Measurement of Association and Dissociation Rate Constants for

Knowledge of the chemical kinetics for the ubiquitous Pb2+/18-crown-6 .... The 18-crown-6 (Sigma) concentration was varied between 1 and 2.9 mM for th...
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Anal. Chem. 2003, 75, 6560-6565

Measurement of Association and Dissociation Rate Constants for Lead(II)/18-Crown-6 Using Square Wave Voltammetry at a Glassy Carbon Mercury Film Electrode Caroline D. Geary and Stephen G. Weber*

Chevron Science Center, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Understanding the rate parameters of metal ion-ligand complexes is necessary for sensing, separations, and responsive materials. The complexation between 18crown-6 and lead(II) is of particular interest due to the potential use of this chemistry in sensors and separations. We have applied square wave voltammetry at a glassy carbon mercury film electrode to this problem. Lead(II) in aqueous solution containing an excess of 18-crown-6, studied with different experimental time scales, yields stoichiometry, binding constants, and rate constants (25 °C). For pulse times longer than 10 ms, the glassy carbon mercury film electrode acts as a planar electrode. For shorter pulse times, a roughness correction factor must be used to calculate dimensionless current because of the increase in effective area due to the droplike nature of the adsorbed mercury. Lead(II) forms a 1:1 complex with 18crown-6 in both nitrate and perchlorate media. Log K for the complex with the nitrate counterion is 4.13 ( 0.09 (SEM); in the presence of perchlorate it is 4.35 ( 0.09 (SEM). The formation rate constants, kf, for the nitrate and perchlorate systems are (3.82 ( 0.89) × 107 and (5.92 ( 1.97) × 106 M-1 s-1, respectively. The dissociation rate constants, kd, are (2.83 ( 0.66) × 103 s-1 with nitrate as the counterion and (2.64 ( 0.88) × 102 s-1 with perchlorate as the counterion. The significant difference in rate constants for the two anions is probably caused by the ion pairing that occurs with lead(II) nitrate. Since the introduction of macrocycles by Pedersen,1 the interaction of 18-crown-6 (1) with Pb2+ has emerged as a system with vast potential in the fields of sensors, extraction, and ion transport.2 Although a qualitative understanding of this system in terms of the macrocycle effect has been long understood and many thermodynamic studies exist for this system in various solvents, few kinetic studies exist. The disparity between kinetic and thermodynamic data for macrocyclic hosts in general has been pointed out in the review literature,2 yet the majority of data that continues to be published is of a qualitative nature or deals with * Corresponding author. E-mail: [email protected]. Fax: 412-624-1668. (1) Pedersen, C. J. Angew. Chem. 1998, 100, 1053-1059. (2) Izatt, R. M.; Pawlak, K.; Bradshaw, J. S.; Bruening, L. R. Chem. Rev. 1991, 91, 1721-2085.

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thermodynamic parameters. Knowledge of the chemical kinetics for the ubiquitous Pb2+/18-crown-6 system would be useful for potential applications. For example, Asher et al.3,4 have proposed using this system in polymerized crystalline colloidal array hydrogel sensors and optrodes for Pb2+ detection. A complete understanding of the dynamics of these sensing materials requires knowledge of metal-crown kinetics. 18-Crown-6 and other crowns have been used in high-resolution separations of metal ions.5-7 Chemical rates are needed for understanding band broadening. Crowns and other metal ion chelators are key elements in photoswitching schemes.8-10 Very little kinetic information exists for these systems.11,12 Stephens et al.12 have used kinetic, equilibria and stoichiometric data to model metal ion binding to a photochromic molecule containing an iminodiacetic acid chelator. Knowledge of the metal-ligand complex association- and dissociation-required rate constants were needed to prove that light could force the dissociation of the metal ion complex. (3) Holtz, J. H.; Holtz, J. S. W.; Munro, C. H.; Asher, S. A. Anal. Chem. 1998, 70, 780-791. (4) Reese, C. E.; Baltusavich, M. E.; Keim, J. P.; Asher, S. A. Anal. Chem. 2001, 73, 5038-5042. (5) Hayashita, T.; Lee, J. H.; Hankins, M. G.; Lee, J. C.; Kim, J. S.; Knobeloch, J. M.; Bartsch, R. A. Anal. Chem. 1992, 64, 815-819. (6) Hayashita, T.; White, J. C.; Lee, J. C.; Bartsch, R. A. Sep. Sci. Technol. 1993, 28, 2607-2620. (7) Turner, N. H.; Barger, W. R.; Mowery, R. L. Book of Abstracts, 210th ACS National Meeting, Chicago, IL, August 20-24, 1995; ANYL-083. (8) Winkler, J. D.; Bowen, C. M.; Kim, H. S. American Chemical Society, Washington, DC, 1996; ORGN-136. (9) Shinkai, S.; Honda, Y.; Ueda, K.; Manabe, O. Bull. Chem. Soc. Jpn. 1984, 57, 2144-2149. (10) Rahman, S. M. F.-u.; Fukunishi, K. J. Chem Soc., Chem. Commun. 1994, 917-918. (11) Zhou, J.; Tang, Y.; Zhao, F.; Song, X. Wuli Huaxue Xuebao 1994, 10, 200203. (12) Stephens, M. R.; Geary, C. D.; Weber, S. G. Photochem. Photobiol. 2002, 75, 211-220. 10.1021/ac034666y CCC: $25.00

© 2003 American Chemical Society Published on Web 10/24/2003

To our knowledge only two studies exist that probe the kinetics of the 18-crown-6/Pb2+ system. Erying and co-workers studied the system in aqueous solution using ultrasonic absorption spectroscopy to investigate the mechanism of complexation.13 Data are interpreted in terms of a two-step mechanism proposed by Chock (conformation change of the crown ether followed by complexation with the metal) that assumes loss of water, and not crown ether isomeric rearrangement, is the rate-limiting step. The formation rate constant was determined by a three-parameter fit to a one-relaxation equation to be 3.3 × 108 M-1 s-1 at 25 °C. Later work by Erying et al. found that the multistep EigenWinkler mechanism correctly interpreted the complexation process for metal ions with crown ethers. Despite being numerically indistinguishable from the Chock mechanism, the Eigen-Winkler mechanism proposed the crown ether rearrangement to be the slow step compared to the complexation. This work was done in DMF and did not include the study of Pb2+ with 18-crown-6. Proton NMR has been used to study the dissociation kinetics of the Pb2+/ 18-crown-6 complex in binary acetonitrile/water mixtures.14 Spectra are fitted to NMR exchange equations to extract the mean interaction lifetime, τ, which is related to kd. For 50% acetonitrile/ water solution, kd was found to be 531 s-1 at 30 °C. A linear dependence of 1/τ with crown ether concentration verified the predominance of a dissociative mechanism. We are interested in measuring the rate constants of this system using a technique capable of measuring rate constants in aqueous solution or organic solvents and with low concentration of metal ion, conditions that have not been reported before. Square wave voltammetry (SWV) at a mercury film electrode is well-suited to the task. SWV is a modern electroanalytical technique noted for its sensitivity and high discrimination against charging currents.15 The theoretical response given by SWV for electron transfer coupled to a preceding chemical reaction (CE mechanism) was published by O’Dea et al.16 This theory has been used successfully to study metal ion-ligand complexation at a hanging mercury drop electrode (HMDE).12,17 Data are in excellent agreement with theory, but this electrode is not without limitations; for example, the HMDE is unstable in organic solvents and violates regulations against use of bulk mercury. An alternative mercury-based electrode is the glassy carbon mercury film electrode (GCMFE). GCMFEs do not have these limitations but retain the benefit of high overpotential for hydrogen that is associated with the HMDE. Despite routine and successful use of this electrode as the working electrode in anodic stripping voltammetry,18,19 the GCMFE is seldom used in direct SWV. This is most likely due to the nature of the electrode, which is a collection of mercury drops with a limited thickness.20 Thus, depending on the parameters used, the (13) Rodriguez, L. J.; Liesegang, G. W.; Farrow, M. M.; Purdie, N.; Eyring, E. M. J. Phys. Chem. 1978, 82, 647-650. (14) Rouhollahi, A.; Amini, M. K.; Shamsipur, M. J. Solution Chem. 1994, 23, 63-74. (15) Osteryoung, J.; Osteryoung, R. Anal. Chem. Symp. Ser. 1986, 25, 3-12. (16) O’Dea, J. J.; Osteryoung, J.; Osteryoung, R. A. Anal. Chem. 1981, 53, 695701. (17) Correia dos Santos, M. M.; Simoes Goncalves, M. L.; Romao, J. C. J. Electroanal. Chem. 1996, 413, 97-103. (18) Economou, A.; Fielden, P. R. TrAC, Trends Anal. Chem. 1997, 16, 186292. (19) Subramanian, G.; Rao, G. P. Rev. Anal. Chem. 1979, 4, 95-109. (20) Frenzel, W. Anal. Chim. Acta 1993, 273, 123-137.

electrode may deviate from the theoretical model, which assumes planar geometry with infinite diffusion both to and from the electrode. Osteryoung and co-workers have studied diffusion into the film for amalgam-forming species as a function of a dimensionless parameter, Λ, where Λ ) l/(DRτ)1/2 (l, film thickness; DR, diffusion coefficient of metal in Hg’ τ, square wave period). For Λ > 3, film thickness is sufficiently large compared to DRτ that the peak position and shape are indistinguishable from those for reversible SWV with unrestricted planar diffusion. Thus, the lowest frequency (longest τ) obeying this condition can be predicted for a given film thickness and metal. There are also restrictions on the highest frequency. Kounaves and Deng21 investigated deviations from theory that occur at high SW frequencies at CGMFEs. They concluded that the decreasing thickness of the diffusion layer is the source of nontheoretical behavior at high square wave frequencies. The maximum frequency that obeys theory depends on the film thickness. For films greater than 3-4 µm thick, the maximum attainable frequency before deviations occurred was found to be around 200-250 Hz. In this work, we have determined that judicious choice of film thickness and experimental time scales allows for the kinetics of a preceding chemical reaction to be studied with SWV at a GCMFE. We have studied 18-crown-6/Pb2+ dissociation kinetics with two different anions in aqueous solution. We have found that the rate constants vary depending on the anion present. This is the first kinetic study of the 18-crown-6/Pb2+ system using voltammetry and the only study using SWV at a film electrode to investigate a CE mechanism. EXPERIMENTAL SECTION Reagents. All reagents were of analytical grade and used as received. Solutions were prepared with deionized water from a Millipore MilliQ Water purification system. Experiments with nitrate as the counteranion were 0.1 M LiNO3 (Baker) and 100 µM Pb(NO3)2 (Baker). Experiments with perchlorate as the counteranion were 0.1 M LiClO4 (Aldrich) and 100 µM Pb(ClO4)2. The concentration of Pb(ClO4)2 was determined by gravimetric analysis using H2SO4 prior to use.22 The 18-crown-6 (Sigma) concentration was varied between 1 and 2.9 mM for the nitrate binding study and 1 and 2.3 mM for the perchlorate binding study. A solution of 0.01 M Hg(NO3)2 (Fisher) in 0.1 M HNO3 (EM) was used to prepare the working electrodes. Instrumentation. Square wave voltammograms for the binding studies were collected using a Cypress Systems model 1090 computer-controlled potentiostat with Cypress 1090 software. The square wave pulse, Esw, was 30 mV and step height, ∆E, was 2 mV; the pulse duration, τ, was 180 ms for the Pb(NO3)2 study and 240 ms for the Pb(ClO4)2 study. For the kinetic studies with Pb(NO3)2 and 18-crown-6, a BAS Epsilon computer-controlled potentiostat with accompanying BAS software was used. For the kinetic studies with Pb(ClO4)2 and 18-crown-6, the Cypress 1090 was used. The working electrodes were prepared using the Cypress System model 1090 computer controlled potentiostat. Procedures. For all electrochemical studies, the voltammetric cell was maintained at 25.0 ( 0.2 °C. Argon presaturated with (21) Kounaves, S. P.; Deng, W. J. Electroanal. Chem. Interfacial Electrochem. 1991, 306, 111-124. (22) Kolthoff, J. M., Elving, P. J., Eds. Treatise on Analytical Chemistry, Part 2; Interscience: New York, 1964.

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deionized water was passed through the solution for 20 min to remove oxygen. The solution was blanketed with argon during data collection. Complexation was studied by the stepwise addition of a concentrated crown ether solution into the starting solution (total metal concentration was maintained at 100 µM Pb(II)). Solutions were degassed and allowed to equilibrate for 15 min prior to scans. Prior to all experiments, the mercury film electrode was tested for reversible behavior by monitoring the current as a function of (1/τ)1/2 in the absence of ligand. For the kinetic studies, the concentration of Pb(II) was 100 µM and the concentration of 18-crown-6 was 2.0 mM. The square wave pulse (Esw) was 30 mV and step height (∆E) was 2 mV, the square wave period (τ) was varied randomly over a range of values. The ranges are specified in the discussion of the data. Experiments were repeated completely three times; that is, different electrodes and solutions were employed, often on different days. A mercury film electrode on glassy carbon was used in all experiments for the working electrode. The mercury film, ∼50 µm thick, was electrochemically deposited on a polished (0.05µm alumina) 1-mm glassy carbon electrode (in-house, Sigradur G glassy carbon). The mercury was deposited electrochemically using a Cypress Systems model 1090 computer-controlled potentiostat with Cypress 1090 software. The charge passed during the deposition was monitored coulometrically. The thickness of the film was calculated from the charge passed during the reduction of the mercury and the geometric area of the glassy carbon substrate. A silver/silver chloride (BAS) reference electrode and platinum grid (in-house) counter electrode were used in all experiments. Errors are reported as the standard error of the mean (SEM). Errors in rate constants were determined from the propagation of error treatment applied to log((1 + K)kd). (K and kd are defined in eqs 2-6 below.) RESULTS AND DISCUSSION Binding constants, stoichiometry, and rate constants for the Pb(II)/18-crown-6 complex have been measured with both nitrate and perchlorate as the counteranions. Different experimental time regimes have been used. For thermodynamic studies, the experimental time scale is sufficiently long compared to the chemical rates such that the system is considered to always be in equilibrium. For determinations of rate constants, the experimental time scale is at or near the kinetic time scale for the preceding reaction. Measurement of all parameters requires that the electrochemical step be reversible. Reversible Behavior of Pb(II) Reduction at GCMFE in the Absence of Ligand. The reduction of Pb(II) at the GCMFE followed the theory for a reversible electron-transfer reaction with planar, semi-infinite diffusion for pulse durations between 10 and 180 ms. A plot of ∆Imax versus τ-1/2 was linear with a fit of ∆Imax ) 0.431τ-1/2 (slope from theory was 0.395 with C ) 100 µM, d ) 1.0 mm, Esw ) 30 mV, and dE ) 2 mV), R2 ) 0.9902. Data collected in this range obey semi-infinite diffusion; the film on the electrode is “thick” (Λ > 3, ∆I ) ψ × Cottrell current). For pulse durations shorter than 10 ms, experimental currents are higher than predicted by theory due to the droplike nature of the electrode resulting in nonplanar diffusion at these thinner diffusion layers (Figure 1 inset). The peak shape for Pb(II) reduction at the GCMFE is given in Figure 1 and is also in agreement with the theory for a reversible, diffusion-controlled system. 6562

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Figure 1. Normalized experimental (9) and theoretical resultant square wave voltammograms for 1.00 × 10-4 M Pb(NO3)2 in aqueous 0.10 M LiNO3. Esw ) 30 mV, dE ) 2 mV, τ ) 30 ms, T ) 25 °C, d ) 1 mm, and l ) 50 µm. Inset: Current vs τ -1/2. Esw ) 30 mV, dE ) 2 mV, and τ varied between 3 and 180 ms.

Figure 2. SWV of 1.00 × 10-4 M Pb(NO3)2 in the absence (a) and presence (b) of crown ether, [18-crown-6] ) 2.90 × 10-3 M in aqueous 0.10 M LiNO3. Esw ) 30 mV, dE ) 2 mV, τ ) 180 ms, and T ) 25 °C.

Determination of Binding Constants. SWV can be used to determine the binding constant and stoichiometry of a metal ionligand complex using the Lingane eq 1:23

∆E ) -

jRT RT ln β ln[L] nF nF

(1)

where ∆E is the shift in reduction potential, β is the formation constant for the complex, j is the stoichiometry of the complex, MLj, and [L] if the concentration of the ligand. The shift in potential is measured by comparing the peak potential for the reduction in the absence of ligand with the peak potential in the presence of an excess of ligand. The reduction of Pb(NO3)2 in the presence and absence of 18-crown-6 in aqueous 0.1 M LiNO3 is shown in Figure 2. Data were collected with a pulse duration of 180 ms. This long pulse allows for the preceding chemical reaction to reach equilibrium within the experimental time scale. Data collected are Nerstian with the peak potential merely shifted along the potential axis in the negative direction. Data were collected until further increases in the ligand concentration affected the magnitude of ∆Imax. When ∆Imax decreases, the response is no longer free of kinetic effects from the preceding chemical step. The regression data for the Lingane plots (∆E1/2 versus log[18-crown-6], see Figure 3) are given in Table 1 for both lead nitrate and lead perchlorate. The slopes indicate formation of 1:1 complexes for both. Log β values (25 °C) were found to be 4.13 ( 0.09 and 4.35 ( 0.09 for the nitrate and perchlorate, (23) Lingane, J. J. Chem. Rev. 1941, 29, 1-35.

Figure 3. Plots of ∆E vs log [18-crown-6] for 1.00 × 10-4 M Pb(II) with varying 18-crown-6 concentrations. (9) Pb(NO3)2 in aqueous 0.10 M LiNO3, Esw ) 30 mV, dE ) 2 mV, τ ) 180 ms, and T ) 25 °C, (2) Pb(ClO4)2 in aqueous 0.10 M LiClO4, Esw ) 30 mV, dE ) 2 mV, τ ) 240 ms, and T ) 25 °C. Table 1. Binding Constants and Complex Stoichiometry from Lingane Plots, ∆E vs -log [18-Crown-6] 100 µM Pb(II) with Excess 18-Crown-6 Log β regression equation R2 (25 °C) Pb(NO3)2 Pb(ClO4)2

∆E ) 0.0303 log [18C6] - 0.1201 ∆E ) 0.0342 log [18C6] - 0.1286

Figure 4. Peak height, ∆ψ, for a CE mechanism as a function of log(λτ) for ∆E ) 2 mV and Esw ) 30 mV for various Log K values. (a-h) 2, 1, 0.5, 0, -0.5, -1, -1.5, and -2.

The rate constants of dissociation and formation are then

j for MLj

0.997

4.13 ( 0.09

1

0.998

4.35 ( 0.09

1

k1

Y y\ zO k

(2)

O + ne h R

(3)

K ) k1/k-1 ) CO(x,0)/CY(x,0)

(4)

-1

where

The preceding chemical step in the work presented here is a metal-complex dissociation with 1:1 stoichiometry, where β ) kf/kd ) [ML]/[M] [L]. Working with an excess of ligand ([L] ) 20[M]), a conditional equilibrium constant, K, can be defined to fit this preceding reaction to the first-order model given in eqs 2 and 4:

K ) 1/β[L] = 1/β[L]T where [L]T is the total ligand concentration.

(5)

(6)

k-1 ) kdβ[L]T

(7)

In SWV, the maximum net current is given by

∆Imax ) respectively. Our data are in good agreement with a recently reported value of Log β ) 4.41 (25 °C) obtained using SWV at a HMDE,24 suggesting that the GCMFE is a viable alternative to bulk mercury electrodes. It is interesting to note that the latter study was done with lead nitrate in aqueous solution with excess tetraethylammonium perchlorate as the electrolyte, and the result more closely matches our perchlorate data. Determination of the Rate Constants. The effect of the preceding chemical reaction on the SWV response for the reduction of an electroactive species has been presented in the literature.16 A general scheme for a CE mechanism is used:

k1 ) kd

nFAD01/2C*ψ(EswEstep) (πτ)1/2

(8)

where ψ is the dimensionless maximum net current, τ is the square wave period, Esw is the pulse height, and Estep is the step height for the waveform. The dimensionless current is constant for a reversible system with set values of Esw and Estep. For a system influenced by the kinetics of a preceding chemical reaction, ψ is not constant, but depends on a dimensionless kinetic parameter. For our system, ψ becomes a function of K[(k1 + k-1)τ]1/2.16 Determination of the kinetic parameters is achieved by measuring the current as a function of the pulse duration. Experimental data are collected over a range of τ values holding ligand concentration constant. ∆Imax values are then normalized to the constant nFADo1/2C*/(πτ)1/2 and referred to a working curve that depends on the product β[L]T and the SW waveform. The constant nFADo1/2C*/π1/2 is experimentally obtained from a linear plot of ∆Imax versus τ -1/2 for the reduction of Pb(II) in the absence of ligand. The working curves are generated by a computer program written from preexisting theory.16,17 It should be noted that there is a typographical error in the cited literature that does not allow the calculation of ψ when log K e 0. In eq 21 of ref 18, the term π1/2 R1′(K2 + 1) should read π1/2 R1′/(K2 + 1). Correcting for this allows for generation of working curves for any log K value (see Figure 4). SW voltammograms for Pb2+ reduction in the presence of 18crown-6 with both counterions are well behaved in the region τ ) 10 to τ ) 120 ms; that is, diffusion to the electrode appears planar, and diffusion into the electrode appears semi-infinite. This (24) Parham, H.; Zargar, B. Russ. J. Electrochem. (Translation of Elektrokhimiya) 2002, 38, 484-487.

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Figure 5. Theoretical curve showing current vs log(λτ) for a CE mechanism with Log K ) -1.43 and [18-crown-6] ) 2.00 × 10-3 M. (9) Experimental data overlaid on curve for 1.00 × 10-4 M Pb(NO3)2 in aqueous 0.10 M LiNO3 with 2.00 mM 18-crown-6. q Esw ) 30 mV, dE ) 2 mV, τ varied between 4 and 120 ms, and T ) 25 °C.

Figure 6. Theoretical curve showing current vs log(λτ) for a CE mechanism with Log Kc ) -1.65 and [18-crown-6] ) 2.00 × 10-3 M. (9) Experimental data overlaid on curve for 1.00 × 10-4 M Pb(ClO4)2 in aqueous 0.10 M LiClO4 with 2.00 mM 18-crown-6. Esw ) 30 mV, dE ) 2 mV, τ varied between 20 and 180 ms, and T ) 25 °C. Table 2. Regression Data for Plots of log (λτ) vs log τ

range of τ values allows for a sufficiently wide “window” on the working curve for the perchlorate case. For the nitrate case, there is a smaller portion of the working curve that is exploited. This is the result of the faster dissociation kinetics of the preceding reaction with this counteranion. To maximize the window for the purpose of decreasing the uncertainty in the rate constants, data at experimentally faster time scales were required. To achieve this, data were collected at shorter pulse durations. In this time scale, diffusion to the electrode is affected by the droplike nature of the mercury on the glassy carbon substrate. The decrease in diffusion layer thickness with shorter values of τ results in an increase in the apparent electrode area and therefore an increase in current. Since the effective area of the electrode is changing with changing τ, the value of nFADo1/2C*/(πτ)1/2 is no longer a constant. Data obtained in this region are therefore normalized by taking a ratio of ∆Imax in the absence of ligand with that in the presence of ligand. Each ∆Imax value in the absence of ligand at a given τ value becomes a reference for the ∆Imax value in the presence of ligand at the same value of τ. For both systems studied, the normalized points are compared to the working curves (see Figures 5 and 6) and log λτ values are determined. Plots of log τ versus log λτ are used to find the value and error in log λ. Log λ values and regression data obtained from plotting log τ versus log λτ are given in Table 2. The intercepts of these plots equal log λ, and slopes should equal 1. In the perchlorate case, there appears to be an outlier at τ ) 180 ms, and removing it brings the slope from 0.87 to 0.92; however, the point cannot be excluded based on the Q test. Although the slope for the nitrate case indicates a better fit, both cases statistically fit the model with 95% confidence intervals (which are shown in Table 2). Log λ is related to kd through λ ) (1 + Κ)kd. Formation and dissociation rate constants for the complexes are given in Table 3. The rate constants can be compared to some degree with published data; however, as solvation plays a large role in this sort of reaction, and the only two studies are not in aqueous solutions, detailed comparison is impossible. The forward rates in all cases do not represent a significant barrier beyond diffusion; that is, all forward rate are less than ∼102 smaller than diffusion 6564

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100 µM Pb(NO3)2 with 2.0 mM 18-Crown-6 τ Range ) 4-120 ms standard lower coefficients error 95% intercept slope

4.88 1.09

0.11 0.06

4.67 0.97

100 µM Pb(ClO4)2 with 2.0 mM 18-Crown-6 τ Range ) 20-180 ms standard lower coefficients error 95% intercept slope

4.08 0.87

0.08 0.07

3.91 0.72

upper 95% 5.10 1.21

upper 95% 4.26 1.01

Table 3. Rate Constants for Pb(NO3)2 and Pb(ClO4)2 with 18-Crown-6 Determined by SWV at a GCMFE at 25 °C

Pb(NO3)2 Pb(ClO4)2

Log K

kd (s-1)

kf (M-1 s-1)

-1.43 -1.65

(2.83 ( 0.66) × 103 (2.64 ( 0.88) × 102

(3.82 ( 0.89) × 107 (5.92 ( 1.97) × 106

controlled. It is interesting to note that Rouhollahi et al.,14 who used a mixed solvent of acetonitrile water, found a dissociation constant that is somewhat lower than the kd we measured in a aqueous solution. This might be expected if rehydration of Pb2+ or the crown ether when the complex dissociates plays a role in the rate-determining step. The rate constants for the nitrate and perchlorate systems are significantly different. To our knowledge this is the first report of an anion effect for Pb2+ complexation with 18-crown-6. Previous studies that have investigated how changes in the chemical environment effect metal ion complexation with crown ethers left unresolved questions about the role of the solvent and conformation changes of the crown ether.13,25,26 However, these studies (25) Strasser, B. O.; Hallenga, K.; Popov, A. I. J. Am. Chem. Soc. 1985, 107, 789-792. (26) Wallace, W.; Chen, C.; Eyring, E. M.; Petrucci, S. J. Phys. Chem. 1985, 89, 1357-1366.

confirm the importance of Coulombic interactions in complex formation and dissociation. Eyring13,26 showed the dependence of changing charge density with increasing ionic size on complexation rates in aqueous solution among ions with noble gas configurations. As charge density decreases, the rate of complexation decreases. Popov et al.25 showed the anion, through the degree of ion pairing, can influence whether unimolecular or bimoleclar dissociation predominates for Na+ dissociation from 18-crown-6 in THF. We hypothesize that electrostatics play a role in the different rate constants for the Pb2+/18-crown-6 system. Aqueous solutions of Pb(ClO4)2 are known to be completely ionized at all concentrations.27 The ion pair Pb(NO3)+ is known to exist even at moderate concentrations. Harrison et al. reported a Kassoc value in water of 1.233 M-1 in the concentration range of 0-1 M at 25 °C.28 The existence of Pb(NO3)+ is consistent with our findings, namely, that the association and dissociation rates are faster for Pb2+/18crown-6 in the presence of the nitrate anion. The formation of an ion pair between the nitrate and lead(II) would, by lowering the charge density of the metal species, facilitate in the dissociation and association of the complex leading to the faster on and off rates observed with this anion.

In conclusion, we have found that the GCMFE is a viable and inexpensive alternative to the HMDE for studying thermodynamic and kinetic parameters of a CE mechanism using SWV. The flexibility of the SW parameters, as well as the ability to control the ligand concentration, should allow this technique to be applied to many CE systems in both aqueous and organic solvents. We have shown the range of time scales can be extended to a few milliseconds even for the GCMFE, which exists as a collection of mercury drops on the carbon substrate. This theory has been used to study Pb2+/18-crown-6 complexation in the presence of nitrate and perchlorate anions. We report the first evidence of an anion effect for Pb2+ complexation with 18-crown-6. This finding is in agreement with previous studies which have reported on the influence of Coulombic interactions on metal-crown complexations.

(27) Sylva, R. N.; Brown, P. L. J. Chem. Soc., Dalton Trans.: Inorg. Chem. (19721999) 1980, 1577-1581. (28) Harrison, P. G.; Healy, M. A.; Steel, A. T. J. Chem. Soc., Dalton Trans. 1983, 1845-1848.

Received for review June 19, 2003. Accepted September 10, 2003.

ACKNOWLEDGMENT We thank the NSF for support of this work through Grants CHE 0078520 and CHE 0315188 and Professor Adrian Michael for his assistance with the computer program needed to generate the working curves.

AC034666Y

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