Rotating Disk Electrode Voltammetry for Studying Kinetics of Metal

Mar 26, 1996 - Two samples (grab samples) of snow were collected on different dates ..... discussions and to the Natural Sciences and Engineering Rese...
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Environ. Sci. Technol. 1996, 30, 1245-1252

Rotating Disk Electrode Voltammetry for Studying Kinetics of Metal Complex Dissociation in Model Solutions and Snow Samples

giving quantitative information about the extent of metal complexation; that is, it can estimate the rate constants for the dissociation of metal complexes and the concentrations of various metal complexes. This technique offers the additional, potential advantage of in situ determination with the least possible disturbance to the chemical equilibria involved.

C. L. CHAKRABARTI,* JIANGUO CHENG, AND WAI FAI LEE

Introduction

Ottawa-Carleton Chemistry Institute, Department of Chemistry, Carleton University, Ottawa, Ontario K1S 5B6, Canada

M. H. BACK Ottawa-Carleton Chemistry Institute, Department of Chemistry, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

W. H. SCHROEDER Atmospheric Environment Service, Environment Canada, 4905 Dufferin Street, Downsview, Ontario M3H 5T4, Canada

Rotating disk electrode (RDE) voltammetry with a mercury thin-film electrode on a glassy carbon substrate combined with anodic stripping voltammetry (ASV) using square-wave, differential-pulse, and staircase waveforms was applied to direct determination of Cu(II) and Pb(II) speciation in model solutions of Cu(II)nitrilotriacetic acid and Pb(II)-nitrilotriacetic acid complexes and in snow samples. The dissociation rate constants of Cu(II) and Pb(II) complexes measured by square-wave voltammetry, differential-pulse voltammetry, and staircase voltammetry were found to be similar. Of the above three waveforms examined for their suitability for the study of Cu(II) and Pb(II) complexes in the above model solutions and in snow samples, staircase voltammetry gave the most satisfactory estimates of dissociation rate constants and diffusion coefficients of the metal complexes. However, the analytical sensitivity of square-wave voltammetry is 2 orders of magnitude higher than that of staircase voltammetry. Such higher sensitivity is required for direct determination of the extremely low concentrations of Cu and Pb complexes found in uncontaminated natural waters and in precipitation samples. The RDE technique combined with ASV is capable of distinguishing labile and nonlabile complexes present in extremely low concentrations in aqueous solutions and in precipitation samples. The RDE technique can do the above differentiation by virtue of its ability to measure metal availability for reduction over a wide range of time scales and by

0013-936X/96/0930-1245$12.00/0

 1996 American Chemical Society

The importance of dissociation kinetics of metal-organic complexes in regulating the bioavailability of metal ions in natural waters under nonequilibrium conditions has been emphasized in the literature on the following grounds (19). The pseudoequilibrium assumption that is generally made is not necessarily valid under natural water conditions, and in some instances, the rate of biogeochemical reactions of metals may be influenced or even controlled by the rates of metal complexation reactions (6). For metals occurring as organic complexes, pseudoequilibrium conditions among dissolved species may be maintained only if the rates of metal complexation reactions are fast compared with rates of metal uptake by biota. If, however, complex dissociation and ligand-exchange rates are slow compared to biological uptake, the rate of metal incorporation into the biota will limited by abiotic chemical kinetics (3). If the exchange kinetics of metal-organic complexes with other cations under natural river conditions are extremely slow, as in the case of Fe(III)-EDTA (as effluents from sewage treatment plants discharged into a river) with other cations (Zn, Cd), then the equilibrium speciation model is not a realistic model of the EDTA speciation because the exchange of Fe(III)-EDTA with other trace metals (Zn, Cd) will not reach equilibrium within the residence time of water in the river (5). Thus, in presence of EDTA, metal speciation in surface waters cannot be evaluated by equilibrium models only; the slow metal exchange kinetics must be taken into account (6-9). For trace metals capable of forming an amalgam, anodic stripping voltammetry (ASV) with a mercury electrode is frequently used as one of the most convenient and sensitive analytical techniques for their chemical speciation in natural waters (10-14). Florence (14) compared direct current ASV with differential-pulse ASV for the determination of ASVlabile copper, lead, and cadmium with and without the “double acidification” procedure and found that the use of direct-current ASV in place of differential-pulse ASV for speciation analysis is limited by the significantly lower sensitivity of the former, but it had the advantage that the kinetics of the stripping step would have little effect on the determination, and hence, the amount of correction necessary in the procedure would be less. Mlakar and Lovric (15) compared different waveforms: square-wave, differential-pulse, staircase, and reverse-pulse anodic stripping measurements with a mercury-plated glassy carbon rotating disk electrode based on the stripping current, and found that the staircase voltammetric results were similar to those * Author to whom correspondence should be addressed; e-mail address: [email protected].

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obtained by linear scan voltammetry. Differential-pulse ASV and square-wave ASV give much higher sensitivity for determination of metals. The higher sensitivity is contributed by partial re-deposition of some of the stripped metal ions that still remain near the electrode surface when a cathodic pulse follows (16). The application of a mercury-plated glassy carbon rotating disk electrode (RDE) combined with anodic stripping voltammetry for measuring dissociation kinetics of metal complexes in natural waters was reported by Shuman and Michael (13). It provides a method for distinguishing labile and nonlabile metal complex kinetically. The advantages of a mercury film rotating disk electrode over a hanging mercury drop electrode are that it provides a totally mass-transfer-limited regime at the RDE. They applied this technique to the measurement of rate constants for copper complex dissociation in marine coastal water samples by spiking the metal ions into the samples and reported a first-order dissociation rate constant for copper chelates of the order of 2 s-1 (17). Others (18) suggested that studies on the lability of metal complexes at environmental concentrations should be done using direct-current stripping voltammetry, which however has much lower sensitivity than square-wave or differential-pulse stripping voltammetry.

Objectives and Scope This paper forms part of a program that makes an approach to the goal of kinetic speciation (19-23). Progress has also been made in developing a comprehensive scheme of metal speciation using ultrafiltration for fractionation of dissolved metals based on molecular weights and characterization of each fraction by its chemical reactivity as manifested by dissociation kinetics of its metal complexes (24-26). The objectives of this research are to examine the applications of the RDE technique for estimating dissociation rate constants and diffusion coefficients of copper and lead complexes in model solutions and snow samples and for establishing an operational definition for labile and nonlabile complexes based on kinetic measurements. This paper summarizes the results of preliminary studies made on the dissociation rates of Cu(II) and Pb(II) complexes in dilute aqueous solutions using the RDE technique in combination with anodic stripping voltammetry (ASV) with a mercury thin-film electrode (MTFE) on a glassy carbon substrate. The RDE technique allows kinetic measurements to be made in situ without greatly disturbing the system or the chemical equilibrium. Anodic stripping voltammetry applied with the waveforms, square-wave or differentialpulse, allows DIRECT determination of metals in natural waters, thereby eliminating the risk of contamination, loss of analytes or change in chemical speciation involved in preconcentration procedures. For preliminary work, CuNTA and PbNTA complexes have been chosen as model systems since their kinetic parameters have been previously studied by other electrochemical techniques.

Theory In the RDE technique, mass transport is by convective diffusion, with the solution transported across the face of the disk electrode in a laminar flow at a rate dependent on the rate at which the electrode is rotated. The time available for a metal complex to dissociate as it moves across the

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disk can be manipulated by varying the rotation rate. The disk is rotated with an electric motor at a rate in the range of 50-4000 rpm. At high rotation rates, there will be a very thin, well-defined, stagnant layer of the liquid close to the disk surface (called the Nernst diffusion layer) in which diffusion is the predominant form of mass transport. Outside the Nernst diffusion layer, convection is the predominant form of mass transport. In both cases, the process rapidly attains a steady state. With increasing rotation rates, the thickness of the diffusion layer continues to decrease till it tends to attain a constant value at extremely high rotation rates. Electrolysis of the uncomplexed metal (assuming that the complex itself is not reduced at the applied potential) is carried out at constant rotation rates in the range of about 50-4000 rpm. The coulombs of electricity passed during electrolysis, Qk, is measured by integrating the oxidation (stripping) current and is a function of the kinetic dissociation rate constant of the metal complex, kd, the ratio of uncomplexed to complexed metal, K, and the rotation rate, ω. The data are plotted as the ratio Qk/Qo or its inverse, as a function of the rotation rate, where Qo is the coulombs of electricity that would pass during electrolysis if all the metal present were reducible. When Qk/ Qo is plotted against ω or ω1/2, Qk/Qo f 1 as ω f 0 because at extremely slow rotation rates all complexes have time to dissociate. At the limit of extremely high rotation rates, there is no time for dissociation, and only uncomplexed metal is reduced at the disk. Therefore,

Qk/Qo f

[M] K ) [M] + [ML] K + 1

as ω f ∞. Kinetic information is obtained between these two limits, either by comparing Qk/Qo versus ω1/2 with the theoretical equation given by Hale (27) or by using a linearized approximation given by Koutecky´ and Levich (28) from which rate constants are obtained from the slope of Qo/Qk versus ω1/2 plots. Considering a 1:1 complex is formed between a divalent metal ion, M, and a ligand, L, its dissociation and the subsequent reduction of the metal ion (if the complex itself is not reduced at the applied potential) during the deposition step may be expressed as: kd

ML y\ z M2+ + L2k f

M2+ + 2e- f M

(in solution) (at the electrode)

(1) (2)

The electrodeposited metal during the electrolysis step is contributed by the free metal ions already existing in the sample and/or is generated by the dissociation of the metal complex, ML. If the dissociation of ML is slow and the reduction of M2+ is fast, the rate constant measured will represent the dissociation rate constant, kd, of the metal complex. In other words, the amount of electricity passed during the electrolysis step, Qk, will reflect the lability of the metal complex. Qk is a function of the kinetic dissociation rate constant of the complex, the ratio of uncomplexed to complexed metal, and the rotation rate of the rotating disk electrode as well as the duration of electrolysis. Qk is measured by integrating the oxidation current (stripping peak area) since the amount of electricity that passes during the electrolysis step would equal the amount of electricity that passes during the stripping step

if there is no re-reduction of the stripped metal (although this is not true for square-wave and differential-pulse voltammetry, the use of the ratio Qk/Qo for the calculation will mostly eliminate the effect of the re-reduction on the estimation of K ()[M]/[ML]) and of kd, where [M] and [ML] are the molar concentrations of the free metal ion and the metal complex, respectively. Qo is the coulombs of electricity that passes during the electrolysis step when the metal complex and uncomplexed metal ions both are reduced at the electrode, and there is no adsorption of the metal on the electrode contributing to the electrochemical processes. Analysis of the data is made by the Hale theory (27), in which the complex dissociation and the complex formation process (eq 1) are assumed as first-order or pseudo-firstorder reactions. According to the Hale theory (27), the ratio of the kinetic limiting current, ik, to the current when the total amount of metal is reducible, io, is expressed as

ik )1 io

/[

1+

D1/6ω1/2 × 1.61[K(1 + K)]1/2kd1/2ν1/6 tanh

)

(

)]

1.61(1 + K)1/2kd1/2ν1/6 K1/2D1/6ω1/2

Qk Qo

(3)

where D, ω, and ν are the diffusion coefficient of the diffusing metal species (it is assumed that D is the same for ML and M2+), the rotation rate of the rotating disk electrode, and the kinematic viscosity (i.e., viscosity/density), respectively. The typical value of ν for aqueous solution is 10-2 cm2 s-1, which has been adopted in this paper. K is the concentration ratio of the uncomplexed metal to the complexed metal (K ) [M]/[ML] ) kd/kf[L]). Qk is the stripping peak area (coulombs) representing the metal accumulated at the disk through kinetic dissociation of the complex, and Qo is the stripping peak area (coulombs) representing the metal accumulated by reduction of both ML + M2+. Qo and Qk are measured by integrating the oxidation (stripping) current. The diffusion coefficient, D, is evaluated from the Levich eq (29) by plotting Qo versus ω1/2:

Qo ) iot )

nFAD2/3Cω1/2 t 1.61ν1/6

(4)

where F, A, and C are the Faraday constant, the electrode surface area, and the bulk concentration of the metal species, respectively. K and kd are obtained by nonlinear regression analysis based on eq 3 (27).

Experimental Section A Princeton Model 384B polarographic analyzer and Rotel 2 rotating disk electrode were used. A mercury thin-film electrode on a glassy carbon substrate (rod of 6 mm diameter) surrounded by epoxy resin (insulator) was used as the working electrode. The rotation of the Rotel 2 electrode was powered by a 3-W motor. The reference electrode consisted of a coiled Ag/AgCl electrode in a Teflon tube fitted with a porous Vycor tip. The counter electrode was made of a coiled platinum wire in a Teflon tube with a porous Vycor tip. Two samples (grab samples) of snow were collected on different dates at a site on the rooftop of the chemistry

building at Carleton University. Following the procedure published earlier (23), the snowmelts were filtered through precleaned 0.45 µm filters (Gelman) immediately after the snow samples melted in order to remove particulate matter from the samples. The pH and the conductivity of the snowmelts were measured with an Accumet 925 pH/ion meter (Fisher Scientific), using a combination glass electrode with an internal calomel reference electrode, and a conductivity Bridge, model 31 (Yellow Springs Instrument Co., Inc., Yellow Springs, OH), respectively. A stock solution of 2.0 M sodium acetate buffer solution was prepared by dissolving an appropriate quantity of sodium acetate (BDH Chemicals) in ultrapure water. This solution was then purified by electrolysis at a potential of -1.4 V versus SCE for at least 48 h. The snowmelt samples were buffered with the sodium acetate buffer solution; the final concentration of the sodium acetate buffer was 0.04 M. The pH of the buffer solution was adjusted to the same value as that of the snow samples before adding the buffer to the samples. The above buffer also served the purpose of a supporting electrolyte. The ultrapure water of resistivity 18.2 MΩ cm-1 was obtained direct from a Milli-Q-Plus water purification system (Millipore Corporation). As described later, the pH and the ionic strengths of all model solutions and samples were held constant in all experiments since any change in the pH and the ionic strength of the samples is likely to change dissociation kinetics of metal-organic complexes (30). Prior to the sample analysis, the rotating glassy carbon disk electrode was polished carefully with 0.05 µm of alumina and then cleaned with an ultrasonic bath for 5 min. The mercury thin-film electrode (MTFE) was formed by plating mercury in situ onto the rotating glassy carbon disk electrode by immersing it into 50 mL of deoxygenated ultrapure water containing the sodium acetate buffer (pH 4.4) and 50 µL of 5000 µg mL-1 Hg2+ (taken as the mercuric nitrate) solution. The rotation rate of the electrode was set to 2000 rpm, and the electrode was held for 5 min at a constant potential of -1.0 V with respect to the Ag/AgCl reference electrode to form the MTFE. After the 5-min deposition period, the MTFE rotation was stopped, and the MTFE formation solution was allowed to become quiescent for 5 s. The MTFE potential was then ramped positive at 100 mV s-1 to 0 V using the square-wave waveform (20 mV pulse height, 50 pulse s-1 frequency) to strip any deposited impurities out of MTFE. The MTFE plating step was repeated three times, and mercury was accumulated into the MTFE. The stripping current was recorded as a function of the applied potential yielding a pseudopolarogram. Using the same instrumental condition as that for the sample analysis, the pseudopolarogram of the blank showed low or undetectable analyte levels and a satisfactory, low background current. The MTFE formation solution was replaced with a deoxygenated sample containing the sodium acetate buffer. The first aliquot of the sample was used to wash the electrodes only; then, a fresh aliquot of the buffered, deoxygenated sample (50 mL) was analyzed. The sample analysis was initiated by depositing the metal from the sample at the MTFE under the conditions of constant potential electrolysis from 0 to -1.6 V versus EAg/AgCl for a period of 120 s at a rotation rate of 2000 rpm, followed by a quiescent period of 5 s for equilibration, and a pseudopolarogram was recorded. Qk and Qo were measured at selected deposition potentials (selected from the plateau

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FIGURE 1. Thickness of the diffusion layer as a function of the rotation rate of the RDE.

FIGURE 2. Pseudopolarograms: (a) Cu-NTA ([Cu(II)] and [NTA] ) 2.05 × 10-7 M) in a model solution (pH 4.4) obtained by square-wave voltammetry with a frequency of 50 s-1; (b) Pb-NTA in a model solution (pH 4.6) obtained by square-wave voltammetry with a frequency of 25 s-1.

region of the pseudopolarogram) using a series of rotation rates in the range of 50-4000 rpm. The accumulated metal was stripped using staircase, square-wave, or differentialpulse waveform, and a positive potential scan going to 0 V versus EAg/AgCl with a scan rate of 10 mV s-1 for the staircase, 20 mV s-1 (frequency ) 10) or 100 mV s-1 (frequency ) 50) for the square-wave, or 10 mV s-1 for the differential-pulse waveform.

Results and Discussion Nernst Diffusion Layer. Figure 1 shows the thickness of the diffusion layer as a function of the rotation rate. The thickness of the Nernst diffusion layer, δ, was estimated using the following equation (31):

δ)

Qo nFADC ) nFADC io t

(5)

where n is the number of electrons involved in the reduction, and F, A, D, C, t, and Qo are as defined earlier. The thickness of the diffusion layer decreases with increasing rotation rates and tends to reach a constant value of 4.5 µm at 4000 rpm. The convective-diffusion model of mass transport is based on the assumption of a very thin well-defined diffusion layer near the electrode surface at high rotation rates (27-29). Figure 1 shows that this assumption is justified. Cu-NTA Model Solution. Figure 2a shows a plot of stripping peak area (coulombs) at a constant rotation rate as a function of applied potential (pseudopolarogram). The overall electrode reaction at the RDE can be written as kd

z Cu2+ + NTA3Cu-NTA- y\ k f

Cu2+ + 2e- + Hg f Cu(0)(Hg) As reduction of Cu2+ occurred at the electrode, Cu2+ was supplied by the dissociation route through the complex, provided the potential of the electrode was insufficient for the direct reduction of the Cu-NTA complex. As the rotation rate was increased, less time was available for the complex to dissociate as it flowed across the electrode. From the pseudopolarogram (Figure 2), two potentials were selected, one corresponding to the plateau for the Cu2+ +

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FIGURE 3. Pseudopolarograms of Cu in snow sample no. 1. (a) b, staircase voltammetry; (, differential-pulse voltammetry; O, squarewave voltammetry with a frequency of 10 s-1; 2, square-wave voltammetry with a frequency of 50 s-1. (b) Extension of b staircase voltammetry of panel a.

2e- f Cu(0) reaction, and the other corresponding to the plateau for the Cu-NTA- + 2e- f Cu(0) + NTA3- reaction. Using staircase voltammetry, Qk and Qo were measured at the applied potentials -0.4 and -1.0 V, respectively. Using square-wave voltammetry, Qk and Qo were measured at the applied potentials -0.6 and -1.4 V, respectively. Diffusion coefficient, D, was calculated from plots of Qo versus ω1/2 using the Levich equation (eq 4). Dissociation rate constants, kd, were estimated using either the Hale equation (27) or the Koutecky´-Levich equation (28). A diffusion coefficient of 2.9 × 10-6 cm2 s-1 and a dissociation rate constant of 8.8 s-1 were obtained. Pb-NTA Model Solution. Figure 2b shows a pseudopolarogram for Pb-NTA in a model solution. There are two well-defined plateaus. Qk and Qo were measured at the applied potentials of -0.80 and -1.20 V, respectively. A diffusion coefficient of 1.2 × 10-6 cm2 s-1 was obtained from eq 4. This value is lower than the value 5.5-9 × 10-6 cm2 s-1 reported for divalent metals in the literature (ref 12, p 360) and also lower than the mean values of 7.3 × 10-6 and 4.8 × 10-6 cm2 s-1 for PbNTA and Pb(NTA)2 reported by Tarelkin et al. (32). This difference may be due to the fact that in eq 4, it is assumed that D is the diffusion coefficient of both M and ML and that the surface area of the mercury thin-film electrode is the same as the geometric area of the glassy carbon electrode surfacesthese assumptions (especially, the latter) are not strictly valid. We also obtained a first-order dissociation rate constant of 0.25 s-1. Snow Sample No. 1. This sample (a grab sample) was collected on January 11, 1994, and had a pH 4.4 and conductivity 30 µS cm-1. Figure 3a shows pseudopolarograms of Cu in snow sample no. 1 using the four waveforms.

FIGURE 4. Plots of Qo versus ω1/2 in snow sample no. 1. b, staircase voltammetry; (, differential-pulse voltammetry; O, square-wave voltammetry with a frequency of 10 s-1; 2, square-wave voltammetry with a frequency of 50 s-1.

Figure 3b is the extension of Figure 3a, the curve for the pseudopolarogram obtained using staircase voltammetry, and shows that there are at least two copper complexes in this snow sample. At an applied potential more positive than -0.4 V, only the free copper ions were reduced, and at an applied potential more negative than -0.8 V, both the free metal ion and the complexed metal were reduced. Figure 3b also shows that the potentials for the reduction of the metal ion and for the direct reduction of metal complex are not well separated. The gross distortion of the middle plateau undoubtedly results from the inability to measure Qk without contribution from the direct reduction of the metal complex. Figure 3a shows that the sensitivity is much higher for the square-wave and the differential-pulse waveform than that for the staircase waveform. The peak height of the stripping current in the square-wave waveform at a frequency of 50 pulse s-1 is 2 orders of magnitude greater than that in the staircase waveform. The higher sensitivity of square-wave voltammetry is due to partial re-reduction of the stripped copper ions remaining near the electrode surface when a cathodic pulse follows, which amounts to partial recycling of the copper ions. The high sensitivity of square-wave voltammetry combined with ASV extends its applicability to direct determination of metals at very low concentrations present in uncontaminated natural waters. Diffusion Coefficient of Copper Species in Snow Sample No. 1. Figure 4 shows the plots of Qo versus ω1/2, where Qo was measured at a deposition potential of -1.0 V versus EAg/AgCl. All the data obtained using these three waveforms fit the Levich equation (eq 4). Table 1 shows diffusion coefficients calculated using the Levich equation (eq 4). Since the same snow sample was measured using the same deposition condition at the RDE, the diffusion coefficient measured using the three waveforms should be the same. However, Table 1 shows that the diffusion coefficients given by these three waveforms differ by 2 orders of magnitude. Generally, the diffusion coefficient obtained by staircase voltammetry is more reliable because of its simple stripping process. For square-wave or differentialpulse stripping voltammetry, the stripping current is increased by partial re-deposition of the stripped metal ions remaining near the electrode surface when a cathodic pulse follows.

Estimation of K and kd for the Copper Species in Snow Sample No. 1. The simplest case is that there is only one metal complex present in a sample, for which the values of K and kd can be obtained by direct fitting of the experimental data to the Hale equation (27) or the Koutecky´-Levich equation (28). However, in natural waters, metals may exist in more than one complex. Theoretically, the contribution of each complex to the total current is additive, and a simple graphical procedure can be used to separate the contribution of the slower from the faster dissociating complex (33). Figure 5 shows the theoretical plots of Qo/Qk and Qk/Qo versus ω1/2 using the Hale equation (27) for a mixture of two complexes, for which one of the complexes has Kf ) 0.5 and kd,f ) 30 s-1 and the other has Ks ) 0.6 and kd,s ) 0.3 s-1, and for rotation rates ranging from 0 to about 4000 rpm (the subscripts f and s stand for ‘fast’ and ‘slow’, respectively). One feature is notable: the curves tend toward a constant value of Qk/Qo at high rotation ratessthe limiting value of Qk/Qo is simply the ratio of [M]/[Mtotal], i.e., the ratio of the kinetically labile metal concentration to the total metal concentration. The value of K is understood then as the ratio of “labile” to “nonlabile” metal and is related to the limiting value of Qk/Qo by Qk/Qo ) K/(K + 1). According to the Hale equation (27), for a complex with a large dissociation rate constant, kd, the plot of Qo/Qk versus ω1/2 should be a straight line with an intercept of 1.0. Hence, in Figure 5, the slope of Qo/Qk versus ω1/2 at high rotation rates can be considered to be due to the fast-dissociating complex only. The values of Qo/Qk for the fast-dissociating complex are transformed by moving in a parallel fashion the linear portion down to the position where its extrapolation to the ordinate equals 1.0. Considering that the composite Qo/Qk is a simple sum - 1.0, of the contributions of the two complexes, the values of Qo/Qk for the slow-dissociating complex are transformed by subtracting the transformed values of Qo/Qk for the fastdissociating complex from the composite value of Qo/Qk + 1.0. Figure 5 clearly demonstrates the success of the data transformation for the two-complex system. For the snow sample no. 1, the pseudopolarogram (Figure 3) shows that there are at least two copper complexes present in the sample. Figure 6 shows the experimental data for the copper complexes in the snow sample, plotted as Qk/Qo, as a function of rotation rate and the Hale equation (27) fitting. The plots show a decrease in Qk/Qo with increasing rotation rates as expected for kinetic dissociation. The experimental data were fitted to the Hale equation (27) using Peakfit Software (Jandel Scientific PeakFit, version 2.01). The lines of the best fit are presented with the data points (Figure 6). Table 1 shows the values of K and the dissociation rate constants obtained from the Hale equation fitting and also the concentrations of copper complexes based on the K values. Although, as stated earlier, the diffusion coefficients calculated using the Levich equation (eq 4) for the three stripping waveforms were quite different, the values of K and kd obtained by square-wave voltammetry are very similar to those obtained by staircase voltammetry. This may be due to the fact that the employment of the Qk/Qo ratio in the Hale theory mostly eliminates the effect of partial re-reduction of the stripped copper ions on the square-wave voltammetry. However, there is a considerable difference in these values between differential-pulse voltammetry and staircase voltammetry. Probably, this difference was due to some change in the sample composition caused by the long (unavoidable) storage of the sample

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TABLE 1

Estimates of Diffusion Coefficients at 20 °C, Concentrations of Copper Complexes, and Their Dissociation Rate Constants in Snow Sample No. 1a waveform square-wave parameter cm2

s-1

D, K ) [M]/[ML] conc, µM

kd, s-1

staircase 10-6

4.8 × Kf ) 0.51 Ks ) 0.64 [Cu] ) 4.5 × 10-2 [CuLf] ) 8.8 × 10-2 [CuLs] ) 7.0 × 10-2 kd,f ) 3.6 × 101

kd,s ) 3.4 × 10-1

frequency ) 10 5.6 × Kf ) 0.49 Ks ) 0.37 [Cu] ) 3.5 × 10-2 [CuLf] ) 7.2 × 10-2 [CuLs] ) 9.6 × 10-2 kd,f ) 6.7 × 101 (3.0 × 101)b kd,s ) 9.5 × 10-1 (4.2 × 10-1)b

a Dissolved organic carbon ) 1.0 mg/L; conductivity ) 30 µS cm-1, pH ) 4.4. 10-6 cm2 s-1.

FIGURE 5. Theoretical plots for a mixture of two complexes, one for which Kf ) 0.5, kd,f ) 30 s-1 and another for which Ks ) 0.6, kd,s ) 0.30 s-1. (a) Plots of Qo/Qk versus ω1/2: b, the composite data calculated at specific rotation rates using the Hale equation; O, the transformed data obtained from the composite data for the fastdissociating complex; ), the transformed data obtained from the composite data for the slow-dissociating complex; s, the linear portion of the composite data at high rotation rates. (b) Plots of Qk/Qo versus ω1/2: b, the composite data calculated at various rotation rates using the Hale equation; O, the transformed data obtained from the composite data for the fast-dissociating complex; ), the transformed data obtained from the composite data for the slowdissociating complex; the solid line is the curve calculated using the Hale equation.

before the differential-pulse voltammetry experiment could be done. Snow Sample No. 2. The sample (a grab sample) was collected on January 12, 1995, and had a pH 4.37 and conductivity of 21.0 µS cm-1. Figure 7 shows the pseudopolarogram of Pb and Cu complexes in snow sample no. 2. For the lead complexes, two plateaus were observed. For determination of the dissociation rate constants of the Pb complexes, Qo and Qk were measured at deposition potentials of -1.35 and -0.90 V, respectively, with respect to EAg/AgCl. The plot of Qo versus ω1/2 shown in Figure 8a gives D ) 3.3 × 10-6 cm2 s-1. Figure 8b shows the plot of Qk/Q0 versus ω1/2 and gives the value of K ()[M]/[ML]) ) 4.0. Figure 8c shows the plot of Q0/Qk versus ω1/2; its linearity and intercept of 1.0 indicate that only one Pb complex was present. A dissociation rate constant of 5.6 s-1 was obtained by the Koutecky´-Levich equation (28) fitting. For the copper complexes, three plateaus were observed in Figure 7b, suggesting that besides free Cu2+ ions there were at least two copper complexes present in

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frequency ) 50

10-5

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b

10-4

1.1 × Kf ) 0.38 Ks ) 0.49 [Cu] ) 3.6 × 10-2 [CuLf] ) 9.4 × 10-2 [CuLs] ) 7.3 × 10-2 kd,f ) 8.4 × 101 (3.0 × 101)b kd,s ) 1.4 (4.9 × 10-1)b

differential-pulse 1.6 × 10-5 Kf ) 1.0 Ks ) 0.86 [Cu] ) 0.064 [CuLf] ) 0.064 [CuLs] ) 0.074 kd,f ) 8.2 × 101 (5.5 × 101)b kd,s ) 2.8 × 10-1 (1.8 × 10-1)b

The values in parentheses have been calculated using D ) 4.8 ×

FIGURE 6. Curve-fitting to the Hale equation for Cu in the snow sample no. 1. b, the composite data; O, the transformed data obtained from the composite data for the fast-dissociating complex; ), the transformed data obtained from the composite data for the slowdissociating complex; the solid line is the Hale equation fitting. (a) Staircase voltammetry; (b) differential-pulse voltammetry; (c) squarewave voltammetry with a frequency of 10 s-1; (d) square-wave voltammetry with a frequency of 50 s-1.

FIGURE 7. Pseudopolarograms of Pb and Cu in the snow sample no. 2 obtained by square-wave voltammetry with a frequency of 50 s-1. (a) Pb; (b) Cu.

the snow sample. For determination of the dissociation rate constants of the copper complexes, Q0 and Qk were measured at deposition potentials of -1.40 and -0.35 V, respectively, with respect to EAg/AgCl. A plot of Q0 versus ω1/2 (not shown) gives D ) 1.8 × 10-6 cm2 s-1. Figure 9a shows the plots of Q0/Qk versus ω1/2 of the composite data

FIGURE 8. Curves for estimation of D (a), K (b) and kd (c) of Pb in the snow sample no. 2. The data were obtained by square-wave voltammetry with a frequency of 50 s-1.

It is capable of giving quantitative information about the extent of metal complexation; that is, it can estimate rate constants for the dissociation of metal complexes and concentrations of metal species present in very low concentrations in aqueous samples. Square-wave voltammetry and differential-pulse voltammetry provide much higher sensitivity than staircase voltammetry and are capable of direct determination of metal species present in natural waters at very low concentrations. The RDE technique offers the additional, potential advantage of in situ determination with the least possible disturbance to the chemical equilibria involved.

Acknowledgments The authors are grateful to Professor J. Buffle for valuable discussions and to the Natural Sciences and Engineering Research Council of Canada and Environment Canada, Atmospheric Environment Service, for financial support.

Literature Cited FIGURE 9. Curve-fitting to the Hale equation for the copper species in the snow sample no. 2. The data were obtained by square-wave voltammetry with a frequency of 50 s-1. (a) b, the experimental (composite) data; O, the transformed data obtained from the composite data for the fast-dissociating complex; (, the transformed data obtained from the composite data for the slow-dissociating complex; the solid line is the Hale equation fitting. (b) O, the transformed data for the fast-dissociating complex; the solid line is the Hale equation fitting. (c) (, the transformed data for the slowdissociating complex; the solid line is the Hale equation fitting. TABLE 2

Estimates of Diffusion Coefficients at 20 °C, Concentrations of Copper and Lead Complexes, and Their Dissociation Rate Constants in Snow Sample No. 2 by Square-Wave Voltammetry (Frequency 50 s-1) parameter

Da ,

cm2

s-1

K ) [M]/[ML] concn, µM

kd, s-1

copper species 10-6

1.8 × Kf ) 0.10 Ks ) 0.79 [Cu] ) 7.1 × 10-3 [CuLf] ) 7.1 × 10-2 [CuLs] ) 9.0 × 10-3 kd,f ) 20 s-1 kd,s ) 3.2 × 10-2

lead species 3.3 × 10-6 K ) 4.0 [Pb] ) 1.2 × 10-2 [PbL] ) 3.0 × 10-3

kd ) 5.6

a These values were normalized by those obtained by staircase voltammetry.

(raw experimental data). Figure 9, panels b and c show the plots of Qk/Q0 versus ω1/2 of the transformed data for the fast-dissociating and the slow-dissociating complex, respectively. The results of the Hale equation (27) fitting are also shown in Figure 9. The dissociation rate constants for the fast-dissociating and slow-dissociating complexes were 20 and 3.2 × 10-2 s-1, respectively. Table 2 presents the results for snow sample no. 2.

Conclusions The RDE technique is capable of distinguishing labile and nonlabile complexes by virtue of its ability to measure metal availability for reduction over a wide range of time scales.

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Received for review June 28, 1995. Revised manuscript received October 30, 1995. Accepted November 1, 1995.X ES950453H X

Abstract published in Advance ACS Abstracts, January 15, 1996.