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Third-body-assisted, binary ion—molecule reactions. The reaction NH+3 + H2 → NH+4 + H
Volume 122, numbe.r 3
6 December 1935
CHEhIICAL PHYSICS LETTERS
THIRD-BODY-ASSISTED, THE REACTION NH;
BINARY + H, --, NH:
ION-MOLECULE + H
REACTIONS.
H. BbHRINGER Mm8046
Planck- Institute for Physic and Astrophystcs. Garchtng. Federal Repubhc of Germany
Received
5 September
-l-he reac~lon from 2U to 298 rate is Increased that a reacllon
1985.
Insruute for Ertraternwrmf
in final form 14 October
1985
AH was stud& m a selected-ion dnft tube as a funcfion of gas density and temperature NH; +H, + NH; K A pressure dependence of the second-order rate coefficient was observed which indicates Hal Lhe reactlon when the intermedlate complexes colhde with a third body. It IS concluded that one has to be aware In general Lhat IS found to be slow at low or moderate density can be slgmficantly faster m a h&-pressure environment.
1. Intraduction In general one assumes that “binary” ion-molecule reactions - e g atom exchange reactions or charge transfer - occur only via a two-body colhsion process and that a pressure-Independent second-order rate coefficrent is sufficient to describe the reactron kinetics This has been found to be correct in almost all experimental studies up to date, where most of these experunents have been conducted at low or moderate gas densities up to about 3 X 1016 cmm3 There are two known exceptrons to thus rule, however In 1969 Bohme et al [l] found a pressure dependen= of the rate coefficrent for the reactron O++Nz-+NO++N
(1)
at a temperature of 82 K in He buffer gas. The result for the rate coefficient has the form kl = 1 65 X lo-r2 + 5.4 X 1 O-2g And in i980 tion
Physrcs
cm3 s-1 cm6 s-l
X
[He]
Johnsen et al. [2] mvestigated the reac-
He+ + H, + products
(2)
and found that the reachon rate is best described as the sum of a second-order and a third-order term
BSrri.nger and Arnold [3] have carned out a detailed study on the kinetrcs of reaction (2) for temperatures from 18 to 400 K and confirmed the previous results Both of these reactions are very slow at thermal energy It 1s also known from early measurements [4] that some slow, excthermic bmary ion-molecule reactions have a rate coefficient that mcreases with decreasing energy. Ferguson and co-workers [S] have explamed this behavior by the existence of an intermedrate reactron complex The increased hfetime of the complex achreved by lowering the temperature favors a reactive decay of the complex into the most exotberrnic channel Other indirect evidence for the formation of long-lived intermediate complexes in ion-molecule collisrons comes from the observatron of three-body association reactions [5] and from the detailed study of the collisronal deactivation of vibrationally excited ions [6] At energies above thermal, evidence for intermediate complexes can be obtained from crossedbeam studies [7]. Taking these observations mto account, one should expect the following kinetic behavior for a slow exothermic ion-molecule reaction. A change in the reacuon kmetics should be observed when the gas dens@ III the experunent is rarsed to the pornt where the lifetime of the complexes becomes comparable to the mverse colhsron frequency. Because of the strong ion-induced-dipole interaction the interrnedia;e 185
Volume 122, number 3
complexes wrll be “hot” compared to the temperature of the background gas and they wrll tend to grve off therr internal energy vra the third-body colhsrons Therefore -he expected effect of high background pressure will he a longer hfetime of the intermediate complexes and thus an enhanced reaction rate coefficient Thrs 1s the behavior which has been observed for the reactions (1) and (2) and we may suspect that rt may be found for marry other slow reactrons Looking for a way to provide more experunental evidence for this assertion we found that the reaction NH3++H2+NH4++H
6 December 1985
CHEMICAL PHYSICS LEl-IERS
(3)
rmght be the ideal candidate for an investigation. It is known to be very slow and rt seems to have an mcreasrng rate coefficrent with decreasing temperature [S-l 11. A study of tlus reaction is also mteresting for other reasons Fehsenfeld et al. [9] and Smith and Adams [lo] have shown that the rate coefficrent of reactron (3) 1s increasing with temperature in the range 80-800 K whtle Lume and Dunn [ 1 l] found again hrgher rate coefficrents at temperatures below 20 K It would be mce to trace the mimmum of the reaction velocity as a functron of temperature and so fill the gap in this most interestmg data set of ion-molecule reactron kinetics. This reaction 1s also very rrnportant for the production of the wrdespread interstellar molecule NH3 [ 121 and rate coefficrents m the temperature range IO-100 K are needed for astro-chemrcal models
NH; by H2 is expected to be more than an order of magnitude hrgher than the reaction probabrhty Thus the reactmg NH; ions are in their ground states. The H2 reactant gas was a room temperature equrlibnum mixture of ortho and para states. The ftrst set of measurements was conducted in pure H,. The disappearance of the NH; signal and the appearance of the product was monitored as a function of H2 pressure. In these measurements the reactions occurred at low enough Hz pressures that no significant pressure dependence was observed and the resultant rate coefficients are close to the lowpressure hut. To observe the pressure dependence more clearly a second set of measurements was carried out with a He-H, rmxture with Hz mixing ratio of 6-10%. Here we measured the rate coefficients for fmed gas pressure by varymg the resrdence tune of the ions through vanatron of the apphed dnft field. During all these measurements the value of E/. (electric field strength/gas densrty) was kept low enough a-1-5 Td ( lo-l7 V cm2) so that the ron krnetrc energy was not sigruticantly enhanced over the thermal value (see theory by Viehland et aI. [15] and discussion in ref [16]). The pnmary ion residence trme was measured drrectly in each expenrnent by a means of a pulsed ran beam mode and the resultant zero-field mobilitres of NH; m H2 were in the range 12.5 f 2.5 cm2 V-1 s-L m the temperature range considered.
3. Results and discussion 2 Experimental A selected-ion dnft tube [ 133 wluch can be operated at temperatures from 18 to 420 K and gas densities up to 3 x 1017 cm-3 was used to study the temperature and pressure dependence of reaction (3) N+ ions were mlected as pnrnary ions into the dnft-tube filled v&h H2 gas or a He-H2 ga_ nrxture The primary rons were raprdly converted to NHf by three successive reactions with H2 [ 141. Smce these first reactron steps are much faster than reactron (3) no sigmficant error rs introduced by takmg N+ mstead of NH; pnmar-y ions. Some of the NH; ions may initially be produced in a vrbrationally excited state because the last addrtion reactron IS sufficiently exothermic by about 1 eV. However, the probabrhty for deactivatron of 186
Frg. 1 shows examples of the observed pressure dependence of the apparent secondorder rate coefficient, k',for reaction (3) k' can be gtven in the form k'=k,+k,m]
,
(4)
where k2 and k3 are constant coefficrents and [M] is the concentratron of the buffer gas Fig 2 summarizes all the results by giving the coefficients k2 and kg as a function of temperature. previous measurements obtamed wrth flowmg afterglows [9,10] at gas densities below about 2 X 1Ol6 crnW3 and from very low density ion-trap expenrnents [l l] are also shown rn the figure. Because of the low dens&es these latter experiments yrelded only the coefficrent k2 There is good agreement between the different measurements.
Volume 122, number 3 I”’
o-
n
NH-;+
42
CHEMICAL.PHYSICS LETTERS ,I
1
11
H,-
NH,+
11
1
I
I,
6 December
4.
11
+ H NH,‘+
ll.6K u
O=-,
5 15 10 gas number density 110” cm-?
The following analytical expressions can be fit to the data: K/n1
k, % 6.4 X lo-!3(T/300 k3 = 1.13 X 10-30(100
5
K)1-g4 K/T)1 g .
for lo-30 for 150-800
K , K , (5)
Fehsenfeld et al. [9] have fitted an Arrhenius expres sron to the high-temperature branch of the data for k2 - wluch 1s physrcally more reasonable - and obtamed A = 1 7 X lo-l1 cm3 s-l for the preexponential factor and E = 0 09 eV for the actrvation energy One has to make sure that (H& dirners do nor interfere m these measurements because they could well mmnc the kinetics of the third-body-assisted reaction by the process NHf+(H2)2-+NH;+H2+H,
H
20
Fig_ 1. Measured rate coefficients for reaction (3) as a function of gas denuty at different temperatures. 0, n in Hz gas; 0, l in He/H2 gas mixture
k, = 1.3 X10 -12(10
Hz-NH,*+
(6)
3
6
10
20
30
60
temperature
100
200 300
600
IKI
Fig. 2 Second-order rate coefficient, kl.and thud-order mte coefficient. k3, for reaction (3) as a function of temperature Previousresults are from rcfs [9-111.
where k,, is a third-order rate coefficrent. X-6 the coefficrent for reaction (6), and Kes the eqmhbrium constant for the dimer concentration. We have drscussed Gus problem for (H-J2 dimers previously [3] and calculated K, by fo-rmulas from Stogryn and Htrschfelder [17] and data from refs. [18,19] We found that k,, istwo or three magnitudes smaller than the observed k3 and concluded that (H2)2 dhners drd not interfere in the present study. The overall reaction that proceeds via an exerted or stabihzed intermediate complex can then be described by the following scheme
ka NH; + H, --_1cNH3+%I* TC
-1
with I
ksPf1
Tr I-
NH3-12 J
NH_pH, (7) 187
Volume 122, number 3
CHEMICAL
PHYSICS
where M is the stabihzmg collision partner. In steady state the macroscoprc rate coefficients are
k
2
=
kd
r$
+ rr-l
z ka$ r
forrc
(8)
Assuming that k, is equal to the encounter lirmt, k,, and k, = kLfl (where p 5 1 is a stabrhsatron efficrency factor) one finds Tc = 4 X 1017k3/p s-I
T= = 6.4 X 108k3/k2/3 s
(9)
With given experimental values and f.l = 1 one obtains for example for a temperature of 50 K the results TV = 1 7 ): 1 O-l2 s and 7r = 12 X 1 0m8 s The reactron probability per collisron 1sP = 1 5 X 10m4 These results lead to the followmg considerations of the reaction mechanism. Results of crossed beam experiments by Ersele et al [20] (who drscuss the geometry and potential energy surface of reaction (3)) and of a study wrth isotopically labeled reactants by Adams and Smith [21] imply that the reaction is impulsrve at high energy and may mvolve the tunneling of an H atom m the complex reaction process at low temperature. One can make a simple quantitative estrmate of tlus process by takmg the barrier height to be penetrated equal to the observed activation energy barrier of 0 09 eV and its width to be about 1 A The tunneling time is then given by the quantum mechanical penetration probability and the vibrational period of the trapped NH$-Hz complex (neglecting a geometric efficiency factor). If the vibrational period is taken to be = lo-l3 s in analogy to the He+-H, polailsation state [22] one gets a reactive transition tune Tr = 5 X 10m8 s which is close to the above value Considering the crude assumptions made one gets a mcely consistent picture for the tunnehng mechanism and obtains severe constraints on the corresponding potential energy surface.
4. Conclusion The present study mcely demonstrates that the mcrease of the rate coefficient with decreasing temperature - as found m numerous ion-molecule reactions 188
LETTERS
6 Demzmber 1985
Table 1 Measured binary reaction rate coeffkxnts at low pressure, kp, estimated third-order rate coefficients, k3. and pressure, p. where the pressure enhancement becomes comparable to kz for some slow ion-molecule reactions at 300 K Reation
k2 (cm3 s-l)
k3 (cm6 s-l)
P (Torr, at 300 K)
0++N2 0; + CH4 co; + 02 AI++02
10-l+ 7 x lo-l2 6 x 10-l’ 5 x 10-l’
10-M lo+9 lo-*’ lo-=
26 18 150 1300
-
1s connected
with an increase
of the lifetime
of the
intermediate reaction complex. The example also shows that a slow, exothermic ion-molecule reaction can become substantially faster at high pressure when the reactron 1s assisted by thud-body colhsions We suspect that most slow, exothermic reactions have an analogous reaction mechanism and should therefore show the same pressure-mduced rate enhancement To give an Idea of the pressure effects that are to be expected we list in table 1 a few slow, exothermrc ion-molecule reactions and the critical pressure at room temperature where the enhancement is comparable to the low-density rate The corresponding cntrcal densrty 1s calculated from w] = kz/k,. The values for k2 were taken from the hterature [23] and the values for k3 were obtained by comparison with measured three-body assocratron coefficients for systems with comparable complexity. All the reactions listed actually show a negative temperature dependence at low temperatures! Most measurements of ion-molecule reaction rate coefficients have been obtamed with flowmg afterglows, dnf-tubes or ion cyclotron resonance spectrometers at den&es below lOI cmm3. It is obvious why hardly any pressure dependence of a reaction classified as bum-y reactlon has ever been detected. But it is clear that one should be careful if one hkes to apply a rate coefficient of a slow exotherrmc reaction to a high-pressure environment, e.g. the loweratmosphere, ratition chemistry or high-pressure dir+ charge There 1s an interestmg application for highpressure reaction experiments, because the question remains whether the apparent bmary rate coeffiiclent can actually grow as large as the collisron lunit at high
pressure.
Volume 122, number 3
CHEMICAL PHYSICS LETTERS
Acknowledgement The experimental
[9]
part of the work was carried
out
at the Max Planck Institute for-Nuclear Physics at Heidelberg and I wish to thank Dr Arnold and the staff of the Institute for their support. I also appreciate helpful comments by Dr J Durup and Dr. T.W Haltquist.
[lo] [ 111 [12] 1131 [141
References [l] D K_ Bohme, D.B. Dunkin, F.C. Fehsenfeld and [2] [3] [4] [S] [6]
[7] [8]
E-E Ferguson, J. Chem. Phys 51(1969) 863. R. Johns-en, A. Chen and M.A. BlondI, J. Chem Phys 72 (1980) 3085. H. Bohrmger and F. Arnold, to be pubhshed E-E Ferguson, D.K Bohme, F C. Fehsenfeld and D B Dunkin, J. Chern Phys. 50 (1969) 5039 E E Ferguson, in Ion-molecule reactIons, VoL 2, ed. J.L Franklin (1972) p 363. H. BG;uL-,-er. M. DurupFerguson, D W Fahey, F-C. Fehsenfeld and Z E Ferguson, J. Chem Phys. 79 (1983) 4201 R Wolfgang, Accounts Chem. Res_ 3 (1970) 48. J-K Kim, L P. Theard and W.T Huntress Jr., J. Chem Phyr 62 (1975) 45
1151 1161
6 December 1985
F C Fehsenfeld, W. Lmdier, AL. Schmeltekopf, D.L Albritton and F_E Ferguson, J Chem. Phys 62 (1975) 2001. D Smith and N.G. Adams, Mon Not Roy. Ash_ Sot. 197 (1981) 377. J k Ltie and G H Dunn, to be pubhshcd. E Herbst and W. Klemperer, Astrophys J. 158 (1973) 505 H Bohrmger and F Arnold, Intern. J Mass Spectxom Ion Phys 49 (1983) 61. F.C. Fehsenfeld, AL Schmeltekopf and E.E Ferguson. J. Chem Phys. 46 (1967) 2802. L.A Wehland, S L Lm and E A Mason, Chem. Phys 54 (1981) 341 H. Bohnnga and F. Arnold. J Chem Phys 77 (1982) 5534.
J. Chem Phys 31 1171 D.E Stogryn and J 0. HiwMp,idcr, (1959) 1531. [181 J-0 Hirschfelder. C F. Cur&s and RB. Bird, Molecular theory of gases and liquids (Wiley, New York, 1954) 1191 B-L Blaney and G E Ewing. Ann Rev. Phys Chem 27 (1976) 553. [201 G. Eisele, k Henglein, P. Botschwina and W Meyer, Ber. Bunsenges. Phys%k Chum. 78 (1974) 1090. 1211 N G Adams and D Smith, Intern J Mass Spectrom IonProc 61 (1984) 133 1221 D G Hopper, J Chem Phys. 73 (1980) 3289 r231 D L. Albritton, At NucL Data Tables 22 (1978) 1.
189
6 December 1935
CHEhIICAL PHYSICS LETTERS
THIRD-BODY-ASSISTED, THE REACTION NH;
BINARY + H, --, NH:
ION-MOLECULE + H
REACTIONS.
H. BbHRINGER Mm8046
Planck- Institute for Physic and Astrophystcs. Garchtng. Federal Repubhc of Germany
Received
5 September
-l-he reac~lon from 2U to 298 rate is Increased that a reacllon
1985.
Insruute for Ertraternwrmf
in final form 14 October
1985
AH was stud& m a selected-ion dnft tube as a funcfion of gas density and temperature NH; +H, + NH; K A pressure dependence of the second-order rate coefficient was observed which indicates Hal Lhe reactlon when the intermedlate complexes colhde with a third body. It IS concluded that one has to be aware In general Lhat IS found to be slow at low or moderate density can be slgmficantly faster m a h&-pressure environment.
1. Intraduction In general one assumes that “binary” ion-molecule reactions - e g atom exchange reactions or charge transfer - occur only via a two-body colhsion process and that a pressure-Independent second-order rate coefficrent is sufficient to describe the reactron kinetics This has been found to be correct in almost all experimental studies up to date, where most of these experunents have been conducted at low or moderate gas densities up to about 3 X 1016 cmm3 There are two known exceptrons to thus rule, however In 1969 Bohme et al [l] found a pressure dependen= of the rate coefficrent for the reactron O++Nz-+NO++N
(1)
at a temperature of 82 K in He buffer gas. The result for the rate coefficient has the form kl = 1 65 X lo-r2 + 5.4 X 1 O-2g And in i980 tion
Physrcs
cm3 s-1 cm6 s-l
X
[He]
Johnsen et al. [2] mvestigated the reac-
He+ + H, + products
(2)
and found that the reachon rate is best described as the sum of a second-order and a third-order term
BSrri.nger and Arnold [3] have carned out a detailed study on the kinetrcs of reaction (2) for temperatures from 18 to 400 K and confirmed the previous results Both of these reactions are very slow at thermal energy It 1s also known from early measurements [4] that some slow, excthermic bmary ion-molecule reactions have a rate coefficient that mcreases with decreasing energy. Ferguson and co-workers [S] have explamed this behavior by the existence of an intermedrate reactron complex The increased hfetime of the complex achreved by lowering the temperature favors a reactive decay of the complex into the most exotberrnic channel Other indirect evidence for the formation of long-lived intermediate complexes in ion-molecule collisrons comes from the observatron of three-body association reactions [5] and from the detailed study of the collisronal deactivation of vibrationally excited ions [6] At energies above thermal, evidence for intermediate complexes can be obtained from crossedbeam studies [7]. Taking these observations mto account, one should expect the following kinetic behavior for a slow exothermic ion-molecule reaction. A change in the reacuon kmetics should be observed when the gas dens@ III the experunent is rarsed to the pornt where the lifetime of the complexes becomes comparable to the mverse colhsron frequency. Because of the strong ion-induced-dipole interaction the interrnedia;e 185
Volume 122, number 3
complexes wrll be “hot” compared to the temperature of the background gas and they wrll tend to grve off therr internal energy vra the third-body colhsrons Therefore -he expected effect of high background pressure will he a longer hfetime of the intermediate complexes and thus an enhanced reaction rate coefficient Thrs 1s the behavior which has been observed for the reactions (1) and (2) and we may suspect that rt may be found for marry other slow reactrons Looking for a way to provide more experunental evidence for this assertion we found that the reaction NH3++H2+NH4++H
6 December 1985
CHEMICAL PHYSICS LEl-IERS
(3)
rmght be the ideal candidate for an investigation. It is known to be very slow and rt seems to have an mcreasrng rate coefficrent with decreasing temperature [S-l 11. A study of tlus reaction is also mteresting for other reasons Fehsenfeld et al. [9] and Smith and Adams [lo] have shown that the rate coefficrent of reactron (3) 1s increasing with temperature in the range 80-800 K whtle Lume and Dunn [ 1 l] found again hrgher rate coefficrents at temperatures below 20 K It would be mce to trace the mimmum of the reaction velocity as a functron of temperature and so fill the gap in this most interestmg data set of ion-molecule reactron kinetics. This reaction 1s also very rrnportant for the production of the wrdespread interstellar molecule NH3 [ 121 and rate coefficrents m the temperature range IO-100 K are needed for astro-chemrcal models
NH; by H2 is expected to be more than an order of magnitude hrgher than the reaction probabrhty Thus the reactmg NH; ions are in their ground states. The H2 reactant gas was a room temperature equrlibnum mixture of ortho and para states. The ftrst set of measurements was conducted in pure H,. The disappearance of the NH; signal and the appearance of the product was monitored as a function of H2 pressure. In these measurements the reactions occurred at low enough Hz pressures that no significant pressure dependence was observed and the resultant rate coefficients are close to the lowpressure hut. To observe the pressure dependence more clearly a second set of measurements was carried out with a He-H, rmxture with Hz mixing ratio of 6-10%. Here we measured the rate coefficients for fmed gas pressure by varymg the resrdence tune of the ions through vanatron of the apphed dnft field. During all these measurements the value of E/. (electric field strength/gas densrty) was kept low enough a-1-5 Td ( lo-l7 V cm2) so that the ron krnetrc energy was not sigruticantly enhanced over the thermal value (see theory by Viehland et aI. [15] and discussion in ref [16]). The pnmary ion residence trme was measured drrectly in each expenrnent by a means of a pulsed ran beam mode and the resultant zero-field mobilitres of NH; m H2 were in the range 12.5 f 2.5 cm2 V-1 s-L m the temperature range considered.
3. Results and discussion 2 Experimental A selected-ion dnft tube [ 133 wluch can be operated at temperatures from 18 to 420 K and gas densities up to 3 x 1017 cm-3 was used to study the temperature and pressure dependence of reaction (3) N+ ions were mlected as pnrnary ions into the dnft-tube filled v&h H2 gas or a He-H2 ga_ nrxture The primary rons were raprdly converted to NHf by three successive reactions with H2 [ 141. Smce these first reactron steps are much faster than reactron (3) no sigmficant error rs introduced by takmg N+ mstead of NH; pnmar-y ions. Some of the NH; ions may initially be produced in a vrbrationally excited state because the last addrtion reactron IS sufficiently exothermic by about 1 eV. However, the probabrhty for deactivatron of 186
Frg. 1 shows examples of the observed pressure dependence of the apparent secondorder rate coefficient, k',for reaction (3) k' can be gtven in the form k'=k,+k,m]
,
(4)
where k2 and k3 are constant coefficrents and [M] is the concentratron of the buffer gas Fig 2 summarizes all the results by giving the coefficients k2 and kg as a function of temperature. previous measurements obtamed wrth flowmg afterglows [9,10] at gas densities below about 2 X 1Ol6 crnW3 and from very low density ion-trap expenrnents [l l] are also shown rn the figure. Because of the low dens&es these latter experiments yrelded only the coefficrent k2 There is good agreement between the different measurements.
Volume 122, number 3 I”’
o-
n
NH-;+
42
CHEMICAL.PHYSICS LETTERS ,I
1
11
H,-
NH,+
11
1
I
I,
6 December
4.
11
+ H NH,‘+
ll.6K u
O=-,
5 15 10 gas number density 110” cm-?
The following analytical expressions can be fit to the data: K/n1
k, % 6.4 X lo-!3(T/300 k3 = 1.13 X 10-30(100
5
K)1-g4 K/T)1 g .
for lo-30 for 150-800
K , K , (5)
Fehsenfeld et al. [9] have fitted an Arrhenius expres sron to the high-temperature branch of the data for k2 - wluch 1s physrcally more reasonable - and obtamed A = 1 7 X lo-l1 cm3 s-l for the preexponential factor and E = 0 09 eV for the actrvation energy One has to make sure that (H& dirners do nor interfere m these measurements because they could well mmnc the kinetics of the third-body-assisted reaction by the process NHf+(H2)2-+NH;+H2+H,
H
20
Fig_ 1. Measured rate coefficients for reaction (3) as a function of gas denuty at different temperatures. 0, n in Hz gas; 0, l in He/H2 gas mixture
k, = 1.3 X10 -12(10
Hz-NH,*+
(6)
3
6
10
20
30
60
temperature
100
200 300
600
IKI
Fig. 2 Second-order rate coefficient, kl.and thud-order mte coefficient. k3, for reaction (3) as a function of temperature Previousresults are from rcfs [9-111.
where k,, is a third-order rate coefficrent. X-6 the coefficrent for reaction (6), and Kes the eqmhbrium constant for the dimer concentration. We have drscussed Gus problem for (H-J2 dimers previously [3] and calculated K, by fo-rmulas from Stogryn and Htrschfelder [17] and data from refs. [18,19] We found that k,, istwo or three magnitudes smaller than the observed k3 and concluded that (H2)2 dhners drd not interfere in the present study. The overall reaction that proceeds via an exerted or stabihzed intermediate complex can then be described by the following scheme
ka NH; + H, --_1cNH3+%I* TC
-1
with I
ksPf1
Tr I-
NH3-12 J
NH_pH, (7) 187
Volume 122, number 3
CHEMICAL
PHYSICS
where M is the stabihzmg collision partner. In steady state the macroscoprc rate coefficients are
k
2
=
kd
r$
+ rr-l
z ka$ r
forrc
(8)
Assuming that k, is equal to the encounter lirmt, k,, and k, = kLfl (where p 5 1 is a stabrhsatron efficrency factor) one finds Tc = 4 X 1017k3/p s-I
T= = 6.4 X 108k3/k2/3 s
(9)
With given experimental values and f.l = 1 one obtains for example for a temperature of 50 K the results TV = 1 7 ): 1 O-l2 s and 7r = 12 X 1 0m8 s The reactron probability per collisron 1sP = 1 5 X 10m4 These results lead to the followmg considerations of the reaction mechanism. Results of crossed beam experiments by Ersele et al [20] (who drscuss the geometry and potential energy surface of reaction (3)) and of a study wrth isotopically labeled reactants by Adams and Smith [21] imply that the reaction is impulsrve at high energy and may mvolve the tunneling of an H atom m the complex reaction process at low temperature. One can make a simple quantitative estrmate of tlus process by takmg the barrier height to be penetrated equal to the observed activation energy barrier of 0 09 eV and its width to be about 1 A The tunneling time is then given by the quantum mechanical penetration probability and the vibrational period of the trapped NH$-Hz complex (neglecting a geometric efficiency factor). If the vibrational period is taken to be = lo-l3 s in analogy to the He+-H, polailsation state [22] one gets a reactive transition tune Tr = 5 X 10m8 s which is close to the above value Considering the crude assumptions made one gets a mcely consistent picture for the tunnehng mechanism and obtains severe constraints on the corresponding potential energy surface.
4. Conclusion The present study mcely demonstrates that the mcrease of the rate coefficient with decreasing temperature - as found m numerous ion-molecule reactions 188
LETTERS
6 Demzmber 1985
Table 1 Measured binary reaction rate coeffkxnts at low pressure, kp, estimated third-order rate coefficients, k3. and pressure, p. where the pressure enhancement becomes comparable to kz for some slow ion-molecule reactions at 300 K Reation
k2 (cm3 s-l)
k3 (cm6 s-l)
P (Torr, at 300 K)
0++N2 0; + CH4 co; + 02 AI++02
10-l+ 7 x lo-l2 6 x 10-l’ 5 x 10-l’
10-M lo+9 lo-*’ lo-=
26 18 150 1300
-
1s connected
with an increase
of the lifetime
of the
intermediate reaction complex. The example also shows that a slow, exothermic ion-molecule reaction can become substantially faster at high pressure when the reactron 1s assisted by thud-body colhsions We suspect that most slow, exothermic reactions have an analogous reaction mechanism and should therefore show the same pressure-mduced rate enhancement To give an Idea of the pressure effects that are to be expected we list in table 1 a few slow, exothermrc ion-molecule reactions and the critical pressure at room temperature where the enhancement is comparable to the low-density rate The corresponding cntrcal densrty 1s calculated from w] = kz/k,. The values for k2 were taken from the hterature [23] and the values for k3 were obtained by comparison with measured three-body assocratron coefficients for systems with comparable complexity. All the reactions listed actually show a negative temperature dependence at low temperatures! Most measurements of ion-molecule reaction rate coefficients have been obtamed with flowmg afterglows, dnf-tubes or ion cyclotron resonance spectrometers at den&es below lOI cmm3. It is obvious why hardly any pressure dependence of a reaction classified as bum-y reactlon has ever been detected. But it is clear that one should be careful if one hkes to apply a rate coefficient of a slow exotherrmc reaction to a high-pressure environment, e.g. the loweratmosphere, ratition chemistry or high-pressure dir+ charge There 1s an interestmg application for highpressure reaction experiments, because the question remains whether the apparent bmary rate coeffiiclent can actually grow as large as the collisron lunit at high
pressure.
Volume 122, number 3
CHEMICAL PHYSICS LETTERS
Acknowledgement The experimental
[9]
part of the work was carried
out
at the Max Planck Institute for-Nuclear Physics at Heidelberg and I wish to thank Dr Arnold and the staff of the Institute for their support. I also appreciate helpful comments by Dr J Durup and Dr. T.W Haltquist.
[lo] [ 111 [12] 1131 [141
References [l] D K_ Bohme, D.B. Dunkin, F.C. Fehsenfeld and [2] [3] [4] [S] [6]
[7] [8]
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189