J . Phys. Chem. 1987, 91, 1618-1622
1618
Gas-Evolution Oscillators. 9. A Study of the Ammonium Nitrite Oscillator’ Mordecai B. Rubin,+ Richard M. Noyes,* and Kenneth W. Smith$ Department of Chemistry, University of Oregon, Eugene, Oregon 97403 (Received: November 6, 1986)
The decomposition of aqueous NH4N02to produce N2 may generate repetitive pulses of gas, but the chemical process itself takes place at virtually the same rate whether or not gas evolution is smooth or pulsed. During times when oscillatory gas evolution was taking place, we found less then 0.4% of NO in the N2 produced; chemical feedback could not have contributed significantly to the oscillations. This absence of a chemical feedback arises because a specific NO molecule is very much more likely to react chemically than it is to escape the solution by entrainment in evolving gas bubbles. Homogeneous nucleation of bubbles of N2 in water takes place at a concentration of 0.012 M, which is about 19 times the equilibrium solubility at 1 atm; this critical supersaturation factor is much less than that previously reported for CO in concentrated sulfuric acid. An energetic analysis of conceivable pathways concludes that the rate-determining step for N2 formation involves nucleophilic attack of NH3 on N 2 0 3just as physical organic chemists have already concluded.
I. Introduction
TABLE I: Percent of Reaction at Various Times
If a chemical reaction produces a dissolved gas, the formation and escape of bubbles often take place in pulses rather than continuously. Most previous studies of the phenomenon have concentrated on the production of carbon monoxide by dehydration of formic acid in concentrated sulfuric acid. The oscillatory behavior was first reported by Morgan., It has now been modeled quantitatively3p4 as a purely physicochemical process involving parameters all but one of which can be measured independently. The chemical reaction is an acid-catalyzeds process which is so nearly irreversible that the net rate is little affected by the release of gas. Another reaction which produces gas is the irreversible decomposition of aqueous ammonium nitrite according to the process
-
NH4+ + NO2- N2+ 2 H 2 0 (A) This reaction is important historically because of its role in the discovery of the element argonS6 Oscillatory behavior was first reported by Degm7 Of course, process A does not take place in a single step. The mechanism is discussed in more detail below. It almost certainly involves the following two component stoichiometric processes: 2HN02 s NO NO, H20 (B)
+
NH3
+ NO + NO2
-
+
+ HNO2 + H20
(C) On the time scale of our measurements, the stoichiometric pair NH4+ NO; is in equilibrium with NH, HNO,, and NO NO2 is in equilibrium with N2O3. The reaction producing N, is almost certainly accelerated by dissolved NO, and NO could be swept out of the solution during a burst of formation of N2gas. It therefore appeared that the behavior of the ammonium nitrite oscillator might be impacted by chemical feedback of a sort not possible with the simpler formic acid dehydration oscillator. The experiments reported here were undertaken to test this hypothesis. N 2
+
+
+
11. Effects of Oscillations and of Stirring on Rates of Reaction The solutions were prepared in triple-distilled water to compositions similar to those developed by Kaushik, Yuan, and Noyes* for a demonstration of the phenomenon. Solution A was 1.78 M in (NH4)2S04and 0.0699 M in H2S04. Solution B was 3.06 M in NaNO, and 3.06 M in NaC10,. Most reactions were run a t 25.0 f 0.05 OC in 100-cm3 round-bottomed long-necked flasks (total volume 150 cm3) fitted with Rcdauiss pressure joints supplied by Witeg Co. of Anaheim, CA. When the theoretical volume of gas would have resulted in ‘Permanent address: Department of Chemistry, Technion-Israel Institute of Technology, Haifa, Israel. *Permanentaddress: Exxon Research and Engineering Co., P.O. Box 5 1 , Linden, NJ 07036.
0022-3654187 I2091 -1618$01.50/0 , I
,
time/min oscillating run nonoscillating run
1
2
5
10
30
60
4.6 5.7
8.8 10.2
20.5 21.0
31.9 32.9
53.5 54.0
67.8 68.2
a pressure increase of more than 0.5 atm, a ballast flask of appropriate volume was connected to the system. In all cases, the appropriate volume of solution B was placed in the reaction flask and bubbled with argon for 5 min followed by an additional 10-min sweeping of the head space before the appropriate volume of solution A was added. This argon sweep was used to eliminate atmospheric oxygen because oxidation of any NO in the evolved gas would have affected the pressure measurements. Pressures were measured with a Celesco KP15 variable-reluctance transducer kit with a 25-psi diaphragm coupled to a chart recorder through a transducer indicator. Response of the system was linear over the pressure range used. Calibration against a water manometer indicated that a 1-V output corresponded to 0.16 atm. The volumes of evolved gas calculated from the reaction stoichiometry and from the total pressure change and known volume of the system always agreed within 5%. Amounts of gas evolved in oscillatory and in nonoscillatory solutions were compared for solutions prepared from 10 cm3 of solution B and 5 cm3 of solution A. In the oscillatory run, the freshly mixed solution was stirred briefly at 240 rpm with a 1/2-in.cylindrical bar magnet which was then slowed to 200 rpm. The oscillations were manifested as successive steps which were initially about 0.01 atm and which became very weak after about 10 min. In the nonoscillatory run, a similar solution was stirred at 300 rpm with a I-in. egg-shaped bar which facilitated gas release sufficiently to inhibit oscillations. Both runs were continued at least overnight in order to estimate a pressure at infinite time, and the fraction reaction was calculated
y.
(1) 74 in the series “Oscillations and Instabilities in Chemical Systems . No. 73 is Ruoff, P.; Noyes, R. M. J . Phys. Chem. 1986, 90, 4700. No. 8 in the series “Gas-Evolution Oscillators” is ref 8. (2) Morgan, J. S. J . Chem. SOC.,Trans. 1916, 109, 274-283. (3) Kaushik, S.M.; Rich, R. L.; Noyes, R. M. J . Phys. Chem. 1985, 89, 5722-5725. (4) Yuan, Z., Ruoff, P.; Noyes, R. M. J . Phys. Chem. 1985, 89, 5726-5732. ( 5 ) Hammett, L. P. Physical Organic Chemisfry;McGraw-Hill: New York, 1940; pp 277-8, 283-4. (6) (a) Lord Rayleigh Proc. R. SOC.London 1894,60, 340-344. (b) Lord Rayleigh; Ramsay, W. Philos. Trans. R . Soc. London 1895, 186, 187-241. (7) Degn, H., informal report at European Molecular Biology Organization Workshop, Dortmund, Oct. 4-6, 1976. (8) Kaushik, S. M.; Yuan, Z.; Noyes, R. M. J . Chem. Educ. 1986, 63, 76-79.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Ammonium Nitrite Oscillator
1619
/// t
0
50
150
100
il
I80
t(min)
Figure 1. Time behavior of two different runs at 25 O C prepared from 1 cm3of solution A and 10 cm3of solution B. Ordinate is fraction of total
gas evolution at the indicated time. Dashed curve represents a run which was stirred continuously. Solid curve represents one where stirring was initiated at times of upward arrows and stopped at times of downward arrows. Note that the amount of gas released when stirring is initiated is roughly independent of the rate of chemical reaction at that time. TABLE I 1 Ratios of NO to N2 in Samples of Evolved Gas Dercent of reaction
oscillating run nonoscillating run
5-10 0.0025, 0.0040 0.0013, 0.0018
54-60
68-73
0.053 0.033
0.047, 0.043 0.039, 0.043
~
at various times up to 1 h. The results are presented in Table
I. The consistent small differences in gas evolved might be due to less supersaturation in the more strongly stirred nonoscillatory solution. More likely, the rates in Table I reflect small differences in the amount of gas escaping before the system could be closed at the start of a run. The important conclusion from Table I is that the rate of reaction is not detectably different whether gas is removed in pulses or continuously. That conclusion is reinforced by the two runs in Figure 1 which were identical except for stirring procedures. The dashed curve represents pressure release from a run which was stirred continuously. The solid curve is from a run where stirring was repeatedly stopped and restarted. As long as stirring was taking place at a particular time, the integrated amount of total gas release was independent of the previous history of stirring. 111. Composition of Evolved Gases Solutions identical with those in the preceding section were run in both oscillatory and in nonoscillatory modes. The reaction flask was connected with a vacuum stopcock to a collection flask filled with argon to 1.2 atm. Excess argon was vented to sweep air out of the connecting volume, and the reaction was allowed to proceed until pressure in the reaction flask had increased about 0.1 atm above that when the two flasks had been connected. The collection flask was then disconnected, and the mass spectrum was scanned three times to determined the relative peak heights of N z and of NO. A separate measurement with an equimolar mixture showed that these two gases had nearly equal sensitivities in the mass spectrometer. We observed no parent peak due to NO,; moreover, separate visual examination of the collected samples showed the gas was colorless. We could easily have detected a fraction of a percent of brown N O z if it had been present even if it had fragmented completely in the mass spectrometer. The results of duplicate oscillatory and nonoscillatory runs are presented in Table 11. The observations in Table I1 do suggest that gas from the weakly stirred oscillating run had somewhat more N O than that from the strongly stirred nonoscillating one. However, during the
Figure 2. Typical trace for determining supersaturation by N2 for a system at 25 "C containing 3 cm3of solution A and 10 cm3of solution B in a total volume of 150 cm3. The stirrer was suddenly turned on at point marked A, and the excess of previously dissolved gas was calculated from extrapolated point marked B. For this measurement, c, = 1.23 X mol c d , and the equilibrium solubility at 1 atm is 6.40 X lo-' mol cm-'.
early stages when oscillations might have occurred, the evolved gas had less than 0.4% of NO, venting of this species from solution could not have had a significant feedback on the physicochemical processes responsible for the oscillations. The mechanistic implications are discussed further in section VII. Up to about 5% of NO was observed in gas evolved during the later stages when oscillationswere no longer possible. Side reaction D may have been responsible. Process D would have increased in importance relative to (A) as the ammonium ion in the original solution was depleted. 3HN02
-+
2N0
+ HNO, + H,O
(D)
IV. Critical Limit of Supersaturation The study of the Morgan, reaction by Smith et aL9 demonstrated that in concentrated sulfuric acid the concentration of dissolved carbon monoxide could be raised to about 0.07 M, but the onset of homogeneous nucleation of bubbles prevented it from rising higher. This critical limit is about 80 times the equilibrium solubility at 1 atm. The oscillatory behavior of nitrogen evolution strongly implies a similar critical limit for onset of bubble nucleation of this gas in water. Figure 2 illustrates a typical measurement of this limit. Solutions A and B were placed in a closed flask similar to those used in sections I1 and 111. Stirring was stopped, and the pressure was allowed to increase for several minutes. Rapid stirring at 800 rpm was suddenly initiated and continued until the rate of pressure increase had again become steady. The trace of pressure was then extrapolated back to the time at which stirring was initiated, and the release of supersaturation could be calculated. The stirring was then stopped, the accumulated gas was vented to the atmosphere, the pressure in the closed system was allowed to rise again, and the stirring was initiated at a selected time. As is illustrated by Figure 1, several traces like Figure 2 could be obtained from a single solution before the rate of the reaction producing gas became too slow for efficient study. Each measurement like that in Figure 2 determines the degree of supersaturation in an individual solution at the time rapid stirring was initiated. If such measurements are to determine the critical supersaturation for nucleation, three criteria must be satisfied by the measurements: (1) The rate of pressure increase immediately before stirring was initiated should equal the limiting rate with continued stirring. (9) Smith, K. W.; Noyes, R.M.; Bowers, P.G . J . Phys. Chem. 1983, 87, 1514-1519.
1620 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 TABLE 111: Pressure Changes and Supersaturations of Solutions Prepared from 10 cm3 of Solution B and Indicated Amounts of Solution A VA/cm3 V.,,,/cm3 V.../cm3 APlV 10Sc./mol cm-3 25 "C I 11 139 0.134 1.1 1 0.138 0.140
1.14 1.16
1
11
139
0.145 0.138
1.20 1.14
1.5
11.5
138.5
0.157 0.150
1.24 1.18
2
12
138
0.164 0.170 0.168 0.166
1.23 1.28 1.26 1.25
3
13
137
0.184 0.174 0.180
3
13
30 ' C 137
0.176 0.172
Rubin et al. TABLE IV: Free Energies of Formation (in kcal mol-') for Species of Potential Significance NH3k) NH3W NH,+(aq) NHz(g) NHzOH(aq) 'izN2(d '/*N2(aq) '/2N20(9) 'i2NZO(aq) NO(d NO(aq)
That limiting rate in the stirred solution is the rate at which gas molecules are being produced by chemical reaction. If pressure above the unstirred solution was increasing at the same rate, the concentration of dissolved gas in that solution had reached a limit which could not be further increased. (2) Any particular solution composition should produce a reproducible upper limit of supersaturation which could not be exceeded regardless of different periods before stirring was initiated. (3) That same limiting supersaturation should be independent of changes in composition which changed the rate of reaction but did not seriously impact the physical properties of the bulk medium or its surface. Table I11 reports the results of a number of measurements like Figure 2 at 25 and 30 "C in a round-bottomed flask with total volume of 150 cm3. Each experiment contained 10 cm3of solution B and 1-3 cm3 of solution A. Because the flask was vented after each measurement of supersaturation, the pressure in the flask was never more than 5% greater than atmospheric. Each measurement was used to calculate c,, the supersaturation in excess of equilibrium solubility at 1 atm.
HNOZ(g) HNOdaq) NOJaq) '/ZNZ03(g) '/2N203(aq) NO,(g) N02(aq) N 03- (a q 1 HZO(1) H+(aq) at pH 5
-9.982 -12.82 -8.25 16.67 16.00 12.390 13.39 -26.43 -56.690 -6.821
TABLE V: Differences in Free Energies of Gaseous and Aqueous Species, [AG,"(gas) - AG,O(aq)l/kcal mol-' NH3 NZ NZ0 NO
1.27 1.20 1.24 av 1.21 i 0.06 1.19 1.17
-3.976 -6.36 -19.00 48.27 -5.60 0.0000 2.179 12.38 13.48 20.719 24.422
2.38 -4.36 -2.20 -3.70
NZ03
HNO2 NO2
1.34 2.84 -1.00 (est)
The values reported by Latimerlo and handbook data on gas solubilities were used to generate most of the desired quantities. The tabulation by Benson" was used for the gaseous species NH,, H N 0 2 , and N 2 0 3 . A value for N203(aq) could be estimated from the studies of H20 Turney', on the equilibrium 2HN02(aq) 2 N,O,(aq) in perchloric acid at 20 "C. We made no effort to correct for temperature change. We could not locate solubility data for the gaseous species NH,, NO2, and N2O4. The estimate for AGfo for NO,(aq) in Table 1V is derived from Table V, showing differences of AGfo in gas and in solution for the other species. The extremes are represented by the very soluble NH, and H N 0 2 and by the minimally soluble N2 and NO. We estimate NO2 to be somewhat more soluble than N 2 0 and doubt the estimate is in error by more than about 1 kcal mol-'. Free energy of formation H + is set at -6.821 kcal mol-' corresponding to pH 5.00, which is near the acidities of the solutions whose behavior we studied. The data in Table IV were used to generate Figure 3 for the possible states of HIoNO3+at pH 5.00. The form is one we have found useful for looking at chemical change in complex systems. Because thermodynamics is only concerned with changes of state, one value can be assigned arbitrarily. We have assigned a free energy of zero to NH4+ + 3H20. We have also arbitrarily assigned e- a free energy of -1 1.593 kcal mol-'; this assignment leads to zero free energy for NO2- 8H+ + H 2 0 + 6e-. All other free energies then follow from the experimental data. For levels in the same vertical column in Figure 3, the most stable one is the lowest. Thus, at pH 5, NH3 is virtually completely protonated while HNO, is largely dissociated. If two levels in different columns are connected by a straight line, all intermediate levels above that line are unstable in their standard states compared to the connected levels and those intermediates will tend to disproprotionate. All intermediate states below that line are stable to disproportionation. Figure 3 permits a number of useful conclusions to be drawn: Because of the extremely strong bond in N,, processes A and C in the Introduction can be regarded as totally irreversible. Process D will go to the right provided N O can escape to the gas phase at about 1 atm, but AGDo would be small in absolute magnitude if the final product were NO(aq). Process B has a rather small absolute AGO and will behave as a reversible reaction. N,O, would be comparable in importance to NO + NO2 if all species were in their standard states, but it will have less relative importance in dilute solution.
+
+
The runs reported in Table I11 do not represent much change in surface area or in volume of solution, but a threefold change in ammonium ion concentration does not change the critical supersaturation significantly. The limited data at 30 "C do not indicate a significant effect of changing temperature. Handbook data indicate that at 25 "C and 1 atm the equilibrium solubility of nitrogen in water is 6.40 X M while the maximum amount of gas which can be released by rapid stirring is about 19 times this solubility. Smith et aL9 report a ratio of about 80 for a similar study of carbon monoxide in concentrated sulfuric acid. The molecules N 2 and CO are of equal mass and isoelectronic with zero or very small dipole moments. The difference in critical supersaturation is tentiatively ascribed to the difference in solvent rather than that in the solute gas. Alternatively, increased hydrogen bonding to the oxygen in CO may somewhat reduce ease of bubble nucleation with this gas. V. Thermodynamics of Possible Reactions
Thermodynamic data are well established for most of the known species containing only nitrogen, oxygen, and hydrogen. The free energies of formation of the various species are presented in Table IV. Values reported are in kcal mol-' with standard states 1 m activity for aqueous species and 1-atm fugacity for gaseous species.
(10) Latimer, W. M. The Oxidation States of the Elemenis and Their Potentials in Aqueous Solutions, 2nd ed.; Prentice-Hall: New York, 1952. (1 1) Benson, S . W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1916.
( 12) Turney, T. A . J . Chem. S o t . 1960, 4263-4265.
Ammonium Nitrite Oscillator
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
T 40-
I ) N 0 2 ( o q ) t 8Ht tH20 t 7e-
30-
20-
- 30
2) NO,(g) t 8H+ +H20 1 7 e -
NHZOH(aq) t 3H' + Z H ~ Ot 2 e -
-20
3) ;N2Oq(g)+8H' t Hfl t
-104
k N 2 0 ( o q lt 5 H t
+ 2 i H 2 0 i 4e-
2)iN20,(q3+ tI
50
- 40
NH2!g)t 2Ht + 3 H p t e-
1621
7e-
7H'
H20 t 6 e-
-201
-301
a
Nzloq) t 4 H ' +3Hz0 t 3e-
-401
iN,(g)t
- 50
t 3 H 2 0 t 3e-
t
H20 t 6e-
5) NO; + 8Ht
4H+
+H20 t 6 e -
Figure 3. Free energies (in kcal mol-') for various states of NO3HIo+at 25 OC. Standard states are 1 M activity for aqueous species and 1-atm fugacity for gaseous species. Electrons are assigned a molal free energy such that levels involving NH,+ and NO2- are both zero.
The species NH, and N H z O H have such large free energies that they cannot be plausible intermediates in the formation of N,. Therefore, NH, or NH4+ must be oxidized directly to some species like H,NNO which could proceed to the final products of reaction. N,O is thermodynamically permissible as an intermediate. N2 NO< However, we doubt that processes like NzO NO, are important. The mechanistic implications of these thermodynamic constraints are discussed in more detail in section VI.
would be in equilibrium with H N 0 2 by rapid process B. We further propose that reaction follows irreversibly after formation of the intermediate species H,NNO. It has been found that N H 2 and N O react to form N 2 H 2 0 at virtually every collision even in gas phase.]' Rearrangement in aqueous solution must be even more facile. If three species are to react, they may do so in a concerted process, or two of them may participate in a prior equilibrium followed by reaction with the third. These alternatives generate four possible sequences designated I to IV.
VI. Kinetics and Mechanism of Reaction A We shall not attempt to review the extensive kinetic literature on nitrosation of primary amines and of amnonia. A good e n t r k is a summarizing paper by Hughes, Ingold, and Ridd.', We accept the conclusions of Abel, Schmid, and Schafranik14 which indicate that the rate of reaction A can be described by
NH, NO2 9 NH, HNO2 NH, + N O ---* HzNNO
-
+
+
+
+
+
+
-
NH, N O e H 3 N N 0 H,NNO + NO2 HzNNO + HNOz
+ NO, * N,03 NH3 + N,03 H3NNO+ + NOzH,NNO+ + NO,HZNNO + HNOz H2NNO + HNOz NH3 + N O + NO2 NO
vA = d[N,] = kion[NH4+] [NO,-] [HNO,]
(2a)
= kmodNH31 [HN02I2
(2b)
-+
Our limited observations seem to be entirely consistent with this conclusion, but we did not attempt a true kinetic study. The rate constants kionand k,,, imply ionic and molecular pathways which may be mechanistically different. However, this system resembles the classic Wohler's synthesis of urea from ammonium cyanate. Frost and PearsonI6 have examined the extensive literature on that reaction and have shown that no kinetic measurements such as salt effects or otherwise could hope to discriminate between kionand k,,,; either expression would fit all data equally well. The transition state for the rate-determining step must have empirical formula H,N303 nH20, where n is zero or an integer. Even though kinetic measurements cannot discriminate between the paths implied by the two forms of eq 2, the necessity to form N-N bonds makes NH, a more plausible reactant than NH,+. We propose that it reacts with N O + N O z or with NZO,; either
*
(13) Hughes, E. D.; Ingold, C. K.; Ridd, J. H. J . Chem. Soc. 1958,88-98. (14) Abel, E.; Schmid, H.; Schafranik, K. Z . Phys. Chem. 1931, Bodenstein Festband, 510-522. (15) Wohler, F. Ann. Phys. Chem. 1828, 12, 253. (16) Frost, A. A,; Pearson, R. G. Kinetics and Mechanism, 2nd ed.; Wiley: New York, 1961; pp 307-316. Unfortunately, a later edition of this important textbook deleted the chapter concerned with mechanistic studies of specific
reactions.
+
---*
(Ia) (Ib) (Ira) (IIb) (IIIa) (IIIb) (IIIc) (IV)
Path I can be rejected for energetic reasons implied by Figure 3. Step Ia is endothermic by 30 kcal mol-] in gas phase and could not possibly take place at the observed rate even if it were rate determining rather than equilibrated as required by the kinetics. If path I1 were plausible, there should be spectrophotometric evidence for H 3 N N 0 in gaseous mixtures of NH, and NO; we are not aware of any such evidence. Path 111 presumably passes through a transition state of the structure H3N+---(NO)---N02- involving a nucleophilic displacement by N H 3 on a nitrogen in Nz03. Concerted path IV involves simultaneous attack by NO, and N O with a presumed transition state of the structure ONO---H---NH2---N0. Although N 2 0 , is in such rapid equilibrium with NO + NO2 that the two paths generate virtually identical kinetics, we can still make a mechanistic discrimination. We made two runs at 25 O C which varied by a factor of 2.5 the amounts of solution A added to a large excess of solution B. The two rates differed by a factor of 6.5, but the two values of (17) (a) Gehring, M.; Hoyermann, K.; Schacke, H.; Wolfrum, J. Symp. (Inr.) Combusr., [Proc.] 1973, 99-105. (b) Gilbert, R. G.; Whyte, A. R.; Phillips, L. F. Int. J . Chem. Kinet. 1986, 18, 721-737.
1622 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
kmolaveraged 6.05 X lo3 L2 mol-, s-I with a range of 15%. These observations lead to the equation
krIIb= 3.0 X IO4 L mol-] s-l
(3)
Presumably klrIais close to the diffusion-controlled limit of 1O1O L mol-' s-l, and the concentrations of various species completely justify the assumption that step IIIa is in a rapid preequilibrium with step IIIb rate determining. If kIllbhas a rather large preexponential factor of about 10" L mol-' s-l, the activation energy of this step is about 9 kcal mol-'. The charge separation in the transition state would, if anything, reduce both the activation energy and the preexponential factor. The AH' for dissociation of gaseous N203 is 9.7 kcal mol-]. Although entropy factors would probably favor the transition state for step IV somewhat over that for step IIIb, it is hard to see how step IV could compete even if its activation energy were virtually zero. Although paths I-IV all have the same formal kinetics, we are in the somewhat unusual position of being able to specify with considerable confidence that path 111 is the one by which reaction occurs. This conclusion is in agreement with the mechanism physical organic chemists have generally a p p r ~ v e d . ' ~ VII. Relevance to Composition of Evolved Gases The kinetic data from section VI permit a more quantitative consideration of the mass spectrometric studies reported in section 111. The runs reported in Table I1 were made with gas evolved from 15 cm3 of solution in which the rate constants from section VI indicate the total rate of N,production was 1.2 X mol s-1. If process C was not too rapid to seriously disturb the equilibrium of process B and if process D had not yet become important, the initial concentrations of NO and of NO2 were equal at 3.6 X mol L-I. The rate of escape of NO gas from the solution, ueSc,was of the form
(4) where A is surface area of solution and k,, is the rate constant for transport through that surface if the compositions of surface and of bulk solution are virtually the same. cm s-I for Kaushik and Noyesis showed that k,, = 2.5 X transport of N2through the surface of concentrated sulfuric acid at 25 "C; we shall assume the same value for water. The spherical portion of the flask used in Table I1 had a volume of 100 cm3, and application of eq 8 and 9 from ref 18 indicates the free solution had a surface area of 19 cm2. Then eq 4 predicts that in this system uescwas 1.7 X IO-* mol s-' and the gas i n the stirred (18) Kaushik, S. M.; Noyes, R. M. J . Phys. Chem. 1985, 89. 2027-2031.
Rubin et al. solutions in Table I1 should have had 0.14% of NO in astoundingly good agreement with the experimental observations. The data for the oscillating solutions in Table I1 suggest that pulsed evolution of gas increased the time-average area of the gas-liquid interface by a factor of 2-3, but the area for the 15 cm3 was never more than about 50 cm2. This semiquantitative argument agrees with the observations better than there was any right to expect. It does encourage a confidence that our theoretical development is valid. VIII. Discussion This study was undertaken in anticipation that escape of bubbles of N, would entrain the NO species essential to production of N,. It is now clear that our expectations were valid in principle, but the anticipated chemical feedback is negligible because of the very different time scales for the gas entrainment and for the chemical reaction. In the example of section VII, a molecule of NO would have an average lifetime of only about 0.5 s before it reacted by the sequence IIIa + IIIb. Even if pulsed gas evolution increased the time-average area of the gas-liquid interface to 50 cm2, the average lifetime for evaporation of that same NO molecule would be about 2 min. Even though evaporation would have been faster during the pulses, the steady-state concentration of NO could not have been significantly impacted. Because chemical feedback is negligible, at least for the compositions employed in sections I1 and 111, there would be no need to invoke it in order to model the system. The oscillations could probably be simulated by the same physicochemical principles employed to model formic acid d e h y d r a t i ~ n .The ~ treatments in sections VI and VI1 suggest that the amount of NO escaping could be made comparable to N, by decreasing the amount of (NH4),S04and increasing that of H2S04in the reacting solution. Although such changes could test some features of our quantitative understanding, it is not clear that we could coax oscillations from a system in which NO was a sufficiently major component of the evolved gas that chemical feedback was important. We believe that a more interesting aspect of the present study involves the measurement of critical supersaturation in section IV. The concentration for nucleation of bubbles of N,in water differs by a factor of more than 5 from that for bubbles of CO in concentrated sulfuric acid. Chemical reactions can be used to create supersaturated solutions of many different gases in different solvents. We believe that homogeneous nucleation of phases is a more important phenomenon than gas-evolution oscillations per se, and a subsequent paper will report studies delineating some of the possibilities in this area.
Acknowledgment. This work was supported in part by Grant No. CHE-8405518 from the National Science Foundation. Registry No. NH,N02, 13446-48-5; N,, 7727-37-9
