Molecular beam reaction of K with HCl: Effect of translational excitation of reagentsJ. Gary Pruett, Frederick R. Grabiner, and Philip R. Brooks Citation: The Journal of Chemical Physics 60, 3335 (1974); doi: 10.1063/1.1681527 View online: http://dx.doi.org/10.1063/1.1681527 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/60/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The effect of reagent translational excitation on the dynamics of the reaction H+Cl2→HCl(v’,J’)+Cl J. Chem. Phys. 100, 1075 (1994); 10.1063/1.466639 Molecular beam reaction of K with HCl: Effect of rotational state of HCl J. Chem. Phys. 70, 5317 (1979); 10.1063/1.437330 Translational excitation of the molecular beam reaction K+HCl→KCl+H J. Chem. Phys. 63, 1173 (1975); 10.1063/1.431454 Effect of reagent vibrational excitation on the rate of a substantially endothermic reaction; HCl(ν′ = 1–4) + Br→ Cl + HBr J. Chem. Phys. 59, 6679 (1973); 10.1063/1.1680052 Molecular Beam Reaction of K with HCl: Effect of Vibrational Excitation of HCl J. Chem. Phys. 55, 1980 (1971); 10.1063/1.1676338

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

155.33.16.124 On: Sun, 23 Nov 2014 12:54:48

LETTERS TO THE EDITOR

The Letters to the Editor section is subdivided into four categories entitled Communications, Notes, Comments and Errata. The textual material of each Letter is limited to 1200 words minus the following: (a) 200 words for a square figure one-column wide. Larger figures are scaled in proportion to their area. (b) 50 words for each displayed equation; (c) 7 words for each line of table including headings and horizontal rulings. Proof will be sent to authors. See the issue of , January 1974 for a fuller description of Letters to the Editor.

COMMUNICATIONS

Molecular beam reaction of K with HCI: Effect of translational excitation of reagents *

J. Gary Pruettt, Frederick R. Grabiner, and Philip R. Brooks~

Department of Chemistry. Rice University. Houston. Texas 77001 (Received 29 January 1974)

The temperature variation of chemical reaction rate constants has traditionally been expressed as k =A exp x(- Ea/RT), where Ea is called the activation energy. Depending on the energy mode which must be activated, various kinetic theory models predict different tempera­ture dependent forms for the pre-exponential factor A, but experimental uncertainties cause any temperature dependence of A to be overwhelmed by the exponential. The determination of the energy modes which must be activated to initiate reaction is sufficiently important that several ingenious techniques have been devised to study reactions under nonequilibrium conditions. Reac­tions studied1 include those intitated by shock waves, flash photolysis, hot atoms, and ions. The possibility of using lasers to stimulate reactions2 now makes eluci­dation of the mechanism of activation of reactions of practical as well as theoretical importance.

Molecular beam techniques have been recognized as the ideal tool for studying such reaction details as the energy mode dependence of the cross section, and the translational energy dependence of several reactions has been reported. 3_6 For the slightly endoergic reaction K + HCI = KCI+ H we have previously reported that vibra­tional excitation of HCI increases the reactive cross sec­tion by about two orders of magnitude. 7 We now wish to report that an equivalent amount of energy placed in rela­tive translation of the reactants results in only a modest (-10 x) increase in cross section.

The apparatus was modified from that previously used6

by adding a nozzle gas beam source, a mass spectrome­ter gas beam monitor, and a differential surface ioniza­tion detector designed to capture most out-of-plane scat­tering. Beams of fast HCI were generated by expanSion of mixtures of HCI and Hz from a room temperature noz­zle source. By varying the mole fraction of Hel the mean HCI speed was varied from 0.6 to 2.2 kM/sec. The velocity distribution of HCI in each mixture was de­termined by time-of-flight measurements. 8 Relative cross sections at five collision energies were obtained by a comparison of integrated product angular distribu­tions, relative HCI denSities, relative K atom fluxes, and relative collision path lengths. Absolute cross sec-

tions were obtained by a similar comparison8 between the lowest energy K + HCI reaction and the well- studied reaction of K + HBr = KBr + H.

The experimental results are shown in Fig. 1, togeth­er with the hard sphere cross section function,9 a= ao(l - E*/ E). The parameter E* is determined by the data to be 10 7 kcal and within experimental error appears to be 11 E, the reaction endothermicity. 10 Earlier cross section measurements for thermal beams ll led us to sug­gest an activation energy, Ea - 1 kcal, in addition to 11 E 30 10 5 kcal but uncertainties in 11 E precluded a unique determination of Ea. The present results do not distin­guish between 11 E and Ea but suggest the sum to be somewhat less than previously assumedo

Comparison of Figo 1 with the results for vibrationally excited (translationally unexcited) molecules6 shows that 8.3 kcal placed in vibration is roughly 10 times more

2.5

2.0

1.5

C\J 0« b 1.0

0.5

4 6 8 10 12

E (kea I I mole)

FIG. 1. Apparent reactive cross section for K+ HCI-KCI + H plotted versus nominal translational energy [defined as E=~ f.1.

(Wk+ W~C1)' where WI is the rms speed of species il. Error bars denote statistical error in relative cross sections; absolute cross sections are uncertain by ~ ± 50% (Ref. 8). The solid curve is 0"= 0"0 (1 -E* IE) with 0"0 = 2_ 5 ,,\2 and E* = 1. 7 kcal/mole.

The Journal of Chemical Physics, Vol. 60, No.8, 15 April 1974 Copyright © 1974 American Institute of Physics 3335 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

155.33.16.124 On: Sun, 23 Nov 2014 12:54:48

3336 Letters to the Editor

effective than if placed in relative translation. 12 (Reac­tive cross sections are -20 and -2 ;"2, respectively.) This effect, of course, has long been postulated for en­dothermic reactions1

,3 and has also been found in the re­cent chemiluminescence experiments of Polanyi and co­workers. 13 Model trajectory calculations14 suggest this to be a general phenomenon for endothermic reactions since the reaction barriers are usually in the exit chan­nel. 14a For this mass combination, however, the exper­imental results would suggest that the barrier is quite late in the exit channel. 14b

It is also instructive to consider the angular momen­tum restrictions imposed on this reaction. As previous­ly pointed outll ,15,16 the large change in reduced mass for this and Similar reactions requires that product ro­tation must carry off almost all of the angular momen­tum originally present as orbital motion of the reactants, so J'n"'" J.wb. Because this reaction is endoergic the energy required for rotational excitation of products must come from initial translation, assuming that the reagents are predominantly in their ground states. One then finds that for reaction to occur, E2: AE+B'hJ'(J' + 1), where primes denote products and other notation is given in Ref. 16(b). These conditions require b:S bo(l - A E/ E)l /2, where bo is the bond length of KCl. Assum­ing that a =71b 2 this predicts that the energy dependence for the cross section is a = 71b~ (1- A E/ E) and suggests that in this case E* be identified with A E and not with Ea as commonly assumed. Since ao is predicted to be too large (24 ;"2 as compared to the 2.5 ;"2 observed) we must conclude that reaction does not occur for all impact parameters satisfying the dynamic constraints. It is not yet clear whether reaction occurS with reduced probabil­ity at all impact parameters less than the maximum al­lowed by the conservation laws, bm , or if the maximum reactive impact parameter is less than bm • 17

*We gratefully acknowledge support of this research by the

Robert A. Welch Foundation and the Alfred P. Sloan Founda­tion.

tNDEA Fellow 1971-1973. Present address: Department of Chemistry, Columbia University, New York, NY.

tAlfred P. Sloan Fellow. l L . D. Spicer and B. S. Rabinovitch, Ann Rev. Phys. Chern.

21, 349 (1970). 2y. S. Letokhov, Science 180, 451 (1973). 3S. B. Jaffe and J. B. Anderson, J. Chern. Phys. 49, 2859

(1960); 51, 1059 (1969). 4M. E. Gersch and R. B. Bernstein, J. Chern. Phys. 55, 4661

(1971); 56, 6131 (1972). 5A. E. Redpath and M. Menzinger, Can. J. Chern. 49, 3063

(1971). BC. Batalli-Cosmovici and K. W. Michel, Planet. Space Sci.

21, 89 (1973). 7T. J. Odiorne, P. R. Brooks, and J. Y. Y. Kasper, J. Chern.

Phys. 55, 1980 (1971). 8J • G. Pruett, Ph. D. thesis, Rice UniverSity, 1974. 91. Amdur and G. G. Hammes, Chemical Kinetics (McGraw­

Hill, New York, NY, 1966). loJANF Thermochemical Tables, edited by D. R. Stull (Dow

Chemical, Midland, Michigan, 1964), and revisions to date. lIT. J. Odiorne and P. R. Brooks, J. Chern. Phys. 51, 4676

(1969). 12Microreversibility then requires the reverse reaction,

H + KCI- Hel + K, to yield mainly excited products. This is consistent with the observations of Siska. (P. E. Siska, Ph. D. thesis, Harvard University, 1970).

13A . M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Faraday Disc. Chern. Soc. (to be pub­lished) and references therein.

14(a) D. S. Perry, J. C. Polanyi, and C. W. Wilson, Jr., Chern. Phys. (to be published); (b) B. A. Hodgson and J. C. Polanyi, J. Chern. Phys. 55, 4745 (1971).

15D• R. Hers chbach , The Vortex, 22, 348 (1961), and Disc. Faraday Soc. 33, 281 (1962).

lS(a) E. F. Greene, A. L. Moursund and J. Ross, Adv. Chern. Phys. 10, 135 (1966); (b) D. R. Herschbach, Adv. Chern. Phys. 10, 319 (1966).

17D. Truhlar [J. Chern. Phys. 54, 2635 (1971)] has used a phase space calculation to fit the nonreactive scattering results of Ref. 16(a). Although his calculation is inconsistent with the present results because t::.E was assumed to be too small, his results suggest a reduced probability of reaction out to bm •

J. Chern. Phys., Vol. 60, No.8, 15 April 1974 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

155.33.16.124 On: Sun, 23 Nov 2014 12:54:48