Anal. Chem. 1997, 69, 783-788
Determination of Aqueous FeIII/II Electron Self-Exchange Rates Using Enriched Stable Isotope Labels, Ion Chromatography, and Inductively Coupled Plasma Mass Spectrometry Gary E. Kozerski,† Michael A. Fiorentino,‡ and Michael E. Ketterer*
Department of Chemistry, John Carroll University, University Heights, Ohio 44118
A strategy is described for rapid on-line measurement of electron self-exchange rates between aqueous FeIII and FeII in aqueous solution using stable 57Fe-labeled reactants, cation chromatography, and inductively coupled plasma mass spectrometry. The self-exchange is monitored by mixing the reactants and performing timewise separations of FeII and FeIII ions. Separations are completed in 30-60 s using a weak phosphonic/carboxylic acid cation exchange guard column and 0.1-0.5 M aqueous HClO4 eluent. The resulting time series of 56Fe and 57Fe chromatograms display systematic changes in isotopic abundances from which the self-exchange rate constant, k11, is obtained. Two different schemes are used for mixing and sampling the reaction mixture; using a peristaltically pumped flow reactor, reaction half-lives on the order of 30 s can be monitored. A series of k11 results are obtained under a variety of temperature (2.0, 21.6, and 25.0 °C) and ionic strength conditions (0.10, 0.50, and 0.55 M aqueous HClO4) which are congruent with three previously published radiolabeling studies for this reaction. Examples of solution-phase electron transfer (ET) processes are abundant in fields ranging from biochemistry to energy storage. The vast importance of electron transfer is reflected in longstanding and continued research in this area of chemistry. Marcus1,2 was the first to establish a concise mathematical description of the single-electron transfer rate constants in solution (k12) as follows:
k12 ) (k11k22K12f12)0.5
(1)
log f12 ) (log K12)2/4 log(k11k22/Z122)
(2)
where k11 and k22 are the self-exchange rate constants for the two redox couples, K12 is the equilibrium constant, and Z12 is the reactant collision frequency. For cases where both reactants are charged, additional expressions have been developed to account for the electrostatic work required to bring the ions together into †
Present address: Dow Corning Corp., Midland, MI 48686. Present address: Department of Chemistry and Biochemistry, University of Texas, Austin, TX 78712. (1) Marcus, R. A. J. Phys. Chem. 1963, 67, 853-857. (2) Marcus, R. A. J. Chem. Phys. 1965, 43, 679-701. ‡
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© 1997 American Chemical Society
a “precursor complex”.3 Reliable values of k11 are crucial in allowing prediction of rates of reaction where the reactants are not members of the same redox couple. Moreover, knowledge of k11 and k22 allows probing of the system’s adherence to Marcus theory and permits certain mechanistic inferences to be made. A common approach is to determine k11 indirectly using the Marcus equations and measuring k12 and K12 using a series of reactants of known k22.4,5 Preferably, a direct measurement of k11 can be made, but this measurement is nontrivial due to the lack of a net chemical change in the self-exchange process (*Ox + Red ) *Red + Ox). Extensively used approaches include NMR relaxation4-12 and isotopic equilibration of radiolabeled reactants.13-18 As with most measurement techniques, these and other approaches for k11 measurement have experimental and practical difficulties which limit the couples and conditions for which k11 can be determined. Stable isotope labeling, combined with separations and mass spectrometry, is a feasible but little-exploited approach for direct measurement of k11. This “stable isotope equilibration” approach is implemented in the same fashion as radioisotope-based procedures yet does not involve the regulatory and radiation safety constraints of the latter. Stanbury and co-workers19 determined k11 for the NO2/NO2- couple in solution using 15N-labeled NO2, ion chromatography, and negative-ion FAB mass spectrometry. We have recently demonstrated the determination of k11 for the aqueous TlIII/I two-electron exchange reaction using 203Tl-enriched reactants, selective precipitation of TlBr, and isotopic measure(3) Macartney, D. A.; Sutin, N. Inorg. Chem. 1983, 22, 3530-3534. (4) Koval, C. A.; Margerum, D. W. Inorg. Chem. 1981, 20, 2311-2318. (5) Vande Linde, A. M. Q.; Juntunen, K. L.; Mols, O.; Ksebati, M. B.; Ochrymowycz, L. A.; Rorabacher, D. B. Inorg. Chem. 1991, 30, 5037-5042. (6) Chan, M. S.; Wahl, A. C. J. Phys. Chem. 1978, 82, 2542-2549. (7) Shprorer, M.; Ron, G.; Loewenstein, A.; Navon, G. Inorg. Chem. 1965, 4, 361-365. (8) Yang, E. A.; Chan, M. S.; Wahl, A. C. J. Phys. Chem. 1980, 84, 3094-3099. (9) Macartney, D. H. Inorg. Chem. 1991, 30, 3337-3342. (10) Hoddenbagh, J. M. A.; Macartney, D. H. Inorg. Chem. 1990, 29, 245-251. (11) Beattie, J. K.; Smolenaers, P. J. J. Phys. Chem. 1986, 90, 3684-3686. (12) Smolenaers, P. J.; Beattie, J. K. Inorg. Chem. 1986, 25, 2259-2262. (13) Prestwood, R. J.; Wahl, A. C. J. Am. Chem. Soc. 1949, 71, 3137-3145. (14) Dietrich, M. W.; Wahl, A. C. J. Chem. Phys. 1963, 38, 1591-1596. (15) Krishnamurty, K. V.; Wahl, A. C. J. Am. Chem. Soc. 1958, 80, 5921-5924. (16) Bonner, N. A.; Hunt, J. P. J. Am. Chem. Soc. 1960, 82, 3826-3828. (17) Jolley, W. H.; Stranks, D. R.; Swaddle, T. W. Inorg. Chem. 1990, 29, 385389. (18) Jolley, W. H.; Stranks, D. R.; Swaddle, T. W. Inorg. Chem. 1992, 31, 507511. (19) Stanbury, D. M.; deMaine, M. M.; Goodloe, G. J. Am. Chem. Soc. 1989, 111, 5496-5498.
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ments by inductively coupled plasma mass spectrometry (ICPMS).20 The primary limitation of both types of isotope equilibration schemes is the requisite chemical separation. It is essential that the separation be accomplished in a time frame that is of the same order as or, preferably, shorter than the self-exchange time scale. Moreover, the separation itself must not cause excessive or irreproducible zero-time exchange (ZTE). The ZTE reflects the degree of exchange occurring during the separation time scale as well as any catalysis of the exchange which may be brought about by the alteration in conditions intrinsic to the separation process. The well-known combination of high-performance liquid chromatography and ICPMS is especially attractive for continuous monitoring of isotopic compositions of the chromatographic eluents. In the present work, we utilize HPLC-ICPMS for the rapid, online measurement of electron self-exchange rates between aqueous FeIII and FeII in perchloric acid solution using stable 57Felabeled FeIII. The aqueous FeIII/II self-exchange process has been the subject of numerous investigations,21-24 which have determined k11 using radioisotope equilibration with separation by selective FeIII precipitation. Owing to the acid dissociation of FeIII-coordinated water, the reaction may proceed by two parallel paths: ka
[*FeIII(H2O)6]3+ + [FeII(H2O)6]2+ y\z [*FeII(H2O)6]2+ + [FeIII(H2O)6]3+ kb
[*FeIII(H2O)5OH]2+ + [FeII(H2O)6]2+ y\z [*FeII(H2O)6]2+ + [FeIII(H2O)5OH]2+
The k11 measured under a given set of conditions, therefore, reflects a composite value for the ka and kb paths. The selfexchange of this particular redox couple has become the subject of extensive theoretical investigation as well as controversy; an inner-sphere “bridging” mechanism has been proposed25,26 for path a to account for what has been perceived as an anomalously rapid self-exchange process. Hupp and Weaver’s electrochemical estimation25 of ka is at least 4 orders of magnitude lower than the directly determined rate for homogeneous solution. Recently, however, Jolley et al.24 examined the pressure dependence of k11 and confirmed that the rates in homogeneous solution are in accordance with an adiabatic outer-sphere mechanism for the ka path and a hydroxide-bridged inner-sphere mechanism for the kb path. Although the aqueous FeIII/II exchange has already been studied extensively, our reasons for pursuing this system are twofold. First, the aqueous FeIII/II couple was chosen to further demonstrate the stable isotope equilibration approach, building upon previous work with aqueous TlIII/I. Since the aqueous TlIII/I couple exhibits a very low k11 of 1.0 × 10-4 M-1 s-1 (25 °C, 1.5 M (20) Ketterer, M. E.; Fiorentino, M. A. Anal. Chem. 1995, 67, 4004-4009. (21) Silverman, J.; Dodson, R. W. J. Phys. Chem. 1952, 56, 846-852. (22) Campion, R. J.; Conocchioli, T. J.; Sutin, N. J. Am. Chem. Soc. 1964, 86, 4591-4594. (23) Brunschwig, B. S.; Creutz, C.; Macartney, D. H.; Sham, T.-K.; Sutin, N. Faraday Discuss. Chem. Soc. 1982, 74, 113-127. (24) Jolley, W. H.; Stranks, D. R.; Swaddle, T. W. Inorg. Chem. 1990, 29, 19481951. (25) Hupp, J. T.; Weaver, M. J. Inorg. Chem. 1983, 22, 2557-2564. (26) Bernhard, P.; Helm, L.; Ludi, A.; Merbach, A. E. J. Am. Chem. Soc. 1985, 107, 312-317.
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HClO4), additional couples need to be examined to probe the upper rate limits of stable isotope equilibration methods; the aqueous FeIII/II couple is expected to produce k11 values of ∼101 M-1 s-1 at ambient temperatures in dilute aqueous acid solution. Second, it is our goal to demonstrate that previous directly measured k11 results for the aqueous FeIII/II couple may be reproduced using independent separation schemes such as HPLC. Such agreement would support the validity of the presently obtained stable isotope equilibration results as well as affirm previously published values. It is also anticipated that HPLCICPMS will be useful in similar k11 studies for additional couples of interest to redox kineticists. EXPERIMENTAL SECTION Elemental 57Fe (>99.9% 57Fe isotopic purity) was obtained from Cambridge Isotope Laboratories. Given the relatively small quantities of this materials which were used in individual kinetic runs, experiments were conducted without dilution of the labeled material with natural abundance Fe. Aqueous 57FeIII stock solutions were prepared by microwave dissolution of the labeled element in HClO4 (70 wt % Baker Optima Grade) in a closed fluorinated ethylene-propylene test tube (Nalgene). Caution: The microwave dissolution step is performed cautiously with 15-20 mL batches using 10 s pulses of 585 W applied power. Natural abundance FeII stock solutions were prepared using Fe(ClO4)2‚ 6H2O (99+%, Alfa Aesar) in aqueous perchloric acid solutions. Total iron concentrations of reactant solutions were determined using inductively coupled plasma atomic emission spectroscopy or ICPMS; the latter technique was performed using Co as an internal standard with summation of all Fe isotope signals. Kinetic experiments were performed by mixing solutions of 57FeIII and natural abundance FeII. Experiments were conducted in 0.10-0.55 M aqueous HClO4 at 0.4-46.6 °C. The reaction temperature was controlled to (0.2 °C with circulating constant temperature baths. For all runs, the FeII and FeIII concentrations were approximately equal; it was not necessary to vary FeIII/FeII at constant [FeII + FeIII], since previous studies21 have demonstrated that the reaction rate is first order in [FeII + FeIII]. The [FeII + FeIII] was varied in the range between 5.0 × 10-5 and 1.5 × 10-3 M. Individual kinetic runs were conducted in one of two possible modes. The first mode, referred to as “static mixing”, is conducted as follows: the thermally equilibrated reactants are mixed manually in a test tube, and the mixture is sampled at known elapsed time intervals using a peristaltic pump, which fills the sample loop of the HPLC system’s load/inject valve. The reaction time is taken as that between mixing and the apex of the unretained FeII peak. After elution of the FeII and FeIII peaks, additional injections of more aged mixture are performed over the first 3-4 reaction halflives. A small portion of the reaction mixture was heated in a hot water bath (90 °C, 5-10 min) to obtain an infinite time, completely exchanged mixture, which was subjected to the same HPLC analysis. Injections are also performed for the individual reactants in order to determine the % ZTE. A second mode, shown in Figure 1, is based on a flow reactor where FeII and FeIII reactants are continuously mixed using a peristaltic pump (ISMATEC Model SA, 0.64 mm i.d. PVC tubing) and a 0.020 in. i.d. PEEK mixing tee (Upchurch P-715). Various temperature-regulated PTFE delay coils, 60-350 cm in length and 0.5-1.0 mm i.d., were used, along with different peristaltic pump speeds in order to regulate the reaction time. The coil volume
Figure 1. Experimental apparatus for measurement of k11 by stable isotope equilibration HPLC-ICPMS in the flow reactor mode. The reactants are mixed online using the peristaltic pump and mixing tee; adjustment of peristaltic pump speed permits monitoring of the exchange at various elapsed reaction times.
and pump speed were judiciously chosen such that data could be obtained in the range of reactant contact times spanning about three reaction half-lives. The delay time between the mixing tee and the sample loop outlet was calibrated for each coil as a function of peristaltic pump speed. The continuously flowing mixture of well-defined reaction time was sampled using the load/ inject valve; two or three chromatograms were obtained at each pump speed, and the process was repeated for several additional reaction delay times. After changing pump speeds and/or delay coils, an equilibration time of about 20 s greater than the selected delay time was observed in order to obtain a steady-state condition in the flow reactor. Additional portions of the mixed reactants were collected at the waste outlet of the load/inject valve and were treated as described above in order to obtain the requisite infinite time results. The FeII and FeIII species were separated using a poly(ethylvinylbenzene/divinylbenzene)-based phosphonic/carboxylic weak acid cation exchange guard column (Dionex CG12A, 4 mm i.d. × 50 mm, P/N 046074). Metal-free load-inject valves and HPLC pumps were used; separations were performed in the isocratic mode with 0.9-2.0 mL/min of 0.18-0.25 M aqueous HClO4. PEEK sample loops of 10 or 50 µL were used, depending on [FeII + FeIII] for a specific experiment, with the larger loop volume being used at lower [FeII + FeIII]. The interface between the guard column outlet and the ICPMS’s concentric glass nebulizer (Meinhard TR-30-C0.5, J.E. Meinhard Associates, Santa Ana, CA) was made using a ∼50 cm length of 0.010 in. i.d. PEEK tubing. ICPMS chromatograms were collected at m/z 56 and 57 using a Perkin-Elmer Sciex Elan Model 500 instrument operating in the peak-hop mode. A peak dwell time of 50 ms along with 5-10 sweeps/reading provided individual chromatographic data points every 0.5-1.0 s. Owing to the relatively high Fe concentrations in the reaction mixtures, no exceptional measures were necessary for reduction of the background 40Ar16O+ and 40Ar16O1H+ signals; a water-cooled Scott-type double-pass spray chamber was maintained at 0-5 °C in all measurements. The ion lens and nebulizer Ar settings were adjusted appropriately to ensure FeII and FeIII chromatographic peaks which did not exceed the ∼106 ions/s
upper limit of the active film multiplier (Model AF561, ETP Scientific, Auburn, MA). The ion lens settings were adjusted without careful consideration of the absolute accuracy of the 56Fe/ 57Fe ratio; owing to the large differences in initial FeII and FeIII isotope compositions, small variations in the degree of mass discrimination were found to be immaterial. The chromatographic data were exported, and boxcar peak integration was performed off-line using a spreadsheet program. RESULTS AND DISCUSSION Chromatographic Separation of Fe Species. FeII was found to be unretained (eluting in 15-20 s at 1.0 mL/min eluent flow rate) at various aqueous eluent strengths in the range 0.15 M < [HClO4] < 0.35 M. FeIII is retained under these conditions to varying degrees; the retention time of FeIII increases as [HClO4] is diminished. An optimized separation of FeII and FeIII could be obtained in 50-60 s using a 0.25 M aqueous HClO4 eluent. At an eluent flow rate of 2.0 mL/min, a similar chromatographic separation was possible, with complete elution of both Fe species in about 25 s. FeIII retention characteristics were found to be reproducible for a given mobile phase flow rate and sample loop volume; slight adjustments in the HClO4 concentration were made as needed in order to yield near-baseline separation of the Fe species after altering mobile phase flow rates and/or sample loop volumes. As is expected, the resolution between FeII and FeIII could be improved by using a 4 mm i.d. × 250 mm analytical column of identical packing downsteam of the guard column; however, the FeII-FeIII resolution is adequate for the needs of the study using the 50 mm length guard column, and hence this more rapid separation mode was used. More details regarding the separation and subsequent kinetic studies are given elsewhere.27 It is also noted that the solution conditions in the reaction mixture are very similar to those of the HPLC mobile phase, which minimizes the chance of the separation affecting the extent of the exchange, through either homogeneous or heterogeneous cataly(27) Kozerski, G. E. Direct Determination of Electron Self-Exchange Kinetic Rate Constants using Stable Isotope Labels, Separations, and ICPMS. M.S. Thesis, John Carroll University, University Heights, OH, 1996.
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heights in the individual m/z chromatograms can be easily rationalized in terms of drift in the Fe concentration sensitivity for individual isotopic signals. This behavior is well-known in practical usage of ICPMS and is of no concern as k11 is extracted using the relative abundances of 56Fe and 57Fe. Determination of k11. The self-exchange rate constants were extracted using the chromatographic data from the FeII peaks; this was done since the FeIII peaks had significantly greater base widths and generally exhibited poorer S/N. The integrated 56FeII and 57FeII peak areas are used to calculate the 56Fe “pseudoabundance”, 56pFe: 56p
Fe ) 56Fearea/(56Fearea + 57Fearea)
(3)
The term pseudoabundance is used to refer to the fact that this quantity does not represent the true 56Fe abundance, as 54Fe and 58Fe are not measured. However, 56Fe and 57Fe account for ∼97% of the total Fe in all mixtures, and the small changes in 54Fe and 58Fe composition can be neglected. The 56Fe pseudoabundance, 56pFe, may therefore be used as the linear observable in calculating F, the fraction exchanged:
(1 - F) ) [56pFet - 56pFe∞]/[56pFe0 - 56pFe∞] Figure 2. Representative chromatographic data sequence for a stable isotope equilibration HPLC-ICPMS kinetic run in the static mixing mode. The last three injections correspond to t ) ∞ aliquots. Self-exchange conditions: 0.10 M HClO4; 298.2 K; [FeIII + FeII] ) 0.000104 M; t1/2 ) 189 s.
sis. When using a separation method requiring a solid support, such as HPLC, the possibility of heterogeneous catalysis at the support surface should not be discounted. Based on measurements of the % ZTE, however, this does not appear to be at issue for the present separation arrangement (vide infra). Kinetic Data. The kinetics of a second-order self-exchange process are governed by the McKay equation, which is described elsewhere.20,28,29 Chromatographic data obtained for a representative kinetic run performed in the “static mixing” mode are depicted in Figure 2. At the initiation of mixing, the FeIII consists of >99.9% 57Fe and
