Anal. Chem. 1996, 68, 829-833
Voltammetric Reduction of Nickel and Cobalt Dimethylglyoximate Dragic V. Vukomanovic, John A. Page, and Gary W. vanLoon*
Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
The determination of cobalt and nickel in aqueous solutions by stripping voltammetry after adsorptive preconcentration is an established procedure. The method is highly sensitive, but there is some controversy concerning the reasons for the excellent sensitivity. Using a variety of voltammetric techniques, we have determined that the reduction of nickel dimethylglyoximate in an ammonia buffer is consistent with an overall process involving 16 or possibly 18 electrons. This hypothesis is confirmed by independently measuring the total quantity of metal adsorptively deposited on the mercury electrode and comparing the amount with the quantity of electricity required for its reduction. Adsorptive stripping voltammetry (AdSV) is a well-established electroanalytical technique for trace determination of aqueous Ni(II) and Co(II) in the form of the dimethylglyoxime complex [M(HDMG)2]. The technique was first described by Pihlar et al.1 in 1981. Since then, more than 10 variants of the method have been developed for a range of samples, with detection limits reaching the picomolar (or part per trillion) level.1-6 There is considerable interest in determining reasons for the excellent sensitivity of AdSV. A reaction scheme describing the AdSV determination of the Ni(HDMG)2 solution has been given by several authors,2,7 and the stripping step has been shown to involve two electrons. However, others have pointed out that the extremely favorable sensitivity of the adsorptive stripping method requires either that mass transfer of the analyte to the electrode surface involve processes other than diffusion or that electron transfer during reduction involve more than two electrons per Ni(HDMG)2 molecule, perhaps through catalytic enhancement. These possibilities have been investigated by several researchers,7-11 and the reasons for the excellent sensitivity remain controversial. The experimental evidence described in the present paper has led us to believe that the “irregular behavior” of the Ni(HDMG)2 complex might be attributed to a larger number of electrons being involved in the reduction of the adsorbed complex. The enhanced (1) Pihlar, B.; Valenta, P.; Nurnberg, H. W. Fresenius’ Z. Anal. Chem. 1981, 307, 337-346. (2) Pihlar, B.; Valenta, P.; Nurnberg, H. W. J. Electroanal. Chem. 1986, 214, 157-177. (3) Torrance, K.; Gatford, C. Talanta 1985, 4, 273-278. (4) Economou, A.; Fielden, P. R. Analyst 1993, 118, 47-51. (5) Westenbrink, W. W.; Page, J. A.; vanLoon, G. W. Can. J. Chem. 1990, 68, 209-213. (6) Zhang, H.; Wollast, R.; Vire, J. C.; Patriarche, G. J. Analyst 1989, 114, 15971602. (7) Weinzierl, J.; Umland, F. Fresenius’ Z. Anal. Chem. 1982, 312, 608-610. (8) Mairanovskii, S. G.; Prochorova, G. V.; Osipova, E. A. J. Electroanal. Chem. 1989, 226, 205-214. (9) Prochorova, G. V.; Henrion, G. V.; Schmidt, R. Z. Chem. 1982, 22, 28-32. (10) Carmen, J. F.; Nieboer, E. Anal. Chem. 1980, 52, 1013-1020. (11) Kissner, R. Fresenius’ Z. Anal. Chem. 1988, 332, 787-790. 0003-2700/96/0368-0829$12.00/0
© 1996 American Chemical Society
electron transfer is associated with the ligand itself, and the reduction products would include those that have been determined to be present when free dimethylglyoxime is itself reduced. EXPERIMENTAL SECTION A Princeton Applied Research Corp. Model 174A polarographic analyzer was employed with a Model 303 static mercury drop electrode (SMDE). The voltammograms were recorded using a Hewlett-Packard Model 7004A X-Y recorder and Bascon Turner Instruments programmable recorder Model 3000. The threeelectrode system consisted of a 15-mL quartz cell with a static Hg electrode, a Pt auxiliary electrode, and a Ag/AgCl/saturated aqueous KCl reference electrode separated from the analytical solution by a Vycor frit bridge. The electrolyte was stirred as required using a 0.9-cm Teflon “spin fin” driven at a rotation rate of 500 Hz. The three Hg drop sizes had areas of 1.18, 1.97, and 2.60 mm2. Three different electrochemical methods have been used in an attempt to determine the diffusion coefficients (Do) of dimethylglyoxime and Ni(HDMG)2. In the first method, polarography was carried out using the SMDE with 2-s drop time; the analyzer was in the dc polarographic mode with scan rate of 2 mV s-1 and a potential range from -0.40 to -1.80 V. The second method followed the current as a function of time using a hanging mercury drop electrode (HMDE) with a drop area of 1.18 mm2. Immediately upon applying a fixed applied potential of -0.85 V, a fresh Hg drop was created in a quiescent solution and the current measured over a 4-s time interval. In the third method, the HMDE was used, and linear potential scan voltammetry was carried out to reduce previously adsorbed complex. Adsorptive preconcentration was done in a quiescent solution at an applied potential of -0.85 V for times ranging from 2 to 14 s. The adsorbed complex was then reduced by applying a negative-going potential scan at a rate of 100 mV s-1. The electrolytes were deaerated and blanketed throughout the experiments with CANOX “oxygen free” grade N2 purified by passage over hot BASF catalyst (30% w/w Cu). The sample and cell manipulations were carried out in a laminar-flow clean hood with a high-efficiency air filter. Graphite furnace atomic absorption spectroscopy (GFAAS) measurements were done using a Perkin-Elmer 603 AAS with an autosampling system and L’vov platform in the pyrolytic graphite atomizer tube. The GFAA program involved atomization at 2700 °C and argon carrier gas operation in the “flow interrupt” mode. The dimethylglyoxime (H2DMG; 2,3-butanedione dioxime) was supplied by Anachemia Chemicals Ltd. It was recrystallized from 95% ethanol, and a 0.1 M stock solution was prepares by diluting the appropriate amount of H2DMG in 95% ethanol. Analytical Chemistry, Vol. 68, No. 5, March 1, 1996 829
dimethylglyoxime differ significantly.12,13 Spritzer and Meites14 have concluded that, in the pH range between 1 and 3, dimethylglyoxime is largely or entirely in the form of the monoprotonated (HDMG-) species. Burger et al.15 claimed that both H2DMG and HDMG- are reduced on the dropping mercury electrode in solutions with pH ranging from 1 to 5. However, Weinzierl and Umland7 reported that H2DMG is polarographically inactive, and the only species that can be (catalytically) reduced are HDMGin acidic media and DMG2- in alkaline media. Spritzer and Meites14 claimed that the reduction of dimethylglyoxime in acidic media corresponded to an 8-electron process,1 with the product being 2,3-diaminobutane. The reduction product was isolated by electrolysis at a controlled potential and identified by infrared spectroscopy, and the overall equation for the reduction was reported1 to be
|
|
CH3CdNHOH+ + 9H+ + 8e- f CH3CHNH3+ + 2H2O CH3CdNOH
Figure 1. Polarographic reduction of free dimethylglyoxime as a function of pH: (a) diffusion current and (b) half-wave potential. Experimental conditions: SMDE; scan rate, 2 mV s-1; drop time, 2 s.
Stock Ni(II) solution was prepared by dissolving 0.5005 g of Ni foil (99.998% purity) in 16.5 mL of 50% HNO3 and diluting to exactly 500 mL with distilled water. Stock Co(II) solution, 1.000 g L-1 in 2.5% v/v HNO3, was provided by BDH Inc. For analytical work, Ni(II) and Co(II) working standards were prepared by diluting the stock solution with a pH 2.0 HNO3 electrolyte. The distilled water was obtained from a well-aged and conditioned three-stage borosilicate glass still. RESULTS AND DISCUSSION Polarographic Studies on Aqueous H2DMG. The electrochemical behavior of uncomplexed dimethylglyoxime (H2DMG) and the Ni(HDMG)2 complex was investigated. One polarographic wave was observed in both acidic and alkaline media. The reduction of dimethylglyoxime was found to be irreversible, and the limiting current for the polarographic wave was diffusion controlled. The height of the polarographic wave (id) was independent of pH in the range between 1.25 and 3.7 (Figure 1a). With further increase of pH, the limiting current rapidly decreased, and at a pH of ∼7, the wave had disappeared. In alkaline media, another wave appeared, so that, between pH 8.9 and 9.3, the id value was constant and very close to that which had been found in acidic solutions. Most of the previous electrochemical studies of free dimethylglyoxime were done in acidic media, and there is some controversy about the dimethylglyoxime species that might exist under these conditions. This is probably a consequence of the fact that literature values for the acid dissociation constants of 830 Analytical Chemistry, Vol. 68, No. 5, March 1, 1996
(1)
CH3CHNH3+
This process is consistent with what has been described16 for the reduction of oximes in general. While eq 1 represents the overall process, the authors also found that a single electron and a single proton were consumed in the rate-determining step. Our studies on the reduction of dimethylglyoxime in aqueous media show that a plot of the half-wave potential for the polarographic wave shifts in the negative direction in acidic solution and in a similar way in alkaline solution (Figure 1b). The consistency of the id value in both acidic and alkaline media, and the fact that the E1/2 follows a consistent linear trend over a wide pH range, suggest that similar reactions might apply under all these conditions, and this could indicate that the electrode process in alkaline media is also an 8-electron process, as has been determined for the acid solution. Linear Scan Voltammetric Studies of the Ni(HDMG)2 Complex. Formation of the Ni(HDMG)2 complex in acidic media is hindered due to protonation of the ligand. In alkaline solution, however, Ni(II) forms a stable complex with dimethylglyoxime, and the complex is slightly soluble in an aqueous alkaline buffer. We found, in close agreement with many others, the optimum medium for analytical purposes to be a 0.1 M NH3/0.1 M NH4Cl buffer with pH 9.3. Under these conditions, the E1/2 for Ni(DMG)2 appears at -1.0 V, and the polarographic wave is well defined. Under the same conditions, free dimethylglyoxime has E1/2 ) -1.67 V; the polarographic wave, however, is not as well defined as that for the complex because it overlaps with the wave due to reduction of the supporting electrolyte. Both free and complexed dimethylglyoxime waves could be observed using conventional polarography or direct linear scan voltammetry without prior depostion on a single mercury drop. Under the latter conditions, beginning at a potential of -0.85 V, and applying a scan rate of 100 mV s-1 on a quiescent solution, a “titration” experiment was carried out. Addition of Ni(II) to buffered 20 mM dimethylglyoxime solution showed a linear decrease in the peak observed (12) Freiser, H. Int. Congr. Anal. Chem. 1952, 77, 830-845. (13) Ueno, K.; Imamura, T.; Cheng, K. L. CRC Handbook of Organic Analytical Reagents, 2nd ed.; CRC Press, Inc.: Boca Raton, FL, 1992; pp 401-410. (14) Spritzer, M.; Meites, L. Anal. Chim. Acta 1962, 26, 58-65. (15) Burger, K.; Syrek, G.; Farsang, G. Acta Chim. Acad. Sci. Hung. 1966, 49, 113-121. (16) Bard, A. J.; Lund, H. Encyclopedia of Electrochemistry of the ElementssOrganic Section, Vol. XIII; Marcel Dekker, Inc.: New York, 1973; pp 314-315.
for free dimethylglyoxime; at the same time, there was a corresponding linear increase in the peak for the Ni(HDMG)2 complex, with a maximum value for the complex occurring when the ratio of ligand to Ni(II) was 2:1. The well-defined Ni(HDMG)2 peaks allowed estimation of areas without any difficulties. However, poorly defined free ligand peaks made estimation of peak area less reliable, especially when the dimethylglyoxime concentration was very small. Within the measurement limitations, the sum of the two peak areas (which correspond to the quantities of electricity during the reduction of either free ligand or complex) during the Ni(II) “titration” was constant. These data are consistent with the view that the reductions of free dimethylglyoxime and the complex Ni(HDMG)2 occur in a similar fashion. If the reduction of dimethylglyoxime involves 8 electrons, it may therefore be surmised that a 16-electron reduction of the Ni(HDMG)2 complex would be taking place. It is also possible that Ni(II) is reduced simultaneously with the ligand in the complex, giving a total of 18 electrons. The above experiment was not sufficiently accurate to enable us to distinguish between 16- and 18-electron processes. Effect of Temperature and pH on the Reduction of Ni(HDMG)2. If the reduction of the Ni(HDMG)2 complex were accompanied by a catalytic process, as has been suggested by several authors,8,9 it would be expected that the reduction current would be highly sensitive to changes in temperature. The catalytic effect has been observed to be as much as 10-20% K-1. Using standard polarographic conditions (20 mM dimethylglyoxime, 4.0 mM Ni in 0.1 M NH3/0.1 M NH4Cl, a drop time of 2 s, and a potential scan rate of 2 mV s-1), the polarographic reduction current was found to increase by only 0.86% K-1. A similar series of experiments using linear scan voltammetry on a single drop resulted in a correponding increase of 1.1% K-1. Another characteristic of catalytic reduction processes is high sensitivity to pH, especially in the case of catalytic hydrogen ion reduction processes. In the case of linear scan voltammetry of Ni(HDMG)2, however, the reduction current associated with the complex remained constant in the range between 8.9 and 9.5. At both lower and higher pH values, the current became much smaller due to instability of the complex and to competition by ammonia or hydroxide ion, respectively. These results, therefore, are further evidence that the enhanced current for the reduction of Ni(HDMG)2 cannot be due to a catalytic effect. Determination of Do Values for DMG and Ni(HDMG)2. Many electrochemical relationships include both n, the number of electrons involved in the reduction, and Do, the value of the diffusion coefficient. Therefore, to determine one of these parameters requires knowledge of the other, as well as additional constants and measured quantities in the expressions. In the first method for Do determination, the integrated form of the Cottrell equation for semiinfinite spherical diffusion was used. The equation describes the quantity of electricity as a function of time during the life of the single drop:
Q(t) )
2nFADo1/2Co*t1/2 π
1/2
+
nFADoCo*t r
(2)
This equation presumes that diffusion to the electrode surface is the limiting feature of the reaction. From the polarographic wave, the value of Q(t) was calculated as the product of the average
current on the diffusion current plateau (id) times the drop time (t ) 2 s). Using the Cottrell equation, a diffusion coefficient (Do) for dimethylglyoxime in 0.1 M NH3/0.1 M NH4Cl buffer was then estimated to be 3.6 × 10-6 cm2 s-1, assuming an 8-electron reduction, and Do values for Ni(HDMG)2 were correspondingly calculated to be to be 2.5 × 10-6 cm2 s-1 assuming a 16-electron reduction and 8.5 × 10-5 cm2 s-1 assuming a 2-electron reduction. Of the two values for the Ni(HDMG)2, the one calculated assuming a 16-electron reduction process was close to that expected for a molecule of similar size.17 The second method for Do determination is one of the most reliable ways of measuring Do values and makes use of it1/2 curves. In this method,18 the HMDE is used, and at a fixed potential, the current decrease was measured as a function of time after applying the potential. We have applied the curve-time relationship used in Shain and Martin’s method:18
i ) nFADoCo*[1/(πDot)1/2 + 1/r]
(3)
If i is plotted vs 1/t1/2, Do may be evaluated from the slope of the straight line assuming a particular n value. We first tested the method using ferricyanide ions [Fe(CN)6]3- in 1.0 M KCl. Under these conditions, the reported16 value for Do is 7.63 × 10-6 cm2 s-1. We obtained the mean Do value of (7.96 ( 0.31) × 10-6 cm2 s-1 for species in 1-, 2-, and 3 × 10-4 M [Fe(CN)6]3- in the same electrolyte. These experiments were carried out in order to assess whether drop creation using the SMDE in the quiescent cell would significantly affect the mass transfer mode. The closeness of results to the reported values indicated that any enhanced mass transfer due to the disturbance of the solution was relatively small (∼4%). Corresponding experiments using free dimethylglyoxime were more difficult because of the high background current observed. However, for Ni(HDMG)2, Do values for 2 and 3 mM solutions could be determined in 0.1 M NH3/0.1 M NH4Cl buffer (pH 9.3) with the HMDE (A ) 1.18 mm2 ). The Do values for Ni(HDMG)2 were found to be 1.83 × 10-6 and 2.54 × 10-6 cm2 s-1, respectively (mean value, 2.2 × 10-6 cm2 s-1), assuming a 16-electron overall reduction. If a 2-electron reduction was assumed, the mean Do would be 1.6 × 10-4 cm2 s-1. The reported19 Do values for many organic molecules of molar mass and size similar to those of Ni(HDMG)2 (molar mass ) 291) are in the range of magnitude of 10-6 cm2 s-1. For example, the molecules 3,3′-dimethoxybenzidine (o-diaminisidine, o-DIA; molar mass ) 492), 2,6-dibromo-p-aminophenol (molar mass ) 267), and 2,6-dichloro-p-aminophenol (molar mass ) 188) have Do values17 (in diluted aqueous H2SO4 solution) between 3.7 × 10-6 and 4.9 × 10-6 cm2 s-1. To our knowledge, there are no molecules in aqueous solutions with Do values as large as those calculated for Ni(HDMG)2 assuming n ) 2. The third method of determining Do values also makes use of the integrated form of the Cottrell equation for semiinfinite spherical diffusion (eq 2). In this case, the quantity of electricity required to reduce the complex that had accumulated over a known period of time at the HMDE was measured by integration of current-time peaks obtained from linear scan voltammetry. The measurements were made on solutions containing different (17) Adams, N. A. Electrochemistry at Solid Electrodes; Marcel Dekker, Inc.: NewYork, 1969; Chapter 8.. (18) Shain, I.; Martin, K. J. J. Phys. Chem. 1961, 65, 254-258. (19) Voorhies, J. D.; Furman, N. H. Anal. Chem. 1959, 31, 381-384.
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Figure 2. Predicted and found Q(t) values for (a) 2 and (b) 5 mmol L-1 Ni(II) in the presence of 20 mmol L-1 dimethylglyoxime. Experimental conditions: HMDE; adsorption for time shown; scan rate, 100 mV s-1. 1, Experimental; O, calculated (n ) 16 electrons); and b, calculated (n ) 2 electrons).
molar ratios of dimethylglyoxime and Ni(II), but there was always an excess of ligand required to form the bis-complex. The effect of varying three Hg drop sizes was also investigated. The quantity of electricity [Q(t)] needed for the reduction of the amount of the Ni(HDMG)2 diffusing to the electrode during the accumulation time period was calculated assuming n ) 16. In all cases, a Do value of 2.0 × 10-6 cm2 s-1 was assumed. The predicted and found Q(t) values for two molar ratios of added ligand and Ni(II) are illustrated in Figure 2. The curves obtained assuming n ) 2 are also shown; clearly, the agreement is substantially better when n ) 16. The proposed postulate of an 8-electron reduction of each coordinated dimethylglyoxime plus a possible 2-electron reduction of the metal center, i.e., 18-electron reduction of the Ni(HDMG)2 complex, is therefore reinforced by the good agreement between the predicted and experimental values of Q(t). Coverage of Ni(HDMG)2 on the HMDE. An additional experiment was carried out in which the Ni(HDMG)2 complex was accumulated on the surface of the Hg electrode by adsorptive preconcentration from a stirred solution under an applied potential of -0.85 V. The potential was scanned from -0.85 to -1.50 V so that reduction peak could be observed. The experiment was similar to that used in the AdSV method for determination of trace Ni and Co in aqueous solutions. Depending on adsorption time, the area of the peak obtained during the stripping step increased but reached a limiting value which is attributed to monolayer coverage of the complex on the Hg surface. By carrying out the experiment using a time which ensures that the limiting (surface832 Analytical Chemistry, Vol. 68, No. 5, March 1, 1996
saturated) value has been reached, it is possible to calculate the number of Ni(HDMG)2 molecules on the surface of the Hg drop from the quantity of electricity in the reduction step, assuming a particular value for n. If the area of the drop is known, then the area occupied by a single molecule of Ni(HDMG)2 on the drop may also be calculated. Assuming a 16-electron reduction of the adsorbed Ni(HDMG)2 molecule, the limiting Qp value corresponds to 1.71 × 10-6 mol cm-2 of complex on the electrode surface. Since the electrode area was 2.8 × 10-2 cm2, and assuming monolayer coverage, each Ni(HDMG)2 molecule would occupy an area of 0.97 nm2, which is not very different from the crystallographic value20 of 0.87 nm2. These results suggest a model where the Ni(HDMG)2 molecules are planar to the electrode surface and closely packed at saturation. If we assume a 2-electron process, the area occupied by a single Ni(HDMG)2 molecule would be 0.12 nm2, which is apparently very different from the reported crystallographic value. Pihlar et al.,2 under the assumption that two electrons were transferred in the overall electrode process, found that each Ni(HDMG)2 molecule occupied 0.15 nm2. Admitting that this was too small for flat orientation, they proposed that the Ni(HDMG)2 molecules in the monolayer were oriented vertically to the electrode surface. An Independent Method for Determination of n. Finally, a series of experiments was carried out to provide independent information regarding the hypothesis that the reduction of Ni(HDMG)2 involved 16 electrons. The similar electrochemical behavior of Ni(HDMG)2 and Co(HDMG)2 encouraged us to apply the experiments to both of the complexes. In all experiments, the initial concentration of dimethylglyoxime was 6.0 mM in 0.1 M NH3/0.1 M NH4Cl (pH 9.3) buffer solutions. Concentrations of Ni(II) and Co(II) from 0.60 to 1.00 mM were chosen so that there was always an excess of ligand present during the experiments, so that all the metal was in the M(HDMG)2 form. The species of interest were adsorbed for 60 s on a HMDE at -0.60 V in the stirred solution. The chosen deposition times as well as the concentration of added Ni or Co have ensured low surface coverage of the HMDE. The Ni(HDMG)2 and Co(HDMG)2 were preconcentrated onto the HMDE during a 60-s deposition period, and then, omitting the stripping step, the drops were collected in a 1-mL polyethylene vial containing from 300 to 500 mL of 0.5 M HNO3. In an individual experiment, 50 Hg drops were collected in this manner in a single vial. Before, at the middle, and after the collection of the 50 Hg droplets, several AdSV experiments were done in an identical fashion to the above, but instead of collecting the Hg drops, linear scan stripping was carried out in order to measure the quantity of electricity needed to reduce the adsorbed Ni(HDMG)2 or Co(HDMG)2. Blank solutions were prepared by collecting the same number of droplets from the same solutions containing complex but with no external potential nor deposition time applied. The samples, the blanks, and a series of standard solutions containing different concentrations of Ni or Co in the presence of 50 Hg drops were analyzed by GFAAS. The Ni and Co contents are given in Table 1. Substraction of blank values for the metal content from the sample values should compensate for the contribution of Ni or Co from the solution layer adhering to the (20) Godycki, L. E.; Rundle, R. E. Acta Crystallogr. 1953, 6, 487-491.
Table 1. Determination of n by Comparison of Stripping Peak Areas with Amount of Adsorbed Complex As Measured by GFAASa
sample
M(HDMG)2 concn/µmol L-1
average peak area per drop/µC
no. of moles per drop ×10-12
n
Ni1 Ni2 Ni3 Co1 Co2
0.68 1.02 1.02 0.68 1.02
3.90 ( 0.15 7.78 ( 0.19 6.37 ( 0.06 4.13 ( 0.05 5.39 ( 0.14
2.12 ( 0.04 4.60 ( 0.12 3.90 ( 0.39 2.42 ( 0.18 3.30 ( 0.16
19.0 ( 0.8 17.6 ( 0.6 16.9 ( 1.7 17.7 ( 1.3 17.0 ( 0.9
a
Errors are expressed as standard deviations.
Hg droplet when transferring it from the electrolysis cell to the collecting vial. By determining the Ni and Co content of the samples and knowing the stoichiometry of the dimethylglyoxime complexes, we have calculated the amount (number of moles) of Ni(HDMG)2 or Co(HDMG)2 adsorbed on the HMDE. Knowing those values and the quantity of electricity needed for reduction of the measured amount of complex (from the reduction peak area), we were able to apply Faraday’s law and calculate the overall number of electrons needed for reduction of an adsorbed molecule. Calculated values are presented in Table 1. Although it is clear that ligand was reduced, the atomic absorption experiments also could not distinguish between a 16and an 18-electron reduction.
ACKNOWLEDGMENT The authors gratefully acknowledge support from the National Science and Engineering Research Council and the School of Graduate Studies at Queen’s University. Thanks are also due to Ms. Chantal Hemens, who carried out preliminary experiments which led to this work. GLOSSARY A
electrode area/cm2
Co*
bulk concentration of analyte species/mol cm-3
Do
diffusion coefficient of oxidized form of the reactant species/cm2 s-1
F
Faraday constant ) 96 485 C mol-1
i
current response/A
n
number of electrons transferred per molecule of reactant
Q
quantity of electricity (charge)/C
r
electrode radius/cm
t
time (defined individually for each method)/s
Received for review June 1, 1995. Accepted December 7, 1995.X AC9505334 X
Abstract published in Advance ACS Abstracts, February 1, 1996.
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