Crossedbeam study of the reactions H3 +(Ar,H2)ArH+ and ArH+(H2,Ar)H3 +C. R. Blakley, M. L. Vestal, and J. H. Futrell Citation: The Journal of Chemical Physics 66, 2392 (1977); doi: 10.1063/1.434276 View online: http://dx.doi.org/10.1063/1.434276 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/66/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Crossedbeam study of the reaction of van der Waals molecule H+(NO)2 J. Chem. Phys. 92, 1657 (1990); 10.1063/1.458100 Crossedbeam study of the reaction H2 + (CO, H)HCO+ at 1.89 eV J. Chem. Phys. 71, 4166 (1979); 10.1063/1.438189 Crossedbeam study of the reaction H3 +(D2,H2)D2H+ J. Chem. Phys. 64, 2094 (1976); 10.1063/1.432434 Crossedbeam studies of the hydrogen exchange reaction: The reaction of H atoms with T2 molecules J. Chem. Phys. 59, 3421 (1973); 10.1063/1.1680488 CrossedMolecularBeam Measurements of the Total Cross Sections of Ar–N2, Ar–Ne, Ar–He, and Ar–H2 atThermal Energies J. Chem. Phys. 45, 240 (1966); 10.1063/1.1727317

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Crossed-beam study of the reactions H3+ (Ar ,H2)ArH + and ArH+(H2,Ar)Ha+ *

c. R. Blakley,t M. L. Vestal,t and J. H. Futrell

Department of Chemistry. University of Utah. Salt Lake City. Utah 84112 (Received 20 September 1976)

The dynamics of the reactions Hi(Ar.H2)ArH+ and ArH+(H2.Ar)Hi were studied over the initial relative translational energy from 0.87 to 9.7 eV and from 0.18 to 6.7 eV. respectively. The reactions were found to proceed via direct mechanisms at all energies studied. Energetic data are presented that suggest Hi is not rapidly relaxed vibrationally upon collision with H2 as previously thought. Rather than being relaxed within a few collisions. the lower vibrational states probably are relaxed with a rate constant on the order of 10- 12 cm3 molecule-I.sec- I.

INTRODUCTION

Proton transfer reactions comprise a class of very simple ion-molecule reactions which have received much attention in the literature. 1 Most information about these reactions consists of rate constants, branching ratios, and heats of formation as determined by mass spectrometry, drift tube, and ion cyclotron resonance techniques. Kinematic information, how­ever, can only be inferred from these data. A more direct approach is to use crossed-beam techniques to directly measure the product angular and energy dis­tributions.

In this paper we report kinematic data on the reac­tions

Hi +Ar- ArH+ +H2'

ArW +H2- Hi +Ar.

(R1 )

(R2)

These reactions are of some interest because they per­mit the comparison study of a simple exothermic pro­ton transfer reaction with its endothermic reverse re­action. Pragmatically, the reactions of Hi are of in­terest because of its use as a reagent ion in chemical ionization mass spectrometry.

EXPERIMENTAL

The crossed-beam apparatus, shown schematically in Fig. 1, is described in detail elsewhere. 2 Basically, it consists of an ion gun which produces a nearly mono­energetic beam of the desired ion which is then crossed at right angles with a beam of neutral molecules. Ion­ic reaction products are energy and mass analyzed in a moveable detector assembly which consists of a 90° cylindrical electrostatic energy analyzer, a quadrupole mass filter, and a secondary electron multiplier. A chemical ionization source is used to generate the re­actant ions and a supersonic nozzle to produce the neu­tral beam. Time averaged, phase sensitive pulse count­ing is used to obtain the. energy spectra of the mass and angular resolved product ions which are then processed off line on a computer.

The high pressure source can be used to produce vi­brationally relaxed reactant ions. The supersonic mo­lecular beam source produces internally relaxed intense neutral beams with narrow velocity and angular spreads and can be "seeded" to produce accelerated beams of heavy neutrals. A neutral beam ionizer has been added

2392 The Journal of Chemical Physics, Vol. 66, No.6, 15 March 1977

so that accurate neutral velocity and angular distribu­tions can be measured with the moveable detector.

REDUCTION OF EXPERIMENTAL DATA

Details of the data reduction have also been described previously.3 Briefly, the experimental data are sum­marized in two forms. In the first of these the contour map of relative intensities normalized for polar cen­ter-of-mass coordinates is plotted superimposed on a Newton diagram4 according to the transformation

I(U, X, <J;)= U2 /V1(T,e, '11), (1 )

where U, X, and <J; are the center-of-mass velocity, polar scattering angle, and azimuthal angle, respec­tively, and V, T, e, and '11 are the laboratory velOCity, energy, polar scattering angle and azimuthal angle, re­spective ly. Because data are obtained in the plane of the reactant beams, the laboratory azimuthal angle can be suppressed. Similarly, since there is azimuthal symmetry in the barycentric system, we can suppress its dependence also. The resulting cartesian velocity contour diagram presents the relative intenSity per unit velocity space in the center-of-mass reference frame. The peak intenSity is arbitrarily set to 100. As dis­cussed elsewhere, 3,5,6 this presentation removes the distortion produced by use of laboratory polar coordi­nates and uncertainties in specifying center-of-mass velocities. It is therefore the most appropriate sys­tem for deducing mechanisms from scattering sym­metry or asymmetry in theE~ experiments. However,

I 25 eM

60· MAGNET

SUPERSONIC NEUTRAL BEAM

~====~\M-~~S~OURCE

"---/E~~~C=:S MOVEABLE DETECTOR

NEUTRAL BEAM /TRAP

FIG. 1. Schematic of the crossed-beam apparatus.

Copyright © 1977 American Institute of Physics

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~Iakley, Vestal, and Futrell: Reactions H; (Ar, H2 ) ArW and ArW (H 2 ,Ar) H; 2393

it is tedious to obtain angular and energy distributions from them.

As an alternative we use the reaction translational exoergicity Q and the barycentric scattering angle X as rectangular coordinates. The appropriate intensity transformation is given by

I(Q, X) =(Tt!T)1/2I(T, e), (2)

where Tf is the relative translational energy of the products, and the translational exoergicity Q is given by

(3)

T; is the initial relative translational energy, t:.Hr is the heat of reaction, and t:.E1nt is the increase in the internal energy of the products over the internal energy initially in the reactants. In this representation the plotted intensities are proportional to the differential cross sections for scattering of products into a solid angle increment on(X) with translational exoergicity between Q and Q+ oQ. The prinCipal advantage of this type of plot is that the angular distributions at each Q

and the distributions over Q at each scattering angle are directly displayed; furthermore, by integrating the distribution of intensities over the scattering angle we may obtain the overall distribution of Q values, I(Q),

or by integrating over Q at each angle we obtain the overall angular distribution, J(X).

The computer programs for analyzing data from crossed-beam experiments have recently been modi­fied to improve the accuracy and resolution of the data. These modifications include corrections for known de­tector discrimination and application of deconvolution techniques to remove distortions of the data caused by the transmission function of the apparatus. 7

Briefly, the known discriminations that are corrected include the change in reaction volume with laboratory observation angle, the change in luminosity of the elec­trostatic prism with energy, and the change in duty time if the energy scan range is changed during the ex­periment. The effective reaction volume changes with observation angle since it is the intersection of two un­equal conical beams.

The general deconvolution problem consists of mea­suring some function f(x) which is related to the func­tion h(x) we would like to determine by the integral

f(x) = i: h(x')g(x-x')dx'=h*g, (4)

where g(x) is the "apparatus" function which is pre­sumed to be known. For this work, the apparatus func­tion for the cylindrical energy plate energy analyzer was assumed to be Gaussian with a calculated standard deviation equal to 1. 8%. The method employed is the Van Cittert solution8

,9 for obtaining an approximate in­version of Eq. (4). This is accomplished by calculating the functions

C;(x) = f(x) -1: hi_1(X')g(x - x") dx', (5)

and the ith estimate of the desired function is given by

The procedure is begun by taking as the zeroth esti­mate for h(x), the measured functionf(x); that is,

ha(x) = f(x). (7)

The procedure may be continued until

(8)

where E is the maximum acceptable error. As is shown by Wertheim, 9 the maximum number of iterations which is useful is limited by noise in the data.

A typical experiment consists of 255 point energy dis­tributions obtained at 20-30 laboratory angles. To speed the construction of the intenSity contour plots, they are generated as 42x42 element arrays. This re­duces the total number of data pOints from about 6000 to 1764, thereby speeding the data reduction process, and permits the plot to be printed on a high speed line printer. The slight loss of resolution caused by the re­duction of the number of pOints is generally more than offset by the speed and ease with which the data are handled. Since the number of elements is held con­stant, the scale of the array in velocity or X, Q space is adjusted to contain the data. Each of the 255 data pOints of the raw energy distributions are allocated to the appropriate array element. Usually, more than one datum is assigned to an element and these points are then averaged to obtain the intenSity value for that ele­ment. This averaging is helpful because it tends to re­duce nOise, which is especially prominent near the lab­oratory origin. Empty elements are filled by linear in­terpolation and the arrays are printed as squares with relative intensities from 1 to 99. Smooth contours are then drawn by connecting elements of equal relative in­tensity. When the data are reduced into the scattering plot using X and Q as rectangular coordinates, the pro­grams also provide I(X) and J( Q) intensity distributions by alternately integrating over the array coordinates.

RESULTS AND DISCUSSION

Hj(Ar,H2 ) ArW

The reaction H;(Ar, H2)ArW was studied at relative translational energies from 0.87 to 9.7 eV. Results typical of the entire energy range studied are shown in Fig. 2, which is a polar center-of-mass normalized intensity plot for reaction at 2.1 eV relative energy. On this figure "CM" denotes the most probable center­of-mass, and 0° denotes the direction of the reactant ion in the barycentric system; the arrow is the termi­nus of the most probable neutral velocity vector. The elastic spectator velocity is indicated by the solid cir­cle inscribed on the figure for which Q = - 0.8 eV.

Since the terminology applied to systems reported in the literature which are reasonably well described by the spectator stripping model1a has mainly involved hy­drogen atom pickup reactions, it is important to define for the present system the terms forward, backward, and small-angle scattering. In each case these terms refer to the direction of the product ion as predicted by

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2394 Blakley, Vestal, and Futrell: Reactions H; (Ar, H2 ) ArW and ArW (H 2 , Ar) H;

H3(Ar,H2)ArH' Tj = 2.1 eV 0"

FIG. 2. Intensity contour plot in polar center-of-mass veloc­ity space for ArB· product at 2.1 eV relative translational en­ergy. "eM" denotes the most probable center-of-mass, 0° is the direction of the reactant ion, and the arrowhead is the ter­minus of the most probable reactant neutral velocity. The elastic spectator prediction is given by the circle.

the simple spectator stripping model. 11 For proton transfer, forward and small-angle products are lo­cated in the vicinity of X = 180°, while back-scattered products will be found at 0° .

For the reaction described ip Fig. 2 there is a sharp peak of intensity in the direction of the reactant neu­tral (at X = 180 0

, corresponding to forward scattering), while a low intensity ridge about the most probable center-of-mass velocity indicates scattering of the product at various angles; as shown in the figure, most of the intensity is well described as forward scattering. Note also in Fig. 2 that the intensity maximum is lo­cated at somewhat higher velocity than predicted by the simple spectator stripping model. Figure 3 illustrates the center-of-mass angular distributions for the ArH+ product at the lowest and highest translational energies investigated, where it is evident that product is strong­ly forward scattered at all energies studied.

These same data obtained at 2.1 eV relative energy are also shown in Fig. 4, where they are plotted in the alternative form using X and Q as rectangular coordi-

IOOr----.----,-----r----.-----r--~

TI = O.87eV-

I (x)

90 180 X (dell)

FIG. 3. Representative barycentric angular distributions for ArB· product at low and high initial relative translational en-ergy.

o

30

60

X

90

(deg)

120

150

180 -2.0 -1.0 00 10

Q (eV)

FIG. 4. Intensity contour plot for ArB· product at 2.1 eV rel­ati ve translational ene rgy using the translational exoergic ity, Q, and center-of-mass scattering angles, x, as rectangular coordinates. The dashed vertical line is the elastic spectator prediction.

nates. The dashed vertical line corresponds to the prediction of the elastic spectator model and X = 0° to the direction of the reactant ion as described above. In this plot, features corresponding to a particular Q show up as vertical ridges. At large scattering angles (small X) the ridge is reasonably centered about the elastic spectator prediction. Clearly, however, for­ward scattered product is formed with considerably more translational energy than the stripping models predict.

As can be seen from Eq. (3), setting aElnt =0, the maximum value of Q possible for ground state reactants is

(9)

Using Henglein's recent value for the proton affinity of argon,12 this reaction is about 0.6 eV endothermic. Hence for ground state reactants, no product should be formed at Q values greater than - O. 6 eV. Imme­diately apparent from Fig. 4 is the considerable amount of product formed at high Q values. This can only mean that a large fraction of the Hi produced in our high pressure source was not vibrationally relaxed. This result was quite surprising in view of several re­ports that excited Hi ions are rapidly relaxed on col­lision with H2. 13-15

The data were obtained using a source pressure of about 0.1 Torr. To estimate the average number of collisions, N, suffered by the Hi ions in our source at this pressure we can use the expression

N=nkT, (10)

where n is the number density of neutrals in the source, k is the collision rate constant, and T is the source residence time. For purposes of this calculation, k may be estimated by the Gioumousis and Stevenson expression16

J. Chern. Phys., Vol. 66, No.6, 15 March 1977

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Blakley, Vestal, and Futrell: Reactions H; (Ar, H2 ) ArW and ArW (H 2 , Ar) H; 2395

100

1(0)

H;(Ar,H2 )ArW Tj = I.leV nH;

o 234

FIG. 5. Q distributions for ArH' product at 1. 1 eV relative translational energy for 0.1 Torr and 0.5 Torr source pres­sures. Qmax denotes the upper limit of Q for ground state reactants. nH3 is the number of vibrational quanta in H; as­suming a constant 0.4 eV quantum size.

(11)

where ex is the polarizability (ex =0. 93x 10-24 cm3 for H2) and 11 is the reduced mass (2 x 10-24 g for Hi, H2). These values yield a value of k of 2.1 x 10-9 cm3 mole­cule-1 • sec-1.

We have not directly measured source residence times on this apparatus. We can, however, calculate reasonable values from diffusion coefficient measure­ments. For ions formed along the axis of a cylinder of radius r, the diffusion lifetime T is given by 7

(12)

where Da is the ambipolar diffusion coefficient. The ambipolar diffusion coefficient pressure product, DaP, has been measured18 to be about 700 cm2 • Torr sec-1

for hydrogen, and r is 0.6 cm for our source, hence we estimate the source residence time to be about 9 Ilsec at 0.1 Torr. Inserting these values intoEq. (10) we obtain N= 66 collisions. Previous results from this laboratory13 and elsewhere14 would predict that Hi ions are fully relaxed in this number of collisions.

To further study this excess internal energy we also obtained data at a source pressure of about O. 5 Torr. From Eq. (12), the residence time is about 45 Ilsec at this pressure; hence from Eq. (10), the average num­ber of Hi, H2 collisions is about 1700. Q distributions for low and high pressure data are compared in Figs. 5 and 6 for approximately equal relative energies. The difference is dramatic; the intensity at high Q is sub­stantially suppressed at high pressure. However, even at this pressure H3 is not fully relaxed into the ground state; it is clear that Hi vibrational relaxation is a much less efficient process than was indicated by earli­er studies.

The structure found in these distributions (Figs. 5 and 6) appears to be significantly outside our experi­mental uncertainties and is probably indicative of spe­cific vibrational tranSitions; however, the combination

of our experimental uncertainty of about ± 0.05 eV in the absolute location of Q = 0 with comparable uncer­tainties in the correct values of the vibrational fre­quencies of Hi and ArW make a detailed analysis diffi­cult. Intensities at Q values greater than - O. 6 eV, however, must result from vibrationally excited Hi re­actant ions. Additionally, some of the structure may be interpreted as evidence for the formation of vibra­tionally excited products. For example, the promi­nent peak near Q=O in Fig. 5 corresponds approxi­mate ly to the Q value expected for the reaction

(R3)

Obviously, a detailed analysis is impossible without a detailed assignment of transitions in these figures. However, one can obtain a crude picture of the vibra­tional energy population of the reactant Hi ions by as­suming that the cross section for reaction is indepen­dent of the internal energy of the Hi and that the prod­ucts are not appreciably excited; then the relative in­tensity at

(13)

would be proportional to the fraction of the Hi with ex­citation energy F!. Further assuming a reasonable value for the Hi quantum of about 0.4 eV, 19 we obtain an approximation of the vibrational distributions of the Hi reactant ions. The results for allof the experiments conducted at low translational energies are summarized in Table I. In view of the several approximations made, the consistency among the various experiments is re­markably good. Taking into account the experimental uncertainty in the absolute values of the measured Q's we may conclude that the average energy of the Hi pre­pared at 0.1 Torr is O. 6± 0.15 eV, and at 0.5 Torr, 0.3±O.15eV.

Q distributions for data obtained at higher energies are shown in Fig. 7. The data for reaction at Tj = 6.7 eV were obtained at 0.5 Torr while the others were ob­tained at O. 1 Torr. If the reactants are in the ground state and the product neutral is not internally excited, the minimum observable Q, Qmln, is given by

100r_----ir-;;;-:-:;~..r_r_--__,

1(0)

-1.0 0 1.0

o (eV)

FIG. 6. Q distribution for ArH' product at approximately equal initial relative energies for 0.1 Torr and 0.5 Torr source pressures.

J. Chern. Phys., Vol. 66, No.6, 15 March 1977

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2396 Blakley, Vestal, and Futrell: Reactions Hi (Ar, H2 ) ArH+ and ArW (H 2 , Ar) H;

T ABLE I. Summary of H; vibrational excitation from analysis of translational exoergicity distributions for the endoergic reaction H;(Ar, H2)ArH+.

F raclional population

Ion source pressure 0.1 torr 0.5 torr

Helative lranslalional energy 0.9 1.1 2.1 1.0 1.7

nH~a E* b

0 0 0.29 0.16 O.2H 0.51 0.55 0.4 0.32 0.32 0.28 0.29 0.29

2 O.H 0.24 0.2H 0.24 0.14 0.14 :3 1.2 O. 11 0.17 0.15 0.06 0.03 4 loG 0.04 0.06 0.05

E' 0.52 0.G5 0.56 0.30 0.2G

aNumber of mean quanta in H; reactant with Hi represented as a triply degenerate harmonic oscillator.

bVibrational excitation energy of Hi, not including zero point energy, assuming a mean quantum of 0.4 eV.

Qmln'" - t:..14 - D (product ion), (14)

where D(product ion) is the dissociation energy of the product ion. Since t:..Hr",P.A. (H2 )-D(ArH), this equa­tion may be reduced to

(14')

where P. A. (H2) represents the proton affinity of hydro­gen. Using Henglein's value of D (ArH+) '" 3.8 eV 10 and the endothermicity of reaction leads to an estimate of Qmln '" - 4. 4 eV as indicated on the figure. The best current experimental value for P.A. (H2) is 4.35 eV, deduced from a measured value for P. A. (02) from photoionization studies20 and the result from two flowing afterglow investigations21-22 which show that P. A. (02) "'P.A. (H2). The intensity below Qmln in Fig. 7 demon­strates that the H2 neutral product carries away some of the energy as internal excitation of the neutral produc t.

Energetic data are summarized in Fig. 8, where the most probable Q values, determined from the peaks in the individual distributions, are plotted versus initial relative energy. The solid diagonal line is the predic­tion of the spectator stripping modelll and Qmax is the upper limit of Q for ground state reactants. The error

FIG. 7. Q distributions for ArH+ product for reaction at mod­erate initial relative energies. The data at T i = 6. 7 eV were obtained at 0.5 Torr and the others were obtained at 0.1 Torr source pressures. Qmln is the minimum expected Q for ground state reactants if all of the product internal energy resides in the ion.

Q(eV)

H;(Ar,H2 )ArH1"

0

Qmax -I

-2

-3

-4 • 0.1 Torr 00.5 Torr

-5LO---2L---4L---6~--8~~IO

Ti (eV) FIG. 8. Plot of observed most probable Q values versus ini­tial relative energy, T i , the error bars represent the full­width at half-maximum of each Q distribution, and the diago­nal line represents the prediction of the spectator stripping model. Qmax denotes the upper limit of Q for ground state reactants.

bars represent the full-width at half-maximum of the Q distributions. For the low pressure data, the ener­getics closely follow simple spectator stripping, even at low energies where the observed Q should be limited by Qmax. The higher pressure results more closely ex­hibit the expected behavior, following spectator strip­ping at higher energies, but showing the limitations im­posed by Qmax at low energies. However, the broad­ness of the distributions and the influence of excess energy are clearly evident in this figure.

ArW(H 2 , Ar) H;

The reaction ArH+ (H2, Ar) H; was studied over the relative energy range from 0.18 to 6.7 eV. ArH+ re­actant ions were produced by mixing a trace of hydro­gen into about 0.1 Torr argon in the ion source. A po­lar center-of-mass normalized intensity map is shown in Fig. 9 for reaction at 1. 9 eV. On this plot, "LO" denotes the laboratory origin, and the dashed lines are the angular limits between which data were obtained. As before, the solid circle denotes the elastic spectator prediction. Generally, this reaction exhibited behavior observed for other exothermic or thermo neutral proton transfer reactions,3 closely following the elastic spec­tator mechanism over the energy range studied.

Barycentric angular distributions for two energies are given in Fig. 10. At the higher energy studied, the distribution is sharply peaked in the direction of the neutral. At the lowest energy, however, there is sub­stantial large angle scattering. This suggests that or­biting collisions may occur, but there is no unequivocal evidence for complex formation.

Q distributions for three energies are compared in Fig. 11. These data are almost identical to the re­sults obtained for the thermoneutral reaction of H; with D 3 in that the most probable Q values are in good 2, . agreement with the predictions of the spectator striP-ping model and that the widths of the distribution are similar. Furthermore, the energy distributions for

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Blakley, Vestal, and Futrell: Reactions H; (Ar, H2 ) ArW and ArW(H 2 ,Ar) Hi 2397

1.geV

FIG. 9. Intensity contour plot in polar center-of-mass veloc­ity for Hi product at 1. 9 eV initial relative translational ener­gy. "LO" denotes the laboratory origin, the dashed lines are the limits between which data were obtained, and the solid cir­cle is the elastic spectator prediction.

this exothermic reaction, even at low translational energies, show only a small fraction of the total inten­sity of Q values greater than Qrnax, indicating either that the ArH+ ions are effectively relaxed into the ground state or, if vibrational energy is present, it is mostly retained in the products. From Eq. (14), Qmtn for this reaction is about - 3.8 eV. Since the product neutral cannot carry away internal energy, the Q distributions should be sharply limited by Qrntn. As can be seen in Fig. 11, the high energy data show this Qmtn limitation quite clearly.

Energetic data are summarized in Fig. 12, where the most probable Q values are plotted versuS initial relative energy. In this plot, the closeness with which the data follow the spectator stripping prediction, in­dicated by the solid diagonal line, is clearly evident. Also evident is the narrowness of the distributions and

100~--~-----.----.-----.----.--~~

I (X)

90 180 X (deg)

FIG. 10. Representative barycentric angular distributions for Hi product at low and high initial relative translational energy.

100

I (Q)

-1.0

Q{eV) o 1.0

FIG. 11. Q distributions for Hi product at three initial rela­tive translational energies.

the lack of intensity above Qmax when compared to the reverse endothermic reaction. We conclude that this reaction is well characterized by the elastic spectator model over this energy range. We cannot, however, decide on the basis of these data whether or not the ArH+ was vibrationally relaxed.

Energy relaxation in H;, H2 collisions

Previous studies13,14 have suggested H:i is rapidly relaxed into the ground state, probably within 10 col­lisions. Most of the conclusions were based upon the reasonable assumption that endothermic reaction chan­nels would be closed out when the total energy available for reaction fell below threshold. For example, D. L. Smith and FutreU13 examined the reaction

D:i +CH3 - CH; +D2 +HD - 0.6 eV (R4)

-CH4D++D2 +1.1 eV

at near thermal translational energies USing a tandem ICR-mass spectrometer as a function of D:i, D2 colli­sions in the source. Since the CH; intenSity fell es-

Q(eV)

-4

o 2 4 6

Tj (eV) 8 10

FIG. 12. Plot of observed most probable Q values versus ini­tial relative energy, T 1• The error bars represent the full­width at half-maximum of each Q distribution, and the diag­onal line represents the prediction of the spectator stripping model. Qmax is the upper limit of Q for ground state reac-tants.

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2398 Blakley, Vestal, and Futrell: Reactions H;(Ar,H 2 )ArW and ArW(H 2 ,Ar) H;

sentially to zero by the time D; had undergone an aver­age of 10-15 collisions, they concluded that D; had no more than 0.6 eV internal energy by the time it had suffered this many collisions. A Iso, since the rate of CHi formation was independent of D;, Dz collisions above an average of five or six, they further concluded that Di is totally relaxed after five or six collisions with deuterium.

Similarly, Leventhal and Friedman14 compared endo­thermic versus exothermic channels in the reactions of Hi with CzHz, CzH4, andCH4, from which they concluded that Hi is probably relaxed after a single collision. Also, Kim, Theard, and Huntress15 determined a de­activation rate constant of 2. 7 ± 0.6 x 10-10 cm3 mole­cule-1• sec-1 for Hi colliding with Hz. Since this rate is about one-sixth of the collision rate, their data quali­tatively agree with those of Smith and Futrell. In sharp contrast, the present data demonstrate that H; is not fully relaxed after a few thousand collisions.

That H; is not readily relaxed into the ground state is supported by the later tandem-ICR study ofR. D. Smith and FutreUz3 on the reaction of D; with Ar. They re­ported that Di was still reacting after an average of 14 collisions at 8% of the low pressure rate. Although superficially disagreeing with the earlier relaxation studies, we note that in this reaction there are no com­peting exothermic channels. Neither are the mech­anisms similar. Most of the other reactions studied involved proton transfer, followed by decomposition. We tentatively conclude then that when there is a multi­ple step process or when there are competing exother­mic and endothermic channels, closure of an endother­mic channel does not necessarily indicate that the total energy available for reaction is below threshold.

A de ac ti vation rate constant kd may be calculated from the relation

(15)

where [Hi*] and [Hi] refer to excited and ground state Hi, respectively, n is the number density of Hz in the source, and T is the source residence time. To esti­mate the relative fraction of excited Hi, we use the data in Table I, taking the average of the various ener­gies. Thus, we estimate that 75% of the Hi are ex­cited at 0.1 Torr source pressure and 47% at O. 5 Torr. As discussed earlier, the approximate source resi­dence times are 9 /-Lsec at O. 1 Torr source pressure and 45 /-Lsec at 0.5 Torr. Inserting these values into Eq. (15), we obtain ka = 9x 10-12 cm3 molecule-1• sec-1

at O. 1 Torr and ka = 9 xl 0-13 cm3 molecule-1 • sec-1 at 0.5 Torr. Reflecting upon the assumptions used in these calculations, these rates should be considered to be order of magnitude estimates.

For comparison, it is instructive to calculate ex­pected excited Hi fractions using the deactivation rate constant measured by Kim, Theard, and Huntress. 15 At 0.1 Torr source pressure, their value predicts an excited fraction of only 0.0002. Clearly, if Hi were relaxed this rapidly, we should not have observed any

difference in the Q distributions between the two pres­sures.

The difficulty appears to be that the ICR experiments measure the average deactivation rate constant for the highly excited Hi ions formed initially by the reaction of H2' with Hz and the analysis implicitly assumes that the deactivation rate is independent of the vibrational excitation of the H3. However, highly excited states of H; may be relaxed rapidly by vibrational-vibrational transfer between H; and H2, while low-lying vibrational states of Hi, which are not close to resonance with vi­brational states of Hz, can only be relaxed by vibration­al-translational transfer. Our results can be inter­preted as implying relaxation rate constants on the or­der of 10-11 cm3 molecule-1 . sec-1 for Hi with about 3 quanta of vibrational excitation and about 10-12 cm3

molecule-1 • sec-1 for relaxation of the lowest vibration­ally excited states. These values are comparable to vibration-translation relaxation rate constants measurec for vibrationally excited neutrals. 24

ACKNOWLEDGMENTS

The authors wish to acknowledge the many helpful discussions with Professor Austin L. Wahrahftig, the assistance of Dr. P. W. Ryan in the early stages of this work, and the technical assistance of Mr. Herb Brant.

* Acknowledgment is made to the Donors of the Petroleum Re­search Fund, administered by the American Chemical Soci­ety, for support of this research.

tPresent address, Department of Chemistry, University of Houston, Houston, TX 77004.

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