J. Phys. Chem. 1985,89, 2027-2031
2027
Gas Evolution Oscillators. 5. Parameters Describing Escape of Molecules and of Bubbles from Solution' S. M. Kaushik and Richard M. Noyes* Department of Chemistry, University of Oregon, Eugene, Oregon 97403 (Received: June 1 , 1984; In Final Form: January 23, 1985)
The quantitative modeling of a gas evolution oscillator requires an understanding of procedures by which dissolved gas escapes a solution either as molecules or in bubbles. A simple method has been developed to measure the rate at which molecules escape from the surface of a stirred solution. That rate is a function of stirring rate, but the data can be extrapolated to determine the rate of equilibration between the gas and a surface maintained at the same composition as the bulk solution. Such measurements indicate that at 25 'C only about one of 2 X lo*gas molecules of N2or of CO will dissolve upon striking a surface of concentrated sulfuric acid. Escape of bubbles can be modeled by use d data from previous hydrodynamic studies. If the critical concentration for homogeneous nucleation has been measured, the modeling of this process is virtually unaffected even by very large variations in the values assigned the parameters in the Volmer equation. Further experimental and computational work will be needed before it will be possible to make a truly quantitative test of our explanation of gas evolution oscillators, but such a test should be possible without the use of any disposable parameters.
Introduction If a chemical reaction in solution produces molecules of a volatile gas, and if the system is stirred only lightly, the escape of gas may take place in repeated bursts separated by several seconds. Although several reactions can generate periodic evolution of gas? the best characterized system is the dehydration of formic acid by concentrated sulfuric acid first reported by Morgan3 almost 70 years ago. The reaction was studied further by Showalter and Noyes4 and by Bowers and Rawji,' and both groups proposed explanations which are no longer viable. Smith, Noyes, and Bowed subsequently concluded on the basis of several different observations that the periodic bursts were the result of a spontaneous homogeneous nucleation of bubbles which occurred only when the solution became supersaturated to about 80 times the equilibrium concentration a t 1 atm. Smith and Noyes' reproduced the qualitative behavior with a computational model which assigned plausible values to a few unknown transport and nucleation parameters. Noyesg then examined the stability of a steady-state distribution of bubble sizes and showed that the oscillatory instability arose because growth of bubbles in solution generated a negative feedback on the nucleation of further bubbles. All presently known purely chemical oscillations are generated by complicated mechanisms involving autocatalysis. Although model computations for such systems exhibit encouraging semiquantitative comparison with experimental observations, present technology is incapable of measuring many of the dynamic parameters necessary for a precise comparison. In contrast to these complex systems, the Morgan' reaction involves trivially simple chemical kinetics, and quantitative modeling should be possible on the basis of a few dynamic parameters associated with the creation of bubble nuclei and with the transport of molecules and bubbles from solution to gas phase. In the present paper, we report some new measurements and calculations which permit improved estimates of these essential parameters. (1) No. 63 in the series "Chemical Oscillations and Instabilities". No. 62 is Bowers, P. G.; Noyes, R. M. 'Oscillations and Traveling Waves in Chemical Systems", Field, R. J.; Burger, M., Ed.;Wiley: New York,1985; pp 473-492. (2) Bowers, P. G.; Noycs, R. M. J. Am. Chem. Soc. 1983,105,2572-2574. (3) Morgan, J. S . J. Chem. Soc., Trans. 1916, 109, 274-283. (4) Showalter, K.; Noyes, R. M. J. Am. Chem. Soc. 1978,100,1042-1049. ( 5 ) Bowers, P. G.; Rawji, G. J. Phys. Chem. 1977,81, 1549-1551. ( 6 ) Smith, K. W.; Noyes, R. M.; Bowers, P. G. J. Phys. Chem. 1983,87, 15 14-1519. (7) Smith, K. W.; Noyes, R. M. J. Phys. Chem. 1983, 87, 1520-1524. (8) Noyes, R. M. J. Phys. Chem. 1984,88, 2827-2833.
Transport of Molecules Models of Molecular Transport. Let cbulk = n / V be the concentration from n moles of a volatile solute in volume V of solution in a closed system which also contains a gaseous phase. If the solution is stirred sufficiently that there are no macroscopic gradients in the bulk below the surface, and if C, is the concentration that will remain when equilibrium has been attained, decay toward equilibrium will follow Here ks (and any other rate constant designated by a single subscript) is a simple first-order constant having dimensions s-l. If A is the surface area of the solution, and if there are no bubbles, the net flux @ex of solute molecules escaping from the bulk solution to the gas phase is given by Here k,, (and any other rate constant designated by a double subscript) has dimensions cm s-l. It is k,, which is evaluated in any experimental study of transport of solute molecules to or from a stirred solution of known bulk concentration. This transport of molecules across an interface between two phases is important to many processes in chemical engineering, and three models for estimating the magnitude of the quantity we call k , are summarized by Sherwood, Pigford, and Wilke: who designated as k, an almost identical quantity.I0 The stagnant film model of Nernst" assumes that there is no mass flow at the interface and that transport involves diffusion through a film of thickness 6 whose magnitude cannot be measured directly. The penetration model of Higbiel* assumes that fluid in the interface is exchanged into the bulk after a time t which is also inaccessible (9) S h e r w d , T. K.; Pigford, R. L.; Wilke, C. R. 'Mass Transfer"; McGraw-Hill: New York, 1975; pp 150-158. (10) The value of C. in our procedure is actually a function of the relative volumes of gas and of solution. A reviewer has objected that it should be replaced by C,,, the concentration in equilibrium with gas at the pressure existing at time 1. Our experimental method with a constant total volume requires that the system be defined as we have done. If the volume of gas were indefinitely large, our C. could indeed be replaced by C=,. In our experiments, the volumes of liquid and of gas were approximately equal. Previous measurement# in sulfuric acid indicated a concentration of about 9 X IO4 M CO in equilibrium with 1 atm (0.041 M) at 25 OC. Then in our experiments Cbuk - C, was about 2% smaller than Cbuk- C,, and our k,, was the same factor greater than the quantity designated k, in the engineering literature. The difference is less than the probable uncertainty in our measurements. (11) Nernst, W. 2.Phys. Chem. 1904, 47, 52-55. (12) Higbie, R. Trans. AIChE 1935, 31, 365-389.
0022-3654/85/2089-2027$01.50/00 1985 American Chemical Society
Kaushik and Noyes
2028 The Journal of Physical Chemistry, Vol. 89, No. 10, 1985
to direct measurement. This penetration model was amplified by the surface-renewal theory of DanckwertsI3 which seems to make the value of k,, a function of stirring rate which must be evaluated empirically. Before we were aware of this existing literature, we had developed an alternative model which resembles the surface-renewal model but which differs in ways which seem to be useful for the problem considered here. Let us postulate the existence of a surface layer of unspecified thickness. If the solution and the gas are not in equilibrium with each other, the average concentration in the surface layer will differ from that in the bulk solution. Within one or two molecular diameters of the phase boundary, the concentration will approximate equilibrium with the gas, and in the interior of the surface layer the concentration will become significantly different from that in the bulk solution. Let CSud be the average concentration in the surface layer. The flux a,, of transport moving the system toward equilibrium will be proportional to Csurf- C,, and we obtain at1
= AktACsurf - C - )
(3)
In this equation, k,, is a rate constant having dimensions cm s-l; it has been used and must apply both to evaporation from the surface of the bulk solution and also to the growth or shrinkage of any bubbles in the solution. in eq 2 must The experimentally observed flux defined as be the same as 3trin eq 3. If the solution could be stirred so efficiently that the concentration was uniform everywhere including the surface layer, k,, would have to be identical with k,,. Therefore, k,, can be estimated by extrapolating measurements of k,, to large stirring rates. Once k,, has been estimated, the same value must be applicable to any other system for which , C can be defined. To the extent that cb,,,k and CsUrf are not exactly equal, , 3 in eq 4 represents the net flux by which mixing of the solution physically transports solute molecules between the bulk and the surface. amx
= Ak"Cbulk
- Csurf)
(4)
Equations 2-4 define the quantities a,,, (P, and 3mx representating fluxes between bulk and gas, between surface and gas, and between bulk and surface, respectively. Because the number of solute molcecules in the surface is always much smaller than the number in either bulk solution or in gas phase, the surface behaves like a transient intermediate in a two-step consecutive p r o ~ e s s , and ' ~ we can say that @ex = 3,,= ,PC is a good approximation a t all times. If the expressions for these fluxes are set equal and rearranged, one obtains This equation is similar to the familiar relation that in an electrical circuit without capacitance the total resistance is equal to the sum of resistances in series. Equation 5 rearranges easily to
The quantities Cbulk,C,, and k,, are subject to direct experimental measurement, and k,, can be estimated by extrapolation of the data to mixing rates so rapid that C,, has become virtually equal to cbulk. At more moderate rates of mixing, k,, will be less than ktr. In such a situation, k , can be calculated by eq 6 and Cbulk - Cwrfcan then be calculated by eq 4. If the concentration were known as a function of distance from the phase boundary, this value of c , , l k - Csurfwould then permit calculation of the thickness of the surface layer such that all of these equations are internally consistent. However, that thickness is not accessible from information presently available to us and is undoubtedly a (13) Danckwerts, P. V. Ind. Eng. Chem. 1951, 43, 1460-1467. (14) Noyes, R. M. "Techniques of Chemistry", Lewis, E. W., Ed.; Wiley: New York, 1974; Vol. 6, part 1 , pp 489-538.
function of stirring rates. Its value is irrelevant to the applications for which this study was undertaken. Experimental Procedures. A reaction flask and a reference flask of equal volumes were immersed in the same thermostat, and the pressure difference between them could be measured as a function of time with a Celesco P7D variable reluctance differential pressure transducer driven by a CD-25 transducer indicator. The output of the CD-25 was connected to a chart recorder. A known volume of 96% aqueous sulfuric acid was added to the reaction flask and stirred by a conventional teflon-coated magnet driven by a rotating magnetic field. The solution was first approximately saturated with Nzor with CO under rapid stirring. No care was taken to ensure that saturation was complete because the method measuring k, was independent of the precise initial concentration of the solution. The stirring was then adjusted to the desired rate by use of a Cole-Palmer Model GP-8204-00 digital tachometer, and both flasks were quickly evacuated to the same pressure and closed off. The difference in pressure between the flasks was then recorded as a function of time. For this arrangement, Cbulk - C, was necessarily proportional to P, - P where P is the pressure above the solution. Then the method of Guggenheim15 permitted k, to be evaluated by means of eq 7 without any information about P,. In this equation, T
k, = -
In
(Cbulk
dt
-
c-1 -_ -
In
(pt+r
- pt)
dt
(7)
is a constant increment of time chosen to be roughly half the duration of the measurements for the system being studied. In order to convert the measured k, to ke, by means of eq 1 and 2, it was necessary to have values of A and V. If the system consists of a spherical flask of known radius R to which the known volume V of solution has been added, we obtain aR3 V = J s ~ R 3sin3 0' do' = -[2(1 3
- cos 0) - cos 0 sin2 01
In these equations 0 is the angle of deviation from the vertical of a line drawn from the center of the flask to the perphery of the surface of the solution. The angle is defined so that 0 = 0 when the flask is empty and 0 = 180° when the flask is full. For the known volume of solution, 0 can be evaluated by Newton's method and A can be calculated by A = a R 2 sin2 0
(9)
Experimental Results. All experiments were conducted either at 25 or 40 OC. Five different pairs of experiments compared rates of escape of N2 and of CO under identical conditions for each pair. Those paired experiments covered a range of stirring rates, temperatures, and volumes of sulfuric acid. In no pair did the values of k, for Nzand for CO differ by more than 9%; and the differences showed no pattern. Runs measuring rates with the same gas under conditions as nearly identical as possible exhibited comparable scatter. For reasons of safety, the remaining experiments were carried out with N2instead of with the isoelectronic C O which is the actual product of the Morgan3 reaction. When we were developing the method, each series of measurements consisted of less than ten runs carried out in a l-L flask without use of a tachometer. Runs with 700 and with 300 mL of solvent (which had equal surface areas) did indicate that at each temperature values of k, at large stirring rates were in the anticipated ratio of 3:7. Estimated values of k,, agreed within about 10%with those reported below for quite different conditions. The more extensive series shown in Figure 1 were obtained with 100 mL of solvent in a 200-mL flask, and stirring rates were measured with the tachometer. Just as predicted by the above analysis, increased stirring rate causes k, to rise to a plateau value which is effectively constant over a range of stirring rates. At ( 1 5 ) Guggenheim, E. A. Philos. Mag. 1926, 2, 538-543.
The Journal of Physical Chemistry, Vol. 89, No. 10, 1985 2029
Gas Evolution Oscillators
sulfuric acid. There is an extensive literature about exchange of energy when a molecule strikes a surface. There have also been many measurements of ammodation coefficients for sticking when gas molecules impinge on a solid surface or on a liquid composed of the same molecules as the gas. However, our very cursory literature search has not uncovered any previous efforts to calculate accomodation coefficients for solution of gaseous molecules in hydrogen-bonded (or other) solvents.
i
4040'C
Transport of Bubbles In a still solution subject to a gravitational field g in cm s - ~ , a bubble of radius r in cm will rise at a velocity U,in cm s-l which rapidly relaxes to a constant value. The situation has been discussed by Levich.17 For small bubbles of the type encountered here, the velocity is given well by
u, = gP9 -
(1 1) 37 In this equation, p is the density of the solution of g cm-3 and 7 is the viscosity in P or g cm-' s-l. Let 2 be the average distance to the surface from a random site in the solution. Then k,, the rate constant for escape of bubbles of radius r, is given by
'"I 1 0
50
100
200 rpm
150
250
300
350
Figure 1. Effect of stirring on rate of escape of N2from 100 mL of 96% H2S04in a 200-mL flask. Abscissa is rate of rotation of stirrer bar in revolutions per minute. Ordinate is k,, = - ( V / A ) d In (Chi, - C,)/dt as determined by eq 7. Open circles are at 25 "C,and filled circles are at 40 "C. Dashed lines indicate estimated values of k,, based on extrapolation of measurements before a significant cone of indentation began to form in the surface of the liquid.
still greater stirring rates, a cone of indentation formed in the center of the surface, and the measured k,, increased again. The plateaus in Figure 1 can be defined with enough confidence to estimate that k, is 2.6 X cm s-l at 25 O C and 3.5 X cm s-l at 40 O C . The reproducibility of separate runs in Figure 1 gives us reason to believe these values of k, are reliable to within about 5%, which is quite sufficient for the modeling tests we wish to undertake. It should be noted that previous model calculation^^-^ assumed k, at 40 O C to be 0.1 cm s-l or almost 30 times as great as the value estimated from Figure 1. The probable accuracy of these k,, values does not justify concern about the 2% correction appropriate before comparison with k, values from the engineering literature.1° Our results also seem to be in the range of those reported previously. Thus, Hutchinson and Sherwood16 used a method somewhat similar to ours to obtain values equivalent to our k , of about cm s-l for several small molecules in water at 25 O C . Their data also imply that k, should approach a limiting value at indefinitely rapid stirring. Their extrapolation is equivalent to k,, = 1.3 X cm s-l for several gases including nitrogen, agreeing within a factor of two with our value in sulfuric acid. This evaluation of k,, permits us to estimate the accommodation coefficient for solution, y, or the probability a gas molecule will be dissolved when it strikes the surface of the sulfuric acid. At equilibrium, the rate at which molecules leave the solution is equal to the rate at which they dissolve, and conventional kinetic theory of gases leads to eq 10 where M is the molecular weight of 28 y = k,,(2T M RT ) /2C, / P,
(10)
g mol-'. Solubility measurements by Smith et a1.6 indicate that at equilibrium at 25 OC C/P= lo4 mol cm-3 atm-' = 9.9 X mol cm-I dyn-I. Then y = 5.4 X
We are surprised that our calculations indicate only about one collision in 200 million leads to solution of a gas molecule in the (16) Hutchinson, M. H.; S h e r w d , T. 836-840.
K. Ind.
Eng. Chem. 1937, 29,
k, = U , / i (12) This rate constant is the same as that assigned the same symbol in a previous development.8 For a solution in a spherical flask of radius R as considered in eq 8 and 9, we obtain
z = ~ ~ 8 1 r R 4 ( c8'0 -s cos 8) sin3 8' de' =
v o
?rR4sin4 8 - R COS 8 (13) 4v The above discussion concerned a still solution. If the system is mixed by stirring, some regions will be pushed to the surface more rapidly than otherwise, and others will be dragged down. However, the rise of bubbles in the gravitational field should provide a unidirectional drift superimposed on the random effects of stirring, and k, should be independent of stirring rate to a good approximation. Our previous approach to modeling these systems7v8assumed k, was independent of bubble size. That assumption simplified the mathematical modeling, but the theoretical treatment present above indicates that k, should be proportional to ?. We have now made a few qualitative observations which confirm that rates of bubble escape are a strong function of size and are of the magnitude anticipated for the known density and viscosity of sulfuric acid. We decided it would require a serious experimental research effort to measure k, values more accurately than they could be calculated from the definitive treatment of Levich.17 Our calculations used g = 980 cm s - ~ ,p = 1.8 g ~ m - ~ , and 7 = 0.14 P, leading to U,/(cm s-l) = 2.7 X lo3 (r/cm)2. The revision to make k, a function of bubble size will seriously impact the quantitative modeling of this system, and some of the implications are mentioned briefly below.
Nucleation of Bubbles Let J be the rate of nucleation of bubbles in cm-3 s-l. The theory as developed by Volmer18predicts that J should vary with the concentration of dissolved molecules according to J = CY exp[-B/(C - C,)2] (14) As C increases from a small value, J remains vanishingly small until it increases almost as a discontinuous step function when a critical concentration is attained. Smith, Noyes, and Bowers6 reported experimental observations which seemed to require that this critical concentration was about 7 X 10" mol cmF3for carbon (17) Levich, V. G. "Physicochemical Hydrodynamics"; Prentice-Hall: E n g l e w d Cliffs, NJ, 1972; pp 432-452. (18) Volmer, M. 'Kinetik der Phasenbildung"; Steinkopf Leipzig, 1939.
2030 The Journal of Physical Chemistry, Vol. 89, No. 10, 1985 TABLE I: Revised Estimates of Kev Parameters at 40 OC previous revised parameter assignment“ value 0.1 0.0035 k,,/cm s-I k,/s-’ 0.7 4.1 X 103?/t cm 4 x 10-9 3104 B/moI2 cm4 “References 7 and 8
monoxide in 96% aqueous sulfuric acid a t 40 OC when the concentration in equilibrium with gas at 1 atm was about 9 X mol In a previous publication,8 we argued that this critical concentration would correspond to the concentration at which dJ/dC was a maximum. At that concentration, p = l.5(Cmlt- C,)’ = 7.1 X l@ molz cm+. Further reflection reveals that this argument is untenable. It leads to the conclusion that the critical concentration is not attained until J = e-l a = 0.2230~where a is the maximum possible nucleation rate a t indefinitely high concentration of dissolved gas. In any real experimental system, we could not obtain an almost discontinuous onset of nucleation at a critical concentration unless J a t that onset was orders of magnitude smaller than a. An alternative argument is to use
In this equation, W, is the reversible work necessary to form a bubble of radius r in equilibrium with dissolved gas at concentration C,P,is the pressure inside that bubble, and u is the surface tension. If we again use C / P = 9.9 X mol cm-l dyn-l and u = 60 dyn cm-’, we obtain fl = 8.2 X mol2 cmd. This factor of lo4 increase from the previous estimate for 0 makes a tremendous difference in the sensitivity of nucleation rate to change in concentration. Let p be the change in log J when C - C, changes by 0.1%. We then obtain P =
2p
X
(C- C,)’ and C- C, = 7 X
0.00043
If 0 = 8.2 X p = 14.9. Then at this concentration J will increase by a factor of lOI5 when C increases by 0.1%. Such a change can fairly be called a discontinuous transition! This analysis suggests that behavior of the system can be modeled very satisfactorily without much concern about specific values of a and 6. Let fl be assigned a value greater than lo6 mol2 cmd and let a be chosen so that J = 1000 cm-3 s-l when calculations should then be C - C, = 7 X mol ~ m - ~Model . almost completely insensitive to the specific values of a and 8. This conclusion is supported by our previous7 failure to observe any difference between the use of eq 14 or of a discontinuous step function.
Discussion Table I presents the values we now propose for some essential parameters and compares them with the preliminary estimates used in our previous7~* efforts to model the Morgan3 reaction. The revisions will certainly influence those modeling efforts.
The reduced value of k,, will mean that most of the product gas will escape the solution in bubbles rather than as individual molecules and that bubbles will grow more slowly than previously assumed with more resulting delay in the feedback which influences the concentration of molecules. The strong dependence of k, on size will keep almost all of the bubbles in solution for nearly the same time after nucleation and ensure that no large bubbles remain much longer than that average time. The revision of /3 will make the onset of nucleation even more nearly discontinuous than before. All of these changes in parameter values will have the effect of making the steady state more unstable and susceptible to oscillation. They should also facilitate modeling the system by the
Kaushik and Noyes single variable differential difference equation method suggested near the end of ref 7. We believe that the present paper has evaluated the parameters associated with transport and nucleation with sufficient accuracy for use in the quantitative comparison of model computations with experimentally observed oscillations. Before such computations can be undertaken, we must make careful measurements of the period and amplitude of gas pulses of a Morgan reaction carried out under well-defined conditions of stirring and of gas leakage from the flask. Such measurements are presently being undertaken. We must also make several revisions of the computational program used previously.’ Among the changes, we shall have to include escape of molecules from the surface of the solution with rate constant k,, as well as change of bubble size with rate constant k,,, and we must note that escape of gas from the space above the solution by means of flow through a capillary involves a relaxation time comparable to the period of an oscillation. Until the program has been thus revised, we can not make quantitative comparisons of our recorder traces with our computations. Once the experimental measurements and computational changes have been effected, the argument developed here predicts that no additional disposable parameters would be available to account for any lack of agreement between computation and experiment! In the meantime and before the additional studies have been completed, our measurements of transport of molecules through surfaces seem to offer sufficient novelty to justify the interim publication.
Acknowledgment. This study was supported in part by a Grant from the National Science Foundation. The use of the digital tachometer to measure stirring rates was suggested by Dr. Ronald Rich. We are grateful for careful critical comments by an anonymous reviewer of a previous manuscript. Those comments contributed to further measurements and a strengthened presentation of our conclusions.
Symbols Used area of surface of solution, cm2 bulk concentration of solution, mol cm-3 critical concentration for homogeneous nucleation, mol concentration in thin layer defined to be surface, mol cm-3 concentration at infinite time in closed system or in equilibrium with bubble of infinite radius, mol cm-) acceleration of gravity, cm s - ~ rate of formation of bubble nuclei, cm-3 s-l rate constant in engineering literature defined to be almost the same as k,, cm s-I rate constant for flux of experimentally observed exchange between bulk solution and gas phase, cm s-] rate constant for mixing solution increment between bulk solution and surface layer, cm s-l rate constant for escape of bubble of radius r, s-I rate constant for escape of molecule from bulk solution, s-l rate constant for transport of molecule from surface to gas phase, cm s-l number of moles of solute, mol pressure of gas above solution at time t , dyn cm-2 pressure in bubble of radius r, dyn cm-2 pressure at infinite time in closed system or in bubble of infinite radius, dyn c n r 2 radius of bubble, cm radius of spherical flask, cm rate of rise of bubble of radius r, cm s-I volume of solution, cm3 work to produce nucleus of radius r, dyn cm average distance of point in solution below surface, cm limiting rate of formation of bubble nuclei at indefinitely large concentration of molecules, cm+ s-I parameter in nucleation rate eq 14, mol2 cm4 probability a molecule striking surface will be dissolved viscosity, g cm-I s-l angle of deviation from vertical of line from center of flask to periphery of surface change in log J when C - C, changes by 0.1%
J. Phys. Chem. 1985,89, 2031-2036 P Q T
density of solution, g surface tension, dyn cm-I time increment in evaluation of k, by Guggenheim method, S
@ex
@nu
atr
2031
flux of molecules exchanging between bulk solution and surface of solution, mol s-I flux of molecules exchanging between surface and gas, mol S-1
flux of solute molecules exchanging between bulk solution and gas phase, mol s-I
Registry No. N2, 7727-37-9; CO, 630-08-0; H,SO,, 7664-93-9.
Vibratlonai Energy Distribution of CDP('Al) from Ketene-d, Photolysis upon Reaction with Cyclobutane. A Chemically Actlvated Methylcyclobutane Study J. W. Simons* and W. C. Mabone Chemistry Department, New Mexico State University, Las Cruces, New Mexico 88003 (Received: October 1, 1984)
The results of a study of chemically activated methylcyclobutaneand methylcy~lobutaned~ from the 337-, 334-, and 313-nm photolyses of ketene or ketene-d2in the presence of cyclobutane, tetramethylsilane, and oxygen are presented. The collisional deactivation of the chemically activated molecules was found to occur in steps of 6 f 2 kcal/mol. A critical examination of the uncertainties in collisional deactivation stepsize determinations in chemical activation systems is given. The vibrational energy distributions of the CH2(IAI)and CD2('A1) at the time of reaction with cyclobutane are determined and discussed. The distributions were found to broaden giving increasing average methylene energies with increasing photon energies and with deuterium substitution on the CH2. An interesting quantum statistical isotope effect on the width of these distributions in going from the 337- to 313-nm photolysis systems is observed and explained in terms of the CH2('AI) and CD2('AI)vibrational frequency modeb. This is an energy partitioning isotope effect on CH2C0 vs. CD2C0 photodissociations. A statistical energy partitioning model for CHzCO and CDzCO photodissociation was found to give generally narrower methylene vibrational energy distributions and lower average energies than observed.
Introduction The vibrational energy distributions in CH2('A1) from ketene and diazomethane photodecomposition have been the subject of several recent chemical activation studies.'" It has been shown that the average energy and width of the energy distribution increases with the excess energy, above the decomposition threshold, deposited in the CH2('A1) precursor. This variation in excess energy has been accomphhed via variations in the photolysis wavelength and the CH2('Al) precursor. The details of the distributions and their relationship to the CH2(lAI)energy distribution a t the instant of formation have not as yet been determined. The effect of isotope substitution on the CH2('AI) energy distributions would be of interest. In the present work, the results of a study of CD2(IA1) energy distributions from ketene-d2 photolyses at 337,334, and 313 nm, in the presence of cyclobutane, to give chemically activated methylcyclobutane-d2, are reported. New results on CH2('AI) energy distributions from ketene photolyses are also reported, which lead to some revisions in the quantitative aspects of our earlier 337-nm results. A critical analysis of the methods of determining collisional deactivation stepsizes and energy distributions in these systems is given.
Experimental Section Materials. Cyclobutane was prepared from 1,4dibromobutane by the method of Whitesides and Gutowski.6 The cyclobutane (1) W. S.Kolln, M. Johnson, D. E. Peebles, and J. W. Simons, Chem. Phys. Lerr., 65, 85 (1979). (2) T. H. Richardson and J. W. Simons, J . Am. Chem. SOC.,100, 1062 (1978). (3) T. H. Richardson and J. W. Simons,Chem. Phys. Lert., 41, 168 (1 976). (4) R. J. Wolf and W. L. Hase, J. Phys. Chem., 82, 1850 (1978). ( 5 ) I. SzilSgyi, L. Zatotai, T.Btrccs, and F. MBrta, J. Phys. Chem., 87, 3694 (1983). (6) G. M. Whitesides and F. D. Gutowski, J. Org. Chem., 41, 2882 (1976).
0022-3654/85/2089-203 1$01.50/0
was purified by low-temperature fractionation and gas chromatographic separation on the analytical column to be described. Ketene and ketene-d2 were prepared by the pyrolysis of acetone and acetone-d6 on a hot wire.' The ketene fraction collected at -195 O C was purified by gas chromatography on a 20-ft, l/&. column packed with 60/100 mesh porapak Q operated at -15 O C . Mass spectrometry gave a ketene-d2 isotopic purity of -95% D. N M R grade tetramethylsilane was tested for purity on the analytical gas chromatography column. Purified oxygen was obtained by condensing commerical grade tank oxygen in a liquid nitrogen trap and taking the middle fraction as this condensed oxygen vaporized. Experimental Procedure. Mixtures of ketene:cyclobutane: tetramethy1silane:oxygen in the approximate ratios of 1:8:2:2 were prepared on a high vacuum system. These mixtures were loaded into conical shaped reactors constructed from Pyrex erlenmeyer flasks with Pyrex windows sealed on the small end. All stopcocks in contact with the reaction mixtures were of the greaseless, teflon plug, O-ring type. Total pressures were varied by varying reactor volumes and amounts of reactants. The 337-nm radiation source was the unfocused output of a Molectron UV-12 nitrogen laser. The source of the 334- and 313-nm radiation was a 500-WOsram point source mercury lamp in an Oriel Optics housing with a quartz lens system followed by a Schott glass UG-11 filter which isolated a band between 250 and 400 nm with -80% transmission between 300 and 350 nm. This filter was followed by a Bausch and Lomb 0.25-m high-intensity monochromator. This system gave a 6-nm fwhm band pass at 334 and a t 313 nm. Photolysis times varied in all cases from -2 h in the smallest reactors to -24 h in the largest reactors. Analysis. Reaction product mixture were analyzed on an Aerograph A-90-P3 gas chromatography unit equipped with a two-secton 'J4-in. column. The first section was 20 ft of 25 wt (7) Hurd and Tallyn, J. Am. Chem. SOC.,47, 1427 (1925).
0 1985 American Chemical Society
