J. Phys. Chem. 1992, 96, 6861-6863 6861

A+B-->O on 1D Lattice with Co(A)=Co(B)=0.02 + A reaction. At P = 1.0, the h = 0.5 for diffusion-limited reaction kinetics is observed, as expected for the diffusion-limited

Conclusions We have observed nonlinear rises of the reaction heterogeneity exponent h with reaction probability P, for A + A - 0 on 1-D, 2-D square, 2-D PC,and 3-D lattices at early times of reaction. For the reactions A + B - 0 and A + B - B on 1-D lattices, similar nonlinear changes of h vs P are also obtained. Our tesults show that the crossover from reaction-limited to diffusion-liited kinetics in small-dimensional media is not smooth and that the lower the dimensionality of the reaction media, the more likely it is to reach a diffusion-limited reaction kinetics within the time scale of the experiment. V.V ' .uo1 .01 .1 1 When the time scale increases, the heterogeneity exponent h approaches that for P = 1.0. In other words, at t - OD, only the Reaction Probability diffusion-limited regime exists, and therefore h values for any P Fi7. h changes with reaction probability, P, for reaction A + B - > 0 will be the same as for P = 1.0, e.&, h = 0.5 for the A + 0. c,(tso) cb(r=o) = 0.02. A - 0 and A + B - B reactions on 1-D media and so on. A+B-->B on 1-D Lattice Co(Ab0.02, Co(Bb0.01 Note Added in Proof. Similar conclusions have been reached very recently in a Letter by Braunstein et al. (Braunstein, L.; Martin, H. 0.;Grynberg, M.D.; Roman, H. E. J. Phys. 1992, A25, L255). Their results include only the A + A - 0 reaction and, furthermore, only for one dimension. Within this small overlapping domain their results are consistent with ours. A preliminary report of our work appeared in Bull. Am. Phys. Soc. 0.3 1 1992, 37, 522. Acknowledgment. This work was supported by NSF Grant DMR-9111622. References and Notes (1) Kopelman, R. Science 1988, 241, 1620. Taitelbaum, H.; Havlin, S.; Kiefer, J. E.; Trus, B.; Weiss, G. H. J. Stat. Phys. 1991, 65, 873. Zumofen, G.; Klafter, J.; Blumen, A. J. Stat. Phys. 1991, 65, 1015. (2) Klymko, P. W.; Kopelman, R. J. Phys. Chem. 1983,87,4565. (3) Argyrakis, P.; Kopelman, R. Phys. Reu. A 1990, 41, 2114, 2121. (4) Kopelman, R.; Parus, S. T.; Prasad, J. Chem. Phys. 1988, 128, 209. Reaction Probability (5) Koo, Y.-E.; Kopelman, R. J. Stat. Phys. 1991, 65, 893. 8. h changes with reaction probability, for reaction A B (6) Taitelbaum, H.; Kopelman, R.; Weiss, G. H.; Havlin, S. Phys. Reu. Figure P, + - A 1990, 41, 31 16. Taitelbaum, H. Ph.D. Thesis, Bar-Ilan University, 1992. B. C,(r=O) = 0.02 and cb = 0.01. (7) Clement, E.; Sander, L. M.;Kopelman, R. Phys. Rev. A 1989, 39, 6472. and many more step have to be simulated which will dramatically (8) Clement, E.; Kopelman, R.; Sander, L. M.Chem. Phys. 1990, 146, increase the CPU time on the computer. This is particularly true 343. (9) Kopelman, R.; Hoshen, J.; Newhouse, J. S.;Argyrakis, P. J. Star. Phys. when a small reaction probability, P, is used. 1983, 30, 335. For the A + B - B reaction on 1-D lattice, Figure 8 indicates (10) Argyrakis, A.; Kopelman, R. Phys. Reu. A 1990, 41, 2114, 2121. that the dependence of h on P follows the same trend as the A (11) Argyrakis, A.; Kopelman, R. Phys. Rev. A 1992,45, 5814.

Determination of the pK, of Bromous Acid'

Roberto de Barros Faria,+ Irving R. Epstein,* and Kenneth Kwtin* Department of Chemistry, Brandeis University, Box 91 IO, Waltham, Massachusetts 02254-91 IO (Received: May 12, 1992: In Final Form: June 30, 1992)

The acid dissociation constant, K, = [H+][Br02-]/[HBrOJ, of HBr02has been determined by measuring the initial velocity of the reaction between sodium bromite and potassium iodide in the pH range 2.9-8, at 25 'C and ionic strength 0.06 M. The pK, values 4.9 and 6.2 that were previously in dispute cannot be valid, because of the first-order dependence of the initial velocity of this reaction on [H'] in the pH range 4.5-8. We obtain a value of KJHBr02) = (3.7 0.9) X lo4 (M),or pK, = 3.43 * 0.05.

Introduction reaction^,^^^ chemists have sought a reliable pK, value for this oxo Because of the central role of bromous acid (HBr02) in the acid. An early estimate of pK,(HBrOJ was obtained in a study Below-Zhabotinsky (BZ)2 and other bromine-based oscillating of the decomposition of bromite solutions in excess Br- in the pH range 3.5-8.Sa5 In that study, the log of the initial velocity was plotted against pH; a change in the slope of the line connecting + Departamento de Quhica Inorghica, Instituto de Quhnica, Univcrsidade the experimental data points at pH 6.26 suggested this value for Federal do Rio de Janeiro, 21941 Rio de Janciro, RJ, Brazil. the pK, of HBr02. 0022-3654/92/2096-6861$03.00/0 8 1992 American Chemical Society 6862 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 Letters Unaware of Massagli et a1.k report,5 Field, Koros, and Noyes (FKN)6 used pKa(HBr02)= 2, based on Pauling's rules for the strengths of oxo acids.' The importance of this value for un- derstanding the BZ reaction should not be underestimated. Tyson, for example, points out that "the rate constant estimates for all the reactions involving HBr02" in the FKN mechanism depend on the value chosen for the pKa of bromous acid.8 Consequently, this value and other FKN kinetics parameters were reinvestigated by Field and Forsterliig? They proposed a pKa value of 4.9, based on experimental results for the kinetics of the conproportionation reaction between bromate and bromite to produce Br02 in 1 M H2S04at 20 OC. Recently, in a study of the kinetics and mechanism of the bromine(II1)-iodide clock reaction, we employed a revised value of pKa(HBrO2).Io Here, we present a more detailed study of the kinetics of the bromine(II1)-iodide reaction, from which this latest pKa value has been obtained. Figure 1. Linear least squares fit of initial velocities, 1/2d([12]+ Experimental Section [13-])/dr,in 0.05 M phosphate buffer: [I-I0 = [Br(III)lo= 1 X M; = 0.15 M. Materials. All reagents (NaC104, NaBrO2.3H2O,and HC104, Aldrich; all others Fisher) were of the highest purity available and were used without further purification. Bromite solutions were prepared by dissolving the required amount of NaBr02.3H20 in 0.1 M NaOH, followed by dilution with deionized water to 0.01 M NaOH. Stock solution titer was checked every week," and the stock solution was discarded after 1 month even if its concentration was not observed to have changed. In a typical analysis we found that the solid reagent had 86% of the bromine atoms as Br02-, the remainder being in the forms Br0,- and Br-. No detectable amounts of BrO- were found. The presence of these impurities in the reagent does not pose a problem, as their reactions with iodide are orders of magnitude slower than the reactions of Br(II1) species. This assumption was checked in separate experiments in which ad- ditional quantities of bromate or bromide were added to reacting solutions; no changes in the initial velocities of these reactions were found. Methods. Reactions were carried out in 0.05 M phosphate 2.7 3.2 3.7 4.2 4.7 5.2 5.7 buffer or 0.05 or 0.025 M buffer made from potassium biphthalate PH Figure 2. Initial velocities, 1/2d([12]+ [I<])/dt, [I-]0= 1 X lo4 M, plus NaOH or HC104. The ionic strength (p) was adjusted with [Br(III)l0= 2.5 X M: (a, *) 0.05 M phthalate buffer, fi = 0.15 NaC104. An Orion Research pH meter, Model 801A, together M, linear least squares fit omitting the point at lower pH; (b, 0)0.025 with a combined pH electrode (Aldrich, Model Z11323-9), was M phthalate buffer, fi = 0.06 M, second degree polynomial fit. used for pH measurements. Kinetics curves were determined at 25 f 0.1 OC in a Hi-Tech SF-3L stopped-flow spectrophotometer. The total iodine con- Over the pH range 6-8, results were obtained using phosphate centration was monitored by measuring the optical absorbance buffer, p = 0.15 M (Table I (given as supplementary material) and Figure 1). A least squares fit of log(initia1 velocity) against at the 12/13- isosbestic point at 470 nm (e, 740 M-I cm-I).I2 Transmittance curves were stored on a diskette and analyzed pH gave a straight line with slope 1.18 f 1.3% and a coefficient with Lotus 1-2-3. For each experiment at least 10 curves were of determination, R2 = 0.9995, indicating a first-order dependence acquired and superimposed on one another on the screen of the of the velocity of reaction 1 on [H+]. (In our previous study of computer. Traces that deviated significantly from the others were the bromite-iodide clock reaction,I0it was noted that phosphate discarded. The remainder, usually more than five, were averaged buffer raised the [H+] order a small amount compared with other and then converted to absorbance. buffers.) For determination of the initial velocities, a quadratic poly- As one descends the pH scale from pH 8, linear behavior is nomial was fitted to the initial part of the kinetics curve and the observed until pH 4.2 is reached (Table I1 (given as supplementary coefficient of the linear term taken as the initial velocity. Two material) and Figure 2, curve a). Investigationsat and below this other procedures were tried to obtain the initial velocity. Taking pH were at first hampered by internal reflectance arising from the tangent to the initial part of the curve manually led to initial Schlieren patterns that occur in the observation chamber upon velocities with much larger uncertainty than those obtained with mixing solutions of very different densities. Because of this effect, the polynomial fit, presumably because fewer experimental points we decided to decrease the ionic strength from 0.15 to 0.06 M. were used. Fitting a straight line by linear least squares to the This change enabled us to measure initial velocities to a pH as very few points in the initial part of the experimental curve gave low as 2.88 (Table 111 (given as supplementary material) and values similar to those of the polynomial fit, but this procedure Figure 2, curve b). was very sensitive to the number of data points selected. Therefore, The very clear curvature for the lower pH values signifies a we believe the polynomial method produced the mmt reliable initial decrease in the sensitivity of reaction 1 to pH below pH 3. If we velocity values. assume that HBIQ is the only species that reacts with I-, the above result suggests that equilibrium 2 starts to be shifted to the left in this range of pH. Results The subject of this study is the reaction 41- + Br(II1) - 21z + Br- HBr02 + I- - HOBr + IO- (3) Letters The Journal of Physical Chemistry, Vol. 96, No. 17. 1992 6863 I Our value of pK,(HBrO,), which differs substantially from the previously considered estimates of roughly 2 and 5,5,9 is quite different from the experimentally determined value 6.2.5 Although it is beyond the scope of this report to provide a complete analysis of the consequences of this new value for modeling the BZ reaction, it is useful to point out that the entire thermodynamic analysis of the FKN mechanism still contains uncertainties not immediately / related to the bromous acid pK,. .-d- For example, a new value for AGfD(Br03-),1.7 kJ mol-I, has %- recently been proposed.16 Insertion of this value into a thermo- c 3 5- dynamic analysis of the FKN mechanism such as TysonV leads \- to a new value of AGrD(Br02),131 kJ mol-’, which is considerably I different from the previous value, 144 kJ mol-’. At least two rate 2- constants of the FKN mechanism, for reactions R2 and RS, would be changed. We calculate kR2= 4.4 X lo7 M-, s-l and kRS= r(*x 10 20 30 40 1 X lo4 M-2 s-l, based on the Tyson treatment,8 and the full set 1 x 10-’/[Hf] (K’) of AGfDvalues.16 In addition, the newly proposed free energy of formation of Figure 3. Linear least squares fit of inverse of initial velocity against bromate ionI6 can also affect previous estimates of the bromous inverse. of [H’] in 0.025 M phthalate buffer: [I-lO = 1 X lo4 M; acid pK,. The new value, 1.7 kJ mol-’, together with K = 1 X [Br(III)l0 = 2.5 X lo-’ M; p = 0.06 M. 10” M-’ for the equilibrium constant of reaction 79 yields a bromous acid pK, of 6.6, which is a much more alkaline value We have kept the initial concentrations of iodide, [I-I0, and bromine(III), [Br(III)l0, constant for all experiments. Therefore, than any previous estimate or experimental finding. if reaction 3 is rate determining, then Br03- + HBr02 + H+ + 2Br0, + H20 (7) [Br(III)lo = [HBr02] + [Br02-] (4) Ours is not likely to be the last word on the pK, of HBrO,. Applications of additional experimental approaches to this and other oxybromine reactions and equilibria are sure to follow before a consensus is reached regarding the full set of rate parameters for all reactions involving HBr02 in the FKN mechanism. where Ka is given by [H’] [Br02-]/[HBr02]. The reciprocal of the initial velocity, Vo = -d[I-]/dt (t = 0), is given by eq 6. Acknowledgment. We thank Dr. Istvgn Lengyel for many helpful discussions. This work was supported by Research Grant 1 Ka 1 CHE-9023294 from the National Science Foundation-and by _-- + (6) Conselho Nacional de Desenvolvimento Cientifico e vo ~3~~~~~~~~lo~~+lo~~-lo~3[Br(~II)lo~I-lo Tecnolbgico-CNPq (Proc. 20208 1 /90-7). Equation 6 shows that we can find K, by dividing the slope of Supplementary Material Available: Tables detailing the data a straight line in a plot of 1 / Vo against 1 / [H+] by its y-intercept used to construct Figures 1-3 (3 pages). Ordering information (Figure 3). In this way we obtain K, = (3.7 f 0.9) X lo4 M is given on any current masthead page. (pK, = 3.43 f 0.05). (To convert the pH readings to [H’], we used the activity coefficient 0.84905 calculated from the analytical References and Notes expression given by Capone et al.I3) (1) Systematic Design of Chemical Oscillators. Part 84. For part 83, see: Rsbai, G.; Epstein, I. R. Submitted for publication. Discussion (2) (a) Belousov, B. P. Ref. Radiats. Med. (Medgiz, Moscow) 1959, 145. (b) Zhabotinsky, A. M. Dokl. Akad. Nauk SSSR 1964, 157, 392. The excellent straight lines obtained in the pH range 4.5-8 rule (3) Field, R. J. In Oscillations and Trawling Waves in Chemical System; out the two previous experimental values 6.2 and 4.9. It is possible Field, R. J., Burger, M., Eds.; Wiley: New York, 1985; p 55. that the true pK, value is still lower than our value, because of (4) Epstein, I. R.; Orbin, M. In Oscillations arid Traveling Waves in the difficulties in measuring initial velocity in the lower pH range. Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley: New York, 1985; p 257. However, our pK, value is internally self-consistent; we obtain (5) Massagli, A.; Indelli, A.; Pergola, F. Inorg. Chim. Acta 1970,4, 593. the same pK, value (within experimental error) when comparing (6) Field, R. J.; Kbrbs, E.; Noyes, R. M. J. Am. Chem. SOC.1972, 94, results from experiments that differ in the total amount of buffer, 8649. ionic strength, and pH range. Moreover, a careful examination (7) Cotton, F. A,; Wilkinson, G. Advanced Inorganic Chemistry, 5th ed.; Wiley: New York, 1988; pp 104-106. of the results of Massagli et al.? who report a pK, of 6.2, reveals (8) Tyson, J. J. In Oscillations and Traveling Waves in Chemical Systems; a curvature similar to that which we found, but the curvature was Field, R. J., Burger, M., Eds.; Wiley: New York, 1985; p 93. overlooked in the linear curve-fitting employed in the data analysis (9) Field, R. J.; Fbrsterling, H.-D. J. Phys. Chem. 1986, 90, 5400. by those authors. (10) Faria, R. B.; Epstein, I. R.; Kustin, K. J. Am. Chem. Soc., in press. (11) Hashmi, M. H.; Ayaz, A. A. Anal. Chem. 1963, 35,908. Using activity coefficients 0.849 05 for H+ and 0.832 65 for (12) Simoyi, R. H. Unpublished studies. Br02-obtained through an analytical expressionI3 and the Davies (13) Capone, S.; De Robertis, A,; De Stefano, C.; Sammartano, S.; equation,14 respectively, we calculate K, = 2.64 X M (pK, Scarcella, R. Talanta 1987, 34, 593. = 3.58) at zero ionic strength. Taking the standard free energy (14) Meites, L. In Handbook ojAnalytical Chemistry; Meites, L., Ed.; MacGraw-Hill: New York, 1963; p 1.8. of formation of bromite ion from the work of Lee and Lister,Is (15) Lee, C. L.; Lister, M. W. Can. J. Chem. 1971, 49, 2822. AGrD(Br02-)= 27.2 kJ mol-I, we find AGf0(HBrO2)= 6.8 kJ (16) Mussini, T.; Longhi, P. In Standard Potentials in Aqueous Solution; mol-]. Bard, A. J., Parsons, R., Jordan, J., Eds.; Dekker: New York, 1985; p 78.