THALLOUS-TWLLPC EXCHANGE IN SYSTEMS CONTAIN- ING BROMIDE, AND THE OXIDATION OF TE3ULOUS ION BY ]BROMIPJE* BY I,. G. CARPENTER,? M. H. FORD-SMITH, R. P. BELL,$ AND R. W. DODSON Chemistry Dept., Brookhaven National Laboratory, Upton, Long Island, New York Received 26th January, 1960 The rate of the thallous-thallic exchange reaction has been measured over a range of bromide concentrations in solutions 0.5 M in acid and ionic strength 0.5 at 30°C. The results conform to the rate law R = ko[Tl+][T13+]+/~2[TlBrf2]+k3[TlBr3]+ k4[TI-k][TIBri] +kg[T1~r~][T1BrZ]. The first-order terms are thought to arise from the reversible oxida- tion of Br- by TlW Their apparent activation energy is 30 kcal/mole. The rate of oxidation of TlI by Br2 has been measured directly. The main features of the two electron exchange between thallous and thallic ions in aqueous perchlorate media have been established at a variety of temperatures and ionic strengths.1-3 The rate is first order in the concentration of each oxidation state, is acid-dependent, and can be written R = k[Tl+]~l3+]+ k'[T1+][TlOH2+]. When anions other than perchlorate are present other terms appear in the rate law and may predominate.Nitrate appreciably catalyzes the reaction.1 Chloride,2, 4 ~ 5 cyanide 6 and sulphate 79 8 have large effects on the rate. These effects have been interpreted as reflecting different kinetic properties (with respect to oxidation- reduction) of the various complex species present. Like chloride and cyanide, bromide forms quite stable complexes with trivalent thallium. The present work9 was undertaken to determine the kinetic effects of bromide in the thallous-thallic electron exchange system and to assign, if possible, kinetic parameters to various possible pairs of reaction partners.Features of interest found which are similar to those previously observed are inhibition of the exchange rate at ligand concentrations smaller than the TllI1 concentration, and marked catalysis at high concentrations. In these regions the rate is first-order in the total concentration of each oxidation state. When bromide is present in about twice the concentration of trivalent thallium there is a pronounced maximum in the exchange rate ; and the reaction order changes, the rate becoming independent of the concentration of TlI. The mechanism responsible for this effect appears to be the reversible oxidation of bromide by trivalent thallium.On this view, the ex- change rate data together with pertinent equilibrium information lead to a prediction of the rate of oxidation of thallous ion by bromine in aqueous solution. The latter was directly measured, and the results are compared with the exchange data. EXPERIMENTAL For experiments at low thallous concentrations the concentrated hydrobromic acid was re- distilled to remove traces of bromine and other oxidizing agents. Thallous perchlorate * Research performed under the auspices of the US. Atomic Energy Commission. t Part of this work is taken from the Ph.D. Thesis of L. G. Carpenter, Columbia $ Visitor from Balliol College, Oxford University, England.Apart from special preparations, the chemicals used were C.P. or reagent grade. University, 1956. 92CARPENTER, FORD-SMITH, BELL AND DODSON 93 was prepared by dissolving thallium metal in nitric acid and fuming off the nitrate with excess perchloric acid. The solid was recrystallized several times from ordinary distilled water and ultimately from triply-distilled water. Thallic perchlorate solutions in per- chloric acid were prepared by anodic oxidation of a solution of thallous perchlorate, as described by Biedermann.10 Diethyl ether was distilled under nitrogen and further purified by passing it through an alumina column. Ordinary reagent-grade ether also proved satisfactory for thallic chloride extractions. Methyl isobutyl ketone (" hexone ") was similarly purified by distillation and chromatography.The stock solutions of the re- agents, usually made up with triply distilled water, were repeatedly analyzed during the course of the experiments. The isotopes used as tracers were 204Tl and 202T1. The 204Tl was obtained as thallous nitrate from Oak Ridge. The 202T1 was prepared by bombarding a mercuric oxide target with deuterons from the Brookhaven 60-in. cyclotron and purified by ether extraction. Steps were taken to ensure and confirm the radiochemical purity of the tracers. The tracers were used in the form of dilute solutions of thallous perchlorate. Exchange reactions were run in vessels immersed in water baths at temperatures con- stant within about 10.05"C. The reaction vessels were variously : polyethylene bottles ; glass stoppered volumetric flasks or mixing cylinders, usually 100 ml in volume ; 100 ml hypodermic syringes.Light was excluded. The vessels were cleaned with sulphuric acid+ dichromate cleaning solution, were thoroughly rinsed with tap water, and then with distilled water (at least ten rinses with the latter). Reaction mixtures were prepared by mixing appropriate volumes of water and the stock solutions. The mixtures were equilibrated in the thermostat for periods of 1 h to about 12 h. Then tracer was added in the thallous form, typically as 1 ml of a 10-4 M Tlc104 solution. At intervals, 5-ml aliquots were removed with a pipette (or sometimes by expulsion through a delivery tube). The TP and TPII were chemically separated, and the amount of tracer in one or both of the fractions was determined.The beta rays from 204Tl were counted with an end-window proportional counter. The gamma and X- radiations from 202T1 decay were counted with a sodium iodide scintillator. Two methods were used to separate the TlI and TlIII fractions : chromate precipitation and solvent extraction. After addition of thallous carrier, thallous chromate was pre- cipitated from an alkaline cyanide medium as earlier described.2 With 202T1 tracer, the TlIII was extracted from chloride media with an equal volume of organic solvent : diethyl ether, from 2.2 M HC1, or hexone, from 0.15 M HCl. Both aqueous and organic phases were counted, in test tubes calibrated with 202T1. Corrections for phase volume change were applied with diethyl ether; none were necessary with hexone.It was found that the aqueous and organic phases had counting efficiencies so nearly the same that correc- tions for differing self-absorption were unnecessary. In consequence, the extent of reaction (x/xo3 in the McKay formulation 11) was given by [(a+b)/a]H/(A+H), where a and bare the concentrations in the reaction mixture of TlIII and TP respectively, and H and A are the counting rates of equal volumes of hexone and aqueous phases. The rate of the exchange reaction was determined graphically from semilogarithmic plots of 1 -x/xco against time according to the McKay expression X The plots were excellent straight lines when the bromide concentration was 2 ca. 3 x (TFII) or > 0.1 M. In many of the runs the thallous concentration was determined during or after the reaction. A 5-ml aliquot of the reaction mixture was added to 5 ml of 6 M HCI, allowed to stand in the dark for several hours, and the TlIII was extracted with two successive portions of hexone.Under these conditions the exchange is catalyzed to completion by chloride, and the counting rates of the aqueous and first hexone samples are proportional to the thallous and thallic concentrations, respectively. The oxidation of thallous ion by bromine was followed by the method of Bell and Ramsden,l2 which had been previously applied to fast bromination reactions of organic compounds involving bromine concentrations in the range 10-5-10-8 M. The potential of a platinum redox electrode against a glass electrode was followed with a Beckman pH meter as a function of time.Measurements were made at room temperature (25fl"C) with 50 ml of vigorously stirred reaction mixture.94 THALLOUS-THALLIC EXCHANGE An excess of thallous perchlorate was added to a dilute solution of bromine contain- ing thallic bromide and potassium bromide. The concentration of free bromide ions was between 10-4 and 4 x 10-3 M, and [TlIII] was at least 20 times [TII]. Under these conditions the measured potential is determined essentially by the more mobile bromine- bromide system and the potential-time curves can be interpreted simply. The instan- taneous drop of potential produced by adding thallous perchlorate was less than 5mV (except in the experiment with IFpr-] = 4 x 10-3 M, where it was 12 mV). The total fall of potential during an experiment was 30-90 mV, corresponding to a decrease of bromine concentration by a factor of 10-1000.The final readings were steady for several hours, and were consistent with the standard redox potentials of the bromine and thallium systems and the complexity constants given by Benoit.13 In almost all experiments the concentrations of Tl(IP1) and Br- did not change significantly during the course of the reaction, and the concentration of thallous ion (-10-6 M) was at least ten times the initial concentration of bromine, so that the reaction should be kinetically of the first order in both directions. If the potentials at times 0, f and 00 are VO, V and Yoo and we write y = 2FV/RT, etc., then if the potential is determined entirely by the brominefbromide system the bromine concentrations are given by [Br2l0: [Br2] : [Br,], = eyo: ey: eyw.If k is the sum of the forward and reverse first-order velocity constants, in practice almost equal to the forward constant, we find k can therefore be obtained from a plot of In [exp (y-ym)- 11 against t. These plots were in fact linear within experimental error, though the point for t = 0 was usually a little high. exP ( - k 0 = Cexp (Y - Y 00) - 1 3 i b P (Y 0 - v w > - 11 * (1) 0 0 . 2 0.4 0.6 0 . 8 a1 against a1 = [TIBr2+11[Tl~II] at 20°C, I = 0.5 and [Hf] = 0.50 M. RESULTS Between 0 and 0.5 h4 bromide the exchange rate varies over about three orders of magnitude, showing an initial decline fo'ollowed by a steep rise to a maxi- mum, a second decline to a minimum, then a continued rise.The experimental data are given in table 1 and fig. 1 and 2. The simplest interpretation of these FIG. 1.-Inhibition of rate of exchange at low bromide concentrations. Plot of rateCARPENTER, FORD-SMITH, BELL AND DODSON 95 effects is that thallous and thallic ions form various bromide complexes which differ greatly in their exchange properties, and that the overall rate is determined by the specific properties of the individual species and by their concentration in the system. We are thus led to consider the bromide complexes of thallous and thallic thallium. [halide], M FIG. 2.Variation of exchange rate with total bromide or chloride concentration. Plot of rate against halide concentration at 30"C, [H+] = 0.50 M, I = 0.50, [TP] = 2-74 x 10-5 M, [TI1111 = 3.08 x 10-3 M.RO = rate in the absence of halide. bromide curve, - - - - - - chloride curve. I_ Thallous bromide, like thallous chloride, is known to be a weak electrolyte. Higher complexes, up to TlBr2- have been reported 14 on the basis of solubility measurements in concentrated solutions. From similar measurements in the present work the thermodynamic equilibrium constants for the reactions T1++ Br- = TlBr, and T1Br-t-Br- = TlBr, were estimated 9 as 7.5 and 1.0, respectively, at 30°C. The first agrees well with other work ; 15 the second can be regarded as only a rough estimate. With an approximate activity coefficient correction the values become 2-9 and 1.0. These are used in the present discussion. There is some disagreement 139 16 as to the existence in aqueous solution of thallic bromide complexes containing more than four bromides.The present discussion is based on the work of Benoit,l3 who reported species up to TlBr; and determined their formation constants at 18°C. We have approximately corrected his values to ionic strength 0.5, using activity coefficients of EaBr3, IBa[ClQ&, and RbN03. It was not possible to correct for the 12" temperature difference. The values adopted for the stepwise formation equilibrium constants of TlBr"+, TlRrt,96 THALLOUS-THALLIC EXCHANGE TlBr,, and TlBr; under the conditions of the exchange measurements are respectively, 4x 108, 2 . 5 ~ 106, 1 x 184, and 5x 102. TABLE 1 .-RATE OF EXCHANGE AT VARIOUS BROMIDE ION CONCENTRATIONS 30°C ; I = 0.50; [Hi-] = 050 [HBrl, M 1.844~ 18-3 1.844 X 10-3 2.767 x 10-3 1.811 x 10-2 1.811 x 10-2 2.767 x 10-3 7-71 ~ 1 0 - 3 7.71 ~ 1 0 - 3 5.57 ~ 1 0 - 3 5-57 ~ 1 0 - 3 5-57 x 10-3 1.219 x 1W2 1.219 x 10-2 1.752 x 10-2 1.752 x 10-2 2.00 x 10-2 2.00 x 10-2 2.25 XlO-2 2.25 ~ 1 0 - 2 3.00 X10-2 3-00 x10-2 3.00 X10-2 340 x10-2 6430 X 10-2 6.00 X10-2 1.00 x 10-1 1.00 x10-1 2.07 X 10-1 2.07 X 10-1 3.07 x 10-1 3-07 X10-1 4.00 x 10-1 4.00 X 10-1 5-04) X10-1 5.00 X10-1 free tBr-I, M 3.2 X 10-8 3.2 X 10-8 4.0 x 10-7 4.0 x 10-7 6.0 x 10-6 6.0 X 10-6 8-5 ~ 1 0 - 5 8.5 ~ 1 0 - 5 2.9 x 10-4 2 9 x 10-4 2.9 x 10-4 1.7 x 10-3 1.7 x 10-3 6-0 x 10-3 6.0 x 10-3 8.35 x 10-3 8.35 x 10-3 1.06 x 10-2 1*06X 10-2 1.80 x 10-2 1.80 X 10-2 1.80 x 10-2 1-80 x 10-2 4.77 x 10-2 4.77 x 10-2 8.77 x 10--2 8-77 X 10-2 1.95 x 10-1 1.95 x 10-1 2.95 X 10-1 2.95 X 10-1 3.88 X 10-1 3-88 X 10-1 488 x 10-1 4.88 X 10-1 1-00 1.846 1.00 1.846 1.50 1.846 1.50 1.846 2.00 9.07 200 9.07 250 3.08 2-50 3.08 3.02 1.846 3.02 1-846 3.02 1.846 3.96 3.08 3.96 3.08 5-68 3-08 5.68 3.08 6-50 3.08 6-50 3.08 7.31 3-08 7-31 3.08 9.74 3.08 9-74 3.08 9.74 3.08 9-74 3-08 19.5 3.08 19.5 3.08 32.5 3.08 32.5 3.08 67.3 3.08 67.3 3.08 99.7 3.08 99.7 3.08 130 3.08 130 3.08 162 3.08 162 3.08 3-01 13.76 3.03 13.62 11.1 410 3.04 13.57 2.16 18.48 2.80 13.1 5 2-80 13.4 2.85 13.1 8 2.92 13.6 2.83 2-86 13.13 13.5 271 13.3 2.75 13.1 2.90 12.78 2.73 12.74 2.85 1274 2.81 2-74 184.8 20.0 86.5 11.6 32.5 2.42 1.21 1.05 4.35 1 -72 11.8 65.0 2-30 10.2 5.6 21.8 7.8 20.8 8-2 23.7 9.0 10.6 17.3 23-7 9.30 13-16 5.00 5.38 1.39 1.43 0.687 0619 0.440 0.387 0.305 0.304 1.03 x 10-6 1.03 X 10-6 7.52 x 10-6 7-63 X 10-6 6.26 x 10-5 6-03 x 10-5 1-99 x 10-5 2.05 x 10-5 8.61 x 10-6 9.86 X 10-6 9-86 X 10-6 8-37 X 10-6 8-56 X 10-6 3.44 x 10-6 4.24 X 10-6 2.50 X 10-6 424 x 10-6 2.40 x 10-6 3.94 x 10-6 2.16 X 10-6 1.85 X 10-6 5.05 X 10-6 3.91 X 10-6 2.02 x 10-6 6.73 X 10-6 3-77 x 10-6 1-62 x 10-5 1.44~ 10-5 5-97 x 10-5 273 x 10-5 1.37 x 10-4 4.45 x 10-5 2-19 x 10-4 6.40 x 10-5 6-27 x 10-5 Rcalc., 1.02 x 10-6 1.02 x 10-6 7.39 x 10-6 7.39 x 10-6 6.66 X 10-5 6.66 X 10-5 M h-1 1-92 x 10-5 1.92 x 10-5 8.97 X 10-6 9.10 x 10-6 10.48 x 10-6 8.37 x 10-6 9.02 x 10-6 3.87 x 10-6 5.01 x 10-6 3.24 X 10-6 4-35 x 10-6 2-49 x 10-6 3-92 X 10-6 1.79 x 10-6 1-79 X 10-6 3-32 X 10-6 3.32 X 10-6 1.96 x 10-6 7.49 x 10-6 408 x 10-6 1.94 x 10-5 1.40 x 10-5 6.15 x 10-5 2.36 x 10-5 1.10 x 10-4 3.57 x 10-5 4-57 x 10-5 4.45 x 10-5 1-60 x 10-4 The concentrations of free bromide and of the various thallium species were calculated by successive approximations from the equilibrium and mass-balance relations.Because the equilibrium constants are not well known the error may be considerable, but the general trends are probably correct. In particular, it is pro- bable that the principal species at [Br-]/mllll] ratios of 1, 2, 3, and 4 are TlBr2+, TlBrZ, TlBr,, and TBr;. Fig. 1 shows the decrease in rate when small amounts of bromide are added at 20°C. Assuming the rate to be expressible as R = Ic~[Tl+][Tl3f]3-J~~[Tlf][TlBr2+],CARPENTER, FORD-SMITH, BELL AND DODSON 97 it follows that a plot of rate against the ratio a1 = [TIBr2+]/[T1111] should be linear and extrapolate to a value kl[Tll][TlrrI] at a1 = 1.The extrapolated intercept at a1 = 1 is zero within experimental error, showing that kl is negligible compared to ko, i.e. that TlBr2+ exchanges with TI+ at a rate negligible compared to that of T P . A reasonable upper limit on the ratio kl/ko would be 0.05. Fig. 2 shows the exchange rate at various total bromide concentrations between 3.08 x 10-3 M and 0.5 My for rJ[r1]=2-78 x 10-5 M and [TIIII] = 3-03 x 10-3 M. In some cases the experimental values were determined at different thallium con- centrations ; the values in the graph have been corrected when necessary by use of the measured reaction orders with respect to [TlI] and fr.III1].For comparison, the dependence 4 of exchange rate on chloride is illustrated by the dashed line. The two systems are very similar at low and high halide concentrations ; there is a striking difference in the region of n = 2. temp. O C 40 38 20 10 20 30 50 TABLE 2.-DETERMINATION OF THE REACTION ORDER WITH RESPECT TO THALLOUS AND THALLIC I = 050, w+] = 0.50 M 5.57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 5-57 x 10-3 5-57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 5.57 x 10-3 5-57 x 10-3 1-85 X 10-2 1-12 x 10-2 2-23 X 10-2 3.09 x 10-1 3.09 X 10-1 7-72 x 10-3 7-72 x 10-3 23.16 x 10-3 1-846 x 10-3 1.846 x 10-3 1-846 x 10-3 1-846 x 10-3 14346 x 10-3 1.846 x 10-3 1.846 X 10-3 1.846 X 10-3 1.846 X 10-3 1.846 X 10-3 1.846 X 10-3 1.846 x 10-3 1.846 X 10-3 1.815 X 10-3 3.692 x 10-3 7.384 X 10-3 6-16 ~ 1 0 - 3 3-05 ~ 1 0 - 3 3-05 ~ 1 0 - 3 3.64 ~ 1 0 - 3 3.64 ~ 1 0 - 3 10.92 X 10-3 2-25 x 10-5 6-40 x 10-5 1-85 x 10-4 1-85 x 10-3 216 x 10-5 1.85 x 10-4 1-85 x 10-3 2.16 x 10-5 1-85 x 10-4 1.85 x 10-3 2-02 x 10-4 2 .1 6 ~ 10-5 1-85 x 10-4 2-61 x 10-4 2.50 x 10-4 2.91 x 10-4 2.15 x 10-5 2-24 x 10-4 4-15 x 10-4 2-49 x 10-3 2-49 x 10-3 1.85 X 10-4 * TlIII order assumed = 1. 3.02 3.02 3-02 3.02 3.02 3 a02 3.02 3.02 3.02 3-02 3.02 3-02 3.02 3.02 3-04 3.02 3.02 LO1 101 2.12 2.12 2.12 0.52 0.96 2-48 12.8 1.72 11.8 ' 65 9.0 67.0 23.3 625 360 385 1890 80.7 46.3 27.0 0.52 2-00 0.89 3.50 x 10-5 4-49 x 10-5 469 x 10-5 5-01 x 10-5 8.61 x 10-6 9.86 x 10-6 9-86 X 10-6 1.46 X 10-6 1.74 x 10-6 1-78 x 10-6 5.82 x 10-6 * 2-36 X 10-7 3.02 x 10-7 3.39 x 10-7 1-96 X 10-6 3.51 X 10-6 0.95 7.21 X 10-6 29 x10-5 3-16 x 10-4 5.00 x 10-4 5-13 x 10-4 1-58 x 10-3 1-02 t T1I order assumed = 0.0.03 002 0.04 007 t t t 1 -02 0.014 When the reaction order was checked in this region, the rate was found to be first order in [TlU1] but closely zero order in [TI1]. Table 2 gives the results of order determinations under various conditions. Measurements were also made at two different T1I concentrations, in ratio ca. 5 : 1, at a number of points in the transition region. From the results, included in table 1, the first- and second-order contributions can readily be evaluated. These are illustrated in fig. 3. It will be seen that the first-order part rises as ulBr$] rises, but drops off less steeply after D98 'r H A LLOU S -T H A LLI C EXCH A NG E the maximum. It then falls approximately with [TIBrJ.The course of the second- order part can be associated with the rise of [TlBr,] and, subsequently that of [TlBr;]. It ultimately rises somewhat faster than the calculated FIBr;}. 0.1 0.01 Id2 Id' I lBr-1, M FIG. 3.-First- and second-order contributions to the rate and the relative populations of complex species. -0-0- net first-order rate constant --a-O- net second-order rate constant multiplied by [TII]. The solid lower curves are, from left to right, the fraction of TlIII present as TI3+, TIBr2+, TlBr,, TlBr, and TlBr,, respectively. The dashed curves refer, correspondingly, to TI+, TIBr, and TIBr;. pi11 = 2 7 4 ~ 10-5 M The temperature dependence of rate was measured at n = 0,2,3, and [Br-] = 0.5.The results are shown in fig. 4. The apparent activation energies are respectively 16.0, 30, 30, and 7.5 kcal/mole. Two sets of measurements pertain to the reactions in the neighbourhood of the maximum, where the mechanism is believed to involve the equilibrium formation of Br2. The first of these comprises experiments with organic additives which react rapidly with Br2. The results are given in table 3. If the organic substrate removes Br2 as it is formed, it would be expected that the exchange would cease and that TITIT would be converted to Tll at the rate with which the exchange proceeds when no organic compound is present. The exchange rate was, in fact, greatly reduced. The last two columns of table 3 confirm the other expectation.In this series of experiments the logarithm of the [TllI1] was plotted against time and good straight lines were obtained initially. As the reaction proceeded the rate decreased ; this deceleration can be attributed to the formation of unreactive TIBr;. The second comprises the results, given in table 4, of direct measurements of the rate at which bromine oxidizes thallous ion. It will be noted that the specific rate is constant over a wide range of conditions, and that it is independent of the free bromide concentration when the latter is varied 40-fold.CARPENTER, FORD-SMITH, BELL A N D I)OL)SON 99 temp. O C 10 20 20 40 40 40 40 40 40 40 50 I I r I 1 3-00 3.10 3.20 3.30 340 3.50 3.60 i/r, KX 103 FIG. 4.-Arrhenius plots.A. [Br-] = 0.50 M C. [Br-] = 9 . 2 4 ~ 10-3 M D. [Br-1 = 0.0 [TI1111 = 3-08X 10-3 M, [TI11 = 2 . 7 4 ~ 10-5 M, [H+] = 0.50 M, 1 = 0.50. B. [Br-] = 7 . 1 6 ~ lO--3 M TABLE 3.-&MPARISON OF BROMINE REMOVAL AND EXCHANGE RESULTS Pr-]/[TlIII] = 3-0 ; I = 0-50; [H+] = 0-50 M additive k, h-1 kr concentration, for decrease of exchange, additive [TIm1] mlq initial initial M [TI"'] h-1 xi03 M x 105 M 3692 3.692 6.16 1 -846 1.846 1.846 3,692 3.692 3.692 3.692 1.846 4.51 4.5 1 0.2 6-60 660 2.55 4.51 451 4.51 4.5 1 2.55 N,N-dimeth yl-aniline phenol N,N-dimethyl-aniline aniline acetanilide ally1 alcohol phenol N,N-dimethyl-aniline aniline 9 9 99 Y, 9 , ,> 9 ) 3.4 x 10--2 3.4 x 10-2 1.8 x 10-1 3.5 x 10-2 1 . 4 ~ 10 1 1.68 x 10--2 6-7 x 10-2 1-18 x 10-1 3-36 x 10-2 1 . 4 ~ 10-1 7.8 x 10-3 1-59 x 10-4 1.06 x 10-3 1.00 x 10-3 2.12x 10-2 267 x 10--2 2-60 x 10-2 2.30 X 10-2 3.94 x 10-2 2.31 x 10-2 2-60 x 10-2 1.10 x 10--1 1-58 x 10-4 9-06 x 10-4 9.06 x 10-4 2.24 X 10-2 2.24 x 10-2 2.24 X 10-2 2-24 X 10-2 2.24 x 10-2 2.24 X 10-2 224 x 10-2 * determined by separate exchange rate studies.100 THALLOUS-THALLIC EXCHANGE TABLE 4.-&TE OF OXIDATION OF THALLOUS ION BY BROMINE room temperature (-25°C) 0.5 1 3.5 1.0 6.6 x 10-4 3.7 x 10-4 0.50" 1.0" 1.0 4.0 x 10-4 1-35 x 10-4 0.50 2-6 1-0 4.0 x 10-3 3-65 x 10-3 0.40 2.9 7.0 3.2 x 10-3 9.5 x 10-4 0.12 1.9 2.0 1-24 x 10-3 6.2 x 10-4 0.04 3.7 1-0 5.4 x 10-4 27 x 10-4 0.02 2.3 1.0 4.0 x 10-4 1-35 x 10-4 mean 248 2.45 2.77 2.4 1 2.8 1 2.74 2.4 1 = 2-59 x 107 M-1 h--I * In this experiment the initial concentrations of bromine and thallous perchlorate were each 1.0 x 10-6 and the results treated by second-order kinetic equations.DISCUSSION The data can be fitted with a simple rate law, in terms of the concentrations of the principal species of TP and TllI1 which are present. Up to [Br-] = 0.2 M a satisfactory expression is R = ko[Tl+][TP+]+ k2[TlBr$] + k3[TlBr3]+ k4[Tl+][TIBr,] +ks[TlBr;][TlBr4]. The values of the specific rate constants at 30°C, I = 0.5 are : ko = 0.69 M-1 h-1; k2= 8 x 10-3 h-1; k3 = 4.5 x 10-3 h-1; 1c4 = 4.6M-1 h-1; k 6 = 2.37~ 103 M-1 h-1. The first term applies to the joint contributions of the unhydrolyzed and hydrolyzed aquo-thallic ions. The fit can be seen by comparing the sixth and seventh columns in table 1. The poorest agreement is at [Br-J = 0.03 My where duplicate runs are discrepant.The system is being further studied in this region of minimum rate, where experimental difficulties were most evident. Above [Br-] = 0.2 M the rates are systematically higher than calculated, which may indicate that activated complexes containing more than six bromines are be- coming significant. On the other hand, the drift would be reduced by a moderate downward revision in the formation constant of TlBr. It appears conclusive that the reaction of TlBr2+ with TI+ is very much slower than that of Tl3+ and TlOH2+. The corresponding situation prevails in the chlo- ride and cyanide systems. One might have supposed that the anion could form a bridge to TI+, by which electron transfer would be facilitated.This is clearly not the case; furthermore, the single anion appears to block whatever electron transfer mechanism operates with the aquated ions. It may be conjectured that the anion alters the orbitals of TIrI1 in such a way that the latter can less readily accept two electrons. Evidence for a strong effect of chloride and bromide on the electron configuration of TllIr has been reported by Figgisy17 who found large chemical shifts in the n.m.r. spectrum of 205Tl when these ions were present. The rapid rise in rate at high bromide concentrations is surely accompanied by a rapid rise in the relative population of species such as TlBry. It is attractive to picture the activated complex as a symmetrically bridged structure such as and to associate the high reactivity with the high symmetry of this arrangement.Such a picture is necessarily speculative at the present time. The main new features of the present work are found in the region where TlBrt and TlBr3 are presumed to predominate and the reaction order becomes zero inCARPENTER, FORD-SMITN, BELL AND DODSON 101 ["I. Weiss 18 has suggested that electron exchanges may proceed through revers- ible redox reactions with a third reactant; the idea is applicable to our results. Consider the reaction TlBr; = Tl++Br,. The equilibrium constant, K = kf/k,, can be estimated from the thallic-thallous and bromine-bromide half-cell potentials 19 to be 2x 18-11 at 25°C and I = 0. Identifying kf with the specific rate k2 of the exchange reaction (interpolated value 3.4 x 10-3 h-1 at 25"), it follows that k, should equal 1 .7 ~ 108 M-1 h-1. The value found (table 4) is 2.7 x lO7M-1 h-1. The agreement is probably within the uncertainties of the equilibrium data. Confirma- tion that the mechanism involves free bromine is given by the results in table 3, which show that when Bra is continually removed from the system the rate of disappearance of TlIIL is closely equal to the thallous-thallic exchange rate when Br2 is not removed. In terms of such a mechanism, the k3r]rlBr3] term in the exchange rate is not compatible, however, with the lack of Br- dependence of the reaction of thallous with bromine. At the concentrations employed the reaction may be written TlBr3 = Tl++Bra+Br-. A calculation similar to the above shows that the observed velocity constant for thallous oxidation (based on TI++ Br2) should in- crease by a factor about 25 when free bromide increases from 10-4 to 4 x 10-3. As table 4 shows, a constant value was found in this range.The discrepancy is not removed by moderate adjustments of the equilibrium constants ; nor, it was found, could it be explained by catalysis on the platinum electrode. Further investigation will be required. Many of our colleagues have aided us in this work. We wish particularly to acknowledge our indebtedness to R. W. Stoenner for chemical analyses and many of the thallium preparations, to J. Hudis for cyclotron bombardments, to D. Christman for purification of the organic solvents, and to J. Galvin and K. T. Brennan for technical assistance. 1 Prestwood and Wahl, J. Amer. Chem. SOC., 1949,71, 3137. 2 Harbottle and Dodson, J. Amer. Chem. Soc., 1951,73,2442. 3 Dodson, J. Amer. Chem. SOC., 1953,75. 1795. 4 E h e r and Dodson, Brookhaven National Laboratory Quarterly Progress Report, 93 5 Brubaker, Groves, Mickel and Knop, J. Amer. Chem. SOC., 1957, 79, 4641. 6 Penna-Franca and Dodson, J. Amer. Chem. 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