- Email: [email protected]
Kinetics of the reactions F+H2S and F+D2S at 298 K
18 December 1998
Chemical Physics Letters 298 Ž1998. 390–394
Kinetics of the reactions F q H 2 S and F q D 2 S at 298 K Avigdor Persky
)
Department of Chemistry, Bar-Ilan UniÕersity, Ramat Gan 52900, Israel Received 10 August 1998; in final form 5 October 1998
Abstract The rate constants for the reactions F q H 2 S and F q D 2 S at 298 K were determined by a competitive method using the reaction F q CH 4 as a reference reaction. The ratios of rate constants k FqH 2 Srk FqCH 4 and k FqD 2 Srk FqCH 4 were determined by a discharge-flow-mass spectrometric technique. By combining the values for these ratios with the value for k FqCH 4 at 298 K, the values k FqH 2 S s Ž1.46 " 0.12. = 10y10 cm3 moleculey1 sy1 and k FqD 2 S s Ž1.42 " 0.12. = 10y10 cm3 moleculey1 sy1 were obtained. The kinetic isotope effect k FqH 2 Srk FqD 2 S was determined directly and the value 1.04 " 0.02 was obtained. The results of this study are compared with previous literature data. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Hydrogen atom abstraction reactions by fluorine atoms, which are usually rapid and very exothermic, are of much interest in molecular dynamics. The interest in such reactions is mainly due to the possibility of designing chemical lasers based on them and of using experimental data for testing basic theories in molecular dynamics. In spite of the considerable importance of such reactions, accurate kinetic data are relatively scarce as compared, for example, to similar reactions with chlorine atoms. This fact can probably be attributed to experimental difficulties resulting from the high reactivity of fluorine atoms and to the occurrence of undesirable secondary reactions w1–3x. The experimental difficulties and resulting inaccuracies of part of the reported experimental data can be illustrated by examining
)
E-mail: [email protected]
the results accumulated over the years for the F q H 2 reaction. This reaction has been investigated by more than 20 research groups, but a significant part of the results is considered to be inaccurate w1–6x. The results of only a few of the research groups have been taken into account in kinetic data evaluations, for recommending the most acceptable kinetic data for this reaction w4–6x. The title reactions F q H 2 S ™ HF q HS, D H0o s y45.3 " 2.0 kcal moly1
Ž 1.
and F q D 2 S ™ DF q DS, D H0o s y45.5 " 2.0 kcal moly1
Ž 2.
are very rapid and highly exothermic Žthe D H0o values indicated above were taken from Table 1 of Ref. w7x.. Agrawalla and Setser w7x found that vibra-
0009-2614r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 1 1 5 4 - 3
A. Persky r Chemical Physics Letters 298 (1998) 390–394
tional levels up to HFŽ Õ s 4. and DFŽ Õ s 6. are populated for reactions Ž1. and Ž2., respectively. The absolute rate constant for reaction Ž1. at 298 K has been determined only by one research group w8x. They carried out the experiments in a fast-flow system and followed the decay of H 2 S with a mass spectrometer under pseudo-first-order conditions with wH 2 Sx 0 < wFx 0 . They obtained the value k FqH S s 2 Ž1.28 " 0.04. = 10y1 0 cm3 moleculey1 sy1 Žthe error limits represent the standard deviation" s .. Two research groups determined relative rate constants at room temperature. Agrawalla and Setser w7x carried out experiments in a fast-flow reactor and measured relative emission intensities from the products of the competing reactions, for a constant concentration of F atoms. From these measurements they obtained the value k Fq H 2 Srk FqCH 4 s 1.9 " 0.2, where k FqCH 4 is the rate constant for the reaction F q CH 4 ™ HF q CH 3 .
Ž 3.
A much higher value for this ratio, 3.2 " 0.3, was obtained by Williams and Rowland, who studied competitive reactions involving thermalized 18 F atoms w9x. A value of 1.4 " 0.2 was obtained by Agrawalla and Setser for k Fq D 2 Srk FqCH 4 . In the present study, reaction Ž3. was used as a reference reaction in the determination of k Fq H 2 S and k Fq D 2 S . We also directly determined the kinetic isotope effect k Fq H 2 Srk FqD 2 S . The results of the present study are compared with the earlier reported results.
2. Experimental section The experimental apparatus and procedure used in this study were similar to those used in our earlier studies of the reactions F q HBr w10x, F q DBr w11x, and F q CH 4 w12x, and therefore they will be described here only briefly. Fluorine atoms were produced by a microwave discharge in a dilute mixture of CF4 in Ar or He, and flowed into the reaction cell through one of its inlets. The F atoms reacted with a mixture of H 2 S Žor D 2 S. and CH 4 , also diluted by Ar or He, which flowed into the reaction cell through a second inlet. The reaction mixture was continuously sampled through a small orifice and analyzed by a quadrupole mass
391
spectrometer ŽBalzers Model QMG 511.. As before w10–12x, the walls of the discharge tube and reaction cell, which were made of quartz, were treated by a 10% HF solution to minimize the heterogeneous recombination of F atoms. The flow rates of the reagents into the reaction cell were controlled by calibrated capillaries and were of the order of 0.005– 0.015 mmol sy1 for H 2 S, 0.012–0.025 mmol sy1 for CH 4 , and 0.003–0.015 mmol sy1 for CF4 . The flow rates of the Ar and He were of the order of 50–100 mmol sy1 . The total pressure in the reaction cell was 1–1.5 Torr. The Ar, He, CF4 , H 2 S and CH 4 were obtained from Matheson and had the stated minimum purities of 99.999%, 99.999%, 99.7%, 99.5% and 99.97%, respectively. The D 2 S was obtained from Merck, Sharp and Dohme and had a stated minimum isotopic purity of 97.0%. The concentrations of the H 2 S, D 2 S and CH 4 were followed by measuring the mass spectrometric signals due to the ions H 2 Sq, D 2 Sq and CHq 4, which have the mass to charge ratios mre s 34, 36 and 16, respectively. Under the conditions where reactions Ž1. and Ž3. compete, the ratio of rate constants k Fq H 2 Srk FqCH 4 is given by the expression k Fq H 2 S
s
k Fq CH 2
ln Ž w H 2 S x 0r w H 2 S x . ln Ž w CH 4 x 0r w CH 4 x .
Ž I.
where wH 2 Sx and wCH 4 x are the concentrations of these reagents at the end of the reaction cell when the reactions with F atoms take place Žmicrowave discharge turned on., and wH 2 Sx 0 and wCH 4 x0 are their concentrations when no F atoms are present Žmicrowave discharge turned off.. In every experiment the background signals due to ions with mre s 34 Žin the presence of CF4 and CH 4 and the absence of H 2 S., and ions with mre s 16 Žin the presence of CF4 and H 2 S and the absence of CH 4 ., with and without discharge, were subtracted from the signals measured when all the reagents were present. In the experiments where reactions Ž2. and Ž3. compete, the ratio of rate constants for these reactions is given by k Fq D 2 S k Fq CH 4
s
ln Ž w D 2 S x 0r w D 2 S x . ln Ž w CH 4 x 0r w CH 4 x .
Ž II .
A. Persky r Chemical Physics Letters 298 (1998) 390–394
392
and in the experiments where reactions Ž1. and Ž2. compete, the kinetic isotope effect is given by k Fq H 2 S k Fq D 2 S
s
ln Ž w H 2 S x 0r w H 2 S x . ln Ž w D 2 S x 0r w D 2 S x .
Ž III .
As in the experiments to determine k Fq H 2 Srk FqCH 4 , also in the last two cases the appropriate background signals were taken into account. The carrier gas in the experiments to determine k Fq H 2 Srk FqCH 4 was either Ar or He. All the experiments which involved D 2 S where carried out only in the presence of He. Ar could not be used because of the interference of signals with mre s 36, due to the isotope 36Ar. All the experiments were carried out at 298 K.
3. Results and discussion
Fig. 2. Plot of ln ŽwD 2 Sx0 rwD 2 Sx. versus ln ŽwCH 4 x 0 rwCH 4 x. for the reaction of F atoms with a mixture of D 2 S and CH 4 at 298 K.
3.1. RelatiÕe rate constants The ratio of rate constants k Fq H 2 Srk FqCH 4 was determined from several sets of experiments in which the extent of reaction was varied over a wide range, by varying the concentration of F atoms. A plot of ln ŽwH 2 Sx 0rwH 2 Sx. versus ln ŽwCH 4 x0rwCH 4 x. is presented in Fig. 1. The straight line in this figure was
Fig. 1. Plot of ln ŽwH 2 Sx 0 rwH 2 Sx. versus ln ŽwCH 4 x0 rwCH 4 x. for the reaction of F atoms with a mixture of H 2 S and CH 4 at 298 K.
calculated by the least squares method. As can be seen, no significant scatter of the points around the line is observed, and the line has a near-zero intercept. This behavior indicates that the calculated rate constant is independent of the extent of reaction and proves that secondary reactions, which might interfere with the determination, are not important under the conditions of our experiments. It should also be noted that changes of flow rates of the reagents over significant ranges did not affect the results to any significant extent and that the results obtained with He as a carrier gas were the same, within the experimental errors, as those obtained with Ar as a carrier gas. The ratio of rate constants obtained from the slope of the line in Fig. 1, according to Eq. ŽI., is k Fq H 2 Srk FqCH 4 s 2.35 " 0.05, where the error limits represent twice the standard deviation Ž"2s .. This value is in between the value 1.9 " 0.2 reported by Agrawalla and Setser w7x and the value 3.1 " 0.3 obtained by Williams and Rowland w9x, but is closer to the lower value of the two. The ratio of rate constants k Fq D 2 Srk FqCH 4 was determined from the plot of ln ŽwD 2 Sx 0rwD 2 Sx. versus ln ŽwCH 4 x0rwCH 4 x., which is shown in Fig. 2. The points in this figure represent several sets of experiments carried out over several days. Again, as in
A. Persky r Chemical Physics Letters 298 (1998) 390–394
Fig. 1, all the points lie on the straight line, calculated by the least squares method, or very near it, and the line has a near-zero intercept. This proves that, also in this case, secondary reactions are not important. The ratio of rate constants obtained from Fig. 2, according to Eq. ŽII., is k Fq D 2 Srk FqCH 4 s 2.29 " 0.05. This value is much higher than the value of 1.4 " 0.2 obtained by Agrawalla and Setser w7x. The value obtained by us for k Fq D 2 Srk FqCH 4 is only slightly lower than the value obtained for k Fq H 2 Srk FqCH 4 and this means that the kinetic isotope effect k Fq H 2 Srk FqD 2 S is near unity Ž1.03 " 0.03.. The kinetic isotope effect was also determined directly from experiments in which F atoms reacted with a mixture of H 2 S and D 2 S. The results of the measurements are shown in Fig. 3 where ln ŽwH 2 Sx 0rwH 2 Sx. is plotted versus ln ŽwD 2 Sx 0 rwD 2 Sx.. Again a straight line with a near-zero intercept is obtained from which, according to Eq. ŽIII., the ratio k Fq H 2 Srk FqD 2 S s 1.04 " 0.02 is calculated. This value is in excellent agreement with the value 1.03 " 0.03 calculated from the individual ratios k Fq H 2 Srk FqCH 4 and k FqD 2 Srk FqCH 4 , and is significantly lower than the value 1.4 " 0.2 reported by Agrawalla and Setser w7x. The near-unity value obtained for the kinetic isotope effect means that isotopic substitution does not
393
have a significant effect on the rate of the reaction. Such behavior could be expected for the F q H 2 S reaction, which is very rapid and probably has a very low barrier, much lower than the zero-point energy of either H 2 S or D 2 S. Similarly, near-unity kinetic isotope effects have been determined for the rapid reactions of F atoms with NH 3 and ND 3 Ž1.1 " 0.2. w13x and for the reactions of F atoms with HBr and DBr Ž1.07 " 0.12. w11x. These values are much lower than the reduced mass effect Ž1.4. predicted by the conventional transition state theory for reactions without a barrier, which indicates that this theory is not applicable for such reactions. 3.2. Absolute rate constants In order to calculate absolute values for k Fq H 2 S and k Fq D 2 S from the relative values determined in this study, the absolute value of k Fq CH 4 is needed. In a recent study w12x we determined the ratio k Fq CH 4rk FqD 2 over a wide temperature range and by combining the results with the earlier results for the kinetic isotope effect k Fq H 2rk FqD 2 w14x and with recommended kinetic data for k Fq H 2 w4,5x, we obtained an Arrhenius expression for k Fq CH 4 . More recently, a new critical evaluation of the available kinetic data for the F q H 2 reaction has been carried out by us w6x. This evaluation led to a somewhat different Arrhenius expression for k Fq H 2 than the one recommended earlier. Using the updated Arrhenius expression for k Fq H 2 , the following expression is obtained for k Fq CH 4 k Fq CH 4 s Ž 1.28 " 0.15 . = 10y1 0 =exp y Ž 215 " 60 . rT cm3 moleculey1 sy1 .
Fig. 3. Plot of ln ŽwH 2 Sx0 rwH 2 Sx. versus ln ŽwD 2 Sx 0 rwD 2 Sx. for the reaction of F atoms with a mixture of H 2 S and D 2 S at 298 K.
Ž IV .
The value obtained for 298 K is k Fq CH 4 s Ž6.20 " 0.50. = 10y1 1 cm3 moleculey1 sy1. This value is about 7% lower than the value reported earlier w12x. Using this value for k Fq CH 4 , the following values are obtained: k FqH 2 S s Ž1.46 " 0.12. = 10y10 cm 3 moleculey1 sy1 and k Fq D 2 S s Ž1.42 " 0.12. cm3 moleculey1 sy1 . The value obtained in the present study for k Fq H 2 S is in good agreement with the value Ž1.28 " 0.04. = 10y1 0 cm3 moleculey1 sy1 obtained by Schonle ¨ et al. w8x. Similar techniques were employed in the two
A. Persky r Chemical Physics Letters 298 (1998) 390–394
394
Table 1 Relative and absolute rate constants for the reactions FqH 2 S and FqD 2 S at 298 K k Fq H 2 S r k FqCH 4
k Fq D 2 S r k FqCH 4 k Fq H 2 S
k Fq D 2 S k Fq H 2 S r k FqD 2 S
Ratio or absolute rate constant
Reference
1.9"0.2 3.2"0.3 2.35"0.05a 1.4"0.2 2.29"0.05a 1.28"0.04 b,c,d Ž1.7"0.4. b,c,e 1.46"0.12 a,c 1.42"0.12 a,c 1.4"0.2 1.04"0.02 a
w7x w9x this work w7x this work w8x w8x this work this work w7x this work
a
Error limits are 2 s. Error limits are 1s. c Units: 10y1 0 cm3 moleculey1 sy1 . d Experimental conditions: large excess of F atoms over H 2 S. e Experimental conditions: large excess of H 2 S over F. These results are considered by the authors to be less reliable than their results under large excess of F atoms.
between the two studies is the fact that while in Ref. w8x the absolute concentration of the F atoms had to be determined, this was not needed in our study. It should also be noted that a small number of experiments were carried out in Ref. w8x under conditions of a large excess of H 2 S over F atoms. The value obtained for the rate constant under these conditions is k Fq H 2 S s Ž1.7 " 0.4. = 10y1 0 cm3 moleculey1 sy1 , but the authors consider this value to be less reliable than their other value. The value obtained by us is in between the two values obtained in Ref. w8x. All the results obtained in the present study are summarized in Table 1, where they are compared with the earlier available data.
b
studies. In both of them a discharge-flow system was used with mass spectrometric detection of the reagents. However, the conditions under which the experiments were carried out were very different. Whereas in Ref. w8x experiments were carried out under pseudo-first-order conditions with the concentration of F atoms in large excess over the concentration of H 2 S, our experiments were carried out under second-order conditions, with the sum of concentrations of H 2 S Žor D 2 S. and CH 4 being larger than the concentration of the F atoms. Another difference
References w1x w2x w3x w4x w5x
w6x w7x w8x w9x w10x
R. Foon, M. Kaufman, Prog. Reaction Kinet. 8 Ž1975. 81. W.E. Jones, E.G. Skolnik, Chem. Rev. 76 Ž1976. 563. J.B. Anderson, Adv. Chem. Phys. 41 Ž1980. 229. R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson, J.A. Kerr, J. Troe, J. Phys. Chem. Ref. Data 21 Ž1992. 1125. W.B. DeMore, S.P. Sander, D.M. Golden, R.F. Hampson, M.J. Kurylo, C.J. Howard, A.R. Ravishankara, C.E. Kolb, M.J. Molina, Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling, Evaluation Number 11 of the NASA Panel for Data Evaluation, JPL Publ., 94–26 Ž1994.. A. Persky, H. Kornweitz, Int. J. Chem. Kinet. 29 Ž1997. 67. B.S. Agrawalla, D.W. Setser, J. Phys. Chem. 90 Ž1986. 2450. G. Schonle, M.M. Rahman, R.N. Schindler, Ber. Bunsenges. ¨ Phys. Chem. 91 Ž1987. 66. R.L. Williams, F.S. Rowland, J. Phys. Chem. 77 Ž1973. 301. R. Edrei, A. Persky, Chem. Phys. Lett. 157 Ž1989. 265.
Chemical Physics Letters 298 Ž1998. 390–394
Kinetics of the reactions F q H 2 S and F q D 2 S at 298 K Avigdor Persky
)
Department of Chemistry, Bar-Ilan UniÕersity, Ramat Gan 52900, Israel Received 10 August 1998; in final form 5 October 1998
Abstract The rate constants for the reactions F q H 2 S and F q D 2 S at 298 K were determined by a competitive method using the reaction F q CH 4 as a reference reaction. The ratios of rate constants k FqH 2 Srk FqCH 4 and k FqD 2 Srk FqCH 4 were determined by a discharge-flow-mass spectrometric technique. By combining the values for these ratios with the value for k FqCH 4 at 298 K, the values k FqH 2 S s Ž1.46 " 0.12. = 10y10 cm3 moleculey1 sy1 and k FqD 2 S s Ž1.42 " 0.12. = 10y10 cm3 moleculey1 sy1 were obtained. The kinetic isotope effect k FqH 2 Srk FqD 2 S was determined directly and the value 1.04 " 0.02 was obtained. The results of this study are compared with previous literature data. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Hydrogen atom abstraction reactions by fluorine atoms, which are usually rapid and very exothermic, are of much interest in molecular dynamics. The interest in such reactions is mainly due to the possibility of designing chemical lasers based on them and of using experimental data for testing basic theories in molecular dynamics. In spite of the considerable importance of such reactions, accurate kinetic data are relatively scarce as compared, for example, to similar reactions with chlorine atoms. This fact can probably be attributed to experimental difficulties resulting from the high reactivity of fluorine atoms and to the occurrence of undesirable secondary reactions w1–3x. The experimental difficulties and resulting inaccuracies of part of the reported experimental data can be illustrated by examining
)
E-mail: [email protected]
the results accumulated over the years for the F q H 2 reaction. This reaction has been investigated by more than 20 research groups, but a significant part of the results is considered to be inaccurate w1–6x. The results of only a few of the research groups have been taken into account in kinetic data evaluations, for recommending the most acceptable kinetic data for this reaction w4–6x. The title reactions F q H 2 S ™ HF q HS, D H0o s y45.3 " 2.0 kcal moly1
Ž 1.
and F q D 2 S ™ DF q DS, D H0o s y45.5 " 2.0 kcal moly1
Ž 2.
are very rapid and highly exothermic Žthe D H0o values indicated above were taken from Table 1 of Ref. w7x.. Agrawalla and Setser w7x found that vibra-
0009-2614r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 1 1 5 4 - 3
A. Persky r Chemical Physics Letters 298 (1998) 390–394
tional levels up to HFŽ Õ s 4. and DFŽ Õ s 6. are populated for reactions Ž1. and Ž2., respectively. The absolute rate constant for reaction Ž1. at 298 K has been determined only by one research group w8x. They carried out the experiments in a fast-flow system and followed the decay of H 2 S with a mass spectrometer under pseudo-first-order conditions with wH 2 Sx 0 < wFx 0 . They obtained the value k FqH S s 2 Ž1.28 " 0.04. = 10y1 0 cm3 moleculey1 sy1 Žthe error limits represent the standard deviation" s .. Two research groups determined relative rate constants at room temperature. Agrawalla and Setser w7x carried out experiments in a fast-flow reactor and measured relative emission intensities from the products of the competing reactions, for a constant concentration of F atoms. From these measurements they obtained the value k Fq H 2 Srk FqCH 4 s 1.9 " 0.2, where k FqCH 4 is the rate constant for the reaction F q CH 4 ™ HF q CH 3 .
Ž 3.
A much higher value for this ratio, 3.2 " 0.3, was obtained by Williams and Rowland, who studied competitive reactions involving thermalized 18 F atoms w9x. A value of 1.4 " 0.2 was obtained by Agrawalla and Setser for k Fq D 2 Srk FqCH 4 . In the present study, reaction Ž3. was used as a reference reaction in the determination of k Fq H 2 S and k Fq D 2 S . We also directly determined the kinetic isotope effect k Fq H 2 Srk FqD 2 S . The results of the present study are compared with the earlier reported results.
2. Experimental section The experimental apparatus and procedure used in this study were similar to those used in our earlier studies of the reactions F q HBr w10x, F q DBr w11x, and F q CH 4 w12x, and therefore they will be described here only briefly. Fluorine atoms were produced by a microwave discharge in a dilute mixture of CF4 in Ar or He, and flowed into the reaction cell through one of its inlets. The F atoms reacted with a mixture of H 2 S Žor D 2 S. and CH 4 , also diluted by Ar or He, which flowed into the reaction cell through a second inlet. The reaction mixture was continuously sampled through a small orifice and analyzed by a quadrupole mass
391
spectrometer ŽBalzers Model QMG 511.. As before w10–12x, the walls of the discharge tube and reaction cell, which were made of quartz, were treated by a 10% HF solution to minimize the heterogeneous recombination of F atoms. The flow rates of the reagents into the reaction cell were controlled by calibrated capillaries and were of the order of 0.005– 0.015 mmol sy1 for H 2 S, 0.012–0.025 mmol sy1 for CH 4 , and 0.003–0.015 mmol sy1 for CF4 . The flow rates of the Ar and He were of the order of 50–100 mmol sy1 . The total pressure in the reaction cell was 1–1.5 Torr. The Ar, He, CF4 , H 2 S and CH 4 were obtained from Matheson and had the stated minimum purities of 99.999%, 99.999%, 99.7%, 99.5% and 99.97%, respectively. The D 2 S was obtained from Merck, Sharp and Dohme and had a stated minimum isotopic purity of 97.0%. The concentrations of the H 2 S, D 2 S and CH 4 were followed by measuring the mass spectrometric signals due to the ions H 2 Sq, D 2 Sq and CHq 4, which have the mass to charge ratios mre s 34, 36 and 16, respectively. Under the conditions where reactions Ž1. and Ž3. compete, the ratio of rate constants k Fq H 2 Srk FqCH 4 is given by the expression k Fq H 2 S
s
k Fq CH 2
ln Ž w H 2 S x 0r w H 2 S x . ln Ž w CH 4 x 0r w CH 4 x .
Ž I.
where wH 2 Sx and wCH 4 x are the concentrations of these reagents at the end of the reaction cell when the reactions with F atoms take place Žmicrowave discharge turned on., and wH 2 Sx 0 and wCH 4 x0 are their concentrations when no F atoms are present Žmicrowave discharge turned off.. In every experiment the background signals due to ions with mre s 34 Žin the presence of CF4 and CH 4 and the absence of H 2 S., and ions with mre s 16 Žin the presence of CF4 and H 2 S and the absence of CH 4 ., with and without discharge, were subtracted from the signals measured when all the reagents were present. In the experiments where reactions Ž2. and Ž3. compete, the ratio of rate constants for these reactions is given by k Fq D 2 S k Fq CH 4
s
ln Ž w D 2 S x 0r w D 2 S x . ln Ž w CH 4 x 0r w CH 4 x .
Ž II .
A. Persky r Chemical Physics Letters 298 (1998) 390–394
392
and in the experiments where reactions Ž1. and Ž2. compete, the kinetic isotope effect is given by k Fq H 2 S k Fq D 2 S
s
ln Ž w H 2 S x 0r w H 2 S x . ln Ž w D 2 S x 0r w D 2 S x .
Ž III .
As in the experiments to determine k Fq H 2 Srk FqCH 4 , also in the last two cases the appropriate background signals were taken into account. The carrier gas in the experiments to determine k Fq H 2 Srk FqCH 4 was either Ar or He. All the experiments which involved D 2 S where carried out only in the presence of He. Ar could not be used because of the interference of signals with mre s 36, due to the isotope 36Ar. All the experiments were carried out at 298 K.
3. Results and discussion
Fig. 2. Plot of ln ŽwD 2 Sx0 rwD 2 Sx. versus ln ŽwCH 4 x 0 rwCH 4 x. for the reaction of F atoms with a mixture of D 2 S and CH 4 at 298 K.
3.1. RelatiÕe rate constants The ratio of rate constants k Fq H 2 Srk FqCH 4 was determined from several sets of experiments in which the extent of reaction was varied over a wide range, by varying the concentration of F atoms. A plot of ln ŽwH 2 Sx 0rwH 2 Sx. versus ln ŽwCH 4 x0rwCH 4 x. is presented in Fig. 1. The straight line in this figure was
Fig. 1. Plot of ln ŽwH 2 Sx 0 rwH 2 Sx. versus ln ŽwCH 4 x0 rwCH 4 x. for the reaction of F atoms with a mixture of H 2 S and CH 4 at 298 K.
calculated by the least squares method. As can be seen, no significant scatter of the points around the line is observed, and the line has a near-zero intercept. This behavior indicates that the calculated rate constant is independent of the extent of reaction and proves that secondary reactions, which might interfere with the determination, are not important under the conditions of our experiments. It should also be noted that changes of flow rates of the reagents over significant ranges did not affect the results to any significant extent and that the results obtained with He as a carrier gas were the same, within the experimental errors, as those obtained with Ar as a carrier gas. The ratio of rate constants obtained from the slope of the line in Fig. 1, according to Eq. ŽI., is k Fq H 2 Srk FqCH 4 s 2.35 " 0.05, where the error limits represent twice the standard deviation Ž"2s .. This value is in between the value 1.9 " 0.2 reported by Agrawalla and Setser w7x and the value 3.1 " 0.3 obtained by Williams and Rowland w9x, but is closer to the lower value of the two. The ratio of rate constants k Fq D 2 Srk FqCH 4 was determined from the plot of ln ŽwD 2 Sx 0rwD 2 Sx. versus ln ŽwCH 4 x0rwCH 4 x., which is shown in Fig. 2. The points in this figure represent several sets of experiments carried out over several days. Again, as in
A. Persky r Chemical Physics Letters 298 (1998) 390–394
Fig. 1, all the points lie on the straight line, calculated by the least squares method, or very near it, and the line has a near-zero intercept. This proves that, also in this case, secondary reactions are not important. The ratio of rate constants obtained from Fig. 2, according to Eq. ŽII., is k Fq D 2 Srk FqCH 4 s 2.29 " 0.05. This value is much higher than the value of 1.4 " 0.2 obtained by Agrawalla and Setser w7x. The value obtained by us for k Fq D 2 Srk FqCH 4 is only slightly lower than the value obtained for k Fq H 2 Srk FqCH 4 and this means that the kinetic isotope effect k Fq H 2 Srk FqD 2 S is near unity Ž1.03 " 0.03.. The kinetic isotope effect was also determined directly from experiments in which F atoms reacted with a mixture of H 2 S and D 2 S. The results of the measurements are shown in Fig. 3 where ln ŽwH 2 Sx 0rwH 2 Sx. is plotted versus ln ŽwD 2 Sx 0 rwD 2 Sx.. Again a straight line with a near-zero intercept is obtained from which, according to Eq. ŽIII., the ratio k Fq H 2 Srk FqD 2 S s 1.04 " 0.02 is calculated. This value is in excellent agreement with the value 1.03 " 0.03 calculated from the individual ratios k Fq H 2 Srk FqCH 4 and k FqD 2 Srk FqCH 4 , and is significantly lower than the value 1.4 " 0.2 reported by Agrawalla and Setser w7x. The near-unity value obtained for the kinetic isotope effect means that isotopic substitution does not
393
have a significant effect on the rate of the reaction. Such behavior could be expected for the F q H 2 S reaction, which is very rapid and probably has a very low barrier, much lower than the zero-point energy of either H 2 S or D 2 S. Similarly, near-unity kinetic isotope effects have been determined for the rapid reactions of F atoms with NH 3 and ND 3 Ž1.1 " 0.2. w13x and for the reactions of F atoms with HBr and DBr Ž1.07 " 0.12. w11x. These values are much lower than the reduced mass effect Ž1.4. predicted by the conventional transition state theory for reactions without a barrier, which indicates that this theory is not applicable for such reactions. 3.2. Absolute rate constants In order to calculate absolute values for k Fq H 2 S and k Fq D 2 S from the relative values determined in this study, the absolute value of k Fq CH 4 is needed. In a recent study w12x we determined the ratio k Fq CH 4rk FqD 2 over a wide temperature range and by combining the results with the earlier results for the kinetic isotope effect k Fq H 2rk FqD 2 w14x and with recommended kinetic data for k Fq H 2 w4,5x, we obtained an Arrhenius expression for k Fq CH 4 . More recently, a new critical evaluation of the available kinetic data for the F q H 2 reaction has been carried out by us w6x. This evaluation led to a somewhat different Arrhenius expression for k Fq H 2 than the one recommended earlier. Using the updated Arrhenius expression for k Fq H 2 , the following expression is obtained for k Fq CH 4 k Fq CH 4 s Ž 1.28 " 0.15 . = 10y1 0 =exp y Ž 215 " 60 . rT cm3 moleculey1 sy1 .
Fig. 3. Plot of ln ŽwH 2 Sx0 rwH 2 Sx. versus ln ŽwD 2 Sx 0 rwD 2 Sx. for the reaction of F atoms with a mixture of H 2 S and D 2 S at 298 K.
Ž IV .
The value obtained for 298 K is k Fq CH 4 s Ž6.20 " 0.50. = 10y1 1 cm3 moleculey1 sy1. This value is about 7% lower than the value reported earlier w12x. Using this value for k Fq CH 4 , the following values are obtained: k FqH 2 S s Ž1.46 " 0.12. = 10y10 cm 3 moleculey1 sy1 and k Fq D 2 S s Ž1.42 " 0.12. cm3 moleculey1 sy1 . The value obtained in the present study for k Fq H 2 S is in good agreement with the value Ž1.28 " 0.04. = 10y1 0 cm3 moleculey1 sy1 obtained by Schonle ¨ et al. w8x. Similar techniques were employed in the two
A. Persky r Chemical Physics Letters 298 (1998) 390–394
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Table 1 Relative and absolute rate constants for the reactions FqH 2 S and FqD 2 S at 298 K k Fq H 2 S r k FqCH 4
k Fq D 2 S r k FqCH 4 k Fq H 2 S
k Fq D 2 S k Fq H 2 S r k FqD 2 S
Ratio or absolute rate constant
Reference
1.9"0.2 3.2"0.3 2.35"0.05a 1.4"0.2 2.29"0.05a 1.28"0.04 b,c,d Ž1.7"0.4. b,c,e 1.46"0.12 a,c 1.42"0.12 a,c 1.4"0.2 1.04"0.02 a
w7x w9x this work w7x this work w8x w8x this work this work w7x this work
a
Error limits are 2 s. Error limits are 1s. c Units: 10y1 0 cm3 moleculey1 sy1 . d Experimental conditions: large excess of F atoms over H 2 S. e Experimental conditions: large excess of H 2 S over F. These results are considered by the authors to be less reliable than their results under large excess of F atoms.
between the two studies is the fact that while in Ref. w8x the absolute concentration of the F atoms had to be determined, this was not needed in our study. It should also be noted that a small number of experiments were carried out in Ref. w8x under conditions of a large excess of H 2 S over F atoms. The value obtained for the rate constant under these conditions is k Fq H 2 S s Ž1.7 " 0.4. = 10y1 0 cm3 moleculey1 sy1 , but the authors consider this value to be less reliable than their other value. The value obtained by us is in between the two values obtained in Ref. w8x. All the results obtained in the present study are summarized in Table 1, where they are compared with the earlier available data.
b
studies. In both of them a discharge-flow system was used with mass spectrometric detection of the reagents. However, the conditions under which the experiments were carried out were very different. Whereas in Ref. w8x experiments were carried out under pseudo-first-order conditions with the concentration of F atoms in large excess over the concentration of H 2 S, our experiments were carried out under second-order conditions, with the sum of concentrations of H 2 S Žor D 2 S. and CH 4 being larger than the concentration of the F atoms. Another difference
References w1x w2x w3x w4x w5x
w6x w7x w8x w9x w10x
R. Foon, M. Kaufman, Prog. Reaction Kinet. 8 Ž1975. 81. W.E. Jones, E.G. Skolnik, Chem. Rev. 76 Ž1976. 563. J.B. Anderson, Adv. Chem. Phys. 41 Ž1980. 229. R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson, J.A. Kerr, J. Troe, J. Phys. Chem. Ref. Data 21 Ž1992. 1125. W.B. DeMore, S.P. Sander, D.M. Golden, R.F. Hampson, M.J. Kurylo, C.J. Howard, A.R. Ravishankara, C.E. Kolb, M.J. Molina, Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling, Evaluation Number 11 of the NASA Panel for Data Evaluation, JPL Publ., 94–26 Ž1994.. A. Persky, H. Kornweitz, Int. J. Chem. Kinet. 29 Ž1997. 67. B.S. Agrawalla, D.W. Setser, J. Phys. Chem. 90 Ž1986. 2450. G. Schonle, M.M. Rahman, R.N. Schindler, Ber. Bunsenges. ¨ Phys. Chem. 91 Ž1987. 66. R.L. Williams, F.S. Rowland, J. Phys. Chem. 77 Ž1973. 301. R. Edrei, A. Persky, Chem. Phys. Lett. 157 Ž1989. 265.