The Journal of
Physical Chemistry
0 Copyright, 1986, by the American Chemical Society
VOLUME 90, NUMBER 1 JANUARY 2,1986
LETTERS The Disproportionation of HBrO,, Key Species of the Belousov-Zhabotinskii Oscillating Reaction Freek Ariese*+ and Zsuzsanna UngvPrai-Nagy Institute of Inorganic and Analytical Chemistry, L.Eotvos University, Budapest, H - 1443 Hungary (Received: April 26, 1985; In Final Form: October 14, 1985)
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+
The rate constant of the disproportionation of HBr02, 2HBr02 HBr03 HOBr, an important step of the BelousovZhabotinskii oscillating system, was measured spectrophotometricallyat 240 nm by using stopped-flow techniques. Its value at [HzS04]= 0.5 M, T = 24 OC was found to be k4 = 2.2 X lo3 M-l . R ough measurements with bromide-selective electrodes led to comparable results. This value is 4 orders of magnitude smaller than the one given by Field, Koros, and Noyes. Consequently, many other rate constants, whose values are known only relative to k4, will have to be changed as well.
Introduction The FKN reaction scheme, as developed by Field, Koros and Noyes,’ is widely accepted as a qualitatively adequate description of the oscillatory behavior of the Belousov-Zhabotinskii reaction. Quantitatively, however, there are still some difficulties due to poorly known rate constants.z Being pioneers in the field and finding only very few experimental data available in the literature, Field and his colleagues were sometimes forced to make rough estimations or to extrapolate data collected under rather different experimental condition^.^ The rate constants of the reactions involving the key species H B r 0 2 were calculated from thermodynamic data, assuming pKa(HBrOz) = 2. Using this value, FKN concluded that the disproportionation of bromous acid is a very fast reaction: k4 = 4 x 107 M-1 S-1 . Forsterling et al.334report an even higher value: k4 = 4 X lo8 M-’ s-l. Massagli et however, have presented evidence that pK,(HBr02) N 6. Sullivan and Thompson6 have pointed out that On leave from the Laboratory of Physical Chemistry, University of Amsterdam, Amsterdam, The Netherlands.
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k4 must be smaller than 6 X IO4 M-I s-l. Noszticzius et a].’ followed the disproportionation of bromous acid with ion-selective electrodes and also arrived at a low value: k4 = 2 X IO3 M-l s-l, 4 orders of magnitude smaller than the one calculated by FKN and in agreement with pK,(HBrO,) N 6. Tyson8 has elaborated a consistent set of “LO” rate constants, based on Noszticzius’ findings combined with other experimental evidence, and has shown that the oscillatory behavior of the Belousov-Zhabotinskii (1) Field, R. J.; Koros, E.; Noyes, R. M. J. A m . Chem. SOC.1972, 34, 8469. (2) Fpld, R. J. In ”Oscillations and Travelling Waves in Chemical Systems ; Field, R. J., Burger, M., Eds.; Wiley: New York, 1985. (3) Lamberz. H. J. Thesis. Universitv of Marburn. 1982. (4j Forsterling, H. D.; Lamberz, H. j.;Schreiber,%. Z . Narurforsch., A
1983. 38A 483. ~
~~
(5) Massagli, A,; Indelli, A.; Pergola, F. Inorg. Chim. Acta 1970, 4, 593. (6) Sullivan, J. C.; Thompson, R. C. Inorg. Chem. 1979, 18, 2375. Noszticzius, E.; Schelly, 2.A. J . Phys. Chem. 1983, (7) Noszticzius, 2.; 87, 510. (8) Tyson, J. J. In “Oscillations and Travelling Waves in Chemical Systems”; Field, R. J., Burger, M., Eds.; Wiley: New York, 1985.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 1, 1986
Letters
I
.?
0.6
.*.... .. .... .... ... ...
0.4
0
20
40
60
TIME,
80
100
500
9
Figure 1. Response of the Br--selective electrode, following the formation of HOBr during the disproportionation reaction; [HBr0210= 4.9 X 10" M.
system can be modelled just as well by using these low rate constants as with the "HI" values given by FKN. The reason is that most measurable features of the oscillating system (e.g., the critical bromide concentration, at which suddenly the autocatalytic oxidation of Ce3+to Ce4+becomes predominant) depend only on the ratio of two or more rate constants and not on their absolute values. Presently, there is still much doubt whether the HI or the LO set is closer to the actual values.2ss Determining the real value of k4 seems to be the clue to this problem.8
z
E
uF 0.2 w
0
. . 3
240
WAVELENGTH, nm
Experimental Section
A stock solution of approximately 0.1 M Ba(Br02)2in 0.1 M NaOH was prepared as described by N o s z t i c z i ~ s .Before ~ each series of measurements some milliliters of the stock solution was treated with A g N 0 3 and Na2S04to remove Br- and Ba2+ions, also following Noszticzius' directions. The bromite concentration was determined spectrophotometrically, using e295 = 114 M-' ~ m - ' . ~The spectrum was identical with the one reported by Forsterling et Polarographical analysis revealed no significant amounts of impurities such as Br03- and HOBr. The purified NaBr02 solution was further diluted with 0.02 M NaOH. After mixing with sulfuric acid the H2SO4 concentration was in all cases 0.5 M. The small effect on the final pH due to N a O H was neglected. For the electrochemical measurements a Radelkis Br--selective electrode was used. Stopped-flow experiments were carried out by using two different instruments: the first a home-made apparatus consisting of a MOM 202 spectrophotometer connected to a memory oscilloscope type Tektronix 564, the second a Beckman Acta M IV recording spectrophotometer provided with a mixing chamber and flow cuvette. In our stopped-flow experiments equal amounts of mildly alkaline sodium bromite solution and 1 M H2S04 are pressed through a mixing chamber into the flow cuvette. Bromite is assumed to be immediately protonated and the disappearance of H B r 0 2 is followed spectrophotometrically. All experiments were carried out at room temperature (24 "C). Results
Electrochemical Measurements. In a first attempt to follow the disproportionation reaction we used the analytical method described by Noszticzius et al.7 A small amount of the purified alkaline bromite solution is injected into a vigorously stirred acidic solution. Bromite, only stable at high pH, is immediately protonated and disproportionates into bromate and hypobromous acid. The increase in HOBr concentration is followed with a bromide-selective electrode; its sensitivity to hypobromous acid can be explained with the corrosion potential theory." (9) Lee, C. L.; Lister, M.W. Can. J . Chem. 1971, 49, 2822. (10) Forsterling, H. D.; Lamberz, H. J.; Schreiber, H. 2. Naturforsch., A 1980, 35A 1354.
Figure 2. (-) Absorption spectrum of 5.74 X M NaBr02 in 0.02 M NaOH; (- - -) absorption spectrum of the reaction products immediately after the disproportionation; [HBr0210 = 5.74 X M; (A) spectrum of HBr02,constructed from the extinction coefficients of Table I, multiplied with 5.74 X lo4 M; (-) spectrum expected for a solution containing 2.87 X lo4 M HBr03and 2.87 X lo4 M HOBr, constructed on the basis of literature data (ref 12 and 14). In all cases optical path length 1.0 cm.
In a typical experiment 1.0 mL of 4.9 X M NaBrOz was injected into 99 mL 0.5 M H2SO4, yielding a starting concentration [HBrOzlq= 4.9 X 10" M. Figure 1 shows the response of the Br--selective electrode. If the disproportionation takes place following clean secondorder kinetics, u4 = 2k4[HBrOZl2,then the half-life is given by T ~ = / 1/2k4[HBr0210. ~ Inserting the FKN value k4 = 4 X lo7 M-I s-I, a half-life of 2.6 ms would be expected, while 7112 = 5 1 s if k4 = 2 X lo3 M-' s-l. Clearly, Noszticzius' low rate constant is much closer to the truth, but from our measurements only a rough estimation (k4 = 6 X lo3 M-' s-l ) could be given. Since the response of our electrode to HOBr was poorly reproducible and proved to deviate considerably from ideal Nernstian behavior, and because calibration was difficult, we could not carry out an accurate quantitative evaluation and we decided to look for better analytical methods. Stopped-Flow Experiments. The disproportionation can be followed spectrophotometrically, provided there is a significant difference in extinction between the starting compound, 2HBr02, and the reaction products, H B r 0 3 HOBr, at the wavelength monitored. As for HBrOZ,however, only the spectrum of the anion BrOzis known and the literature values for the analogous couple BrO-/HOBr (e330 = 303 M-I cm-' and 32 M-' cm-l,l2 respectively) show that especially low-energy absorption bands can change considerably upon protonation. A spectrum of HBrO, could be obtained in the following way: At different wavelengths the transmission of the reaction mixture was recorded while equal amounts of alkaline 4.2 X M NaBrOz solution and 1 M HzSO4 were pressed through the cuvette. Setting the transmission equal to 10"d[HBfilo X 100% (neglecting this way the small amount
+
(1 1) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J . Am. Chem. SOC. 1983, 104, 6194. (12) Betts, R. H.; Mackenzie, A. N. Can.J . Chem. 1951, 29, 666.
The Journal of Physical Chemistry, Vol. 90, No. 1, 1986 3
Letters TABLE I: Apparent Extinction Coefficients of HBrOz at Various Wavelengths wavelength, nm transmission, % c(HBrOJ,” M-l cm-I
220
10
952
240
26 58 75 88 95
557 225
260 280 300 330
0.05
0.04
z
-
0.03
ii.
0.02
119
U *
53 21
L I+
’c(HBrOz) was calculated via cdc = -log T/100, inserting d = 0.50 cm and c = [HBr0210= 2.1 X M.
0.01
J 80
a
z
Em m
H
f
E3
TIME, s
0
22
b
I
d
I
18 16
8
6
10
12
8
Figure 4. (a, top) Decrease in extinction at 240 nm during the disproportionation; [HBr0210= 1.2 X lo4 M; optical path length 1.0 cm. The observed extinction at t = 0 is smaller than expected due to the rather long pathway between mixing chamber and cuvette. (b, bottom) Reciprocal plot of 4a according to eq 1.
20.
4
I
TIME,
rl
N
2
8
h
no significant change in extinction.
0
In the ultraviolet region, however, there are some possibilities to follow the reaction accurately. Figure 2 shows that a considerable change in extinction can be expected at 240 nm: t(HBr02) = 560 f 40 M-’ cm-’, while €(products) = 100 f 10 M-I cm-I. (Some minutes after the reaction AE240 showed again a slow increase, probably due to some slow side reactions; ~ ( p r o d u c t s ) ~ ~ = 100 f 10 M-’ cm-’ was found if the extinction was measured within half a minute after the reaction.) In a typical stopped-flow experiment, [HBr0210= 2.1 X M, we observed an increase in transmission as shown in Figure 3a. From this plot the extinction at time t can be calculated, which must be equal to AE240t = e(HBr02)240d[HBr021 t + ~(prod)~4od([HBrO~lo - [HBr021t)
.J
U
0
cy
N
w
Y
4. 2 . 0 0
0.1
0.2
0.3
0.4
TIME, s
Figure 3. (a, top) Increase in transmission at 240 nm during the disproportionation; [HBr0210= 2.1 X M; optical path length 0.50 cm. (b, bottom) Reciprocal plot of 3a according to eq 1.
of H B r 0 2 that has already reacted before entering the cuvetteI3) we can calculate the apparent extinction coefficients for HBr0, at the various wavelengths. The data are listed in Table I and the resulting spectrum is shown in Figure 2, on the same scale as the spectrum o f t h e alkaline Br02- solution and that of the products of the disproportionation reaction (HBr03 HOBr). L a m b e d tried to follow the disproportionation at X = 330 nm, but Figure 2 shows that this was not a very lucky choice; when we tried to follow the reaction at this wavelength we could observe
+
(13) This would lead to a systematic error of *lo%, since the dead. time of this fast stopped-flowapparatus was approximately 20 ms while r l j 2= 100 ms.
and if the time dependence of [HBrO,] is given by 1 [HBr02], = [HBrO2lo-l + 2k4t we get
Indeed, transforming AE24ot into this reciprocal plot against time we obtained good straight lines with slope 2k4 (see Figure 3b). The average value over six runs was k4 = (2.3 f 0.4) X lo3 M-1 s-1 A second series of experiments was carried out by using the other, more sensitive but slower, stopped-flow apparatus. Now smaller starting concentrations were taken. In a typical experiment equal amounts of 2.4 X lo4 M NaBrO, and 1 M H2SO4 were
4
J . Phys. Chem. 1986, 90, 4-6
mixed. The decrease in extinction at 240 nm is shown in Figure 4a. Again we used eq 1 to construct a reciprocal plot against time (Figure 4b). The average value found after 11 runs was k4 = (2.2 f 0.3) X lo3 M-' s-I, for HBrO, starting concentrations ranging to 2 X M. from 2 X If we have another look at Figure 2 we see that the observed product spectrum (dashed line) agrees fairly well with the sum of the literature spectra of bromate and hypobromous acidIzJ4 (full line). This shows that the main products of the reaction are indeed equal parts of HBr0C and HOBr, and is an extra indication that the reaction we followed must be the disproportionation of HBr02 and not some other unidentified secondary or side reaction.
Discussion Spectrophotometrical measurements indicate that the rate constant for the disproportionation of bromous acid is k , = (2.2 f 0.3) X lo3 M-' s-'. The main source of error lies in the uncertainty about the extinction coefficients of starting compound (14) Bridge, N. K.; Matheson, M. S . J . Phys. Chem. 1960, 64, 1280.
and products. Measurements with ion-selective electrodes led to comparable results. Our data are in full agreement with the values reported by Noszticzius et al.' Thus it seems that from now on the LO set of rate constants as elaborated by Tyson' should be used for calculations and computer simulations. Available literature data on indirectly determined rate constants should be reinterpreted. More precise values for the rate constants of a number of elementary steps can be obtained by relatively simple laboratory experiments, since thermodynamic consistency requires that these reactions, too, must be some orders of magnitude slower than previously assumed. Finally we would like to emphasize that, no matter how useful computer simulations can be, satisfactory outcome of computations should not keep the scientist from checking his assumptions in the laboratory as well.
Acknowledgment. Thanks are due to Dr. MiklBs Jaky and the Central Research Institute for Chemistry in Budapest for laboratory facilities, and to Prof. Endre Koros for useful comments. F.A.'s stay in Budapest was made possible by the kind cooperation of the University of Amsterdam and the L. Eotvos University.
Interactlons between Hydrocarbon Surfaces in a Nonpolar Llquld: Effect of Surface Properties on Solvation Forces Hugo K. Christenson Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, ACT 2601, Australia (Received: September 6, 1985)
The force between hydrocarbon surfaces has been measured in the model nonpolar liquid octamethylcyclotetrasiloxane. The surfaces were prepared by either (i) adsorbing hexadecyltrimethylammonium bromide (CTAB) from solution or (ii) depositing a compressed Langmuir-Blodgett film of dioctadecyldimethylammonium bromide (DOAB) on a mica substrate. The results show how surface roughness affects solvation forces, leading to a reduced range (compared to bare mica surfaces) for DOAB or a complete smearing out for CTAB, in which case a van der Waals type attraction is found. For both surfaces the contact adhesion is consistent with Lifshitz theory. The results indicate that the interaction of (uncharged) rough surfaces may be adequately described by a van der Waals potential
Introduction A number of recent publications have dealt with direct measurements of the force between molecularly smooth mica surfaces immersed in a range of nonpolar liquids.'-3 As predicted theoretically4 and by computer simulations of model liquids between solid walls,5 the interactions at small separations are dominated by structural or solvation effects arising from packing restrictions imposed by the two surfaces. In liquids consisting of near-spherical molecules of limited flexibility, such as tetrachloromethane or octamethylcyclotetrasiloxane (OMCTS), the solvation force is a decaying oscillatory function of surface separation with a period close to the mean molecular diameter of the liquid. About 10 oscillations are measurable before the amplitude becomes comparable in magnitude to the van der Waals force, which is found, as predicted theoretically: in the limit of large separations. Liquids with flexible molecules such as the n-alkanes show fewer oscillations, and at least for the longer chain homologues like tetradecane,' the period of the oscillations is close to the mean thickness of the alkyl chains. In polar and hydrogen-bonding liquids the (1) R. G. Horn and J. N. Israelachvili, J . Chem. Phys., 75, 1400 (1981). (2) H. K. Christenson, J . Chem. Phys., 78, 6906 (1983). (3) H. K. Christenson, Chem. Phys. Lett., 118, 455 (1985). (4) D. J. Mitchell, B. W. Ninham, and B. A. Pailthorpe, Chem. Phys. Lett., 51, 257 (1977). ( 5 ) J. H. Lane and T H. Spurling, Chem. Phys. Lett., 67, 107 (1979). (6) B. W Ninham, J . Phys. Chem., 84, 1423 (1980). (7) J. N . Israelachvili, J . Colloid Interface Sci., in press.
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force is also dominated by structural effects at short In spite of the occurrence of solvation forces, it has been found experimentally that the contact adhesion between mica surfaces in nonpolar liquids is well predicted by the Lifshitz theory of van der Waals forces.2 A substantial body of knowledge is thus emerging on the forces between mica surfaces in nonpolar liquids, but little work has been done with other surfaces. Horn and Israelachvili have reported measurements of the force in OMCTS between mica surfaces made hydrophobic by adsorption of the cationic surfactant hexadecyltrimethylammonium bromide (CTAB). I They concluded that the measured forces, at least beyond the second oscillation (from contact), were similar to those found between uncoated mica surfaces. Horn and Israelachvili did not, however, use adequate control of the water content of the liquid, and in light of the large quantitative effects of water on the forces between bare mica surfaces in nonpolar liquids,lJJOthis throws some doubt on the validity of the results. Recent measurements of the hydrophobic attraction in water have shown a large dependence of the strength of the interaction on the nature of the hydrocarbon In particular, (8) H. K. Christenson and R. G. Horn, Chem. Phys. Lett., 98,45 (1983). (9) H. K. Christenson and R. G. Horn, J . Colloid Interface Sci., 103, 50 (1985). (10) H. K. Christenson, J . Colloid Interface Sci., 104, 234 (1985). (1 1) J. N. Israelachvili and R. M. Pashley, J . Colloid Interface Sci., 98, 500 (1984).
0 1986 American Chemical Society
