J . Phys. Chem. 1985,89, 3050-3053
3050
Traveling Waves in the Nitric Acid-Iron( II)Reaction Gyorgy Bazsat and Irving R. Epstein*t Institute of Physical Chemistry, Kossuth Lajos University, H-4010 Debrecen, Hungary, and Department of Chemistry, Brandeis University, Waltham. Massachusetts 02254 (Received: February 12, 1985)
Traveling waves of brown FeN02+may be observed in an initially homogeneous mixture of nitric acid and iron(I1). The waves are obtained by first scavenging HN02 from the mixture with hydrazine or azide and then initiating at a given point with a drop of nitrite solution or electrochemically. Both one- and two-dimensional waves have been generated and their velocities studied as functions of initial reactant concentrations. The one-dimensionalwaves travel several times more rapidly going down a narrow tube than going up. This remarkable, but apparently general, behavior is attributed to the effects of convection induced by the exothermicity of the reaction.
Introduction
Traveling waves have now been observed in a variety of chemical reactions. Although they encompass a broad range of chemistry, all reactions which have been found to exhibit traveling waves-the Belousov-Zhabotinskii (BZ) system,’-, ferrous-br~mate,~iod a t e - a r ~ e n i t e , ~chlorite-iodide,6 and hydroxylamine-nitric acid7-have two common features. They are autocatalytic, and they possess bistable steady states in a stirred tank reactor (CSTR). Recent theoretical treatments, particularly of the BZgIo and arsenite-iodate waves,” have yielded significant insights into the nature of these waves and how their velocities depend upon reactant concentrations. One of the best characterized autocatalytic reactions is the oxidation of iron(I1) by nitric acid. The batch reaction is marked by the transient formation of the brown FeNOZ+intermediate, the basis of the brown-ring test of qualitative analysis.12 The kinetics of this clock reaction have been modeled successfully by a seven-step mechanismI3 which takes into account the successive reduction of NO< to NO2, H N 0 2 , and NO, the formation of the F e N 0 2 +complex, and reactions among the various oxynitrogen species. Extension of that mechanism to allow for the flow of reactants gave an accurate simulation of the bistability observed in CSTR experiment^.'^ We report here the existence of traveling waves in the Fe(I1)-HNO, reaction. Waves have been observed in the usual one-dimensional (test tube) and two-dimensional (Petri dish) geometries, and their velocities have been studied as a function of the initial reactant concentrations. Under these circumstances, the behavior is similar to that found in other wave-propagating systems. However, when the one-dimensional waves are studied in a geometry which permits wave propagation either upward or downward, a surprising new phenomenon is observed. We describe this “gravity effect” and offer a tentative explanation of its origin.
Two-dimesional waves were observed in glass Petri dishes of 120-mm diameter with a millimeter scaled paper support to allow wave position to be read as a function of time. Procedure. Reaction mixtures were made by mixing the appropriate volumes of 10 M nitric acid, 0.5 M ferrous, and 1 X lo-, M hydrazine solutions. Addition of hydrazine renders the mixture stable for several hours in the absence of external initiation of the autocatalytic oxidation reaction. Tubes were filled with glass syringes through a silicon rubber tube from the lower end to eliminate air bubbles. The tube was clamped after filling was complete. The reaction was initiated at the upper or lower end of the tube by dipping a glass rod into 0.01-0.1 M N a N 0 2 solution and then touching it to the reaction mixture. The position of the wave was read visually off the ruled scale. All experiments were carried out at room temperature (25 f 1 “C) without thermostating. Results
One-Dimensional Waves. In the absence of the hydrazine inhibitor (azide may also be used), the autocatalytic reaction which produces the brown FeN02+occurs more or less homogeneously throughout the tube after an induction period. Attempts to induce a wave result in a rapid color change which propagates too rapidly for quantitative measurement. However, if the H N 0 2 is first removed by the scavenger, then no change is observed in the solution until reaction is induced by a glass rod which has been dipped into a nitrite solution. After an induction period of about 5 min, a brown piston-shaped region forms at the end which has been touched and moves along the tube at a constant velocity. The front of the wave is relatively diffuse, while the rear boundary is quite sharp. The intensity profile of the brown color along the “piston” resembles the mirror image of the spectrophotometric kinetic curve of the reaction in
Experimental Section
Materials and Apparatus. Stock solutions (10 M) of nitric acid were made by dilution from 65% H N 0 3 (Carlo Erba, RPE) which had been purged with nitrogen gas for 30 min. The ferrous solutions were prepared by dissolving (NH4)2Fe(S04)z-6H,0in slightly acidic (H2S04) water. This salt, N a N 0 2 , and N2H4. H2S04 were of analytical grade (Reanal, Hungary) and were used without further purification. The one-dimensional propagation experiments were performed i.d. and 1.2-mm wall thickness except in glass tubes of 2.5” where otherwise specified. The “standard” tube was bent so that it had two elbows and three 30-cm straight sections. A length scale was painted on the side, and the straight sections were held vertically by laboratory pincers. In one set of experiments thermocouples were placed about halfway down a straight tube to record the temperature. Kossuth Lajos University University.
1 Brandeis
0022-3654/85/2089-3050$01.50/0
( I ) Field, R. J.; Noyes, R. M. J . Am. Chem. SOC.1974, 96, 2001. (2) Showalter, K.; Noyes, R. M.; Turner, H. J . Am. Chem. SOC.1979,101, 7463. (3) Jorne, J. J . Am. Chem. SOC.1980, 102, 6196. (4) Showalter, K. J . Phys. Chem. 1981, 85, 440. (5) Gribschaw, T. A.; Showalter, K.; Banville, D. L.; Epstein, I. R. J. Phys. Chem. 1981, 85, 2152. ( 6 ) Weitz, D. M.; Epstein, I. R. J . Phys. Chem. 1984, 88, 5300. (7) Gowland, R. J.; Stedman, G. J . Chem. SOC.,Chem. Commun. 1983, 1038. (8) Reusser, E. J.; Field, R. J. J . Am. Chem. SOC.1979, 101, 1063. (9) Schmidt, S.; Ortoleva, P. J . Chem. Phys. 1980, 72, 2733. (IO) Rinzel, J.; Ermentrout, G.B. J . Phys., Chem. 1982, 86, 2954. (11) Hanna, A,; Saul, A.; Showalter, K. J . Am. Chem. SOC.1982, 104, 3838. (12) Swift, E. H. “A System of Chemical Analysis for the Common Elements”; W. H. Freeman: San Francisco, 1939; pp 485-486. (13) Epstein, I. R.; Kustin, K.; Warshaw, L. J. J . Am. Chem. SOC.1980, 102, 3751. (14) Orbln, M.; Epstein, I. R. J . Am. Chem. SOC.1982, 104, 5918.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 3051
Traveling Waves in the Nitric Acid-Iron(I1) Reaction
lmin
Figure 3. Three replicate determinations of temperature as a function of time at the midpoint of a vertical tube of length 12 cm and i.d. 8 mm with thermocouples built into the wall. Chemical composition as in Figure 1. Figure 1. Three replicate determinations of distance (I) from point of initiation as a function of time ( 1 ) after mixing reagents in a glass tube of 2.5-mm i.d. Initial concentrations: HN03, 3 M; Fe(II), 0.2 M; N2H4, 1 X 10-4 M. Arrows indicate the direction of wave propagation. Drawing at upper left shows shape of tube. Iml I I"+
1LW.
IZW'
:(J--lg e
OJ
50
yx)
150
Zoo
tlrm"
Figure 4. Distance-time plot under the same conditions as in Figure 1 but with tubes filled with silica gel: X, 2,s-mm-i.d. tube; 0, 1.3-mm4.d. c
Figure 2. Distance-time plot under the same conditions as in Figure 1 but with a more elaborately structured tube.
TABLE I: Wave Velocities at Different Initial Concentrations' velocity, mm/min up down down [HN0310, M [Fe(II)lo, M 8.7 43.5 0.16 40 3 10 55 0.20 60 3 15 57.2 0.24 67 3 75 12.7 77.5 3 0.32 3 0.40 92 20 87.5 2.5 0.16 52 8.8 48 2.5 0.20 54 13.5 62 2.5 0.24 71 11.2 84 11.3 100 0.32 72 2.5 2.5 0.40 80 16.2 115 2.4 0.20 55 10.5 58 2.2 0.20 51 8 67 50 7.6 57 2.0 0.20 1.8 0.20 40 1.7 2.2 0.20 36.4 1.6
'Fixed conditions: tube i.d. 2.5 mm, [N2H4I0= 1 X lo4 M. a closed system.13 The length of the brown region is roughly proportional to its velocity; slowly moving waves give narrow rings. The position of the wave was measured periodically and the velocity calculated as a function of time. The results of three repeat experiments in our standard tube geometry are shown in Figure 1.
While the constancy of the velocity within each segment of the tube is heartening, the sizable differences in wave velocity between the upward and downward directions is surprising, to say the least. Experiments at different concentrations or with the wave initiated at the lower end of the tube give similar results. The downward traveling wave is always faster than the upward traveling wave
tube. TABLE 11: Influence of Tube Diameter on Wave Velocity" velocity, mm/min i.d., mm 2.5 2.1 1.3 0.6
o.d., mm 4.5 4.5 3.5 2.5
down 50-60 50-60 30 2.5
UP
10-15 7-10 6 0.7
'Fixed conditions: HNO,, 3 M; Fe(II), 0.2 M, hydrazine, 1 X lo4 M. by a factor of 4-10. The velocities obtained in a n even more elaborately structured tube are plotted in Figure 2. The effects of varying the initial reactant concentrations are summarized in Table I. The well-defined brown wave is obtained only in a relatively narrow range of initial concentrations. Hydrazine concentrations in the range 4 X 10-5-4 X lo4 M had no effect on the wave velocities, though they did influence the induction times a bit. Varying the concentration of the nitrite solution used as initiator also affected only the induction times. The reaction is strongly exotehermic, and it seems reasonable to consider whether temperature gradients generated by the heat released may play a role in the "gravity effect" on the wave velocity. The role of hydrodynamics in nonlinear kinetic phenomena has been emphasized recently by Epstein et al.I5 and by Laplante et a1.,16 who point out that even very small temperature gradients can be enough to support convective motion. A trace of the temperature vs. time for the standard concentrations used in Figure 1 is shown in Figure 3. The maximum in temperature (15) Epstein, I. R.; Morgan, M.; Steel, C.; Valdes-Aguilera, 0. J. Phys. Chem. 1983,87, 3955. (16) Laplante, J. P.; Micheau, J. C.; Gimenez, M. J . Phys. Chem. 1984, 88, 4135.
3052
Bazsa and Epstein
The Journal of Physical Chemisrry. Vol. 89, No. 14. 1985
TABLE 111: Wars Rommlon Velocllin In Different Ruction-Diffusion Syslems
system
rance of mcasd velocities. mm/min I
BZ BZ BZ
5-10 3-5 1-4
bromate-ferroin iodate-arsenite chlorite-iodide
1-22 1-5
HN03-NHzOH H NO,-Fc( I I )
0.3-3 0.02-9 3C-llS‘ 8-2@ 0.7‘
ref
I 2
3 4
5 6 7
this work this work this work
‘Downward in vertical lube. ’Upward in vertical tube. “Upward or downward with silica gel added.
F i p w 5. I’ho~ogr;iphr in+dimcnsion;il >\;I\C> u i i h diifereni Ihyer thicknesse-. C h e m c n l c o m p i l i o n as in Figure I .
coincides with the passage of the brown wave front. Careful visual observation of the waves shows that the fronts, especially during upward motion, are not smooth but show evidence of macroscopic disturbance. To test further the notion that heat generated in the reaction has a significant effect on the wave velocity, we performed two further sets of experiments. By decreasing the tube diameter, one increases the rate a t which heat is dissipated through the walls instead of into the liquid. Table I I shows that the tube diameter does indeed have a marked influence on the velocity, though the gravity effect remains. One way to inhibit convection is to increase the vismsity of the solvent. By filling the tubes with fine glass powder or with silica gel before introducing the reactants. we were able to eliminate the gravity effect completely. Figure 4 shows a typical set of results. Under these conditions, the waves are quite narrow (
