J. Phys. Chem. 1082, 86,66-70
66
sors has been proposed to account for the atypical behavior of the REMPID fragmentation patterns of the alkyl iodide molecules with increasing laser pulse energy. A key finding of the present study is that the n-propyl and n-butyl cations do not isomerize appreciably (to isopropyl or tert-butyl cations, respectively) within the 5-ns laser puke duration but absorb the 368-nm radiation and photodis-
sociate, whereas the isopropyl and tert-butyl cations are essentially transparent at this wavelength and thereby persist without fragmentation. Acknowledgment. This work has been supported by NSF Grants CHE 78-25187 and CHE 77-11384, hereby acknowledged with thanks.
Klnetics of the Reactions of Methoxy and Ethoxy Radlcals wlth Oxygen D. Outman,'' N. Sanders,? and J. E. Butler Chemkby Divhbn, Nevel Research Laboratory. Washington, D.C. 20375 (Received: September 4, 1981)
Rate constants have been obtained as a function of temperature for the gas-phase reactions of methoxy and ethoxy radicals with oxygen. The alkoxy radicals were produced by the 266-nm photolysis of the corresponding nitrites, and their concentrationswere monitored by using laser-induced fluorescence. The CHBO+ O2reaction was studied from 140 to 355 "C, and the rate constants obtained were used to derive an Arrhenius expression, 6.3 X lo7exp(4.6 kcal/RT) M-' s-l. The C2HS0+ O2reaction was studied at two temperatures, and the rate constants obtained were 4.8 x lo6 M-' s-l (23 "C) and 5.9 x lo6 M-l s-l (80 "C). Upper limits for the rate of the isomerization reaction, CH30 + M CHzOH + M,are calculated, and the possible use of the results of this study in atmospheric smog modeling is discussed.
-
Introduction Alkoxy radicals are important reaction intermediates formed during the gas-phase oxidation of most hydrocarbons. In the early, low-temperature stages of combustion these labile intermediates form largely through the decomposition of peroxidic species:
ROOR' -* RO.
+ R'O.
(1)
Subsequent reactions of these radicals ultimately produce such products as aldehydes, ketones, and alcohol^.^,^ In photochemical smog cycles, alkoxy radicals are produced from the oxidation of nitric oxide by alkylperoxy radicals:
ROz
+ NO
--+
RO.
+ NOz.
(2)
Under atmospheric conditions RO- can react with oxygen
RCH20.
+02
---*
RCHO
+ H02
(3)
isomerize or d e c ~ m p o s e . ~ Although the reactions of alkoxy radicals have been the subject of numerous studies, our present knowledge of the reactivity of these intermediates is still largely based on indirect kinetic measurements. The primary obstacle to performing direct studies has been the lack of a suitably sensitive method for dynamically monitoring these free radicals under well-defined reaction conditions. Recently (1) On sabbatical from the Department of Chemistry, Illinois Institute of Technology, Chicago, IL 60616. (2) NRL/NRC Postdoctoral Research Associate (1979-1981). Present address: E u o n Research and Engineering Co, Linden, NJ 07036. (3) Pollard, R. T. In "Comprehensive Chemical Kinetics";Bamford, C. H., Tipper, C. F. H., Eds.; Elsevier: New York, 1977; Vol. 17, Chapter 2. (4) Bradley, J. N. "Flame and Combustion Phenomena"; Methuen: London, 1969. (5) Pitts, J. N., Jr.; Finlayson, B. J. Angew. Chem., Int. Ed. Engl. 1975, 14. 1 and references therein.
Inoue, Akimoto, and Okuda have observed and analyzed the laser-induced fluorescence (LIF) spectra of three simple alkoxy These studies have now provided the spectroscopic information needed to use LIF as a diagnostic method in future chemical kinetic studies of the reactions of the three radicals, CH30, C2Hs0, and C2H30. The first direct study of an alkoxy radical reaction was reported by Sanders, Butler, Pasternack, and M~Donald.~ The investigation involved the production of CH30 using pulsed UV laser photolysis of C H 3 0 N 0 and the subsequent monitoring of the decay of CH30 by LIF in the presence of different reactant gases. A rate constant for the reaction with NO was obtained,1° as were upper limits on the rate constants of nine other reactions, all at room temperature. We wish to report that this same experimental procedure has now been used with a heated reaction vessel to study the reactions of CH30 and C2H50with oxygen at several temperatures. Prior studies of RO + O2reactions have all been of the simplest of the series, namely CH30 + O2 CHzO + HOz (4) Three recent publications have focused on reaction 4, reporting rate constants at various temperatures."-13 All
-
(6) Inoue, G.; Akimoto, H.; Okuda, M. J. Chem. Phys. 1980,72,1769. (7) Inoue, G.; Akimoto, H. J . Chem. Phys. 1980, 74,425. (8)Inoue, G.; Okudo, M.; Akimoto, H. J . Chem. Phys. 1981,75,2060. (9) Sanders, N.; Butler, J. E.; Paaternack, L. R.; McDonald Chem. Phys. 1980,48, 203. (IO) The room-temperaturevalue for the CH90 + NO rate constant reported in ref 9 is valid only for the 15 i 5 torr of SF, buffer gaa pressure used in the experiments on this reaction. Subsequent work at other pressures confirms that this reaction is in the falloff region at 15 torr. N.D.S. thanks Dr. L. S. Batt of Aberdeen University for pointing out the likelihood that the mechanism of the CHsO + NO reaction under the conditions of the earlier study waa primarily the pressure-dependent recombiantion process. (11) Barker, J. R.; Benson, S. W.; Golden, D. M. Int. J. Chem. Kinet. 1977, 9, 31. (12) Batt, L.; Robinson, G . N. Int. J . Chem. Kinet. 1979, 9, 1045.
This article not subject to U.S. Copyright. Published 1982 by the American Chemical
Society
The Journal of Physical Chemlstty, Vol. 86, No. 1, 1982 07
Reactions of Methoxy and Ethoxy Radicals
used indirect approaches in which rate-constant ratios involving k4 were deduced from measured pressure profiles and stable end-product concentrations on system in which CH30 was produced by a thermal or steady photolysis source. Assumed mechanisms and rate constanta for the reference reaction as well as other participating elementary reactions were used to yield the desired rate constants for reaction 4. All three studies determined k4 near 150 OC, the values ranging from 1.3 X loe to 4.3 X lo6 M-' s-l. Reported values from other indirect methods not specifically designed to derived k4 are reviewed in ref 13.
Experimental Section The experimental facility is nearly identical with that used previously to study CH30 reaction^.^ Briefly, the quadrupled output from a Nd:YAG laser (266 nm, 3 mJ/pulse, 10-ns pulse width, Quanta Ray DCR-1A) is used to photodissociate CH30N0 or C2H60N0in a heatable fluorescence cell. A frequency doubled, flash-lamppumped dye laser (294-323 nm, -1-ps pulse width, Chromatix CMX-4) which provides the probe beam is counterpropagated coaxial to the photolysis beam. Both lasers and the gate of the boxcar averager CpAR Model 162/ 164)were actuated at a 10-Hz rate synchronous with the power line. The delay between the photolysis and probe laser pulses was set by the sum of a fixed delay (or advance) and a continuously swept delay generated by the boxcar. A 3-419 dead time between triggering and fving of the CMX-4 dye laser was accommodated by providing an external delay between the Model 162 timing pulse and the input pulse to the Model 164 gate generating circuit. A typical measured decay required about 1000 s. The near-UV-induced fluorescence from the alkoxy radicals at the center of the cell is collected by a 1:l f/2 telescope, passes color filters (Hoya UV-32 and Schott BG-3 for monitoring CH30 fluorescence and Schott GG375 and Hoya B-390 for monitoring C2H60fluorescence), and is focused onto the cathode of an RCA lP28A-Vl photomultiplier. The excitation wavelengths used to monitor CH30 and C2H60concentration were 3039 f 2 A (assigned6 as A 2A1, u3/ = 2 X 2E,u3/1 = 0) and 3228 f 2 A (assigneda as A X (3-0) in the corresponding C-0 band series), respectively. These wavelengths are among the recorded peaks which we observed in the laser-induced fluorescence excitation spectra of the two radicals. These spectra were in agreement with those identified and assigned by Inoue et a1.6p8 Gases used in each experiment (RONO, 02,N2) were blended before flowing into the fluorescence cell. A constant slow flow of all gases (-0.5 L/min at 40 torr of total pressure) was maintained during experiments to avoid accumulation of reaction products. Pressures were measured with a Baratron Model 170M capacitance manometer. Methyl and ethyl nitrites were prepared from the corresponding alcohols and nitrosylsulfuric acid.' Commercial N2 and O2 (Air Products, 99.998% N2 and 99.6% O2 (oil free)) were used without purification. The heatable reaction cell consists of a 17-cm long, 4-cm 0.d. heated Pyrex tubular section surrounded by heating mantles made of nichrome wire and fibrous alumina/glass ceramic in~u1ation.l~The gas mixture enters at one end of this section and exits at the other. The four 2-cm diameter windows used to paw the photolysis and probe laser
-
-m
e C
3
r X
0
r e
t 100
200
300
t i m e ( m i c r oSecond 8 )
Figure 1. Observed firstorder CH30 concentration decays for the reaction of CH30 0,: (a) 40 torr of N, (b) 1 torr of O2 39 torr of N, (c) 10 torr of 0, 30 torr of N, (d) 20 torr of 0, 20 torr of N2, (e) 30 torr of O2 i10 torr of N, (1) 40 torr of 0,.
+
+
+
+
- -
(13) Cox, R. A.; Dement, R. G.; Kearsey, S. V.; Batt, L.; Patrick, K. G. J . Photochem. 1980, 13, 149. (14) The design of the cell is essentially identical with one in use by Dr. A. R. Ravishankara, Molecular Sciences Group, Engineering Experimental Station, Georgia Institute of Technology, Atlanta, GA, who graciously provided us with the detailed plans for ita construction.
10
20
30
40
10
20
30
40
pressure O 2 (torr)
Figure 2. Plots of the first-order decay constants vs. the 0,pressure used to obtain the bimolecular rate constants for the reaction of CH30 wRh 0,.The uncertainty in the slope is f15% except for 335 OC
(f20%).
light and to observe the LIF are on glass flanges attached two-thirds of the distance down the heated section from the end where the gas mixture is admitted. The temperature along the axis of the heated section can be measured by a thermocouple inside a movable glass tube which can be placed anywhere along the axis of the reaction cell. Because the external heating is not completely uniform in the immediate vicinity of the photolysis and observation windows, small temperature differences exist along the cell axis in this region. These differences are not detectable below 70 "C but grow with increasing temperatures to create an increasing uncertainty in the absolute temperature at the observation point which reaches f10 OC at 350 OC.
Results Sets of experiments were performed to measure the CH30 + O2and C2H60+ O2 rate constants as a function of temperature. At each temperature, concentration decay
68
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
Gutman et al.
TABLE I: Measured Decay Constants and Bimolecular Rate Constants T , "C 140 202 290 335
23 80
1 0 - ~ k *s-',
(o,, torr)
CH,O t 0, Reaction 1.65 (O.O), 2.13 (0.97), 3.0 (lo), 3.8 (20), 5.0 (30), 6.1 (40.4) 1.53 (O.O), 1.45 ( l . O ) , 2.6 (lo), 3.4 (20), 4 . 9 (30), 6.6 ( 4 0 . 5 ) 1.39 (O.O), 1.85 ( l . O ) , 3.6 (lo), 5.0 (20), 7.4 (30), 8.6 (40.5) 2.7 (O.O), 3.0 ( l . O ) , 4.8 (lo), 6.8 (20), 7.1 (30), 10.0 ( 4 0 . 4 ) C,H,O + 0, Reaction 1.9 (O.O), 4.6 ( l o ) , 6 . 2 (20), 9.5 (30), 14.3 (40.4) 2.3 (O.O), 4 . 2 (8), 7.9 (21), 10.9 (30), 12.9 (40.4)
10-6k, M-1 s - l
2.8 3.6 6.4 7.6
4.8
Y
5.9
profiles were recorded with between 0 and 40 torr of O2 present (See Figure 1). The first-order decay constants (kl)obtained from such experiments were plotted vs. O2 pressure, and a second-order rate constant was obtained from the slope of the line drawn through each data set (see Figure 2). All experiments were performed at a total pressure of 40 f 1torr. Nitrogen was used as the added diluent to assure that diffusion losses of the radical from the observation volume would be constant in all experiments. The alkyl nitrite pressure was kept constant at -40 mtorr during each set of experiments. A summary of the experiments performed and the results obtained is given in Table 1. Quenching of the LIF by 0 2 prevented the use of O2 pressures above 40 torr (at this pressure of 02, the fluorescence intensity was reduced by a factor of 40-80 from that observed with 40 torr of N2). On the basis of the integrated fluorescence signal and the measured fluorescence lifetime for CH30(A 2A1),4we can place an upper limit on the quenching rate by O2of 1 X lo6 torr-' s-l (3 X cm3 s-l molecule-') or slightly smaller than the absolute quenching rate reported by Ohbayashi, Akimoto, and Tanaka.15 This quenching by O2 limited measurements to temperatures at which the reaction rate constant was at least 2 X lo6 M-l s-l An upper temperature limit of -340 "C was imposed on the CH30 + O2 experiment by the onset of rapid pyrolysis of CH30N0. A t 380 "C there was no detectable CH30N0 (no LIF which depended on the photolysis process). We did, however, observe the presence of CH30 (significant LIF without photolysis) at 380 "C, indicating that CH,O can be detected in a purely thermal system by LIF. Thus, the further use of LIF to conduct quantitative kinetic studies of low-pressure thermal reactions which produce and consume CH30 may be possible. The observed LIF from C2H50decresed significantly as the temperature was raised above 50 "C and was 10 times weaker at 150 "C than a t room temperature. This precluded measurement of the C2H50+ O2rate constant at temperatures exceeding 80 "C. The magnitude of the effect can be traced neither to pyrolysis of ethyl nitrite nor to the broadening of the absorption spectrum of the ethoxy radical at elevated temperature. Previous studies of alkyl nitrite photolysis have shown that decomposition by @ cleavage of the primary alkoxy products is significant if the photolysis occurs at modest pressures and at wavelengths shorter than 350 nm. These observations have been cited as evidence for a branched photolysis mecha-
I 1.5
I
2.5
2.0
3.0
1000 K/T
Flguro 3. Arrhenkrs plot of the measured alkoxy-oxygen reaction rate 0,) and the previously constants (e = CH30 0,; A = C2H,0 0,(0 = ref 1 2 A = ref 11; 0 = ref 13). reported values for CH,O The filled circle with arrow Is the upper limit from ref 9. Parameters of the fltted line are log A = 7.8 and E , = 2.6 kcal mol-'.
+
+
+
nism involving production of highly excited alkoxy radic a l ~ . It~ is ~ possible that the observed thermal loss of ethoxy LIF signal in our experiment results from increased decomposition of a large fraction of nascent ethoxy radicals with internal energies close to that needed to undergo fragmentation rather than collisional relaxation. The measured rate constants were independent of the amount of alkyl nitrite present and the intensity of the photolysis laser. Because of the poor detection sensitivity caused by O2quenching, it was not possible to test whether the measured second-order rate constants were pressure independent. Other studies of the CH30 + O2 reaction have reported no pressure dependence and have concluded that this reaction involves a direct H-atom transfer.12J3
Discussion Comparison with Other Studies. The measured rate constants for both alkoxy radical reactions are shown in Figure 3 together with other reported values of the CH30 + O2rate constant obtained from experiments which were specifically designed to study this reaction. There have been no prior values reported for the C2H50 + O2reaction. The present work provides the first direct measurement of any RO + O2rate constant and the first measurements for CH30 + O2above 170 "C. We have derived an Arrhenius expression for k4 which is based on the results of this study at high temperatures and an average room-temperature value (8.0X lo6M-' s-l) obtained by Cox et al. from 13 determinations of this rate constant at 25 "C over a wide range of experimental cond i t i o n ~ .It~ is ~
k4 = 6.3
X
lo7 exp(-2.6
kcal/RT) M-ls-l
798.
(A)
This expression is almost identical with one offered by Cox et al., based on a strong weighting of the same room-temperature point and value from virtually all prior studies of this reaction at elevated temperatures. There is confirming evidence for the accuracy of this room-temperature value. In the earlier direct study of reaction 4 by Sanders et al., an upper limit of 1.0 X lo6 M-' s-l was ~ b t a i n e d .While ~ reaction was actually ob~~~~~~~~
(15) Ohbayashi, K.; Akimoto, H.; Tanaka, I. J.Phys. Chem. 1977,81,
3.5
~
~
(16)(a) McMillan, G. R. J. Am. Chem. SOC.1962, 84, 4007. (b) Christie, M. I.; Hetherington, P. M. J. Photochem. 1976/77, 6, 285.
Reactions of
Methoxy and Ethoxy Radicals
The Journal of Physical Chemistry, Vol. 86,No. 7, 7982 69
TABLE 11: Estimates of RO t 0, Rate Constants at 300 K
R
logA"
CH,O C*H,O n-C,H,O i-C,H,O n-C,H,O i-C,H,O
7.8 7.6 7.6 7.3 7.6 7.6 7.3
S-C,H,O
k,C min-'
k,M-'s-' 2.6 1.3 1.3 0.0 1.4 1.1 -0.2
8X 4x 4x 2x 4X 6x 3x
lo5 lo6
4
X
2x 2x
lo6 107 lo6 lo6
1x 2X
lo5 lo6 lo6 107 lo6 lo6
3x 1 x 107
107
From log[A/(M-' s-I)] = 7.3 + log n (obtained from A factor of the CH, t 0, reaction and n = 3 for CH,O. n is the number of equivalent H atoms which can be lost in reaction 3. From EA = 12.63 t 0.34 a€€'~. Numbers obtained from eq A and a comparable expression for the C,H,O reaction ( 4 . 2 x l o 7 exp(-1.3 kcal/RT) M-' s-l) obtained from low-temperature C,H,O + 0, experiments and estimated A factor in Table 11. Thermochemical data to calculate AH"R obtained from ref 29 and 30. Calculated for air at 300 K.
served, it was too slow at room temperature to permit the measurement of an accurate rate constant. Taken as an approximate value of k,, this observed rate constant agrees well with Cox's value. The agreement between the two Arrhenius expressions, both anchored at the same roomtemperature point, indicates that the results of the direct studies taken collectively are in agreement with our observations. RO + O2 Reactions in the Lower Troposphere. The oxidation of organic pollutants in the troposphere proceeds in large part via the formation of alkoxy radicals, reaction 2, and their subsequent loss by reaction 3 (RO + 02), unimolecular decomposition, or i s o m e r i ~ a t i o n . ~ JThe ~-~~ need for accurate rate parameters for alkoxy radial reactions (including the RO O2reaction) in modeling photochemical smog cycles was recently emphasized.22 Bec a w of the present absence of such information, these rate constants are often estimated from thermochemical considerations or adjusted to provide agreement between smog mechanisms and smog-chamber observation^.'^^^^ Estimates of RO + O2rate constants based on thermochemical calculations and existing experimental data have been estimated to be uncertain by a factor of ~ 8 0 . ~ ~ We have recalculated estimates of RO O2 rate constants by using the same procedure followed by Baldwin, Barker, Golden, and Hendrya but with the results of this study as input data. By assuming that the A factors vary only because of a symmetry property, as did these authors, one can use the data from this study to calculate the parameters of a linear relationship between the activation energies and AHRovalues (the standard enthalpies of reaction for reaction 3). This expression can then be used to calculate estimates of the activation energies for a series of RO + O2 reactions. The estimated rate constants and details of the calculation are given in Table 11. The estimates in Table I1 are similar to those presented by Baldwin et al. as case 111 (where a signficant lowering
+
+
.
(17) Carter, W. P. L.; Lloyd, A. C.; Sprung, J. L.; Pitts, J. N. Jr. Znt.
J. Chem. Kinet. 1979,9,45.
(18) Niki, H.; Daby, E. E.; Weinstock, B. Adu. Chem. Ser. 1972,113, 116. (19) Demerjian, K. L.; Kerr, J. A.; Calvert, J. G. Adu. Enuiron. Sci. Technol. 1974, 4, 1. (20) Baldwin, A. C.; Barker, J. R.; Golden, D. M.; Hendry, D. G. J. Phys. Chem. 1977,81, 2483. (21) Graedel, T. E.; Farrow, F. A.; Weber, T. A. Atmoe. Enuiron. 1976, 10, 1095. (22) "Chemical Kinetic Data Needs for Modeling the Lower Troposphere"; Herron, J. T.; Jiue, R. E.; Hodgeson, J. A., Eds.; US. Department of Commerce: Washington, DC, 1979; NBS Spec. h b l . (US'.) No.557.
of the activation barrier with increased exothermicity was assumed) but are about tenfold higher than those of their case I (where the authors wumed a 4 kcal mol-' activation energy for all RO + O2 reactions). The lower estimates from the case I treatment were used by Baldwin et al. in their modeling of the atmospheric reactions of butane and propene.20 Similar lower estimates were used by Carter et al.17 in their modeling of smog-chamber experiments. Since the estimates of the rate constants given in Table I1 for the reactions of propoxy and butoxy radicals with O2are extrapolated from the experimental values obtained for the analogous methoxy and ethoxy reactions and since the thermochemistry of all of the reactions in the C1-C4 series is quite similar, the uncertainty in the estimates cannot be large, probably less than a factor of 3. In the atmosphere, the reactions of C4 alkoxy radicals with O2 have rates comparable to those of other loss processes, particularly i s o m e r i z a t i ~ n .The ~ ~ ~fact ~ ~that ~ the alkoxy reactions with O2 are significantly faster than previously believed will require a readjustment in the preceived importance of these reactions in smog mechanisms and in the estimated magnitude of the rate constants of the other competing alkoxy radical loss processes. Possible Isomerization of CH30. Radford has found that the hydroxymethyl radical is far more reactive with O2than is CH30 and has also observed that at 650 K H 0 2 is rapidly produced during the low-pressure pyrolysis of (CH3)2O2 (a source of CH30) in the presence of 02.25 These results have led to his suggestion that RO + O2 reactions may under certain circumstances proceed first by isomerization, e.g. CH30 CH20H (5) followed by rapid reaction of the hydroxymethyl radical (6) CH2OH 02 CH2O HOz
-
+
+
Batt, Burrows, and Robinson have recently estimated the rate constant for reaction 5, and they have questioned the likelihood that isomerization competes favorably with direct reactions.26 In our studies, the first-order decays of the RO fluorescence recorded in the absence of a second reactant are upper limits to the rate of isomerization of the radical since isomerization would cause a loss of the fluorescing species. Unimolecular falloff curves for the decomposition reaction CH30
M
CH20 + H
(7)
have been calculated by Adams, and they indicate that this reaction is in the second-order region up to 1000 torr at 900 K S n Isomerization has virtually the same activation energy as the decomposition route but is predicted to have a lower A factor.% It is still likely that the isomerization reaction would be in the low-pressure region below 100 torr at all temperatures above 25 "C. Therefore we interpret our upper limits in terms of a second-order isomerization process. At room temperature we have measured CH30 fluorescence decays in the presence of N2 or SF6at pres(23) Carter, W. P. L.; D d , K. R.; Lloyd, A. C.; Winer, A. M.; Pitts, J. N., Jr. Chem. Phys. Lett. 1976,42, 22. (24) Baldwin, A. C.; Golden, D. M. Chem. Phys. Lett. 1978, 60, 108. (25) Radford, H. E. Chem. Phys. Lett. 1980, 71, 195. (26) Butt, L.; Burrows, J. P.; Robinson, G. N. Chem. Phys. Lett. 1981, 78, 467. (27) Adams, G. F. In 'Proceedings of the 15th JANNAF Combustion Meetings"; Newport, RI, Sept 1978; CPIA Publication 297, Feb 1979.
J. Phys. Chem. 1982, 86, 70-73
70
sures from 10 to 100 torr. The observed decay constants in the presence of N2 and SF6did not vary with pressure, which permits us to conclude that the second-order isomerization process must contribute less than 10% to the overall decay process at the highest pressure studied. Since the fluorescence decay constants were typically 2 X 103s-l, the decay constant due to isomerization at 100 torr is less than 200 s-l. Radford has observed CH30 fiist-order decays in a flow reactor experiment conducted at a total pressure of 0.5 torr of He. The measured decay constant, 40 s-l, is interpreted as an upper limit to the isomerization rate at room temperature. If our upper limit of 200 s-l is scaled to the lower pressure of Radford's experiments, we conclude that under his experimental conditions the homogeneous isomerization reaction has an upper limit of 1 s-l. Therefore, the loss of CH30 observed by Radford in the flow reactor experiments was not due to any significant extent to a homogeneous isomerization process. At elevated temperatures, up to 340 "C, our experiments were conducted at various pressures up to 40 torr of Nz
or SF6with the same results observed; the first-order loss of CHBOwithout a second reactant present was again less than 2 X lo3 s-l. This not only indicates no significant isomerization rate at 340 OC (also 20 kcal mol-1).26~28 Acknowledgment. We thank Dr. J. R. McDonald of the Naval Research Laboratory for advice and encouragement throughout the course of this work. N.D.S. was an NRC/NRL Cooperative Research Associate (1979-1981). D.G. was a visiting fellow at NRL (1980-1981) under the IPA program. (28) A h , G. F., US.A r m y Bellietic Research Laboratory, Aberdeen Proving Ground, Aberdeen, h4D 21005, private communication. (29) Batt, L.; McCuUoch, R. D.;Milne, R. T. Int. J.Chem. Kinet. 1975, SI, 441. (30) Howard, C. J. J. Am. Chem. SOC.1980,102,6937.
Thermodynamlc Processes, Tlme Scales, and Entropy Productiont Victor Falrgn,' Michael D. Hatiee, and John Ross Depertment of Chemistry, Stanford University, Stanford, Californle 94305 (Received: September 8, 1981)
We analyze time-dependent processes in thermodynamic systems by obtaining the entropy production in terms of the relaxation times of these processes. The various physically possible limits of these times and their ratios lead to a classification into reversible, both quasistatic and otherwise, and irreversible processes. In one of these limits, it is possible for a reversible process not to be quasistatic, but this limit is physically not interesting. For the case of heat conduction, that limit requires infinite thermal conductivity, a m, such that the flow of heat is not zero as T Te,. As an application, we compare the efficiency and power output of a Carnot cycle defined with nonquasistatic reversible branches and that of an irreversible Carnot cycle.
-
-
I. Introduction Thermodynamics establishes a clear-cut division between reversible and irreversible processes. In a reversible process, the total change of entropy of the system and its surroundings is zero, and in an irreversible process, the total entropy increases. As a consequence we have that in a reversible process a system proceeds along a continuous succession of equilibrium states. During such processes, the intensive variables (temperature, pressure, chemical potentials) are continuous across the boundary of the system, from the system to the surroundings. If a reversible process proceeds from an initial to a f i i state, and is then followed by a reversible process returning the system from that final state to the initial state, then no net change has occurred in the system or the surroundings. Any process which varies from any of these conditions is termed irreversible. A reversible process is an idealization in that it is a limiting case of a real process which is in general irreversible. Processes in real systems have associated time This work wm supported in part by the National Science Foundation and the Air Force Office of Scientific Research. * Departmento de Fisica Fundamental, UNED, Ciudad Universitaria, Madrid-3 (Spain). A Fellowship from the U.S.-Spanish Committee for Scientific and Technological Cooperation is gratefully acknowledged.
scales: the characteristic time of the process itself and the relaxation times of the components of the system and its surroundings. Consider the conduction of heat from the surroundings to a system by linear heat conduction dQ/dt = a(T,, - T ) (1.1) where dQ/dt is the flow of heat per unit time, a is the thermal conduction coefficent, T,, is the temperature of the surroundings, and Tis the temperature of the system. For this process we have a time scale for the heat flow, which is determined by the properties of the thermally conducting medium, and internal relaxation times of the system and surroundings. The flow of heat becomes reversible in the limit T Tex. At finite a,we then have dQ/dt 0, or, the process occurs through a succession of infinitesimally separated equilibrium states. In this limit, the reversible process is quasistatic; that is, it proceeds infinitely slowly.' Any process of thermal conduction with T # T,, is irreversible. The extension of this analysis to thermal engines implies that reversible cyclic processes take an infinitely long time and hence cannot generate power. For finite thermal
-
+
(1) J. Kestin, 'A Course in Thermodynamics",Blaisdel, Waltham, Mess., 1966, W. J. Moore, 'Physical Chemistry",Prentice-Hall, Englewood Cliffs, N.J.,1965; V. Fried, H. F. Hameka, and U. Blukis, "Physical Chemistry",Macmillan, New York, 1977.
0 1982 American Chemical Society
