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Chemiluminescent reaction of oxygen atoms with dimethyl disulfide and dimethyl sulfide

 

作者: Ubaradka B. Pavanaja,  

 

期刊: Journal of the Chemical Society, Faraday Transactions  (RSC Available online 1994)
卷期: Volume 90, issue 6  

页码: 825-829

 

ISSN:0956-5000

 

年代: 1994

 

DOI:10.1039/FT9949000825

 

出版商: RSC

 

数据来源: RSC

 

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(6), 825-829 Chemiluminescent Reaction of Oxygen Atoms with Dimethyl Disulfide and Dimethyl Sulfide Ubaradka 6. Pavanaja, Hari P. Upadhyaya, Avinash V. Sapre, Kuchimanchi V. S. Rama Rao* and Jai P. Mittal Chemistry Division, Bhabha Atomic Research Centre, Trombay, Bombay400 085,India Broad chemiluminescence spectra in the range 240-460 nm with a sharp peak at 308.5nm are obtained from the reaction between oxygen atoms [O("P)] with dimethyl disulfide (DMDS) and dimethyl sulfide (DMS). The emitting species are identified as OH (A'C') and SO, ("8, 'B). The photon yields are found to be 3.3 x lob6 and 4.4 x for DMDS and DMS, respectively. Computer simulations were carried out to elucidate the reaction mechanism. Reactions of oxygen atoms with various organosulfur com- pounds are of importance in atmospheric and environmental chemistry.' Many reduced sulfur compounds, mainly dimethyl disulfide (DMDS) and dimethyl sulfide (DMS), are released into the atmosphere from oceanic, biogenic (algae, bacteria, plants) and anthropogenic (wood, pulp mills, pet- roleum refineries, sewage treatment plants) source^.^^^ OH radicals and O(3P) are mainly responsible for the atmo-spheric oxidation of the above compounds and contribute to the formation of SO, ,thus increasing the acidity of the atmo- sphere.,~~The present work was undertaken as an extension of our earlier work on the chemiluminescent reaction of O(,P) with CS,.' Reactions of O(,P) with DMDS and DMS have been studied earlier by several workers and negative temperature dependences of the rate constants have been rep~rted.~,~Moreover, chemiluminescence can be used to detect reduced sulfur corn pound^.^^^ SO, chemiluminescence was observed in the reaction of 0, with DMDS" and in the reaction of O(3P) with DMS." The primary reactions of DMDS and DMS with O(,P) are known to be direct addi- tion of an oxygen atom to the reduced sulfur compounds, followed by rapid unimolecular decomposition.' r 0 I*IICH,SSCH, + 0 -+ LCH,SSCH,] +CH3S0 + CH3S; AH = -142 kJ mol-' (la) r o i* CH3SCH, + 0 -+ CH,SCH, +CH,SO + CH,;L " 1 AH = -129 kJ mol-' (lb) Both of these reactions are exothermic with fairly high rate constants.lo The small negative activation energy for these reactions is also consistent with an addition mechanism.' In the present work chemiluminescent emission from the reac- tion of oxygen atom with DMDS and DMS is observed.The emitting species are identified as electronically excited OH radicals and SO, molecules, formed as a result of secondary reactions, mainly that of SO and CH, with oxygen atoms. Mechanisms are proposed for the formation of the emitting species based on the experimental results. The photon yields are estimated for both reactions as described by Fontijn et ~1.'~ Experimental Most of the experiments were performed in a discharge flow tube in the pressure range 1-1.5 Torr. Some experiments were also performed in a beam-gas configuration, the apparatus being described elsewhere.' The diameter of the flow tube used was 34 mm and the distance from discharge cavity to the observation zone was ca.60 cm. The flow tube was pumped by a 20 dm3 s-l rotary vacuum pump. Oxygen atoms were generated in a microwave discharge (Raytheon 100 W, 2450 MHz) cavity. Three gas compositions were used: (1) Pure 0,, (2) Ar-0, (2-3%) mixtures and (3) Ar-N,O (2-2.5%) mixtures. All gases used were of high purity (Indian Oxygen Co., IOLAR grade, >99.99%). DMDS and DMS (Fluka Chemical Research) were distilled under vacuum. Any traces of water were removed by storing the liquids over anhydrous Na,S04 overnight and then subjecting them to several freeze-pumpthaw cycles prior to use. Before carrying out the experiment the entire flow tube was heated to ca.200 "C with a heating coil and was continuously pumped out to remove any traces of moisture in the flow tube. DMDS and DMS were injected directly into the observation zone. The total gas pressure in the observation zone was monitored by a capacitance manometer (Datametrics 1174, Edwards). The reagent inlet pressure was monitored by a strain gauge (Membranovac 1VS Leybold). NO was injected in the inter- action zone for the titration of oxygen atoms. The relative O(3P) concentrations were monitored using the standard NO + 0 reaction by measuring the NO; emission at 525 nm. NO was prepared by adding an FeSO, solution to an acidic KNO, solution, purified using trap-to-trap distillation and was used after it had been passed through a dry ice and acetone slurry trap.Light from the observation zone was col- lected and focused on the slit (0.25 mm) of a stepper motor driven monochromator (Jarrel-Ash model 82- 140,0.3 m, pro- vided with two gratings, one for the 200-400 nm range and another for the 400-800 nm range). The dispersed light was measured by a photomultiplier tube (Philips XP2254B) and an electrometer amplifier (Keithley 61 7). The resolution of the detection system was ca. 0.2 nm. The spectral data acquisi- tion was performed by an IBM-compatible personal com-puter. The photon yields were estimated by comparing them with the standard NO + 0 afterglow as described by Fontijn et aZ.I3 Results and Discussion Spectra Dimethyl Disu&de A strong emission in the near-UV was observed in the reac- tion of DMDS (10 mTorr) with O(3P)[Fig.l(a)]. The emis- sion spectrum extended from 250 to 460 nm, with a vibrationally resolved peak at 308.5 nm. The broad spectrum 826 J 26. "." I 1 III 3.0- h .In C.-2 2.5-2 Y.+2.0- 4-.- InC .-E 1.5- 1.o-Ii ' I ' I' I ' I ' I ' 1.1 r' ' 1 240 260 280 300 320 340 360 380 400 420 A/nm Fig. 1 Emission spectra from the reaction of oxygen atoms gener- ated from Ar-O, (2%) discharge, with (a) DMDS (10 mTorr), (b) DMS (3 mTorr), at a total pressure of 1.2 Torr. Inset: Vibrationally resolved spectrum in the range 305-309 nm. is very similar to that observed by Glinski and Dixon" in the reaction of DMDS with 0, and Tabares12 in the reac- tion of thiophene with oxygen atoms.Both groups attributed the observed emission to electronically excited SO, (3B, 'B). From the similarity of the spectra, it is concluded that the emitter is electronically excited SO,. The SO, spectrum is vibrationally unresolvable in our system, probably due to the high vibrational temperature of the SO, formed in the reac- tion. The emission in the range 306-309 nm shows vibra- tional features, shown in Fig. 1 (inset), which can be attributed to the 0-0 band of the A-X emission from OH (Table l).14 In the discharge of pure O2 and Ar-0, mixtures, production of singlet oxygen [O,('A,)] and small amounts of 0,cannot be ruled out and DMDS is known to give chemi- luminescence with O3,lo hence it is desirable to confirm the reacting species.For this, pure O(3P) as generated by an Ar-N,O discharge', where neither 0, nor singlet oxygen are produced. Under these conditions, the shapes of spectra are similar, confirming that the reaction of O(3P)gives che- miluminescence with DMDS and DMS. To confirm that OH* emission is purely from the reagent and not from trace amounts of moisture in the flow tube or in the argon, a blank spectrum (no reagent, i.e. DMS or DMDS was added) was recorded, which showed no signal at 308.5 nm. Dimethyl Suljide A very similar spectrum was observed in the reaction of DMS (3 mTorr) with 0 atoms generated in 2% 0, in Ar at a total pressure of 1.2 Torr [Fig. l(b)].A vibrationally resolved peak was observed in the range 306-309 nm [Fig. 1 (inset)]. Lee et al." observed SO, chemiluminescence in the reaction of DMS with O(3P),but did not report the spectrum. Wit# very similar arguments it is concluded that the emitters are electronically excited SO, and OH. Pressure Dependence Studies The dependence of chemiluminescence intensity on the DMDS, DMS and O(3P) concentrations was studied by Table 1 0-0 Bandheads of the A-X system of OH* l/nm obs. lit. assignment 306.5 306.4 Rl -306.7 R2 307.8 307.8 Q1308.5 308.9 Q2 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 keeping the concentration of one of the reactants constant and varying the others at argon flow rates of 20-30 Torr dm3 s-'. The SOY emission was measured at two wavelengths, 290 and 330 nm, and the OH* emission was followed at 308.5 nm.The results are summarised in Fig. 2 and 3 at concentra- tions from 0-300 mTorr (DMDS) and 0-12 mTorr (DMS). For lower concentrations of DMDS/DMS the chemilumin- escence intensity grows almost linearly with the DMDS/DMS concentration, but at higher substrate concentration it reach- es a maximum and then decreases. Similarly the O(3P) concentration was varied at constant DMDS and DMS con- centration [Fig, 2 (inset) and 3 (inset)]. A linear dependence on O(3P)concentration at low pressure was obtained, but at high O(3P)concentrations the intensity tended to level off. A similar pressure dependence was observed for Ar-N,O dis-charge, where 0,and singlet oxygen [O,('Ag)] were absent, on addition of DMDS or DMS. However, the work was carried out for Ar-0, (2%) discharge since signals were much better for these mixtures.These results show that the chemilumescence is very sensi- tive to the concentrations of O(3P)and DMDS or DMS. The maximum intensity is seen at a pressure of 3 mTorr for DMS and 16 mTorr for DMDS. The decreases of intensity beyond these pressures are due to complex reactions involving various intermediates. A similar type of behaviour has been I 11 lo nv) c.-C 3 -5 20 Y >. c.-In a-CI C.-I I I I 0.0 0.1 0.2 0.3 DMDSrorr Fig. 2 Chemiluminescence intensity us. DMDS pressure [Ar-O, (2%) at 1.2 Torr] at wavelength (a)290 nm, (b) 330 nm, (c) 308.5 nm.Inset : Chemiluminescence intensity us. relative O(3P) pressure (at DMDS = 10 mTorr and Ar-O, < 10%)at wavelength (a) 290 nm, (b) 330 nm, (c) 308.5 nm. 3 h .g 2 3 f W >.c.-E' c .-C i0 1 I I I 0.000 0.004 0.008 0.012 DMS/Torr Fig. 3 Chemiluminescence intensity us. DMS pressure [Ar-O, (2%) at 1.2 Torr] at wavelength (a)290 nm, (b) 330 nm, (c) 308.5 nm. Inset: Chemiluminescence intensity us. relative O(3P)pressure (at DMS = 3 mTorr and Ar-0, < 10%) at wavelength (a) 290 nm, (b) 330 nm, (c) 308.5 nm. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 reported by Tabares and Ureiia', for the OH* intensity dependence in the reaction of furan with oxygen atoms. To discover whether there was some contribution from the primary reactions to the observed emission, experiments were performed in beam-gas configuration in a molecular beam apparatus.No emission was observed under such conditions, which ruled out the possibility of production of OH* and SO; in the primary processes. CH,SCH, + 0 -+CH,SCH, + OH (i) CH,SSCH, + 0 -+ CH,SSCH, + OH (ii) These reactions are endothermic and hence the production of OH* is energetically unfavorable. The DMDS and DMS pressure dependences show a sharp increase and exponential decrease. Chemiluminescence Photon Yields As we will see later, the oxygen atoms and DMDS or DMS molecules are principally consumed in the fast bimolecular reactions (la) and (lb) with a very small fraction of oxygen atoms participating in the further reactions of the products of these reactions.The chemiluminescence is obtained from the secondary products, SO; and OH*, formed in their electronically excited state. It is of interest to determine the photon yield for total reaction, i.e. the number of chemiluminescence photons, N,, , generated for every DMDS/DMS molecule consumed in the reaction (Nreacted), For equal concentrations of DMDS/DMS and 0 atoms, we have Nreacted = (N;klz)/(1 + NOklz) "N No where No is the initial concentration of either reactant, k, is the rate constant for the reaction (la) or (lb) and z is the time domain of the flow reactor within the viewing zone. The total number of photons from SO, is given by NSO, = A,6, LnLzdt where A,*,, is the Einstein coefficient for the SO; molecules: the values for 'B and are 1.6 x lo3 and 123.5 s-', respec-tively.' ' The integration is carried over the time domain z to obtain Nsoz.While numerical integration has been carried out for the complex reaction scheme, we prefer to evaluate N,, experimentally. This was done by comparing the chemilumin- escence from the sulfide reaction with that from the standard NO + 0 reaction, adopting the method described by Fontijn et all3 The reference chemiluminescence photons, NNO2, is given by NNOz = A:,, ngo2 dt = k:,,, Ni zl where Ago, = 1.6 x lo4 s-','~ is the Einstein coefficient for NO: and Go,is the total chemiluminescent rate constant for the reaction NO + O.', At high values of A:,,, the rate of the reference reaction is essentially controlled by relatively slow NO + 0 recombination reaction and the above equa- tion holds for the equal concentration of NO and 0,as in the present case.The ratio NSoZ/NNo2 is experimentally evaluated, after due consideration of the spectrally overlapping regions. Since we have and @ = (NSOz/NNOz)k&+O NO Owing to the complex reaction mechanism, as elaborated in a later section, the chemiluminescence intensity and hence the photon yield varies with substrate concentration. However, the photon yields are 3.3 x lo-, for DMDS and 4.4 x for DMS, respectively, at their intensity maxima.t Chemiluminescence Mechanism It is well known that the formation of electronically excited SO, in the reaction of DMDS with 0, and in the reaction of DMS with O(,P) is due to reaction of the initially generated SO e.g.M0 + SO -SO;; AH = -548 kJ mol-' (iii) This channel has sufficient energy to generate the product SO, in the upper electronic level. The reaction of O(,P) atoms with episulfide also exhibits SO, afterglow," for which the following mechanism is pro- posed : O+ AH = -276 kJ mol-(iv) Reaction (iv) is followed by reaction (iii)". Lee et a!." con-sidered the direct formation of SO in the endothermic reac- tion 0 + CH,SCH, + 2CH, + SO; AH = 84 kJ mol-i (v) but ruled this out on the basis of the overall negative activa- tion energy observed for the consumption of 0 atoms in the reaction with DMS.The formation of C,H, and SO in the primary reaction 0 + CH,SCH, + C,H, + SO; AH = -293 kJ mol-' (vi) may be considered on energetic grounds but was not sup- ported by the mass-spectrometric results, which showed no evidence for C,H, at low pressure." Lee et a!." concluded that the primary step in the reaction mechanism is reaction (lb) followed by reaction (2) (later). The production of electronically excited OH cannot be accounted for as a result of reactions (i) and (ii) since the energy requirement is large. A possible reaction to explain the formation of OH* is M0 + H -OH; AH = -427 kJ mol-' (vii) where M is a third body, mainly Ar in the present experimen- tal condition. Production of H atoms was reported by Lee et al." in the reaction of O(3P)with DMS, viz.CH, + O(,P) -+ H,CO + H; AH = -293 kJ mol-' (viii) 7 The cumulative errors in the evaluation of photon yields are CQ. 10%. The H atoms generated can react with O(,P) atoms to give OH*. Based on the above considerations, we propose the follow- ing reaction scheme. CH,SSCH, + 0 +CH,SO + CH3S; k, = 1.3 x lo-'' cm3 molecule-' s-' (14 CH,SCH, + 0 +CH,SO + CH, ; k,, = 5 x lo-" cm3 molecule-' s-l l7 (W MCH,SO -CH, +SO; k, = 5 x S-' (2) CH, + 0 -,H,CO + H; k, = 1.4 x lo-'' cm3 molecule-' s-' '7p18 (3) 0 + H -OH*; k, = 2.3 x cm3molecule-' s-' l9 (4) OH* &OH + hv; k, = 1.5 x lo6 S-' 20,2' (5) MO,+H-HO, ; k6 = 3.2 x 10-l~cm3molecule-1 s-' 17v2, (6) SO+OLSOf; @=1.3; k, = 2.7 x cm3molecule-' s-' 23 (7) SO? --LSO, + hv; k8 = 123.5 S-' l5 (8) CH, + 0, LCH,O,; k, = 3.7 x cm3 molecule-' s-' l7 (9) These rate constants are the values recommended in the ref- erences mentioned.The second-order rate constants for the reactions of 0 atoms with H, and SO and 0, with CH, and H [reactions (4), (7), (9) and (6)] are dependent on the third-body (M) con-centration in the fall-off region. The rate constants for these reactions are taken from ref. 17 [the pressure of M (Ar) being 1.5 Torr here]. In the above mechanism, we consider as the primary step the reaction of O(3P) atoms with DMDS or DMS, i.e. reac-tions (la) and (lb). The primary radical products generated trigger the entire reaction sequence, resulting in the observed chemiluminescence.With both sulfide molecules, the rate- controlling step for SO formation is the slow unimolecular dissociation of CH,SO [reaction (211. Reaction (lb) for DMS gives a direct primary route for generation of CH, radicals, which are precursors for OH* [reactions (3) and (4)]. This facilitates the much higher emission intensity from OH* as observed in the DMS reaction. In the reaction scheme, the dimerization of CH, radicals is not considered because (i) their concentration is too small compared to that of 0 and 0, and (ii) the reaction rate con- stant k,,,, (1.4 x lo-'' cm3molecule-' s-')~"'~is larger than kCH, +CH3 (5.9 x 10-'' cm3 molecule-' s-1).24*25 Numerical Simulation The reactions in the above mechanism lead to various coupled differential equations. To elucidate the exact profile of the different transient species in the flow system, these coupled differential equations have been solved numerically using the program EPISODE developed by Hindmarsh and Byrne.26 All the equations have been solved taking dV/u as dt, where dV is the volume element in the flow direction of the observation zone and u is the bulk linear flow velocity.A typical concentration profile of all the species for 15 mTorr of 0 and 15 mTorr of DMDS is shown in Fig. 4. The concen- tration of CH,SO increases up to 10 ps (or the corresponding volume element) and subsequently reaches a steady state. Similarly, the steady state is reached for CH, and SO? after J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 10 ms. In the case of SO, H and OH*, the steady state is not attained even after 200 ms. As the residence time in the obser- vation zone is <2 ms in the present experiments, a steady-state condition cannot be imposed. The concentration profiles in Fig. 4 show that the major depletion of 0 atoms and sulfide molecules occurs by their mutual reaction. The 0 atoms are promptly and almost entirely consumed [Fig. qb)] in ca. 100 ps, leaving very few 0 atoms to sustain the second- ary reaction sequence [Fig. 4(c)-(g)]. The unavailability of 0 atoms €or further reaction is the principal reason for the low photon yields. When the relative 0-atom concentration is increased, greater accessibility of 0 atoms for the secondary reactions becomes feasible and the photon yields do increase.The exothermic chemical system dynamics can be optimised, in principle, to achieve a better photon yield for a selected channel. Taking the DMS + 0 system as an example,27 we can take advantage of the primary generation of CH, and, under conditions of abundant supply of 0 atoms, drive the system so as to convert the major fraction of the products of the primary reaction (lb)to generate OH*. Since the concen- tration of the emitting species is entirely dependent on the decomposition channel of CH,SO, it is desirable to assess the decomposition rate of the radical under our experimental conditions. The unimolecular decomposition rate constant (5 x lo-, s-') and the bond-dissociation energy (209 kJ rnol-'), for the CH,SO radical suggest that this radical is very stable with respect to decomposition.The exothermicity of the formation reaction of CH,SO [reactions (la)and (lb), may result in some vibrational excitation of CH,SO, which in turn may enhance its decomposition rate. To discover whether the CH,SO undergoes decomposition with the above or higher rate constants, a similar simulation was per- formed taking k, in the range of 5 x 10-5-5 x lo5 s-'. The photon yields calculated for different values of k, are com- pared with the experimental observed values. The experimen- tal photon yield matches the simulated value for k, = 5 x s-'. This shows that the majority of CH,SO disso-ciates with the lower rate constant only, and the participation of vibrationally excited CH,SO can be ruled out in the light of this explanation.In the reaction scheme CH,, which is a precursor of OH*, is also formed in reaction (lb). So we may expect the ratio OH* :SO! to be higher for DMS than that for DMDS. Experimentally it has been observed that the ratio of area under the curve for OH* and SO! in the case of DMS is ca. three times higher than that for DMDS. By simulation (in the case of DMS the recombination reaction of CH, is also con- sidered as the CH, concentration is much higher in this case 1o4 tls Fig. 4 Computer simulation showing time-domain concentration of different species (at DMDS = 15 mTorr and 0 = 15 mTorr).(a) CH,SO, (b)DMDS or 0,(c)SO, (d) SO;, (e)CH,, (f)H, (9)OH*. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 4.0 15.0 4 4 10.0 2.0v 20 25 30 35 40 45 50 DMDS/mTorr 0.0 0 10 20 30 40 50 DMDS/mTorr Fig. 5 Computer simulation of SO! (a)and OH* (b)emission inten- sity us. DMDS pressure. Inset shows a magnified view of the tailing portion. than for DMDS) studies the same ratio was obtained, which further confirms the mechanism proposed. The nature of the emission intensity curve can be simulated with the help of the EPISODE program, if the intensity is considered to be proportional to the photon density of the emitting species. The simulation thus arrived at with respect to DMDS pressure is shown in Fig. 5. The curve shows a linear rise and an exponential fall, similar to that obtained experimentally.To discover the contribution of the quen- ching term, if any, in the fall-off region, a similar simulation was carried out taking a typical collisional quenching rate constant for diatomic and triatomic molecules for OH* and SO;, respectively. Both show a similar intensity pattern with variation of DMDS pressure. Conclusion Formation of electronically excited SOz and OH in the gas- phase reaction of oxygen atoms with DMDS and DMS is reported. Broad chemiluminescence spectra in the range 240-460 nm with a sharp peak at 308.5 nm are obtained. The emission intensities show a linear dependence on DMDS/ DMS/O concentration in the low-pressure region.However, at higher oxygen or reagent concentrations the emission intensity reaches a maximum and then starts to decrease. A similar trend was observed for computer simulation of the pressure dependence of the chemiluminescence intensity. The maximum photon yields are found to be 3.3 x and 4.4 x for DMDS and DMS, respectively. The authors thank Dr. V. K. Kelkar for help with the com- puter programming and one of the referees for his suggestion on evaluation of photon yields. References 1 G. S. Tyndall and A. R. Ravishankara, Znt. J. Chem. Kinet., 1991,23,483. 2 F. Yin, D. 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Gaydon, The ldentijcation of Molec-ular Spectra, Chapman and Hall, London, 3rd edn., 1965. 15 F. Su, J. W. Bottenheim, D. L. Thorsell, J. G. Calvert and E. K. Damon, Chem. Phys. Lett., 1977,49, 305. 16 V. M. Donnelley and F. Kaufmann, J. Chem. Phys., 1977, 66, 4100. 17 R. Atkinson, D. L. Baulch, R. A. Cox, R. F. Hampson Jr., J. A. Kerr and J. Troe, J. Phys. Chem. Ref Data, 1992,21, 1125. 18 R. Zellner, D. Hartmann, J. Kanthauses, D. Rhasa and G. Weibring, J. Chem. SOC., Faraday Trans. 2, 1988,84,549. 19 W. Tsang and R. F. Hampson, J. Phys. Chem. Ref: Data, 1986, 15, 1087. 20 K. R. German, J. Chem. Phys., 1975,63,5252. 21 W. H. Smith, J. Chem. Phys., 1970,53,792. 22 K. L. Catleton, W. J. Kesseler and W. J. Marinelli, J. Phys. Chem., 1993,97,6412. 23 I).L. Singleton and R. J. Cvetanovic, J. Phys. Chem. Ref. Data, 1988,17,1377. 24 I. R. Slagle, D. Gutman, J. W. Davies and M. J. Pilling, J. Phys. Chem., 1988,92,2455. 25 A. F. Wagner and D. M. Wardlaw, J. Phys. Chem., 1988, 92, 2462. 26 A. C. Hindmarsh, G. D. Byrne, Lawrence Liuermore Laboratory, Report UCID-30112, Rev. 1, April, 1977. 27 H. P. Upadhyaya, U. B. Pavanaja, A. V. Sapre, K. V. S. Rama Rao and J. P. Mittal, 3rd Int. Con$ on Chemical Kinetics, July 12-16, 1993, NIST, Gaithersburg, USA. Paper 3/05549C; Received 15th September, 1993

 

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