303 O K .
For conditions corresponding to A(2) of Table I, Underkofler (27) cited a voltammetric peak height of 30.9 pA. It is uncertain whether this value is average or root-meansquare, nor is it a t all clear whether his reported current is in-phase or total. For the sake of some comparison, however, a value of 0.72 pA results if our 0.49 pA in-phase current (Table I) is multiplied by 0.060/0.041 to correct for area. The difference between 0.72 pA and 30.9 pA is rather substantial and difficult to explain, particularly in view of precautions exercised in the present study and some knowledge of the dependence of I ( w t ) on factors affecting the pre-electrolysis step (uide infra). Reproducibility of Phase-Selective Stripping. Table I1 lists stripping peak currents for ten measurements on a test solution of 1 x 10-6M CdC12 in 0.1M KC1 in order to assess overall measurement reproducibility. For each of these runs pre-electrolysis was carried out for 5.0 min a t -0.90 V us. Ag/AgCl with 600 rpm stirring. Stripping was accomplished a t 50 Hz with A E = 19.3 mV (rrns) using a measured working electrode area of 0.041 cm2. Each analysis was performed by extruding a separate drop (5.0 minor divisions using a Metrohm EA842-120 capillary) from a completely refilled micrometer reservoir. Reproducibility of the cell mass transport characteristics, the precision of electronic control and measurement, and reproducibility of the micrometer electrode constituted potential sources of error afflicting each run. The 1.20% average deviation which resulted for replication in this set of ten runs is fairly respectable precision at this concentration level (112 parts/billion). Stripping P e a k Currents us. Concentration. In Underkofler and Shain's reports which were referred to earlier (5, 27), phase selective stripping currents were cited for Cd(I1) in 0.1M KC1 a t trace metal levels ranging from 10-6M to 10-lOM. In this part of their investigation they report a 450-pA peak current for 1 x 10-6M Cd(I1) under conditions which correspond to 7 = 5.0 min, A E = 7.07 mV (rrns), and f = 100 Hz. The 3-electrode cell employed by these authors utilized synchronous magnetic stirring and did not differ substantially in configuration or size (5, 27, 28) from the arrangement employed in the present study. Nonetheless, such currents appeared extraordinarily large in the light of our own results ( u i d e infra). Eisner e t al. (6) reported PSAS data a t the HMDE for 5 x 10-7M Cd(I1) in 0.1M KC1. Normalizing their experiment [uir., A E = 5.0 mV (peak) f = 80 Hz, 7 = 1.0 min] (28) G. S. Albertsand I . Shain,Ana/. Chem.. 35, 1859 (1963).
ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 13, N O V E M B E R 1973
2181
0
/
1 35
40
l
,
'Erequen:y
( A € = 19 mV (rrns); T = 5 min; [ C d ( l l ) ] = 1 x 1 0 - 6 M plated at -0.90 V v s . SCE; T = 303 O K ; rest period 60 sec.; 20-ml solution vol-
' scan rate
Table 1 1 1 . Recorded RMS In-Phase Peak Stripping Current YS. [Cd(ll)] in 0.1M KCla C, molar
x x 1x 5 x 1 5
Plating time, min
10-6
10
10-7
10
10-7 10-8
10 10
i,, PA
[ip/ f l ] x 1o5
4.76 2.50 0.52? 0.263
4.76
Mean % meandev
5.00 5.22 5.25 5.06 3.5
" A l l runs were made at 100 Hz, I€= 7.07 mV (rrns); HMDE area = 0.041 cm2; T = 303 O K ; 20-mi solution volume; and 1 1 , l mV sec stripping scan rate.
-'
to match that of Underkofler and Shain (57, Eisner et al.'s measurements yield a peak current of 31.9 pA, which is lower by a factor of about 14. From an analytical standpoint, it is unfortunate that neither set of authors is clear whether they determined their currents to be "peak," "average," or "root-mean-square," although both report AE as peak, or peak-to-peak. It is an interesting aside in considering these earlier results that a more suggestive possibility emerges if one assumes that the 450 pA value of Underkofler and Shain is a peak value, rather than average, or rms, and that of Eisner et al. is root-meansquare, in which case the latter author's value is about 1h.o that of Underkofler and Shain's; on the other hand, it is about %O if the converse is true. This confusion regarding sensitivity is discouraging to anyone wishing to apply this method in actual analysis. To resolve this point, measurements were made to determine the Cd(I1) analytical sensitivity a t several solution levels encompassed by both the aforementioned investigations. Our resulting rms currents which are an average of three replicate runs each using a 10-minute pre-electrolysis time (7) are summarized in Table 111. A peak gurrent (in-phase) us. [Cd(II)] plot of these data yielded a straight line over this 20-fold concentration change with an average [ip/.C] X lo5 = 5.06 f 3.5%. A regression analysis of these data yielded a slope of 4.98 X lo4 and correlation coefficient of 0.99996. It is perhaps noteworthy in view of previously reported work to direct attention to the magnitudes of the currents in Table 111. A t the micromolar Cd(1I) level, the present 2182
* ANALYTICAL C H E M I S T R Y ,
/
I
I
l
1
l
l
l
l
l
l
IO
l
l
5
l
l
l ~ 20
l
l
l
M ~ l l ~ v o l tI sR M S )
(Hz)]
Figure 1. In-phase rrns faradaic stripping current vs. frequency for Cd from 0 . 1 M KCI
ume: 1 1 , l mV sec-
l
5
0
,/2
Figure 2. 0.1M
In-phase rms stripping current vs. A€ for Cd from
HCI
f = 70 Hz; T = 5 min; [ C d ( l l ) ] = 1 X plated at -0.90 V vs. SCE; T = 303 O K ; rest period 60 sec; 20-ml solution volume; 11.1 mV sec - scan rate
'
study yielded a peak current of only 4.76 FA. This current magnitude was corroborated in parallel measurements in which the HMDE(K) was replaced by the HMDE(Pt). For the same experiment, the earlier measurements would be expected to yield 900 pA ( 5 ) and 63.7 p A ( 6 ) , respectively. Phase-Selective Stripping Current us. Frequency. One anticipates from the theory underlying ac polarography (12, 20) that observed ac stripping peak heights should increase linearly with d/2. Except for the i, us. w 1 / 2 linearity in the 5- to 60-Hz range recently reported by Velghe and Claeys (11) for their 18-min drop time experiments, no additional work has appeared to suggest the upper limit of frequency linearity in the cadmium case. Using large values of w can offer substantial sensitivity increase if one is t o judge from the indications of Equation 2, and an accurate indication of the response a t higher angular frequencies would be analytically useful. Frequency results which were obtained for 1 x 10-6M Cd(I1) a t an applied AE of 19.0 mV (rrns) are plotted in Figure 1 for T = 5.0 min. These data points which are for the in-phase current component are linear u p to about 400 Hz. A t the potential of the reverse scan (-0.90 V us. Ag/ AgCl), it was possible to balance the quadrature current component to zero with the LIA a t each frequency value studied, although above about 500 Hz this null adjustment became progressively more difficult to achieve. For the low frequency portion of the curve, application of a linear least-squares analysis produced a slope of 0.652 with a correlation coefficient of 0.997. What seems in this case to be the most plausible explanation for the departure from linearity which commences a t about 376 Hz is the onset of a "G(o)'' dependence which becomes manifest for quasi-reversible processes a t high frequencies (12). In other words, Smith's criterion ( 1 2 ) for ac polarographic reversibility expressed by Equation 4 is not satisfied a t frequencies above the breakpoint.
[i(y)'2] 5 0.01
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Peak Current us. AE. Insofar that one can assume that an expression similar in its principal form to Equation 2 also applies to peaks obtained in stripping analysis, it is evident that peak height and hence sensitivity should in-
VOL. 45, NO. 13, N O V E M B E R 1 9 7 3
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Figure 4. Effect of solution volume on peak height
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Conditions same as for Figure 3 data, except 600 rpm stirring rate
f = 100 Hz: T = 5 rnin; [ C d ( l l ) ] = 0.982 X 10-6M plated at -0.90 V vs. AglAgCl; T = 303 O K ; rest period 60 sec: 30-117 solution volume; 43.2 rnV s e c - ' scan rate: A€ = 7.07 mV (rrns)
crease with increase in applied ac voltage. Figure 2 depicts the in-phase peak current us. A E behavior for micromolar Cd(I1) in 0.1M KC1, and it can be seen that the linear functional relationship is preserved a t low applied AE's. The departure from linearity occurs a t about 4.0 mV (rms) or 5.7 mV (peak). This is in fairly good accord with the 8 / n prediction from ac polarographic theory (12) for a perfectly reversible process. The departure from linearity is gradual, and apart from the fact that large applied AE's lead to generation of a rich harmonic content in the observed currents, it is clearly evident from Figure 2 that increased analytical sensitivity is achievable a t large applied ac signal amplitudes. From the analytical point of view, the accumulation, or collection step assumes a level of importance equal in weight to that attached to the analysis step. Experiments described below were intended to provide an indication of the effect of several cell parameters on peak height for the Cd(II)-O.lM KC1 system. While these results were obtained for a well defined electrode process using conventional apparatus and procedures and should be repeatable by other investigators, it is remindful that sensitivity and performance are indeed dependent on the individual investigation. Sensitivity us. Stirring Rate. Under otherwise fixed conditions during pre-electrolysis, the efficiency governing collection of the trace metal into the microspherical electrode is dependent on the rate of stirring which in turn controls mass transfer to the electrode, and the thickness of the diffusion layer. The hydrodynamic characteristic of particular (and usually complicated) cell configurations virtually precludes prior knowledge of the functional response to be expected. Figure 3 presents results obtained in the present study using the Metrohm cell and magnetic stirring accomplished with a variable speed motor ( r i d e supra) whose speed was measured with a "Strobotac." The test solutions each consisted of 30 ml of 0.982 x 10-6M CdClz in 0.1M KC1. Data from 275 to 730 rpm were obtained using an electrode area of 0.041 cm*, A E = 10 mV peak, and f = 100 Hz; a 60-second rest period separated the collection step from the analysis itself, which was accomplished a t 43.2 mV sec-1. The very evident linear dependence illustrated in the Figure 3 plot was unexpected. An analysis of these data gave a correlation coefficient of 0.998, slope
60
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and intercept equal to 0.00137 and 0.954, respectively. Peak Height us. Solution Volume. Since the accumulation step conforms closely to the model of macroscale controlled potential electrolysis, theory for that technique (1-3, 18) would suggest that the amount of trace metal removed during the time T should be a function of A / V , or the ratio of electrode area to solution volume. That is, for the fixed stationary area of the HMDE(K), sensitivity (or peak height) should increase with decrease in solution volume. This expectation was confirmed in a series of measurements in which the volume of solution (0.982 x 10-6M CdClz in 0.1M KC1) was varied from 15 to 60 ml a t constant electrode area (0.041 cm2). The results, which depict a smooth variation in response, are shown in Figure 4. A sizable decrease in peak height occured between 15 and 30 ml; following this, the response is essentially flat, rising gradually to a maximum a t 50-ml volume. Several replications of this experiment under varying conditions always produced the maximum a t 50 ml. The jacketed cell used in all this work was comprised of a shallow angle conical lower section topped by a larger cylindrical reservoir. Addition of 50 ml to the cell placed the liquid surface exactly a t the breakpoint between the lower and upper cell geometries. It is submitted that the small added fluid turbulence imparted to the solution by this abrupt change in geometry accounts for the slight maximum in peak height a t 50 ml. At larger volumes, the peak current seemed to return to the previously established monotonic decrease in current with added volume. The temptation to employ extraordinarily large A / V ratios t o achieve sizable increases in analytical sensitivity is, from a measurement point of view, to be eschewed; under such conditions sizable amounts of material are removed in each analysis with considerable degradation in analytical precision. Effect of Scan Rate. In their phase selective study of the Fe(III)/Fe(II)-oxalate process a t the stationary mercury electrode, Underkofler and Shain ( 5 ) varied the rate of voltage scan used in the direct voltammetric sweep. They found that all curves were identical for scan rates up to 150 mV sec-1, beyond which they became distorted. This insensitivity to scan rate was claimed to be in accord with the planar diffusion model used and arose if the time rate of change of the scan voltage was much smaller than the applied signal frequency, W . This point was examined for the substantially different mass transport case involving the Cd(I1)-Cd(Hg) system under conditions otherwise similar to those employed for the Figures 3 and 4 data,
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO. 13, N O V E M B E R 1973
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Effect of scan rate on peak height and width at half
height Conditions same as for Figure 3 data, except 600 rprn stirring rate Curve A Peak height (left ordinate) Curve B Width at half height (right ordinate)
except for the use of 600-rpm stirring and a 30-ml cell volume. The scan-rate data are plotted as Curve A in Figure 5. I t is evident that for the Cd(Hg) system, the peak height is strongly affected by scan rate. Incrementing the rate over the range from about 10 to 90 mV sec-1 halves the peak magnitude with the decrease occurring almost linearily a t low scan rates. From about 90 mV sec-I upwards, the peak height diminishes more slowly with the slope approaching zero a t the 164 mV sec-1 level. The width (in millivolts) of the peak a t half-height is an important reflection of the ac reversibility of the electrode process and is an important consideration when attempting to achieve maximum resolution between close-lying peaks. Peak widths corresponding to each data point of Curve A were averaged and plotted us. scan rate to yield Cupve B, Figure 5 . Only a t the very low scan rates is there an indication that the width approaches the 45-mV value which reflects a reversible peak in ac polarography (12) for n = 2. For chemical analysis where sensitivity and narrow peaks are especially to be desired, it is therefore apparent from Figure 5 that the amalgam stripping procedure is best carried out in the region of small voltage sweep rates.
CONCLUSION Hanging mercury drop electrode results for cadmium using phase-selective anodic stripping techniques are not very numerous in the literature, and clear indications of the Z ( w t ) dependence of cadmium on individual parameters such as those in Equation 2 are absent or scattered. From the present study, it was concluded that the micrometer-type HMDE can produce electrodes of quite reproducible working area if reservoir refill is made before complete Hg depletion. For micromolar Cd(I1) in 0.1M KCl as a test system, per cent relative error in peak height for ten completely independent measurements was f1.20, which included uncertainty in cell mass transfer characteristics. Because of literature inconsistencies pertaining to measured stripping current us. trace cadmium concentration, i. e., analytical sensitivity, particular attention was accorded the Z ( w t ) response to changes in this variable.
2184
Experiment showed that the in-phase peak current component increased linearily with the Cd(I1) solution concentration. At the micromolar Cd(I1) level, in-phase i, values recorded in this study were about %SO those currents tabulated earlier by Underkofler and Shain and about y13 those obtained by Eisner et al. for the same system in 0.1M KC1. Similarly lower values were obtained in independent measurements with the HMDE(Pt) from which we conclude that our lower i, values did not originate because of diffusional loss of plated Cd into the capillary thread of the micrometer electrode. The phase-selective anodic stripping method is extraordinarly sensitive, and in the present study of micromolar Cd(I1) the lowest instrumentation sensitivity was used. We can only conclude that the earlier claims for sensitivity are overstated and may have arisen from uncorrected instrument gain. Increase in applied frequency, w , led to increased current, and indeed in-phase i, us. w1/2 proved linear up to about 400 Hz, beyond which the current. increased more slowly. Peak stripping current also increased linearly with superposed ac voltage, AE, up to about 5.7 mV (peak), which a t the 100 Hz used here is not an unreasonable departure from the 8/n mV rule applicable to low frequency reversible ac polarographic processes. Thus, while an equation similar to Equation 2 is not available to specifically describe the ac stripping of a metal from an amalgam microelectrode, currents obtained in the present study seem to exhibit nonetheless the same functional dependence on w1I2, A E , and electroactive metal ion concentration as portrayed by Equations 1 and 2 for the planar and spherical diffusion models, respectively. Achieving good precision for the overall two-step ac stripping analysis requires control of the parameters which govern the accumulation, or preconcentration of the trace material. With the apparatus and procedures employed here, the in-phase faradaic peak current increased linearly with the rate of magnetic stirring. For large volumes of test solution, i . e . , large values of the volume-toelectrode area ratio ( V I A ) ,the peak height is virtually insensitive to V, but, as anticipated, peak height and thus analytical sensitivity increased rapidly as VIA decreased; in the present study this increase was noted when VIA dropped below 730 for T = 5.0 min. The effect of voltage scan rate on stripping Cd(Hg) was also studied, and it was found that i, decreased to 113 its value when the scan rate was increased from 20 to 164 mV sec-1.
ACKNOWLEDGMENT The authors wish to express their gratitude to William Ehmann for providing a sample of ultra-pure cadmium foil for analysis of the cadmium stock solutions and to Barbara Barker for precise water conductance studies. Received for review January 15, 1973. Accepted May 31, 1973. Funds provided by the University of Kentucky Research Foundation enabled construction of the polaragraph/potentiostat used in this study. One of us (P.H.D.) expresses his gratitude to the University of Kentucky for University Fellowship support during the present investigation.
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, N O . 1 3 , N O V E M B E R 1 9 7 3
