S. M. Kaushik, Zhi Yuan, and Richard M. Noyes University of Oregon, Eugene. OR 97403 If molecules of avolatile material are created by a reaction in homogeneous solution, the releaseof gas may take place in repetitive pulses rather than continuously. Our explanation of the phenomenon (1-3) involves homogeneous nucleation which commences only when the soluti& becomes grossly supersaturated. The subsequent growth and escape of bubbles so reduces the supersaturation that several seconds elapse before homogeneous nucleation is again possible. The hest-characterized eas evolution oscillator is the dehydration of formic acid inlconcentrated sulfuric acid. Oscill a t o r ~behavior was first observed bv Morean (4)and confirmed by Okaya (5).It was further studiei by'~owersand Rawii (6)and hv Showalter and Noves . (7). . . Smith. Noves. and Bowers (8)characterized the system and showed that the behavior could he reproduced semi-auantitativelv . hv. computation (I). The phenomenon is best studied quantitatively by pressure measurements in a flask connected to the atmosphere hy a capillary leak. The visual effects accompanying such a study are sufficiently dramatic that it seemed appropriate to develop a small demonstration in an open container. Use of the Morgan (4) reaction for such a demonstration would require some care because it involves foamed evolution of voisonous carbon monoxide from warm concentrated sulfuric acid! We report here a less unpleasant concoction which exhibits a t least as dramatic behavior. althoueh for a shorter time. The suggested demonstration is based on the decomposition of aqueous ammonium nitrite according to
78
Journal of Chemical Education
NH,'
+ NO,-
-
N,(g)
+ 2H,O
(A)
The oscillatory potential of this reaction was first reported by Degn (9) and was studied qualitatively by Smith (10). The subsequent discussion will show that the chemistry is more complex than is implied by the simple stoichiometry of the above eauatiou.
Condllons for the Demonsiratlon The demonstration suggested here is scaled for vresentation to a small group, h d could be shown to a large class by means of television monitorinp. I t involves the mixing of two solutions prepared from readiiy available materials. Solurion A roncisls of 26.4 i:111.200 md, of (NII4l2SO,in 100 g 199 ml., ot 0.200 molar HIW+ Solutim B cmsisrs of 27.6 g (0.400 moll oiNnNO, ond 4Y.Ue (U.4UO molr ufsnhvdnur NaCIOnm 100 e water. ~ l a e e i l . 2mL (i2.7 e) of Solution A in a 100-m~ beaker e) and stir eentlv with a m&ne$c stirrine bar. Add 13.1 -~ - mL 117.7 e,
- .
-
~~~~
~~~~~~
~~~
of Solution B. The order for mining is not important. The resulting solution is 2 m each in NH4+and in NOS- and is also 2 rn in NaClOd and somewhat less than 0.2 N in H2S01. The pH of the freshly mixed solution is about 3.2 Bursts of gas evolution begin in about 10 t o 15 s. The solution suddenly turns a milky white from the many small bubbles. It froths up and then subsides, becoming almost clear except for a few lame bubbles on the walls of the container. Successivebursts occur with a perid of 8 to 10 s, and 30 to 35 strong bursrs can bc uhcninrd during about 5 min. As the reartian progresses in rh~s ~
~~~
~~
~~
unthermostated system, the solution warms and the period hecomes somewhatshorter. In the later stages, the bursts are more clearly defined if the stirring speed is reduced. The photographs in Figure 1 were taken at different times during a demonstration and illustrate how much the appearance of the solution changes. Figure 2 is a record of pressure change in a thermostated flask connected to the atmosphere through a capillary leak. Factors which Deserve Attention
If conditions are properly adjusted, the successive pulses of gas evolution can he rather dramatic. However, we have found that little prior testing is necessary to develop the most effective conditions. Several factors deserve to be noted. The solutions do not need to be prepared with the accuracy of primary standard analytical reagents, but deviations in concentration of more than a few percent mav have sianificant effects. Even though the solution is buffered by the excess of nitrite, and even though hydrogen ion aoei not appear in eqn. (I),we have found that hehavior is rather sensitive to the amount of acid taken. The large concentration of sodium perchlorate enhances the demonstration for reasons which are not obvious. Apparently it acts by a salt effect on the rate of reaction. We did
not find conditions under which sodium sulfate was as effective as sodium perchlorate was. Large concentrations of salt increase the surface tension somewhat. However, in some experiments in a closed flask we obtained fairly strong oscillations even after adding several drops of the detergent Triton X-100. The detergent altered the surface tension in the opposite direction from the salt, and surface tension changes donot appear to be involved in the dramatic enhancement of oscillations by sodium perchlorate. The above instructions call for making an amount of each solution 10 times what is needed for a single demonstration. We found that solutions could he stored a t least two weeks without losing their effectiveness. I t should be possible to store Solution A almost indefinitelv. " . hut we are less confident about Solution B. The scale of the demonstration could undoubtedly he altered, but hehavior is dependent upon a surface-to-volume ratio which does not scale simply. Any quantitative studies ofthis reaction should he made in thermostated systems, and 30°C is a good temperature. We deliberately developed this demonstration for ambient conditions. Stirring is probably the most important single factor in an effective demonstration. The length of our stirring rod was one inch. which was a maior fraction of the diameter of the beaker. kt the start of a hemonstration, we stirred rapidly for about the first five seconds in order t o mix the reagents and then slowed the rate to one to two full revolutions per second. We slowed the rate somewhat more as reaction progressed. The reaction container should be carefully cleaned, although a few bubbles on the walls do not detiact seriously. Scratches on the surface serve as nuclei for bubble formation and should be avoided. If the surface has heen treated with Dri-Film (a silicone preparation trademarked by General Electric Company and distributed by Pierce Chemical Company), the demonstration is appreciably enhanced. The size and shape of the container are not unduly important. We tried a variety of conditions and even carried out a demonstration in a wine glass to relate the behavior to the damped pulses sometimes observed after a bottle of champagne has been suddenly opened. Prlnclples which are illustrated
The above demonstration involves hehavior which will be unanticipated from the prior experience of many students. The reason for performing such a demonstration is that it
Figure 1. A demonstration likethat described. Plate (a) shows a freshly mixed solution in which reaction is proceeding but in which gas evolution has not begun. Plate (b) shows a burst of gas evolution in which the frdhing has approximately doubled the volume of the coments of lhe flask and completely changed its appearance.
Figure 2. Record of pressure in a 100-mL flask connected to me atmosphere by a leak consisting of 5 cm of 0.5-rnm capillary tubing. The flask was in a thermostat at 30°C. and the base line correspondsto the same pressure inside the flask as outside. The pressure was measured with a Celesco P7D variable reluctance differential pressure transducer driven by a CD-25 transducer indicator. The output of the CD-25 was fed to a chart recorder, This record shows 29 clear pulses. The final burst came when stirring was stopped.
Volume 63
Number 1 January 1966
77
can be used to illustrate a number of basic principles from classical obvsical chemistrv. These orincioles include the homogeneo& nucleation or one phaHe in another, the distance over which diffusion can influence a system, the most stable configuration of two phases in contact, the effect of a gravitational field on the behavior of a chemical svstem. and the effect of feedback on a reaction sequence. ~ i e s p*incie ples all have a long tradition, but they often receive rather little attention in modern courses of physical chemistry. Homogeneous Nucleation of a Phase Let a spherical bubble of radius r with internal pressurep, exist in a medium under hydrostatic pressure Phwhere P, > P h . Let a be surface tension or Gibbs free energy per unit area of the surface between the gas and the liquid. The volume, V, and area, A, of the bubble are given by eqns. (1) and (2).
If the bubble were to e x ~ a n dreversiblv hv an increment dr, i t could perform P V expansion war-k Gainst its surroundinps, but the ex~ansionwould require aA surface work to create new surface. Theses two work terms are given by eqns. (3) and (4). expansion work = (P,
- Ph)dV= (P, - Ph)4ar2dr
(3)
surface work = odA = o8rrdr
(4) When the bubble is in a state of equilibrium with its surroundings, the expansion and surface work terms will be equal in magnitude and opposite in sign. We then obtain eqn. (5).
+
P, = Ph 2olr
(5)
'l'ua first approximation, we cnn assume C = #where C is t h e c ~ ~ n r m t m t i oofndissolved molecules in equilibrium with gas at pressure P, and x is the Henry's law constant. Then eqn. (5) can be rearranged to eqn. (6).
In this equation, Chis the concentration a t equilibrium with gas a t pressure P h and reqis the radius of a bubble in equilibrium with solution a t concentration C. For a solution at concentration C, any bubble smaller than re,. will lose molecules to the solution and will shrink until it eventually diinppears. If any buhl~leis larger than re?, molecules will evaporate into it from the solution and it wdl grow. Such growthbill either dilute the solution enough to establish a new equilibrium a t a larger bubble size, or else the bubble will escape physically from the solution. Equations (3) and (4) compare the work terms involved with interactions between a bubble and the surrounding solvent. The treatment regards the bubble itself as the system. If we want to know the work necessary to create a bubble in a solvent, we should consider both the work to force solvent from the cavitv and the work to form the surface. Both of these work teims are positive1 if the system is now defined to include both the solution and the bubble. Then the total work, W,, to create a bubble of radius r is given by eqn. (7).
'
This argument differs from that developed on p. 1521 of reference ( 1 ) . We believe the present one is more correct. The two treatments lead to conclusions of the same form but which differ bv a factor of 3 in magnitude. Because of the near discontinuity of ihe nucleation process, the difference is unimportant. 78
Journal of Chemical Education
The neglect of P V term assumes P, >> Ph, which has been shown to be true for creation of bubble nuclei in a specific real system (8). Let J, be the rate at which bubbles of radius r would be created spontaneously per unit volume of solution. The exact evaluation of J, probably goes beyond the range of what is possible with present theories, but we expect J, to be of the form of eqn. (8).
In this equation, a is assumed to be independent of r . If a bubble smaller than re. is created, we have seen that it will rapidly redissolve. g hire fore, spontaneous homogeneous generation of macroscopic bubbles in a solution at concentration C will require creation of bubbles larger than re,. If we combine eqns. (€4, (7), and (8) and let J be the rate of formation of bubbles with radii re,, we find eqn. (9).
This form of equation was first proposed by Volmer ( 1 1 ) . As C - Ch increases from less than fito a larger value, eqn. (9) behaves almost as a step function. Calculations reported elsewhere (3)for a specific system suggest that an increase of 0.1% in C mieht increase J bv a factor of lO'5! Homogeneous nucleation can be regarded as discontinuous when a critical concentration has been attained. E x c e ~for t that critical concentration, detailed numerical values of pa. rameters are almost irrelevant. This discussion has been concerned with spontaneous homogeneous nucleation of bubbles. Such a ohenomenon is \.eri. difficult to study experin~entallybecause of thr vlrtual impossit~lit\~uf'eliminatinr mirroscooic dust oarticles which can serve as heterogeneous nuclei-for bubble formation. However, these particles should be removed from solution hy the bubhles whose tcrrmation they nucleated. Some of the early pulws in Figure 2 fall nearer to the base uressure than do the later ones: We do not have a certain explanation of this effect but suggest that depletion of dissolved pas may have been more complete in the early pulses because-heten;. genevus nucleation centers were also present then. Recauscof the difiitulty of eliminating heterogeneous nucleation in a .iolurim of dissolved gas, homogeneous nucleation has been a notorim~slydifficult subject to study. In a gasevolution oscillator, thedissolved gas is created molrculr by molerul~in a chemical reaction. \Ve believe such r~rocedures offer new opportunities for studying the phenomenm 01 nucleation. We haw used the deh\,dmtion of formic acid in concentrated sulfuric acid (8)to show that homogeneous nucleation of carbon monoxide begins at about 0.07 M. A solution saturated at one atmosphere pressure is a t a coocentration of about 0.0009 M. Homogeneous nucleation begins only when the concentration of dissolved molecules would be in equilibrium with gas at about eighty atmospheres! At this concentration, re, for a bubble nucleus is calculated to be about 150 A.We do not know whether these critical supersaturations and nucleus sizes will be general for other gases and other solvents.
-
Distance of Influence by Diffusion Some perceptive students may note that there are always hubbles on the walls of the container. The pressures in these visible bubbles cannot be much more than one atmosphere, and the solution near them must he in equilibrium with this pressure. However, the argument presented immediately above says that the solution suddenly turns milky because i t is supersaturated to a concentration that would be in equilibrium with 80 atmospheres. The paradox can be resolved by noting that the distance a
molecule diffuses in time t is of the order of JiSt where D is the diffusion coefficient. For small molecules in aqueous solution, D is a few times 10-5 cm2 s-1, and the period of an oscillation is about 10 s. Therefore, the visible bubbles only influence the solution for distances of about 0.1 mm, and the remaining volume may become grossly supersaturated. Most Stable Configuration of Two Phases
If two phases are in contact, there is an energy associated with the surface between them. Other things being equal, the most stable state of the svstem will he that in which the total surface area is a minimum. Any breaking of one large bubble into smaller ones will increase surface area. The eauilibrium state will consist of a single large bubble. Another way to make the same point is to note that any population of bubbles is unstable with respect to a single large bubble. Suppose a solution initially contained several bubbles each of which was of radius re, as given by eqn. (6). If one of the inevitable statistical fluctuations made one bubble a little smaller than the others, it would shrink until it disappeared. If a fluctuation made one bubble a little larger, it would grow by depleting the dissolved gas in the solution and making the other bubbles too small to be in equilibrium. "Unto every one that hath shall be given.. . ; b u t from him that hath not shall be taken away even that which he hath" (12).
Another aspect of the same principle is embodied in the folk wisdom that "the heer remembers.'' If a bottle of beer is given a sharp jolt and then opened, it will foam up badly. Even if the opening is delayed for an hour or more, some people allege that the beer "remembers" its trauma. Shock and cavitation phenomena associated with the jolt will create many bubble nuclei in the saturated solution, and they will respond when opening the bottle reduces the hydrostatic pressure Pb. These nuclei will ultimately disappear by the processes described in the preceding paragraph. However, those bubhles with radii very close to re, will respond only slowly and will persist as nuclei in case of a subsequent onenine of the bottle. This ex~lanationsuggests that the ";llemo&"of the heer could Or ~lestroyedby'karming it and then recoolinr so that everv bubbleu,ould havediffrred from re, at some time during the cycle. Dynamic Effects of a Gravitational Field
Although the discussion has concentrated on formation of bubhles in a liquid solution, it would apply equally to any other phase transition such as forming a solid precipitate or forming droplets in a gas. The pulsed behavior requires that most of the bubhles be uhvsicallv removed from the solution so that they do not interfere with the building of supersaturation toward a new burst of nucleation. That removal occurs because the solution is much denser than the gas in a bubble and because the svstem is in a gravitational field. If the reaction of this demonstrati& were started in an orbiting satellite at zero gravity, there would be a burst of nuclea~ionafter abuut l5seconds creating a large numt)er of m a l l hul~hlr.ithroughout thesolution. Those hubblesu~ould then grow as the reaction progressed, but there would be no periodic bursts of gas formation such as are observed in the demonstration. After the chemical reaction was over, the bubbles would coalesce to a single large one just as discussed above. Just as reducing gravity could prevent pulsed behavior in a system which would otherwise exhibit it, increasing gravity might cause pulsed behavior to appear. If chemical reaction produced molecules of a solid denser than the solution, running the reaction in an ultracentrifuge might generate successive "snowstorms" as crvstallites formed and settled out.
Effect of Feedback in a Chemical Mechanism
None of the above discussion explains why bubbles are evolved in repetitive pulses rather than continuously. Molecules are being formed by chemical reaction and are being incorporated into bubbles which eventually leave the solution. One might expect a steady state in which the flux of molecules was constant from chemical formation to escape in bubbles. The mechanism being discussed can he summarized in four general steps. A-M M eN
where j = 0,1,2,3, . . . .
The first s t .e (ean. ~ . (10)) renresents the chemical reaction pnxlucing dtw~lvedmolecules, M. Equatlon (11)represents the formation of nuclei. N. The kineticsof this step involve a virtual step function as discussed above, but theonly impurrant point is that thr rate of reaction 01 111) is faster the the concentration of M. The last two steps describe the alternative behaviors of bubbles, B,, which are j increments lareer than nuclei with N Bn. Reaction (12) . . reore. sents the growth of a bubble by evaporation into i t of molecules of dissolved gas. Reaction (13) represents physical escape of bubbles from solution into gas phase. Reactions (10) and (13) can be regarded as irreversible for all values of j. However, reactions (11) and (12) go to the left for small j a t reduced concentration of M. As molecules are produced by reaction (10). the concentration of M builds up until nucleation bv. step . reaction (11)begins almost discontinuously. The first nuclei and small k b b l e s have small surface area and grow slowly. Eventually, they get big enough that the totaleffect of all reactions (12) is toconsume M faster than reaction (10) is producing it. Then the delayed negative feedhack reduces the concentration of M so much that reaction (11) shuts off. That concentration of M is further reduced as the bubbles erow and escane. Then the cycle begins again. This mechanistic discussion is nurelv but i t . - aualitative, . illustrates how a delayed step in areaction sequence can feed back to inhibit a nrevious ster, in the same sequence. Parameters are being evaluated ( j )in order to test whether the explanantion outlined here is able to describe the quantitative dynamics of the system.
-
-
Potential Chemical Complications
The argument has assumed that physical processes of bubble nucleation, growth, and escape are sufficient to explain the phenomenon of pulsed gas evolution. Present evidence (8) is that such an explanantion is satisfactory for the Morgan (4) reaction based on dehydration of formic acid. The demonstration described here may be more complicated. Reaction (A) is not sufficient to describe everything that is hanoenine. Some fumes of brown NO1- annear .. .. durine+ the reaction suggesting that NO is also evolved and reacts with the air. Moreover. the nH drifts from about 3.2 to 4.0 as should also invoke reaction proceeds. he fu~lkxp~anantion reaction (B).
-
3HN0,
-
ZNO + NO,-
+ Ht + H,O
(B)
Very qualitative observations (10) suggest that the ammonium nitrite reaction exhibits oscillations only when the pH is such that reactions (A) and (B) are going at comparable rates. Volume 63 Number 1 January 1986
79
Even though the detailed chemistry of this system is not vet understood, the pulsed gas evolution can he explained semiqt~nntitilti\,rlyhy the arguments dwelopcd nlwve, and this rcaction offers an excellent illustration of several important principles of physical chemistry. This work was supported in part by a grant from the National Science Foundation. This paper is No. 68 in the series "Chemical Oscillations and Instabilities." It is also No. 8 in the series "Gas Evolution Oscillators." The immediately preceding numbers are in press in the Jour. Phys. Chem.
80
Journal of Chemical Education
Literature CHed ( I ) Smith, K. W., md Noyes, R. M., J. Phys. Chem., 87.1520 (1983). (2) Noyes. R. M., J. P h w Chem., 88,2827 (1984). 13) Kaushik. S. M.. and Noyes, R. M.. J. Phys. Cham., 89.2027 11985). (4) Morgan. J. S.,J. Chem Soc.. Trans., 109,274 (1916). ( 5 ) Okaya,T.,Ploe.Phv~.-Molh.Soc. Jpn., 1,43119191. (6) Bowem.P. %and RaWi,G., J.Phy8. Chem..81,1549 (1977). 17) Showaltar, K.. and Noyes, R. M.. J. Amer. Cham. Soe.. 100.1042 (1978). (8) Smith, K. W., Noyea, R. M., end Bowers, P. G., J. Phw. Chem., 87,1514 (1983). . Worhhshap, I91 Degn. H.. informal report at Europcan Molecular B i ~ l o g organization Dortmund, October 4-6.1976. 110) Smith. K. W., PhD thesis, University ofOregon, 1981. (11) Volmor, M.,"Kinetikder Phascnbildung?Stainkopf,Leipzig. 1939. 112) Maftheai: 26129.
