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fluoroalkane matrices. A similar matrix effect on the spectral resolution was observed for n-C6HI4+as is mentioned before. The matrix effect may solve the controversy about the presence and absence of the substructure as well as a small difference in the seven-line splittings reported by two groups.6 As is expected from our previous results for branched alkane cations,2the unpaired electron of HME+ must be mainly confined to the central C-C bond so that large couplings (29 G) can be expected from the six protons in the trans C-H bonds while the small ones (4 G) arise from the remaining 12 protons with the 60’ conformations. Similar 6-proton couplings with rigid CH3 protons in C-C cr radicals have already been determined by ENDOR studies in our laboratory for the deprotonated cations of a-aminoisobutyric acid.12 The averaged 6-proton couplings for the two CH3 groups are 22.1 and 3.3 G for the (12) H.Muto, M. Iwasaki, and Y. Takahashi, J.Chem. Phys., 66,1943 (1977).
trans and the 60’ conformations, respectively (pc = 0.45). This must give a firm basis for the spectral identification of HME+ with a rigid staggered structure. Conversion of Radical Cations to Neutral Radicals. Preliminary experiments indicate that [H(CH2),H] in CFClzCF2Clconverts predominantly into CH3CHCH2CH3 (I) by proton loss upon warming to 11G120 K. Formation of I rather than CH3CH2CH2CH2(11) is somewhat surprising, but one cannot exclude the possibility of deprotonation via the form having a large spin density on the proton attached to the C2 atom. Although they are less probable, one cannot exclude the possibilities of isomerization from I1 to I after deprotonation from the C1 atom and of H abstraction by matrix radicals from undamaged n-C4Hloto form I. Further studies on the reactions of alkane cations are now in progress. +
Acknowledgment. The authors thank Dr. H. Muto for his cooperation in the experiments at liquid helium temperature.
Chemical Waves In the Acidic Iodate Oxidation of Arsenite Thomas A. Gribschaw, Kenneth Showalter,” Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506
Debra L. Banville, and Irving R. Epstein* Department of Chemistry, Brandeis Universiyy, Waltham, Massachusetts 02254 (Received: March 20, 198 1; In Final Form: May 20, 198 1)
After a brief induction period, an unstirred, initially homogeneous solution containing arsenite and iodate at pH -2 may give rise to a single wave of chemical reactivity. The waves have been studied in thin layers and in narrow tubes of solution. The wave is apparently initiated at a region of high I2 concentration, where autocatalytic production of I- begins and spreads into the rest of the solution by diffusion. Waves were also electrochemicallyinitiated in thin layers of solution at a negatively biased Pt electrode. A simple reaction-diffusion model is given to illustrate wave propagation in such a system. Introduction The development and propagation of chemical waves in an initially homogeneous solution is a subject of considerable interest.l Studies of chemical wave behavior have thus far been confined almost entirely to bromate systems.2 The development of a general theory of such waves will require the existence of several systems, preferably rather different chemically from one another, in which waves may be observed. Epik and Shub3reported, some 25 years ago, that the oxidation of arsenite by iodate is capable under appropriate conditions of generating a chemical wave. No quantitative study was done, however, and no convincing explanation of the reaction-diffusion behavior was developed. It does not appear that this phenomenon has been investigated further since 1957. In this paper, we describe our initial experiments in a detailed investigation of the reaction-diffusion behavior (1) (a) Kopell, N.;Howard, L. Stud. Appl. Math. 1973,52, 291-328. (b) Winfree, A. T. In “Theoretical Chemistry”; Eyring, H.; Henderson, D.; Academic Press: New York, 1978, Vol. 4, pp 1-51. (2) (a) Field, R.J.; Noyes, R. M. J. Am. Chem. SOC.1974,96,2011-6. (b) Orbin, M.Ibid. 1980,102,4311-4. (c) Showalter, K. J.Phys. Chem. 1981,85,440-7. (3) Epik, P.A.; Shub, N. S. Dokl. Akad. Nauk SSSR 1955,100,50343. Shub, N.S. Ukr. Khim. Zhur. 1957, 23,22-6.
in the iodate oxidation of arsenite. Experiments similar to those conducted by Epik and Shub using an open glass cylinder have been carried out. We also report on the electrochemical initiation of waves in a thin f i i of reaction mixture. In addition, a numerical simulation based on a simple reaction-diffusion model is presented. Experimental Section Solutions were prepared with doubly distilled water and reagent-grade chemicals. In the tube experiments iodate and arsenite solutions were prepared in a sulfate-bisulfate buffer and were thoroughly mixed before being poured into tubes of 11cm length and 1.0 cm diameter. The induction time 7 is defined as the time between mixing and the first appearance of the brown ring at the top of the tube. Wave velocities were measured by recording the times at which the wavefront passed predetermined points marked on the tubes. Experiments were also carried out in which waves were initiated at a negatively biased Pt wire electrode. Reaction mixtures were prepared by pipetting appropriate volumes of stock solutions. Iodate reagent was added last by rapid delivery pipet and complete delivery was defined as time zero. The reaction mixture was throughly mixed and then spread over the bottom of a thermostatted petri dish. A
0022-3654/81/2085-2152$01.25/00 1981 American Chemical Society
The Journal of Physical Chernistty, Vol. 85, No. 15, 1981 2153
Letters
x
c
-$
03-
z
I
% 02-
P
01 -
0 0032
0128
[KIO,]
0 256
(M)
Figure 2. Wave velocity and induction time as a function of [IO3-lO in solutions wlth [H,AsO,], = 0.05 M. Numbers to the rlght of each curve give the pH of the buffer solution employed.
Figure 1. Waves in a tube: left: excess iodate, [IO3-lO= 0.03 M, [H,As03] = 0.05 M, pH 1.80; right: excess arsenite, [IO3-I0= 0.030 M, [H3AsO3]o = 0.094 M, pH 1.50, 0.5% starch.
Plexiglas cover served as a holder for two Pt wire electrodes (B & S Gauge No. 26) which were connected to a variable voltage source. The center Pt electrode was negatively biased at -1.0 V against a Pt electrode near the edge of the dish. The electrodes were positioned and the power supply was turned on at 1.0 min after time zero. The central electrode was visually monitored until a dark region of solution surrounding the electrode signaled the initiation of a wave. Once the wave appeared, the power supply was turned off. The wave front position as a function of time was recorded by taking photographs at timed intervals.
The Arsenite-Iodate Reaction The reaction between arsenite and iodate in acidic aqueous solution was first shown to be autocatalytic by Eggert and Scharnow4 some 60 years ago. The reaction may be viewed as involving two overall processes
+ IO3- + 6H+ = 31z + 3Hz0 H3As03 + Iz + H 2 0 = H3As04 + 21- + 2H+ 51-
(A) (B)
In the presence of excess iodate ([103-10/[H3A~0310 > 1:3), the overall reaction is (2(A) + 5(B)), or 5H3As03 + 2103- + 2H+ = 5H3As04 + I2 + H 2 0
(1)
to design an analytical procedure for the determination of I-. Reaction A, which is the well-known Dushman reaction,6 proceeds rapidly once significant amounts of Ihave been produced, and in a stirred system the reaction is marked by the sudden appearance of a brown color typical of I2or 13-. Process B, the Roebuck reaction,’ is significantly more rapid than process A and, if there is arsenite remaining in solution, we may obtain the overall reaction (A) + 3(B), or 3H3As03+ IO3- + 51- = 3H3As04 + 61-
Iodide is written on both sides of eq 2 to emphasize that because process A is rate determining for eq 2, the reaction is autocatalytic in the product I-. The I2 produced by process A is consumed rapidly in process B and the color appears only fleetingly.
Results “One-Dimensional” Configuration. In a thin tube, after an initial induction period a brown area appears a t the top of the initially colorless solution. When iodate is in excess, the boundary of the colored region moves down the tube, so that the entire solution eventually becomes colored. With excess arsenite, a narrow ring propagates down the tube maintaining a roughly constant width, finally disappearing when it reaches the bottom. Both the high iodate expanding wave and the high arsenite ring wave are shown in Figure 1. In Figure 2 we show the variation of the induction time and wave velocity with the initial iodate concentration and pH. At pH’s below about 1.2, the wave velocity cannot be measured because the color change initiates before the residual convection due to mixing is complete. At low iodate, there is a rough inverse dependence of 7 on [IO3-I0
Bognir and S&osi5have made use of this rapid transition (4) Eggert, J.; Scharnow, B. Z. Elektrochem. 1921,27, 455-70.
(2)
(5) Bbgnar, J.; SHrosi, S. Anal. Chim. Acta 1963,29, 406-14. (6) Dushman, S. J. Phys. Chem. 1904,8,453-82. (7) Roebuck, J. R. J. Phys. Chem. 1902,6,365-98.
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Letters
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\
IO3 [IO;]/M
e 4 5 4 0 A 3 5
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0 2 0
a I’”
v 1 5
z
P
I
e 2 5
W
‘0-
I 0
10
20
30
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TIME/min
Figure 4. Wave front position as a function of time. Reaction mixture composition and temperature same as Figure 3 with [IO3-] varled.
the waves accelerate once initiated.
Figure 3. Waves in thin film of solution. Central wave initiated at negativeiy biased electrode at 2.6 min. Photograph taken at 8.0 min. Reaction mixture composition: [NaIOJ = 2.5 X M, [NaAs03] = 3.75 X I O 3 M, [H2S04] = 1.00 X M, and 0.5% starch. Temperature = 25 OC and solution depth 0.8 mm.
in agreement with that found by Eggert and Scharnow4 for the stirred reaction. A significant [H+] dependence is also evident, though it does not appear to be as sharp as the 1/[H+I2dependence8that one might expect if the sole determinant of the induction time were the rate of the Dushman reaction. Further evidence that process B is important in initiating the wave is found in our observation that increasing [H3As03],, decreases the induction time. In Eggert and Scharnow’s stirred reactions, this period is nearly independent of the initial arsenite. The waves are not affected by visible light. Carrying out the reaction in a dark room with or without a region in the middle of the tube exposed to a narrow beam of light resulted in no departure from either the usual induction time or point of initiation of the waves. “Two-Dimensional“ Configuration. The dependence of wave velocity on [IO3-]was also investigated in the petri dish experiments. A typical experiment is shown in Figure 3. Measurements were made on waves initiated a t the negatively biased Pt electrode. Wave position as a function of time was determined by averaging right angle diameters of the dark region. In six experiments, [IO37 was varied with the other reactant concentrations held constant. Wave initiation occurred a t approximately the same time in each experiment. The average initiation time was 2.67 min with an average and maximum deviation of 0.28 and 0.58 min, respectively. The results for this series of experiments are shown in Figure 4. The experimental distance vs. time data are corrected so that the initiation time for each experiment corresponds to the origin. Each of the curves in Figure 4 is slightly concave upward, demonstrating that (8)Liebhafaky, H.A.; Roe, G. M. Int. J . Chem. Kinet. 1979, 11, 693-703.
Discussion The development of a wave of chemical reactivity in an unstirred, but initially homogeneous medium is a remarkable and significant phenomenon. Such a process clearly must involve the coupling of reaction and diffusion. Epik and Shub3 emphasize the “autocatalytic” role of H+in the system, but our experiments in buffered solutions, where the pH changes by
