Experimental Study of the Phase-Selective Anodic Stripping Analysis for Trace Concentrations of Gallium E. D. Moorhead and P. H. Davis Departments of Chemical Engineering and Chemistry, The University of Kentucky, Lexington, Ky. 40506
An experimental study was undertaken of several analytlcally important factors whlch affect the alternating current phase-selective anodic stripping (PSAS) of gallium into acidified NaSCN(NaC104) supporting electrolytes using the micrometer hanglng mercury drop electrode. The dependence on the concenof the In-phase peak current magnitude (ip) tration of bulk Ga( ill), thiocyanate concentration, ionic strength, pH, applied ac voltage amplitude, frequency, electrode area, pre-electrolysis time, temperature, and electrode potential scan rate Is reported. The shift in peak potential and change in peak width at half-height is reported for variations In ionic strength and added NaSCN. The response of ipto pH, pre-electrolysis stirring rate, ionic strength, and applied frequency differed from expectations based on previously published work. Eight replicate mea4.5M NaCIO4 surements of 59.5 ppb Ga in OSM NaSCN yielded a re1 std dev of 0.91%. The overall results obtained using several base electrolyte compositions suggest that the PSAS method is a potentially attractive technique for the rapid assay of tissue-sequestered trace gallium.
+
The rather undifferentiated nature of aqueous Ga(II1) ( I , 2)-viz. (near) uv-visible transparency, single stable oxidation state, kinetically slow complex formation [signifi, cant with complexing organic chromophores ( 3 ) ]etc.-has posed historical problems with regard to gallium measurement a t trace and ultratrace levels. Generally, it has been customary and convenient (4, 5 ) to employ radioanalytical methods and to endure the long count times and calculational procedures required to achieve analytical precision a t the part-per-billion (ppb) or sub-ppb level. As an alternative physical method, neutron activation affords the required sensitivity (6, 7), but instrument cost and rather long exposure time in an available high flux reactor restricts its generality. Atomic absorption spectrometry would also seem to be an attractive alternative but, in the case of gallium, it is actually of marginal utility; one reported detectability limit (2943.6-A line, air-acetylene) is only about 1100 ppb ( 8 ) ,although modern flameless excitation techniques may be able to improve this figure. The above difficulties, which pose serious obstacles in quantifying ultratrace gallium in sarcomatous tissue and bone ( 4 , 5, 9-12), were recently placed in more elaborate perspective by Zweidinger, Barnett, and Pitt ( 3 ) .In their analytical approach, anion exchange was employed first to separate GaCl4-I from acid-digested tissue (or bone). After ascorbic acid reduction of interfering Fe(III), gallium was measured fluorometrically as the Ga(II1)-Lumogallion complex extracted into isoamyl alcohol. Although Zweidinger et al. report a useful fluorescence detection limit of ca. 30 ppb, their multistep procedure is lengthy (12 hours per run); even using predigested samples, only 15 gallium measurements could be accomplished per day, which is partially accounted for by the 1-hour time period required to form the Lumogallion complex. We have had the opportunity on several past occasions 622
ANALYTICAL CHEMISTRY, VOL. 47, NO. 4. APRIL 1975
to investigate some aspects of the electrometric analysis of gallium (13-18). I t seemed that the basic measurement requirements developed in those studies (15, 18, 19) of reversible Ga(II1) reduction could be combined with phaseselective anodic stripping (PSAS) techniques (20) to produce a rapid, rather easily instrumented method which would be useful for general studies of trace gallium, as well as for gallium’s tissue uptake and serum distribution. Several features which were uncovered in the present investigation merit expanded study, but we feel that our preliminary results, despite their identification with a rather narrow set of solution conditions, may have some immediate utility in the design of clinical assay procedures.
EXPERIMENTAL Apparatus. A custom-built multipurpose polarograph/potentiostat conctructed of linear, solid state devices was used throughout this investigation. An integral, low-pass, 2-pole, 5.0-Hz Butterworth active filter (Analog Devices, Model 704L2B) was used to precondition the x-axis sweep signal which drove a Hewlett-Packard 7000A x-y recorder. An operational amplifier with capacitive input and feedback served as a variable gain, frequency independent, coupling amplifier to isolate the total ac cell current (quadrature plus faradaic) component. This amplifier output was externally coupled to an Ithaco 353 CQ lock-in-amplifier (LIA). A Wavetek Model 750 digital phase meter aided in the fine-tuning of the LIA system. The root mean square in-phase (faradaic) component from the LIA was then fed to the recorder y-axis. A final phase adjustment step was performed during the 30-second pause between electrodeposition and reoxidation, or stripping, and consisted of adjusting the “channel 1” in-phase output of the LIA to recorder zero in a region (the deposition potential) corresponding to maximum quadrature current. Ac signals superposed on the cell were derived either from the internal 100 Hz k 0.1% sinusoidal generator (Conner-Winfield H200 LB) or from an external HewlettPackard 3300/3304 generator. To compensate for some frequency dependence of the overall system and to correct for other unavoidable small offsets, known calibration currents were injected into a precision resistance network which replaced the cell. The recorder calibration markers thus derived served as fiducial marks for measurement of in-phase stripping peak currents. In those sections of the paper which depict the variation of peak current with frequency, ionic strength, etc., each current point reported is the average of at least four replicate measurements. A calibrated Kemula-type (Metrohm E-410) micrometer hanging mercury drop electrode [HMDE(K)]of 0.0260 cm2 area served for all measurements except those relating to area dependence. The thermostated (30 “C), jacketed cell (Metrohm EA-876-20) was fitted with a standard Metrohm cell cap. The tapered joints assured reproducible cell geometry which is a critical factor for the precise replication of results. Before each measurement, the cell contents were deoxygenated for at least 15 min with a humidified stream of H.P. argon. A NaC1-saturated, H-form Ag/AgCl reference half-cell was used. The probe tip, which was terminated with a porous Vycor plug, was separated from the reference half-cell by an integral salt reservoir filled with concentrated ( 7 M ) NaC104. Test solutions were magnetically stirred a t 600 rpm using a 3-mm x 12-mm Teflon-coated spin bar. This was driven by a larger bar magnet affixed to an inverted Sargent synchronous rotator. A simple wooden jig was used to reproducibly fix the motor position beneath the cell, and it was oriented so that the cell spin bar was slightly off center to avoid undesirable vortexing at the HMDE. The peak height dependence on frequency was measured using both our custom-built instrument and a Princeton Applied Research Model 174 polarograph with Model 51 ac accessory to serve
as a check. In those instances where data were amenable to regression analysis (linear, exponential, etc.), it proved convenient to use a Hewlett-Packard 9100A/9125/9120 desk top computer combination. Reagents. The present studies required solvent water of reasonably high purity. This was prepared by redistilling water which had already been double-distilled from a pair of tin-lined Barnstead stills. Subsequent redistillation from borosilicate glass was made first from dilute alkaline permanganate, then again neat. The product was stored in a sealed polypropylene bottle. Principal reagents were stored as stock solutions in polyethylene bottles protected from light; this proved to be a very necessary precaution in the case of light-sensitive NaSCN. Reagent Ga(C104)~.6Hz0 was obtained from G. F. Smith Co. Experimental runs verified that our particular lot of this material was acceptably free of trace metal interferences. Stock solutions of the Ga(C104)3were standardized by back titrating excess added EDTA with a solution prepared from H.P. bismuth metal. British Drug House was the source of "Analar" grade HClOI, and NaC104, while NaSCN was J. T. Baker reagent grade. The latter materials were prepurified of trace metal contaminants by controlled-potential electrolysis [Wenking, Model 68TS1] at a stirred mercury pool electcode for at least 24 hr; or, in the case of concentrated stock NaSCN (21), by passage through a column packed with Corning CPG-550 porous glassimmobilized 8-hydroxyquinoline (Pierce Chemical). To lessen possible contamination by laboratory air, all cleaned glassware as well as electrodes were kept stored in a large air-tight (and dust-free) Plexiglas cabinet constructed especially for this purpose. All glassware was cleaned by soaking in 25% " 0 3 followed by thorough rinsing with quadruply distilled water. Despite moderately rigorous efforts at purification, it proved virtually impossible to generate in our laboratory base electrolyte solutions totally uncontaminated by lead, copper, or zinc. Consequently, in assessing the effect of most variables, it proved expedient t o adopt test solutions of 8.55 X 10+M in Ga(C104)3,except where otherwise specified.
RESULTS AND DISCUSSION Among the principal hallmarks of anodic stripping analysis (ASV) (22-26) are its extraordinarily low limit of detection for mercury-soluble heavy trace metals and its very wide linear dynamic range. Both of these features plus the speed and basic simplicity of the method make it potentially attractive for instrumented tissue affinity studies. Phase-selective anodic stripping (PSAS) used in the present study (20) represents a modification of dc stripping analysis in that a mV-level sinusoidal signal is superposed on the dc potential sweep. The resulting ac current after appropriate signal conditioning results in a gaussian, or near-gaussian peak readout of the in-phase faradaic current component proportional to bulk trace metal concentration. Inclusive equations to account for the influence of all possible variables underlying the two-step phase-selective procedure are probably underivable in tractable form. Nonetheless, Delmastro and Smith's equations (27-29) derived for the simpler case of linear single sweep ac polarographic reduction of an amalgam-forming metal at a stationary microspherical electrode serve as an instructive guide. These are written here as Equation 1, which applies to a chemically uncomplicated, kinetically fast (reversible) charge transfer process.
Y
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I
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-08
-57
l
I
A
[ ,
-CL
I
-39
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0
- 1
3
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[VCIIS
1s
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Figure 1. Phase-selective anodic stripping voltammogram of 59.5 ppb W W Base electrolyte of 0.5MNaSCN plus 6.5MNaC104 at pH 2 [HC104]. f = 50 Hz, A € = 10 mV (rms), v = 24.9 mV sec-', T = 5.0 min plus 30-sec rest period, A = 0.0260 cm2. Impurity peaks a, b, c identified as Pb, Cu. and Zn,
respectively
case of cadmium. For similar processes that are kinetically slower or quasireversible, relative to the ac modulation frequency, considerably more complicated extensions of Equation 1 apply (28). General Current-Voltage Behavior of Gallium. In perchlorate solutions of 5 pH 3 and numerous other base electrolytes, gallium is oxidized or reduced totally irreversibly (13, 15, 19) (low pH's are required to avoid hydrous oxide formation). T h e usual drawn-out dc current-voltage curve a t ca. -1.1 volts vs. Ag/AgCl occurs 300 mV to 350 mV more negative than the estimated thermodynamic halfwave (E1/2) potential of the metal (vide infra) and is severely masked by proton reduction. This problem can be conveniently bypassed by using base electrolytes comprised of acidified (HC104)NaSCN-NaC104 to catalyze the gallium charge transfer process (15). The resulting large rate increase (19, 30) produces kinetically reversible, or nernstian, current-voltage behavior. When such electrolyte combinations are employed in conjunction with the phaseselective stripping method, analytically useful peaks are produced such as the one shown in Figure 1 for 59.6 partper-billion gallium. These peaks are subject to a number of measurement parameters, and the response to several of these is discussed below. Effect of Thiocyanate on Peak Height. Because thiocyanate plays a rather important role in the kinetic reversibility of the gallium electrode reaction, we thought it desirable to obtain first a n accurate notion of the stripping dependence on this anion. Moorhead and Frame (15) demonstrated that in 6.OM NaC104 supporting electrolytes containing 2mM Ga(II1) both dc and ac polarographic reduction currents increase sharply and nearly linearly over the range 0.0 to 0.1M NaSCX. De Levie ( 3 1 ) and more recently Tur'yan and Makarova (32) have ascribed this SCN-salt dependence as mechanistically in accord with a reaction of surface-adsorbed SCN- with bulk aquo Ga(II1) to form an easily reduced, partially desolvated, labile intermediate (32). [GaWzO), (SCN)x(3-X~fls,rjace The PSAS thiocyanate dependence obtained here for 8.55 X 10+M Ga(II1) in a constant ionic strength ( J ) NaC104 electrolyte at pH 2 is illustrated in Figure 2, curve A. T h e shape of this curve closely duplicates earlier results for reduction of millimolar Ga(II1) (15, 33). For the initial, rather abrupt rise in i,, a regression analysis yielded a slope of 56.2 PA M-I with a correlation coefficient, r, equal to
-
where
An elaboration of the Equation 1 symbolism will not be re-iterated here since it conforms to ordinary electrochemical usage and was recently discussed (20) in detail for the
ANALYTICAL CHEMISTRY,
VOL. 4 7 , NO. 4 . A P R I L 1975
623
8 0 8 i - o=- " ; 70
A
I
i
0 ---C 6 5 00
05
I 5
2 0
N a S C U [Mclar;
Figure 2. Dependence of PSAS peak height on thiocyanate concentration at 7.0Mconstant ionic strength
Figure 3. Effect of thiocyanate on peak potential (E,,)and peak width at half-height ( Wl,2)
Initial base electrolyte composition and measurement parameters the same Initial base electrolyte comprised of 7.OM NaC104 at pH 2. f = 50 Hz. A € = as for Figure 2. Curves A and C obtained for 8.55 X 10-6MGa(lll);Curves B 10 mV (rms), Y = 24.9 mV sec-', A = 0.0260 cm2. Curve A: 8.55 X 10-6M Ga(C104)3, i = 2.0 min plus 30-sec rest period. Curve B: 8.55 X ~ o - ~ M and D correspond to 8.55 X lO-'MGa(lll) Ga(C104)3, i = 5.0 min plus 30-sec rest period
0.999. A repetition of this study for 8.55 X
Ga(II1) (curve B ) yielded a slope of 5.60 with r = 0.995. The sharp bendover of Curve A in the vicinity of 0.15M SCN- is pronounced, and its morphology agrees fairly well with Frame's earlier dc polarographic measurements (15) a t pH 1 and 6.OM NaC104 [virtually identical thiocyanate dependence as depicted by Figure 2 was recently obtained by Demerie et al. (34) using direct dc pulse polarography]. At the higher SCN/Ga ratios of Figure 2, curve B, the peak current requires a higher thiocyanate concentration before leveling off. That is, i, continues to increase up to 0.6M NaSCN. From the dependence of i, on [Ga(III)], which is discussed later, proportionately lower thiocyanate concentrations may be required to achieve maximum sensitivity for trace metal levels much below 1 X 10-6M. Thiocyanate Effect on Peak Width ( W l / z ) .From classical ac polarographic theory (35) the width a t half height (W1/2)of a reduction peak is an important factor governing resolution and is equivalent to 90/n mV (25 "C) for an ideally reversible process, n being the number of equivalents of charge per mole of reaction. A less clear-cut relationship would prevail if the process were quasi-reversible, or if the charge transfer reaction were governed by coupled slow chemical reactions (35, 36). Peak width is also obviously important with regard to the resolution of PSAS peaks. Their half-width's in the present study were found to be strongly thiocyanate dependent. Figure 3, curve A is a plot of W1/2 vs. [SCN-] obtained from peaks used to construct curve A of Figure 2. The small PSAS peaks obtained a t 0.01M NaSCN were 45 mV wide a t half-height and were clearly not reversible. An abrupt narrowing of the peaks reflecting an increase in rate resulted when NaSCN was increased 10-fold, and a t 0.2M NaSCN W1/2 was 35 mV, a value which remained unchanged up to 2.OM. Curve B of Figure 3 shows that pretty much the same response is obtained a t 8.55 X 10-7M Ga(III), with the exception that the entire curve is moved upward toward larger Wllz's. Thus, W112 = 58 mV for 0.01M NaSCN decreasing to a limiting value of ca. 38 mV beyond 0.2M. The limiting W1/2 figures for both studies approach fairly closely the predicted reversible ac polarographic values ( 3 5 ) .As demonstrated previously for cadmium (20), both i, and W1/2 depend on scan rate. On the basis of evidence presented later, the Figure 3 scan rate ( Y ) 624
ANALYTICAL CHEMISTRY, VOL. 47, NO. 4 , APRIL 1975
of 24.85 mV sec-l for gallium probably could not be greatly exceeded without distorting the two curves. Thiocyanate Effect on Ep.Curves C and D of Figure 3 which were obtained for v = 24.85 mV sec-l depict the shift in E , with increasing thiocyanate for 8.55 X loc6 and 8.55 X 10-7M Ga(III), respectively. Both sets of data appear to give a reasonable fit to an equation of the type E , = a exp {b[SCN-]I. For curve C, the respective a and b parameters were found by an exponential least-squares fit to be 42.8 and 0.181; for curve D, 16.41 and 1.03. Associated correlation coefficients were, respectively, 0.879 and 0.783. Such an exponential variation in E , very likely has empirical significance only since, over the range of thiocyanate studied, there is an obvious change in reaction mechanism and this is probably accompanied by Ga-SCN complexation as well. I t is noteworthy, however, that the exponential change in E , toward more negative values is rather smooth and does not seem to reflect the abrupt change in W1/2 depicted by curves A and B. Variation of Zp with Ionic Strength. From earlier studies involving the direct reduction of Ga(II1) (dc and ac polarography, dc pulse, chronopotentiometry, etc.), it is abundantly evident (13-19, 30, 34) that electrocatalyzed reversible behavior is inextricably bound to the use of high ionic strength background electrolytes. For example, with kinetics-sensitive ac polarography, there is no evidence of peak development below ca. J = 1 (0.1M NaSCN, 1.OM NaC10,; 50 Hz), although in the region 1 I J 5 7M there is rapid emergence of a nernstian-type peak whose height increases monitonically with J (15). Accordingly, a qualitatively similar J dependence was anticipated for the stripping of dissolved gallium from the HMDE. In fact, quite different behavior was found. Data collected in two independent measurements are plotted in Figure 4 which reveals a pronounced maximum in the i, vs. J curve. The ascending branch qualitatively resembles the aforementioned dc (15, 34) and ac (33) polarographic results, except that the Figure 4 data would appear to be shifted toward lower J values, suggesting a higher sensitivity of the anodization process toward increased ionic strength. The rapid drop off in peak magnitude beyond the maximum a t J = 5 cannot be unequivocally accounted for without some further study since there is no certainty a t this time whether it is related to the stripping process itself or the associated plating step. However, since deposition
7 20 r ---
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30
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o n ? Slrenglh
Figure 4.
60
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Initial base electrolyte consisted of 0 5M NaSCN plus 2 OM NaC104 at pH 2 Measurement parameters same as for Figure 2, except that A € = 2 50 mV (rms). 8 55 X 10-6MGa(C104)3
7r -
Dependence of PSAS peak height on ionic strength
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Figure 5.
Change in PSAS peak potential with increasing ionic
strength EP data obtained from curves used to construct Figure 4
Table I. Variation of P S A S P e a k Height with Pre-electrolysis Time ( T ) Q T ~ min. ,
1.oo 1.25 1.50 2 .oo 2.50 3.50 5.50
i,,
u A (rml
0.535 0.692 0.824
1.10 1.37 1 .a4 2.35
[ i p / r cGa1x inJ
0.626' 0.648' 0.642" 0.644' 0.641' 0.615
0.500 8.55 X 10-6M Ga(II1) in 0.5M NaSCN, 4.5-W NaC104, p H 2; j' = 50 Hz, 1E = 2.50 mV (r.m.s.); Hg area = 0.0260 cm2, preelectrolysis potential = -0.85V vs. Ag/AgCl; u = 24.9 mV sec-l r includes 30-sec rest period. Average of these data 0.640, re1 std dev = 1.77%.
from stirred solution is a dc process, the latter possibility seems rather implausible a t this time. Because i, is least sensitive to a change in total salt in the region of the maximum, practical PSAS analyses of Ga(II1) in 0.5M NaSCN are probably best carried out near an ionic strength of 5.OM to ensure maximum precision. Ionic S t r e n g t h Effect on Ep. Achievement of a welldefined gaussian ac voltammetric peak requires, for a dynamic measurement of this kind, that the redox process be sufficiently fast kinetically that, for all practical purposes, the interrelationship between electrode potential and the interfacial concentration of electroactive species remains nernstian. Under such circumstances E , can be identified with the polarographic El/* and, hence, indirectly with the standard electrode potential, E O G ~For . numerous reasons, direct measuremeni of E O G ~for the amalgam, liquid, or solid metal is difficult (33, 37-41). There remains some uncertainty, e.g., as to whether it should be assigned the value -0.52 V [von Bergkampf ( 3 7 ) ] -0.56 , V [Stelling ( 3 9 ) ,Saltman and Nachtrieb (4111, or -0.58 V [Challenger ( 4 0 ) ] ,all vs. NHE. Figure 5 shows a smooth dependency of E , vs. J , the data for which were taken from the averaged peaks of the Figure 4 study. Obviously, part of this change in E , with increasing J can be ascribed to anticipated changes in junction potential and solution activity coefficients. That i, increases and W1/2 decreases with increasing J , also reflects an increased kinetic rate of reaction. The dashed line in
Figure 5 represents a reasonable extrapolation of these data. Assuming that the electrode potential of the NaClsaturated Ag/AgCl reference can be taken as +0.22 V vs. NHE a t 30 OC in the region J I1,the -0.78 V vs. Ag/AgCl intercept a t J = 0 would indicate a "formal" potential of -0.56 V vs. NHE for the Ga(III)/amalgam couple in the presence of 0.5M NaSCN. This agrees with Stelling's amalgam studies and also with Saltman and Nachtrieb, except that the latter's figure pertains to Ga3+aquo 3e = Gao(solid)in HC1 media and does not reflect the free energy of amalgamation. P e a k Height vs. Pre-electrolysis Time ( 7 ) . Preconcentration at the HMDE (usually by controlled-potential preelectrolysis with constant stirring) underlies the sensitivity offered by the anodic stripping technique and, under ordinary circumstances, a simple increase in T provides the compensation required for more dilute trace metals. For short deposition times corresponding to the removal of a small fraction of the trace material, it can be assumed that the deposition current, I d , remains nearly constant (26). Thus the I ~ product T and the amalgam metal concentration, as well as the PSAS peak heights should linearly increase with 7 . Table I lists the variation in L, with T which was obtained with a pH 2 solution made up of 8.55 X 10+M Ga(III), 0.5M NaSCN, and 4.5M NaC!04 [2.5 mV root mean square, 50 Hz]. A least-squares treatment of the current data affirmed the linearity of i, vs. T below 2.75 min [r = 0,9999, slope = 0.5503. Thus, from the slope, i,/r CR,,]~averaged 6.43 X lo4. The departure from linearity for times in excess of 2.75 min probably reflects some progressive deterioraT amalgam contion in the proportionality between I ~ and centration. A second possibility relates to the use of the HMDE(K) and the 1957 finding by Nikelly and Cooke (23).They showed from their experiments that i p d C should approach a limiting value vs. T when the pre-electrolysis deposition rate approached the diffusion rate of the plated metal into the capillary. Although not undertaken in the present study, the use of an HMDE(Pt) would enable verification of this point. Gallium is recognized as only slightly soluble in mercury, and this fact could be construed as a third possibility, viz., that deviation from linearity may reflect gallium saturation of the HMDE(K). This is deemed
+
ANALYTICAL CHEMISTRY, VOL. 4 7 , NO. 4 . APRIL 1975
625
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0
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5
,
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Mlcrometer D i v i i i o n s
Figure 6. Increase in electrode area and magnitude of PSAS peak current vs. number of micrometer divisions Solution: 8.55 X 10-6MGa(C104)3, O.SMNaSCN, 6.5MNaC104,pH 2. f = 50 Hz, A€ = 2.5 mV (rms), u = 24.9 mV sec-’, 7 =.2.0 min plus 30-sec rest period. Curve B left ordinate; Curve A right ordinate rather unlikely by virtue of the construction of the HMDE(K) whose thread provides a diffusive path to relieve a tendency of the drop to saturate, as shown by Nikelly and Cooke (23), and because the low level of collected gallium is unlikely to exceed its solubility (13, 4 2 ) . Current Dependence on Electrode Area. As shown by Equation 1 for reversible reduction based on convergent diffusion to a microspherical electrode, I ( w t ) varies linearily with electrode area, A, a dependence which also holds for quasi-reversible processes as well (35).Whether the linearity prevails when the same method is applied to anodic stripping seemed of considerable empirical interest because of its bearing on analytical sensitivity. For direct current ASV and divergent diffusion, Reinmuth ( 4 3 ) accounted for the ro2, or area dependence [ro = electrode radius] incorporated in the Randles-Sevcik Equation ( 4 4 , 4 5 ) and the rO3volume, or concentration dependence of the deposited metal to show that direct current stripping peaks should increase linearly with the first power of ro. Since a Kemula-type micrometer-driven capillary was employed in our PSAS work, it was of preliminary interest to measure the electrode area generated by a given number of micrometer screw divisions and to compare this with the corresponding currents. After charging the HMDE(K) with Hg, the capillary was immersed in a solution composed of 0.5M NaSCN and 6.5M NaC104. The screw was then advanced, say, 5.0 minor divisions, and the drop dislodged. The area was determined from the mass of ten such drops which were assumed to be spherical. The measurement was repeated for 6 divisions, etc. The area results are shown as curve A of Figure 6. Part of the curvature below A = 0.0175 cm2 probably arises from manifestation of some micrometer non-linearity, plus the fact that a fractional part of a micrometer division was required to advance the mercury thread back to the capillary orifice, both of which could contribute sizable non-linearity at very small drop areas. The measured PSAS current peak height vs. the number of micrometer divisions is given by curve B. The general similarity of the two curves is evident. The correlation coefficient, intercept, and slope for the linear regions above five micrometer divisions were 0.999, 0.122, and 0.0280 for curve A, and 0.999, 0.0124, and 0.00278 for curve B. A direct plot of i, vs. A yielded a straight line above 0.020 cm2 with r = 0.989 and a slope of 32.1 FA cmP2. 626
ANALYTICAL CHEMISTRY, VOL. 47, NO. 4 , APRIL 1975
I 0
1
0
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,
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,
,
,
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,
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.
I
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,
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Figure 7. Increase of PSAS peak currents with increase in the rms amplitude of applied ac voltage Solution 8 55 X 10-6MGa(C104)3. 0 SMNaSCN, 6 5MNaC104, pH 2 Measurement parameters, except A€, same as for Figure 6 A = 0 0260 cm2
Peak Dependence on AE. The I ( w t ) dependence on the amplitude of the superposed ac voltage (Equation 1) is a useful relationship in PSAS analysis as shown by earlier studies of cadmium (20) and, consequently, it was desirable in the case of gallium to test the range of i, vs. /1E linearity. These results are illustrated in Figure 7 for 8.55 X 10-6M Ga(II1) in a base electrolyte 6.5M in NaC104 plus 0.5M NaSCN adjusted to pH 2. For this study, a 50-Hz signal was applied and the PSAS peaks were scanned at 24.9 mV sec-l. The i, vs. LIE dependence proved to be linear up to about AI? = 2.8 mV (root mean square). In view of the moderately high scan rate and divergent diffusion, this is in surprisingly good accord with the 8/n value predicted from ac polarographic theory for a perfectly reversible process (35).Analysis of the Figure 7 limiting slope in the range 0.0 to 2.8 mV yielded a correlation coefficient of 0.995 and a slope of 0.65. Dependence on’ Stirring Rate. Regardless of the electroanalytical method chosen for the analysis step, providing data readout is linear with amalgam concentration (barring complications introduced by intermetallic compound formation) the PSAS functional dependence on the preelectrolysis stirring rate, u, would be expected to be the same as that reported for dc stripping, viz., i, should increase linearly with u1I2 (see ref. 26, Equation 6). A seemingly unequivocal and interesting exception to this has been noted, however, in the PSAS analysis of Cd using the same cell arrangement where a linea u dependence was found (20) for stirring rates up to 700 rpm. Table I1 presents the stirring rate results obtained for 8.55 x lO-‘jM Ga(II1) in a pH 2 solution made up of 0.5M NaSCN and 4.5M NaC104. To provide more efficient magnetic coupling at high rpm with the internal stirring bar, a Metrohm non-jacketed cell was employed (room temperature ca. 24 “C) which enabled the achievement of stirring rates in excess of 1300 rpm measured with a General Radio “Strobotac.” Hydrodynamic instability and vortexing were pronounced at rotational speeds much in excess of 800 rpm. This was not serious at lower speeds. A plot of i, vs. u1’2 (not shown) for u < 700 rpm proved linear with a correla-
Table 11. Increase i n P S A S P e a k Height with Increase i n the Pre-electrolysis Stirring Rate (u)a u , rpm
222 300 355 403 475 555 660 7 50 910 1200 1310
u1l2,
(rm)1’2
14.90 17.32 18.84 20.07 21.79 23.56 25.69 27.39 30.17 34.64 36.19
i , , P A (rms)
iplu1/2
0.733 0.932 1.04 1.13 1.24 1.39 1.50” 1.52’ 1 .GOC 1.58 1.50
15.63b 18.58b 18.12b 17.76b 17.57b 16.95b 17.13 18.01 18.85 21.92 24.13
lO-5M Ga(II1) in 0.5M NaSCN, 4.5M NaC104, p H 2; f = 50 Hz, AE = 2.50 mV (rms); Hg area = 0.0260 cm2; pre-electrolysis potential = -0.85 V vs. Ag/AgCl; Y = 24.9 mV sec-l, T = 2.0 min. * Average of these data 17.44; re1 std dev = 6.28%. CDeviation of these i,’s from the linear plot excluded them from inclusion in the std dev calculation ( b ) . a
tion coefficient of 0.999, and slope and intercept equal to 0.0744 and -0.367, respectively. Effect of pH. Moorhead and Frame in an earlier study ( 1 5 ) observed that current peak magnitudes for the ac reduction of Ga(II1) a t the DME were pH insensitive in the range 0 5 pH 5 2.0 but decreased to zero between pH 2 and 3, a fact which they ascribed to hydrous oxide formation. Demerie et al. ( 3 4 ) recently observed essentially similar pH behavior in their direct derivative pulse polarographic study of gallium. It seemed plausible, therefore, that reversible controlledpotential accumulation prior to stripping should follow essentially the same pH dependence. The same response to pH would not necessarily apply, however, to the re-oxidation process. To estimate this, the cell was filled with a measured volume of solution comprised of 8.55 X 10-6M Ga(III), 0.5M NaSCN, and 4.5M NaC104. The initial pH of this solution was adjusted to 0.50. The cell pH was then incremented by adding fixed aliquots of a second solution whose composition differed only in that it had been adjusted to pH 12 with electrolytically purified NaOH and contained no Ga(II1). Peak currents obtained after each addition (the cell was deaerated each time) were then volume-corrected for the change in cell Ga(II1) concentration. Because [H+]/[Ga]~,lk1 10 throughout the study, the employment of buffering agents was considered unnecessary, and indeed to be avoided anyway to eliminate undesirable competitive complexation with Ga(II1). The results are shown in Figure 8, where each point is an average of five replications. The morphology of this curve, which resembles a titration curve, is substantially different from the earlier, simpler relationship found for ac polarographic reduction of mM gallium (vide supra). Since the ac phase-selective method is rate sensitive (351, one could speculate that the 33% current drop between pH 1.0 and 1.7 of Figure 8 reflects some change in the oxidation mechanism from one aquo Ga(II1) complex ion to another having a smaller diffusion coefficient. Alternatively, one could also speculate (as suggested by one Reviewer) that there occurs a mechanistic change in which n for the oxidation changes from 3 to 2. This seems implausible for a number of reasons, not the least of which is the fact that such a change in n should produce a 55% change in i, (Equation l ) ,not 33%. The numerical spread in published Ga(II1) stepwise hydrolysis constants, pK1, is extensive ( 2 , 46). It may be sig-
3-
3
4
PH
Figure 8. Variation of peak current with measured pH Initial solution: 8.55 X 10-6M Ga(CIO4)3, 0 . 5 M NaSCN, 4.5M NaC104, pH 0.51. Measurement parameters same as for Figure 6. Each point is the average of five replicate runs
nificant that the values 1.22 and 1.75 reported by Ahmarin for pK1 and pK2 (47) lie within the narrow pH region of current decrease. Particularly since trace levels of gallium are involved, it seems unwise a t this time, however, to carry such reasoning too far. At least for more concentrated solutions, it is unlikely that mononuclear cations exist in significant concentration above pH 1. A t higher pH’s, there is a pronounced tendency to form condensed polynuclear moieties. Haladjian (48), for instance, presented quite detailed evidence to show that mononuclear hexaquo Ga(111) is in equilibrium with the polymeric species [Gaz, (OH)J,. H20Ixm+for all [OH-]/[Ga3+] ratios where m was found to range upwards without bound. Moreover, the complexity of interpretation in the present case is substantially compounded by the presence of complexing NaSCN and the possible tendency for Ga(II1) to associate with C104-. Well-defined narrow peaks characteristic of reversible anodization were obtained in both regions A and B of Figure 8. On the other hand, above pH 2.8 (region C), the peaks became progressively shorter, wider, and more irreversible. The peak potential, which remained virtually unchanged a t ca. -0.763 V vs. AgIAgC1 from pH 0.5 to 2.8, underwent a very rapid shift toward more negative values above this figure, which probably reflects the onset of condensation and hydrous oxide formation in the interfacial region. Ipvs. Applied Frequency. For purely reversible redox processes, the magnitude of i, varies linearly with the square root of angular frequency, w . The same theory ( 3 5 ) predicts a more complicated frequency dependence for the quasi-reversible case, Le., where k , &*. Under such circumstances Z(wt)rev is multiplied by a “G-function” in frequency, given by Equation 2, where X = k , (e-.] ed))/ D112;j= n F ( E d c - E1/21ev)/RT,
-
+
and the other terms carry their usual electrochemical significance (20, 35). For complete reversibility, (2w)112/X
