Study of the 2Ar+Ar+ 2=Ar+Ar+ 3 reactionD. L. Turner and D. C. Conway Citation: The Journal of Chemical Physics 71, 1899 (1979); doi: 10.1063/1.438544 View online: http://dx.doi.org/10.1063/1.438544 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/71/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The repulsive wall of the Ar–Ar interatomic potential reexamined J. Chem. Phys. 92, 1030 (1990); 10.1063/1.458165 A new potential fitting procedure with application to Ar–Ar J. Chem. Phys. 65, 490 (1976); 10.1063/1.432745 Collision diameter and well depth of the Ar–Ar interaction J. Chem. Phys. 58, 2659 (1973); 10.1063/1.1679553 Vibrational Levels of Ar2 and the Ar–Ar Pair Potential J. Chem. Phys. 54, 3645 (1971); 10.1063/1.1675394 Scattering of HighVelocity Neutral Particles. XVI. Ar–Ar, Ar–He, and Ar–H2 J. Chem. Phys. 51, 968 (1969); 10.1063/1.1672164

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:

130.160.4.77 On: Sat, 20 Dec 2014 08:07:03

Study of the 2Ar+Ar~ =Ar+Ar~ reaction D. L. Turner and D. C. Conwaya)

Department of Chemistry. Texas A&M University. College Station. Texas 77843 (Received 19 March 1979; accepted 17 May 1979)

Equilibrium constants for the reaction 2Ar + Art = Art + Ar have been determined mass spectrometrically from 144 to 217'K. Assuming Art to be linear. tJ.H'2oo = - 5.06±O.08 kcallmole. tJ.S '200 = - 20.3±O.4 callmole deg. and Do(Art - Ar) = 5.05±O.11 kcallmole. The tJ.S' is too negative for the "loose cluster" model in which it is assumed that the Art is freely rotating in the Art cluster. It is concluded that Art is probably linear. The rate constant for the formation of Art was computed and compared to experimental results at 77 and 298'K.

I. INTRODUCTION

It has been postulated l that the formation of Ar; by the reaction

2Ar + Ar+ !.! Ar+ + Ar 2 ~1 3

(1)

is the cause of the deterioration of laser power at high pressures in the Ar excimer laser. This is a result of the electron denSity being reduced at high pressures by the dissociative recombination process

Ar; + e- ~ neutral products , (2)

which is generally extremely rapid for most clustered ion species. I Werner et al. fit their room temperature peak electron density data in Ar with the rate constants k l =4. 2x10-33 cms/sec and k 2=3. 6x10-5 cm3/sec. Liu and Conway2 determined kl to be 3. 2x10-30 cms/sec at 77 OK in a drift tube mass spectrometer. The two values of kl appear to be in disagreement because kl is not ex­pected to have such a strong temperature dependence. The purpose of this research was to measure the ther­modynamic data for Reaction (1) and use the data to esti­mate k l .

II. EXPERIMENTAL PROCEDURE

The Ar was ionized by a 2 Ci titanium tritide radio­active source in a flow system. The apparatus and ex­perimental procedure were the same as described pre­viously3 except the inlet window was a 2. 5 jJ.m Pt foil with a 25 jJ.m diam orifice. Attempts were made to use the electrodepositied Au foil window with the 9 jJ.m ori­fices used in the NO+· N2 work, 3(b) but very few Ar~ ions could be detected at 298 or 195 OK. 4

III. RESULTS

Each mass spectrometrically measured ion intensity was divided by the square root of ion mass to obtain the corrected intensity I(~). This sensitivity correction is to account for relative transit times in the active region of the mass spectrometer. 5 The equilibrium constant for Reaction (1), i. e., K, is I(Ar;)/I(Ari)PAr, where PAr is the Ar pressure in mmHg (133 Pa=1 mmHg). It is seen (Fig. 1) that K is independent of PAr' The reaction time was increased by reducing the Ar flow rate from

alTo whom correspondence should be addressed.

the normal 1000 to 500 cc/sec. K was the same at both flow rates at 144 and 195°K. A van't Hoff plot of K is shown in Fig. 2.

IV. ANALYSIS OF DATA

The equilibrium constant data were analyzed by itera­tion on a digital computer by a method described pre­viously.3(a),5 The ion structures, the Ar; stretching fre­quency, and a model for the frequency distribution of the weak vibrational modes of the ions are used as input data to the computer program. In vibrational model I, all frequencies are assumed to be the same, whereas in model II, the frequencies are assumed to be distributed over a factor of 5 in a geometrical series. The Ari bond length Re was taken to be 2.45 A, S,7 and the fre­quency of the stretching mode Ws to be 300±30 cm-I • 7

Two Ar; geometries were used to estimate the rotation­al entropy; a linear model with 2. 5 A between Ar nuclei and a T structure with 2. 45 A between two Ar nuclei which are 3. 45 A from a third nucleus. 8

The derived entropy change for Reaction (1), i. e. , 6.So, was used to compute the Ar; vibrational frequen-

1.0

h ¥

01 E . E

0.Q1

0.001

b-

3.0

I

/ A

B

"

C

:lI '" D

E

6.0 9.0 12.0

PAr(mm Hg)

FIG. 1. K vs PAr' Temperatures in OK are as follows: (A) 144.4, (B) 159.8, (e) 178.1, (D) 195.3, and (E) 217.3.

J. Chern. Phys. 71(4), 15 Aug. 1979 0021-9606179/161899-03$01.00 © 1979 Arnerican.lnstitute of Physics 1899

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:

130.160.4.77 On: Sat, 20 Dec 2014 08:07:03

1900 D. L. Turner and D. C. Conway: 2Ar + Ar; = Ar + Ar; reaction

1.0

0 I~

OJ I

0.1 E E

:.::

0.01

0.001 4.6 5.0 5.4 5.8 6.2 6.6

liT x 103 (OK1)

FIG. 2. van't Hoff plot of K. From the slope, till ° = - 5.11 ± 0.07 kcal/mole for Reaction (1).

cies. These were used to correct t:.Ro to 0 OK to obtain Do(Ari-Ar). 'The results are given in Table I. It was computed3(a).5 that less than 1 x 10-3 of the Ar; ions dis­sociate after entering the mass spectrometer.

V. COMPUTATION OF k1

The rate constant kl =Kk_ h where K was obtained from the 200 OK thermodynamic data in Table I, cor­rected for the change in heat capacity via the vibration­al frequencies corresponding to each model. 9 The k_l was computed by the RRKM method in the semiclassical approximation, i. e. ,

(3)

Here, Qv is the vibrational partition function, Eo is the zero point energy sum, and sand t are, respectively,

the number of vibrations and active rotations of the Ar;, which is assumed to be linear. The collision rate con­stantk2 is 2lTe(0!/1l)1/2, where Ci is the Ar polarizability (1. 63 x 10-24 cc) and Il is the Ar-Ar; reduced mass. 10

The Do in Table I is used for the activation energy Ea. Q R and a are the rotational partition function of the adiabatic rotations and the symmetry number in QR, re­spectively' for Ari. Q'R and a+ refer to the activated complex. r /1 is the moment of inertia ratio. Equa­tion (3) is the corrected 11 version of an earlier equa­tion given by Marcus and Wieder. 12 The a+Q~/a QR fac­tor corrects for the fact that when the energized Ari forms the activated complex at constant angular mo­mentum; part of the adiabatic rotational energy is used to break the Ari-Ar bond. 13 However, this means the activated complex can be formed from states with less energy in the active modes, so decomposition can occur from an energy region with reduced level density. For linear molecules, the level density correction l1 consists of replacing the (Ea + Eo) factor given in the first paper 12

by [Ea + Eo + RT(l -rim. In using Eq. (3), it was assumed that there are no

active rotations in the energized Ari (t = 0). When Ari and Ar collide to form an activated complex, the activa­tion energy E'j is J 2(J + 1)2n4/81l20!e2. 14 We obtain the average value of r, i. e., (r), from the relation15

~~ (2J+ l)exp(-E;/kT)dJ= 8lT2(~;)kT , (4)

from which (J+) = ll(lTO!e2/2kT)1/2. This value of (I') and the assumed Ar; linear structure given above were used to compute 1'/1. The computed values of k_l and kl are given in Table II for the following Ar; models: (a) frequencies chosen with approximately the same fre­quency distribution as CO2 to fit the entropy data, (b) vi­

brational model I results, and (c) vibrational model II results (Sec. IV).

VI. DISCUSSION

After subtracting the computed translational and ro­tational contributions from t:.S200 , the vibrational con­tribution to t:.S200 is 10.7 cal/mole deg for the linear Ar:i structure and 2. 5 cal/ mole deg for the T structure. These correspond to an Ari "internal" entropy of 11. 5 and 3.3 cal/mole deg, respectively. If Ari were a "loose cluster," the internal degrees of freedom would consist of an Ari stretching mode, an Ari-Ar stretch-

TABLE I. Quantities computed at T = 200 OK from the experimental K data.

Arj - (t:.ST)b - (tillT)b yO Do(Ari-Arlb D.(Ari-Arlb

structurea (cal/mole deg) (kcal/mole) (cm- I ) (kcal/mole) (kcal/mole)

Linear 20.3±0.4 5. 06±0. 08 90.4±12d 5.05±0.11 5.15±0.11

T 20.6±0.4 5.12±0.09 244±22e 4.62±0.11 5.4±0.3

anefined in the text. byalues are averages of vibrational model I and II calculations. Standard deviations have been increased by half the difference in the two vibrational model calculations.

C A rj vibrational frequency for vibrational model 1. "Maximum frequency for vibrational model II is 206 cm-I. "Maximum frequency for vibrational model II is 640 cm -1.

J. Chern. Phys .• Vol. 71, No.4, 15 August 1979

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:

130.160.4.77 On: Sat, 20 Dec 2014 08:07:03

D. L. Turner and D. C. Conway: 2Ar + Ar; = Ar + Ar; reaction 1901

TABLE II. computed values of k_1 (cm3/sec) and k l (cm6/sec).

Arj model

A

B

C

Experimental

Arj vibrational frequencies (cm-I)

200, 100, 59(2)

90.4(4)

206, 120.6, 70.5, 41. 2

77.3°K

k_1 x 1021 kl X 1031

3.22 3.68

3. 84 4. 82

2.95 3.29

32a

298 oK

k_1 X 1012 kl X 1032

8.65 6.96

9.23 7.46

8.44 6.78

0.42b

"Reference 2. ~eference 1.

ing mode, and two Ari internal rotations. Because the Ar; rotational entropy is computed to be 14.3 cal/mole deg at 200 oK, the Ari entropy is too small for the loose cluster model to be valid.

The Oi-N2 bond energy of 5.51 kcal/mole was found to be in agreement with that predicted by a simple elec­trostatic model in which all the positive charge is on the Oi. 16 The most stable structure was found to be T shaped, which would probably be the most stable struc­ture for Ari if the bonding is electrostatic, i. e., if essentially all the charge is on two atoms. However, the the N2 polarizability parallel to the bond is 4/3 the po­larizability of Ar and Ar does not have a quadrupole mo­ment. (The charge-quadrupole interaction contributed 2.4 kcal/mole to the Oi-N2 bond energy.) Therefore, we feel the bonding in Ari is probably covalent with the charge spread over all three atoms. 17 Since the half­filled AO in Ar+ is a 3p AO, one expects Ar; to be linear with two electrons in a au bonding, two electrons in a u, nonbonding, and one electron in a au antibonding MO composed mainly of the three 3pz AO's. Additional evi­dence in favor of the linear structure is the fact that the Ar; vibrational frequencies obtained from the entropy data for the T structure are O. 8 of the Ari stretching frequency w. for model I and range up to twice Ws for model II (Table I). Because Do(Ari-Ar) = 5 kcal/mole, whereas Do(Ar-Ar+) = 26-30 kcal/mole, 5-7 these Ar; frequencies appear to be too large. The Ari stretching frequencies are not expected to be larger than W s, and the Ari bending mode frequencies are expected to be much smaller than w.. This frequency problem is ex­pected for any nonlinear structure because of the larger rotational entropy.

If some of the vibrational modes become internal rotations in the "energized" Ara (excitation energy >Ea+RT[1-r/IJ) or if energized Ara is T shaped, the value used for (8 - 1) + t /2 in Eq. (3) should be reduced. To determine the sensitivity of kl to this change, the rate calculations were repeated for the T shaped Ar; us­ing the same values of a+Q'R/uQR and r /1 as used for the linear Ar;. The new kl values were 5-10 times smaller at 77. 3 oK and 3 -4 times smaller at 298 oK, in better agree me nt with the results of Werner et al. I Of course, a+Q'R/aQR and r/I were not computed correctly in the latter computations. If anharmonicity corrections were introduced, the Ar; vibrational level density would be increased, which would increase the theoretical kl val­ues. On the basis of the rate constant computation, it is concluded that the temperature dependence of kl is small,

as expected, so one (or both) experimental measure­ments of kl is (are) in error by more than an order of magnitude.

ACKNOWLEDGMENT

The authors wish to thank the Robert A. Welch Foun­dation for its generous support of this research.

IC. W. Werner, E. Zamir, and E. V. George, Appl. Phys. Lett. 29, 236 (1976).

2Wei-cheng F.' Liu and D. C. Conway, J. Chern. Phys. 62, 3070 (1975).

3(a) D. C. Conway and G. S. Janik, J. Chern. Phys. 53, 1859 (1970); (b) D. L. Turner and D. C. Conway, J. Chern. Phys. 65, 3944 (1976).

'With O2 at room temperature, O2• ions could not be detected, but O2• ions could. These "small hole" windows exhibit this charge discrimination effect for certain gases. Ulbricht ob­served this effect earlier [W. H. Ulbricht, Jr., Ph. D. thesis, Texas A & M University (1978) (unpublished»).

5Harry H. Teng and D. C. Conway, J. Chern. Phys. 59, 2316 (1973) .

6W. J. Stevens, M. Gardner, A. Karo, and P. Julienne, J. Chern. Phys. 67, 2860 (1977).

7T. L. Gilbert and A. C. Wahl, ~. Chern. Phys. 55, 5247 (1971); W. R. Wadt, J. Chern. Phys. 68, 402 (1978); H. H. Michels, R. H. Hobbs, and L. A. Wright, J. Chern. Phys. 69, 5151 (1978). Wadt's calculations were ab initio with con­figuration interaction, whereas Michels et al. used the X", method. The results are Similar: R.=2.48 and 2.43 A and ws=293 and 298 cm-I.

BThis makes the third nucleus 3.0 A from the top of the T. 9At 77°K, each value computed for K with ~Cp assumed equal

to zero is within 40% of the value used. The difference is much less « 5%) at room temperature.

10K. Yang and T. Ree, J. Chern. Phys. 35, 588 (1961); H. Eyring, J. O. Hirschfelder, and H. S. Taylor, J. Chern. Phys. 4, 479 (1936).

HR. A. Marcus, J. Chern. Phys. 43, 2658 (1965). 12G. M. Wieder and R. A. Marcus, J. Chern. Phys. 37, 1835

(1962). 130. K. Rice, Statistical Mechanics Thermodynamics and Kinetics (Freeman, San Francisco, 1967), pp. 499, 500.

I'S. Glasstone, K. J. Laidler, and H. Eyring, The Theory oJ Rate Processes (McGraw-Hill, New York, 1941), p. 133.

15Reference 14, p. 131. 16G. S. Janik and D. C. Conway, J. Phys. Chern. 71, 823

(1967) . 17The bonding in small homomolecular clusters is expected to

be covalent, whereas for large clusters, it is expected to be electrostatic. In the case of O2., the transition to electro­static seems to be at 0 6-02 [D. C. Conway, J. Chern. Phys. 52, 2689 (1970»).

J. Chern. Phys., Vol. 71, No.4, 15 August 1979

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:

130.160.4.77 On: Sat, 20 Dec 2014 08:07:03