Anal. Chem. 1995, 67, 4004-4009
This Research Contribution is in Commemoration of the life and Science of 1. M. Kolthoff (1894- 1993).
Measurement of TI(III/I)Electron SelflExchange Rates Using Enriched Stable Isotope Labels and Inductively Coupled Plasma Mass Spectrometry Michael E. Ketterec* and Michael A. Fiorentino Department of Chemistry, John Carroll University, University Heights, Ohio 441 18
An approach is described for measuring electron self-
exchange rate constants (kll) in solution based upon stable isotope-labeled reactants, chemical separations, and inductivelycoupled plasma mass spectrometry. The technique is demonstrated for the exchange between TIIrl and TI1aquo ions in aqueous HCIO4. Ti111is prepared using 203n-enrichedT l 2 0 3 (203nabundance, -36%), and "lI is prepared from natural abundance Tl reagents (natural 203nabundance, 29.52%). The exchange is monitored by mixing the labeled and unlabeled reactants and performing timewise separations through selective precipitation of as m r . Isotope abundances are measured in the TlBr precipitate and 'ITr1solution phases using ICPMS with minimal sample preparation; an NIST 981 (common lead) spike is added, and the 208Pb/206Pb is measured as an intemal standard to correct for mass discrimination. Ihe se€f-exchangerate constant is determined from a McKay plot obtained from the 20sT1 abundances of either oxidation state. A k 1 1 of (1.0 f 0.1) x M-l s-l was obtained in 1.5 M aqueous HC104 at 25 "C.The obtained K11 compares favorably to a value of 1.1 x M-' s-l based upon a previously published study of this exchange reaction using radiolabeled (204Tl) reactants. Research into solution-phase electron transfer reactions has been an active and productive area of study since MarcuslJ first laid his theoretical framework. Marcus's theory describes single electron transfer rate constants (klz) for solution-phase reactants as follows:
where kll and k22 are self-exchange rate constants for the two redox couples, K ~ is z the equilibrium constant, and 212 is the reactant collision frequency. For systems where both reactants are charged, additional corrective terms are used to account for the electrostatic work required to bring the reactants together (1) Marcus, R A J Phys. Chem. 1963, 67, 853-857. (2) Marcus, R A. J. Chem. Phys. 1965, 43, 679-701.
4004 Analytical Chemistry, Vol. 67, No. 27,November 7, 1995
into a "precursor complex". More recently, Macartney and Sutin have also proposed extentions to these equation^.^ Accurately known k l l values are important when comparing theoretical rate predictions for cross-reactions with experimental values, which enables inferences to be drawn about reaction mechanisms and the intrinsic properties of the reactants. Furthermore, accurately determined kll values are preferred to the alternative of relying on the Marcus correlation's validity while using cross-reaction data to evaluate a given k l l , which has shortcomings which are mentioned else~here.48~ Unfortunately,direct measurement of kll is dficult, since no net chemical change takes place in the electron exchange (*Ox Red = *Red Ox). Numerous elegant procedures have been used to measure k l l , includingloss of optical activity of chiral complexes,6infrared measurements of complexes with 2H-labeled ligands? and electrochemical exchange between solution-phase and electrodeadsorbed reactants.8 Extensively used procedures include NMR r e l a x a t i ~ n * ~and ~ ~ ~isotopic -~~ equilibration of radiolabeled The aforementioned procedures all entail certain experimental and practical difficulties, which have tended to limit the systems and conditions for which kll has been directly determined. A plausible but little-exploited approach for kll measurement is to incorporate stable isotopelabeled atoms into either the Ox or the Red species, perform timewise separations of an Ox/Red
+
+
(3) Macartney, D. A; Sutin, N. Znoq. Chem. 1983,22,3530-3534. (4) Koval, C. A; Margerum, D. W. Inoq. Chem. 1981,20, 2311-2318. (5) Vande Linde, A M. Q.; Juntunen, IC L.: Mols, 0.; Ksebati, M. B.; Ochrymowycz, L. A; Rorabacher, D. B. Znoq. Chem. 1991,30,5037-5042. (6) Farina, R; Wilkins, R G. Inoq. Chem. 1968, 7, 514-518. (7) Meyer, T. J.; Taube, H. Znorg. Chem. 1968, 7, 2369-2379. (8) Lee, C. W.: Anson, F. C. I n o q . Chem. 1984, 23, 837-844. (9) Diehich, M. W.; Wahl, A C. j . Chem. Phys. 1963, 38, 1591-1596. (10) Chan, M. S.; Wahl, A. C. J. Phys. Chem. 1978, 82, 2542-2549. (11) Shprorer, M.; Ron, G.; Lowewenstein, A; Navon, G. Znorg. Chem. 1 9 6 5 , 4 , 361-365. (12) Yang, E. A: Chan, M. S.; Wahl, A C.J. Phys. Chem. 1980,84, 3094-3099. (13) Macartney, D. H. Znorg. Chem. 1991, 30, 3337-3342. (14) Hoddenbagh, J. M. A; Macartney, D. H. Znorg. Chem. 1990,29,245-251. (15) Takagi, H.; Swaddle, T. W. I n o q . Chem. 1992, 31, 4669-4673. (16) Silverman, J.; Dodson, R W. J. Phys. Chem. 1 9 5 2 , 5 6 , 846-852. (17) Krishnamurty, IC V.; Wahl, A C.J Am. Chem. SOC.1958,80, 5921-5924. (18) Bonner, N. A; Hunt, J. P. J. Am. Chem. SOC.1960, 82, 3826-3828. (19) Jolley. W. H.; Stranks, D. R; Swaddle, T. W. Znorg. Chem. 1 9 9 0 , 2 9 , 385389. (20) Jolley, W. H.; Stranks, D. R; Swaddle, T. W. Znorg. Chem. 1990,29,19481951. (21) Jolley, W. H.; Stranks. D. R.; Swaddle. T. W. Znorg. Chem. 1992, 31, 507511. 0003-2700/95/0367-4004$9.00/0 0 1995 American Chemical Society
mixture, and monitor the change in stable isotope abundances of Ox and/or Red using mass spectrometry. Stanbury et al.22 recently used this approach for determiningk11 for the NOdN02couple; 15N-labeledNO2, separationsvia ion chromatography,and negative ion FAB mass spectrometry were used. While this, in principle, is identical to the well-known radioisotope exchange procedure, the stable isotope approach is advantageous for two reasons. First, large advances in separation science have taken place since radioexchange studies were fkst performed. Newer techniques such as reverse-phase and ion-pair HPLC, ion chromatography, and continuous liquid-liquid extraction are all potentially suited to performing the requisite separations. Another relevant factor is that ICPMS enables pragmatic determinations of elemental isotope abundances to be made directly in solutions with microgram per liter levels of analyteF3 A key limitation of both radiotracer-basedand enriched stable isotope schemes for k l l measurements is the requirement for timewise separations of Ox and Red. Ideally, the separation process is accomplished in a time frame which is negligible compared to the time scale of the exchange. Moreover, the separation process must not cause an excessive degree of “zerotime exchange”, which is the apparent degree of exchange occurring as a result of the separation process. Ultimately, separation processes and zero-time exchange, along with reactant concentrations, determine the upper rate limits of either stable or radiolabeled isotope-based measurement schemes. The present study was undertaken to demonstrate the concept of using enriched stable isotope labels, chemical separations, and ICPMS isotope abundance measurements as a practical, versatile means of measuring k l l . We have chosen the well-characterized two-electron exchange of Tl(III/I),
as an appropriate reaction to demonstrate the concept. Using radiolabeled zMTllll,Prestwood and WahlZ5were able to measure kll using a variety of selective precipitations. This reaction is ideal as a demonstrative example since the reactants are not air sensitive and the exchange takes place over a relatively long time scale (i.e., several hours to a few days). We have undertaken a study of kll for the above reaction using 20Tl-labeledTho, and separation by selective precipitation of Tll as TIBr, to lay the framework for a useful means of studying many additional selfexchange reactions of contemporary interest. We demonstrate herein that the time dependencies of Tl isotope abundances contain encoded kinetic information about the self-exchange process and that kll may be obtained through the experiment. EXPERIMENTAL SECTION
2°Tl-labeled 1 2 0 3 (97%2oTl) was obtained from Cambridge Isotope Laboratories. Based upon cost considerations,1part (w/ w) of the labeled material was mixed with about 9 parts of the natural abundance T1203(Alfa Products) to produce the labeled TllI1 starting material for most experiments. This labeled (22) Stanbury, D. M.; deMaine, M. M.: Goodloe, G. J. Am. Chem. SOC.1989, 111. 5496-5498. (23) Jarvis, K. E.: Gray, A L;Houk, R S. Handbook oflnductiuely Coupled Plasma Mass Spectromety; Blackie: Glasgow. 1992. (24) Mackay, H. A C.Nature 1938,142, 997-998. (25) Prestwood, R. J.; Wahl. A. C. J Am. Chem. SOC.1949,71, 3137-3145.
material had a zOTl abundance of -36-37%, which compares to the naturally occurring 2oTl abundance of 29.52%. solutions were prepared by microwave dissolution of labeled TlzO3 in HC104 (70%, Baker Optima Grade) in a closed fluorinated ethylenepropylene test tube (Nalgene). Caution: The microwave dissolution step is petjiormed cautiously with 2-3 mL batches, using 5-10 s pukes of 50-100 W applied power. Tl’ solutions were prepared by dissolution of natural abundance Tl2C03 (Aldrich, 99.999%) in HC104. Tllll solutions were filtered through PTFE syringe filters to remove small amounts of undissolved T1203; all solutions were diluted with deionized water to produce the desired HClO4 and TI concentrations. Thallium concentrations of all solutions were established by ICPMS using Pb as an internal standard. Most kinetic experiments were conducted in 1.5 M aqueous HClO4 at 25 f 0.2 “C, with a [TlIII TI1] of -0.05 M, and with the TlI’I and T l I concentrationsbeing approximately equal. Additional studies were conducted with unequal Tllll and Tll concentrations, at a [TlrI1 TlI] of -0.025 M, in 3.0 M HC1O4, and using a ‘W tracer prepared from smaller relative amounts of 97%20Tl-labeled Yzo3. Reaction mixtures were formulated by mixing equal volumes of TII1l and Tll solutions in a small test tube, which was placed in a constant temperature bath. One hundred microliter aliquots were withdrawn; these were mixed with 25 pL of 2 M aqueous NaBr in the barrel of a 3 mL disposable syringe to form a TlBr precipitate; 2 mL of additional 2 M aqueous NaBr was added, and the mixture was filtered through a 0.2 pm PTFE syringe filter. The degree of zero-time exchange was somewhat sensitive to the precise steps used in forming and rinsing the precipitate; it was found to be important to perform these steps in a consistent, reproducible manner. The Tl’II-containing filtrate was collected and diluted to 10 mL with 5%v/v aqueous nitric acid. The TlIBr precipitates were dissolved by slowly passing 2 mL of aqua regia through the syringe filter; the aqua regia solution was collected and diluted to 10 mL with deionized water. The TlrI1 and TI1 reaction mixture products were appropriately diluted with a solution of 0.6 mg/L NIST 981 Pb in 5%v/v aqueous nitric acid; the optimal TI concentration for isotope abundance measurements was -0.5 mg/L. The same dilution and analysis scheme (see below) was also used to measure the isotopic composition of all TllI1 and Tll reactant solutions. Isotope abundance measurements were conducted using a Perkin-Elmer Sciex ELAN 500 ICPMS instrument. This instrument utilized an unpumped (freeaspirating) Meinhard TR-3GCO.5 nebulizer; the deflector and CEM detector have been replaced by an active tilm multiplier (Model AF561, ETP Scientitic,Auburn, MA). Ion lens settings were initially adjusted to produce a 2oy11/ z03n within &4% relative to the value for naturally occurring Tl.A duplicate abundance measurement was made for each sample; each measurement collected signals for a total of 30 s per m / z using peak hopping (one measurement per mass spectral peak) and a dwell time of 50 ms. Signals were collected at m / z 203, 205, 206, and 208. The NIST 981 Pb internal standard, with a certified zosPb/z06Pb value of 2.1681 f 0.0008, was used to correct for mass discrimination in the observed z0y11/203Tlratio using the raw ion intensities i203-i208 and the equation shown below:
+
+
(20””n/”””n),,,
= (i205/i203),,,(2.1681)/~i208/i206~,~,
(3) Analytical Chemistty, Vol. 67,No. 21, November 1, 1995
4005
seriously affect the observed exchange rate; it is desirable to demonstrate agreement of the observed rates using different separation conditions. For the TI(III/I) system, Prestwood and WahP found agreement between rate constants obtained using precipitation of TI0 using Br- and CrOdZ-as well as precipitation of ll(III) hydroxide. To further investigate this concern, a series of kinetic runs were conducted at varying concentrations of bromide (0.5, 2.0, 4.0 M); this modification to the separation process produced rate constants which were indistinguishable. Kinetic Data. The kinetics of a second-order self-exchange process are described by the McKay equation:24
5
2'25 L
2.1
t, 0
45
90
Scan Number
Figure 1. Drift in the degree of mass discrimination observed for the 208Pb/206Pb of the NlST 981 internal standard. The certified value for this ratio is 2.1681 f 0.0008.These data were collected over a single 9 h time frame and are typical of changes in mass discrimination during operation.
Reagent blank subtraction and detector dead-he corrections were found to be unnecessary. Isotope abundances were calculated from COYnlZ0Tl),,,.
&,,[Ox+ Redlt = -ln(l
- F)
(4)
where F is the fraction exchanged. The zero-time exchange is given by the yintercept of a plot of ln(1 - F) or log(1 - F) vs time. Prestwood and WahP5 have shown that reproducible degrees of zero-he exchange and/or incomplete separationsdo not impede self-exchange rate measurements, since these effects do not alter the slope of the McKay plot. kll is obtainable using the McKay equation and the isotope abundances of either oxidation state:
RESULTS AND DISCUSSION
Mass Discrimination of Isotope Measurements. The problem of mass discrimination in quadrupole ICPMS is well known; furthermore, variations in the degree of mass discrimination occur during operation. Measurement of an isotope ratio for an internal standard element has been used as a basis for mass discrimination correction in quadrupole and magnetic sector ICPMS; several g r o u p ~ ~ ~have - ~ Oused TI as an internal standard for measurement of Pb isotope ratios, and Ga has been used as an internal standard for measurement of Zn isotope rati0s.3~Based upon the success of this form of internal standardization, Pb has been used as an internal standard for correction of measured TI isotope ratios. With the ELAN 500,mass discrimination correction was found to be essential to produce isotope data suitable for the intended kinetic application. Figure 1depicts a typical example of changes in mass discrimination for the Pb internal standard observed over a 9 h time frame. Since these changes in Pb mass discrimination emulate changes in TI mass discrimination,n Figure 1implies that using uncorrected zOVn abundances would produce anomalous kinetic plots. Table 1 illustrates isotope abundances measured for kinetic starting materials and completely exchanged solutions; the distributions of relative precisions (expressed as the range of two measurements) are typical of those found for all solutions investigated. 'Ilrir-'lliSeparationProcess. The change in solution conditions required to separate the two oxidation states can itself (26) Longerich, H. P.; Fryer, B. J.; Strong, D. F. Spectrochim. Acta 1987,42, 39-48. (27) Ketterer, M. E.; Peters, M. J.; Tisdale, P. J. J. Anal. At. Spectrom. 1991,6, 439-443. (28) Ketterer, M. E. J. Anal. At. Spectrom. 1992,7, 1125-1129. (29) Walder. A J.; Platzner, I.; Freedman, P. A J. Anal. At. Spectrom. 1993,8, 19-23. (30) Walder, A. J.; Koller, D.; Reed, N. M.; Hutton. R C.; Freedman, P. A J. Anal. At. Spectrom. 1993,8, 1037-1041. (31) Roehl, R; Gomez, J.; Woodhouse, L. R J. Anal. At. Spectrom. 1995,I O , 15-23.
4006 Analytical Chemistry, Vol. 67, No. 21, November 7, 1995
In the above expression, COTl), is the isotope abundance measured at time t expressed as a fraction of unity, CoYn)o is the abundance measured at t = 0 (i.e., immediately upon mixing), and CoYn)ifin is the abundance found at infinite time (i.e., after driving the reaction to completion). It was found that the self-exchange process could be readily monitored using the zOTl abundance data from either oxidation state. Figure 2 illustrates this point for three distinct self-exchange formulations. The experimental curves for Z O V n abundance vs time are in accordance with the simplified second-order rate process expected by the McKay equation, and the information contained in the TImrand TI1 curves is very similar. When the reaction is monitored to completion, the isotope abundances for the two oxidation states approach an equilibrium value which is (within the experimental uncertainty of the measurements) the concentration-weighted average of the initial values. Figure 2A depicts the results of run 2; the TI111 and TI' concentrationsare close to equal, as are the relative changes in 2oVnabundance for the two oxidation states. The effect of using unequal TI"' and TI1concentrations is evident in Figure 2C; in this case, the and TIi concentrations were 0.0263 and 0.0159 M, respectively. As expected, a larger relative change in the isotope abundance is observed for the TI1 fraction. The effect of using lower relative enrichments of TI111 in the starting material was examined; this produces a smaller observable change in isotope abundance over the course of the exchange. Figure 2B depicts the results of run 8, in which a TllI1 mixture with an initial zOTl abundance of 66.93%was used; this solution was prepared from a mixture of -1 part 97%203TI-enrichedTI203 and 24 parts natural abundance Tl20,. Clearly, the self-exchange is still observable; the relative changes in isotope abundance with time are, as expected, smaller, and the errors in the individual
Table 1. Isotope Abundances (Fractional Abundances of zorTl)afor Starling Materials and Products and Percent Zero-Time Exchange for the TI1I1-TI'Self-Exchange Process in Aqueous HClO, Tlrlr abundance0
run
hypothet
measd
1 2 3 4 5 6 7 8 9 10
0.6420 (0.0003) 0.6420 (0.0003) 0.6500 (0.0003) 0.6500 (0.0003) 0.6448 (0.0016) 0.6448 (0.0016) 0.6693 (0.0005) 0.6693 (0.0005) 0.6380 (0.0005) 0.6380 (0.0005)
0.6507 (0.0006) 0.6522 (0.0008) 0.6638 (0.0001) 0.6626 (0.0010) 0.6540 (0.0006) 0.6535 (0.0006) 0.6758 (0.0011) 0.6733 (0.0022) 0.6436 (0.0007) 0.6437 (0.0002)
W l
TIr abundance0
abundanceid, measd
0.6760 (0.0007) 0.6766 (0.0010) 0.6803 (0.0004) 0.6788 (0.0004) 0.6750 (0.0002) 0.6745 (0.0002) 0.6877 (0.0002) 0.6884 (0.0002) 0.6609 (0.0014) 0.6627 (0.0004)
% ZTE
hypothet
measd
TI1abundanceid, measd
yllr
a 1
0.7048 (0.0011) 0.7048 (0.0011) 0.7054 (0.0001) 0.7054 (0.0001) 0.7048 (0.OOOl) 0.7048 (0.0001) 0.7048 (0,0001) 0.7048 (0.0001) 0.7058 (0.0003) 0.7058 (0.0003)
0.6988 (0.0001) 0.6995 (0.0012) 0.6993 (0.0002) 0.6960 (0.0010) 0.6980 (0.0002) 0.6978 (0.0003) 0.7022 (0.0035) 0.6980 (0.0009) 0.6818 (0.0002) 0.6804 (0.0001)
0.6768 (0.0009) 0.6764 (0.0005) 0.6808 (0.0004) 0.6800 (0.0015) 0.6765 (0.0001) 0.6762 (0.0004) 0.6897 (0.0005) 0.6877 (0.0011) 0.6616 (0.0017) 0.6612 (0.0003)
24.5 27.0 41.6 51.1 26.4 26.5 29.8 25.9 24.3 24.0
18.3 19.3 26.9 34.2 21.5 21.3 16.9 29.7 51.4 56.2
All samples analyzed in duplicate; figures in parentheses reflect the range of the two values.
0.71
O:*O
'
'
'
wg 0
0.7
'
'
'
"
'
'
A-
@a
0.69 0.68 0.67 0.66 0.65 Q)
0.7
0 C
a
2
0.69
3
9
F v)
0.68
a
0.67 0.69
0 L
4
0.68
0.67 0.66 0.65 0.64
-2
0
60
120
180
Time (Hours)
Figure 2. Temporal changes in 205TIabundance (mass discrimina(0)and TIi (0)over the course of tion-corrected) observed for TI111 kinetic runs. Duplicate points represent isotope abundance measurement-stage replication. (A) Kinetic run 2, [TIIi1]and [TI1]approximately equal; 1.5 M HC104; 25 "C; 1.9 T P tracer formulation; (B) kinetic run 8, [TI1I1] and [TI1]approximately equal; 1.5 M HC104; 25 "C; 1:24 TI11' tracer formulation; (C) kinetic run 10, unequal [TIIii], [TI1];1.5 M HC104; 25 "C; 1.9 TI1i1tracer formulation.
abundance measurements are more pronounced. While no experiments were conducted with still lower degrees of relative 1" enrichment, ' it is believed that the formulation of run 8 shown in Figure 2B represents a realistic limit for quantitative determination of rate information. Extraction of k l l . Rate constants were obtained from McKay plots of log(1 - F) vs time, as described by eq 4. Examples of these plots are shown in Figure 3. The McKay plots were found
0
120
60
180
Time (Hours)
Figure 3. McKay kinetic plots of log(1 - F) vs time obtained for TIi11(0)and TI1(0).Duplicate points represent isotope abundance measurement-stage replication. Plots A-C correspond to the kinetic runs depicted in Figure 2A-C.
to be linear over the course of the 2-4 half-lives which were monitored. At longer reaction times, larger relative differences in log(1 - fl for duplicate isotope ratios are observed; this is expected given eq 5. The effect of using a lower relative T P enrichment is evident (run 8, Figure 3B). The slopes of the McKay plots were determined using weighted least-squares regression models without an intercept term; the omission of the intercept is appropriate based upon eqs 4 and 5. In obtaining the values of log(1 - f l ,the value of C0Tl)o was taken as that observed with the first sampling of the reaction mixture, typically 1-3 min after mixing. The CoyIl)idn was obtained from the isotope abundance of a completely exchanged Analytical Chemistry, Vol. 67, No. 21, November 7, 1995
4007
Table 2. Kinetic Results Obtained for the TI1I1-TI1Self-Exchange Process in Aqueous HC104. kii
tll2
run
[TP],M
[TI'l, M
2 0 j T l , b 3111
[HC1041, M
yll'
TI'
1 2 3 4 5 6 7 8 9 10
0.0234 0.0234 0.0117 0.0117 0.0260 0.0260 0.0251 0.0251 0.0263 0.0263
0.0271 0.0271 0.0131 0.0131 0.0243 0.0243 0.0271 0.0271 0.0159 0.0159
0.6420 0.6420 0.6500 0.6500 0.6448 0.6448 0.6693c 0.6693c 0.6380 0.6380
1.50 1.50 1.50 1.50 3.00 3.00 1.50 1.50 1.50 1.50
36.3 39.6 78.8 71.8 57.4 62.1 39.5 37.5 38.4 44.8
40.0 37.2 76.0 71.6 59.6 61.4 34.4 40.7 46.0 47.0
a 1 1 1
1.06 9.72 x 9.85 x 1.08 6.71 x 6.20 x 9.55 x 1.01 1.19 1.02
10-4 10-j 10-5
10-4 10-5 10-j 10-5 10-4 10-4 10-4
Tl' 9.61 x 1.03 x 1.02 x 1.08 6.47 x 6.27 1.10 9.29 9.92 9.70 x
10-4 10-4 10-5 10-5 10-4 10-5 10-5 10-5
a Half-livesare in hours, and self-exchangerate constants are in M-' s-l. * Initial values of the 2ovIl abundance (expressed as a fraction of unity) for 3 1 1 1 material used in the run. c All 3 1 1 1 reactants were formulated from -1 part 97%203T1-labeled1 1 2 0 3 and -9 parts natural 3 2 0 3 , except for runs 7 and 8; this reactant was prepared from -1 part 97%20311-labeled T I 2 0 3 and -24 parts natural 1 2 0 3 .
portion of reaction mixture, prepared as described in the Experimental Section. Weighted least-squaresregression was performed using [ foTl), - C0Tl)i,fin] as weighting factors. The half-life and k l l were obtained from the slope, m:
The la relative uncertainties in individual k l l measurements are expected to be -3-5% based upon the relative uncertainties in [Tlnr+ TI']and t1/2. Presented in Table 2 are concentration parameters as well as tllz and kll results for 10 kinetic runs. The kll values derived from runs 1-4 and 7-10 provide a composite value of (1.0 f 0.1) x M-l s - l at 25.0 "C in 1.5 M HC104; this value compares very favorably to a kil of 1.1 x M-' s-l, which was obtained graphically from results presented by Prestwood and WahLZ5The average k l l values obtained from Tl1I1 and Tl]were indistinguishable at the 80%confidence level, as can be seen from Table 2. Based upon the limited data of Table 2, isotope abundance monitoring of either oxidation state would appear to suffice for determining k l l using the technique described herein. It is certainly appropriate to investigate isotope abundance changes in both oxidation states when attempting to use this technique for new redox couples. The effect of changing from 1.5 to 3.0 M HClO4 is seen in the results of runs 5 and 6; a composite k l l of (6.4 f 0.3) x W5M-I s-1 is obtained at 25.0 "C in 3.0 M HC101. This decrease in k l l parallels the decrease in k l l with increasing HC104 concentration observed by Prestwood and WahLZ5The change in the observed k l l may be interpreted in terms of changes in the work required to form the precursor complex and/or dimunition of the importance of the hydroxide-bridged inner-sphere reaction path. Although a rigorous test of the rate law was not conducted, the expected changes in tllz were produced by changes in [TIe1 TP],and the rate constants for runs 1-4 and 7-10 are in close agreement. It follows from the results of runs conducted at different [H+l and I T P I + TIr] that the technique is capable of producing interpretable rate constants which have chemical significance.
+
4008 Analytical Chemistry, Vol. 67, No. 21, November 1, 7995
Zero-Tie Exchange. The degree of zero-time exchange was established by using a modified form of eq 5
In this expression, C o q ) h , refers to the hypothetical value of the isotope abundance at t = 0; this is simply the 205T1abundance measured for the applicable reactant prior to mixing. As is seen in Table 1, the observed CoYn)o values were systematically different from foq)h,, which indicates that zero-time exchange exists in all cases. The effect of the zero-time exchange is to "consume" part of the observable difference between (2Oq)hm and (2OTl)idn; provided the Ox/Red separation is reproducible, one can circumvent a large zero-time exchange by using a larger relative isotope enrichment in the labeled reactant. The percent zero-time exchange (ZE) values shown in Table 1 were determined by substituting eq 8 in eq 4; weighted linear regression parameters, including an intercept, were determined for eq 4. Weighting was again performed using [(20Tl)r COTl)i,finlas weighting factors; the y-intercept obtained corresponds to log(1 - FZTE).The ZTE values were fairly consistent for a given set of conditions; they are obviously iniluenced by the reactant concentrations. The differences in ZI'E observed between run 7 and run 8 for TI'are most likely due to the low degree of relative TI111 enrichment used. Figure 4 illustrates the lack of any apparent relationship between k l l and ZTE. Although similar investigations will be needed in extending our approach to additional redox couples, this finding suggests that the technique presented herein is rather tolerant of incomplete separation and/or separation-induced exchange. A plausible interpretation of the physical significance of the zero-time exchange is that it reflects a brief period of accelerated electron transfer between Tllll and TI1. This may arise due to a bromide-bridged homogeneous inner-sphere pathway; halide ions are known to catalyze the self-exchange reaction between aquo metal ions such as C ~ ~ ~ ( a q ) ~ + / C u ~ (Itaisq )also +.~~ possible that the exchange is accelerated by the presence of TI1Br(s) particles, which are in contact with the exchanging solution for a few seconds until the filtration is completed. (32) Sisley, M. J.; Jordan, R. B. Inorg. Chem. 1992,31, 2880-2884.
0 0
20
40
80
60
100
Percent Zero-Time Exchange Figure 4. Plot of k11 vs observed percent zero-time exchange for eight kinetic runs, 25 "C,1.5 M HCIO4. Varying [TI111TI1]conditions influenced the YOT E . Numerical symbols indicate the TI oxidation state being monitored.
+
CONCLUSION We have demonstrated that kll can be measured using enriched stable isotope labels, chemical separations, and ICPMS. For the 'lllnll reaction studied, the self-exchange rate found by this technique is in good agreement with those obtained from analogous radiotracer experiments. The stable isotope method appears to be insensitive to varying degrees of zero-time exchange and to the relative concentrationsof the two redox forms; changes in isotope abundancesfor both redox forms are readily monitored, and it is found that the rate constants derived from either oxidation state are indistinguishable. With mass discriminationcorrected
ICPMS isotope abundance measurements of 0.1-0.5% RSD, kinetic events can be monitored with as little as a -3% relative change in isotope abundance over the course of the reaction. This method may potentially be extended to the study of other redox couples which can be suitably prepared in metal-ion labeled form and for which a suitable separation of the redox forms can be developed. Of obvious interest is extending the method to faster exchange reactions. Work in progress involves identifying the upper rate limits of the technique, comparing results of this technique to kll values obtained by NMR line-broadening methods, and measuring k11 for some systems of theoretical interest where kll has not been characterized to date. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research (28639GB3). This work was also supported by the Society for Analytical Chemists of Pittsburgh (Starter Grant Award) and John Carroll University. The ICPMS instrument is a donation of VWR Corp., which the authors gratefully acknowledge. The authors also thank M. L. Waiwood for preliminary studies. J. P. Guzowski, B. Ohlson, and K. Humphries assisted with the isotope abundance measurements. Scienfzj5cParentage offheAuthor. M. E. Ketterer, Ph.D. under C. A Koval, Ph.D. under F. C. Anson, Ph.D. under J. J. h g a n e , Ph.D. under I. M. Kolthoff. Received for review March 23, 1995. Accepted August 21, 1995.a AC950285B ~~~
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Abstract published in Advance ACS Abstracts, October 1, 1995.
Analytical Chemistry, Vol. 67, No. 21, November 1, 1995
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