The vibrational activation energy of the reaction Br(2P32 ) with CH3F

Chemical Physics 42 (1979) 345-353 0 North-Holland Publishing Company

THE VIBRATIONAL

ACTIVATION

L.N. KRASNOPYOROV,

ENERGY OF THE REACTION

E.N. CHESNOKOV

Br(‘P,,,)

WITH CH,E

and V.N. PANFlLOV

Institute ojChernical Kinetics mcl Cornbrtstion, USSR Acudemy ojSciences, Siberiun Brunch, Novosibirsk 630090, USSR

Received 28 December 1978

The influence of cw COJaser vibrational excitation of CH,F molecules on their reactions with bromine atoms, generated by light of various wavelengths, has been investigated. It was found that vibrational excitation accelerates the reaction Br (‘Ps,J f CH,F and does not influence the reaction Br (‘P& -I- CH,F. The vibrational activation energy of Br (‘P,,J + CHaF was found to be 12.5 f 2.5 kcdl mole-‘.

The purpose of the present work is to investigate quantitatively the role of the vibrational energy in surmounting the activation barrier in the Br + CH,F reaction.

1. Introduction

The activation energy is one of the main characteristics of reactivity of the particles involved in elementary reactions. Together with the preexponential factor it determines the reaction rate constant which describes quantitatively the reaction kinetics as long as the degrees of freedom of the reacting particles are in equilibrium. The probtem becomes more complex if there is no equilibrium. At low pressures, where energy transfer is slow, and at high temperatures, where the reaction is too fast, it becomes insufficient to know only the activation energy and the pre-exponential factor. The role played by a particular kind of energy in surmounting the activation barrier is very important for a quantitative description of the elementary reaction process under nonequilibrium conditions. The reactivity of electronicaliy excited Br(‘P,,J atoms with respect to CHJF has been investigated in refs. [ 1, z]. It was shown that the activation energy decreases with the excitation energy, besides, a decrease in the pre-exponential factor by 2.6 orders of magnitude is observed. In refs. [3,4] it has been Found that the reaction

rate increases

when CH,F

2. Technique Two different experimental techniques have been used in this work: One to study the photobromination acceleration at vibrational CH,F excitation, the other to determine the CH,F vibrational temperature. The experimental setup used to measure the reaction acceleration (partially described in refs. [l, 3,4] is given in fig. 1. The reaction was carried out in a 50 cm long cylindrical quartz vessel, 2 cm in inner diameter, with NaCl windows. It was connected to the ion source or a MX- 1303 massspectrometer via a 10 ,Upinhole. The Br, dissociation was induced by light of various wavelengths selected from a DRSh-500 mercury lamp spectrum by glass lilters. Vibrationally excited CH,F molecules were obtained upon absorption of radiation of a cw COJaser operating on the rotational line P(20) of the 00”1-02”0 transition. at 1046.85 cm- ’ frequency, coinciding with the rotational line Q( 12.2) of the vg vibration of the CH,F molecule (up to 23 W). To attenuate the infrared

is

An isotopically selective CH,F photobromination (with respect to carbon isotopes) has been carried out in refs. [S, 61 under cw laser irradiation. vibrationally

excited by a cw COJaser.

345

346

h

to

ion

Source

--0ft724cs-spectrometer

._

Fig. I. Block-diagram of the experimenral setup for investigation of vibrational excitation effects on the reaction Br + CH,F. (I) CO&ser; (2) auenuator; (3) power meter; (4) reaction vessel; (5) quartz plate; (6) filters; (7) lens; (8) mercury lamp.

irradiation we used a two-plate KRS-5 polarizer. The reaction rate was derived from the time dependence of the CH2FBr concentration resulting from the fast stage CHIF + Br2 4 CH,FBr + Br which followed the discussed reaction Br + CH3F + HBr + CH2F. CH,FBr observation was done by counting the ions on the in/e 114 line of the mass-spectrum. The pulses were accumulated for IO-15 min every 50 s. The experimental setup for measuring vibrational

temperatures iS given in fig. 2. The vibrational temperature was calculated from measurements on all the vibrationally excited CH,F molecules by the method of double infrared resonance [7-g]. The cw CO,-laser radiation, interrupted with a 46 Hz frequency, went to a 37 cm long cell with 2 cm inner

diameter through an attenuator and a Ge plate. The magnetic lield-tunable He-Ne-laser (3.39 /1) radiation also went to the cell after reflection by the Ge plate. A i-/4 plate was used to transform the two Zeeman +components of the He-Ne-laser radiation

into linearly polarized components, perpendicular to each other. The required component was selected after the reflection from the Ge plate by using a polarizer behind the cell. The intensity of the

He-Ne-laser radiation was measured by a Ge-Au photoresistor, cooled with liquid nitrogen. To improve the signal-to-noise ratio we employed a 64-channel averaging system [lo]. Subject to the experimental conditions we made 200 to 2000 signal accumulations. The quantity of excited CH,F molecules was

Fig. 2. Block-diagram of rhc experimental setup for measurements of vibration&y excited CH,F molecule concentration. (1) He-Ne-laser in solenoide; (7) i/4 plate; (3,4) obturators; (5) CO&ser; (6) attenuator; (7) Ge-plate; (8) power meter; (9) cell; (10) quartz plate; (11) polaroid; (12) detector.

L.N. Krctsrtopyoruu er ul./Actioation energy ojtlw

measured as follows. The He-Ne-laser was tuned by a magnetic field to the CH,F absorption line near 1450 Gs [S]. The cell was lilled with a CH2F-Ar gas mixture, the He-Ne-laser radiation was chopped and the transmitting radiation intensity J was measured. Then the chopped CO,-laser radiation (1045.85 cm-‘) passed through the cell and the modulation of the He-Ne-laser radiation was measured. If J,, is the intensity of the entering He-Ne-laser radiation and J is that inside the cell, then J = J, exp ( -II&),

(1)

where ttOis the concentration of CH,F molecules in the ground state, G is the absorption cross section, 1 is the cell length. Then the modulated signal AJ is (at Atz,,GI< 1) AJ = - An,~45, exp ( - w,crl),

(2)

where An, is the decrease of the ground state CH,F concentration (the increase in the upper level population by the transition absorbing the He-Ne-laser radiation is negligible because of the large value of the quantum). Hence we have Att,/rt, = -AJ/necrlJ.

(3)

Alongside with the decreasing population of CH,F ground state due to absorption of the CO,-laser radiation, the modulated signal can also be influenced by a decrease in the totai concentration of CH,F molecules, an increase of the absorption line width and a redistribution of the rotational levels of the CH,F ground state resulting from thermal heating along the celfs axis. The above effects are proportional to the pressure of the absorbing CH,F gas and thus can be excluded by extrapolation of the ratio At~,,/t~, to zero pressure. It has been found experimentally that over the CH,F pressure range from 0.05 to 0.25 Torr and at CO&ser radiation up to 23 W the dependence of An&-, on PcHJF is within the limits of experimental errors. Thus the above effects resulting from heating are negligible and the quantity An,,, determined from eq. (3) can be considered equal to the increase of the vibrationally excited molecules, II*, over their equilibrium concentration.

reucrim

Br (‘P,,,)

+ CH,F

347

3. Experimental resu!ts Reaction acceleration studies under CH,F vibrational excitation were carried out at the following concentrations: 6 x 1013-10’h cmm3 (CH,F), 8 x IO” cm-‘(BrZ), 2.3 x lOi cme3 (Ar). The CO,-laser radiation intensity in the cell varied from 0 to 23 W. The temperature was 40-160 “C. As shown in refs. [ 1.21 under such conditions comparable contributions to the total CH3F photobromination rate can be made by reactions of bromine atoms both in the ground (‘P,,,) and electronically excited (‘P& states. It was interesting to study the influence of the CH,F vibrational excitation on the reactions with Br(‘P& and Br(‘P,,,) atoms separately. It is known that under light with wavelengths shorter than 4000 A only ground state bromine atoms are produced, whereas longer wavelengths produce excited atoms [ 1l] as well. Therefore, the effect of vibrational excitation on the Br(‘P,,,) + CH,F reaction was studied under light with a wavelength 4360 A which forms both Br(‘P,,?) and Br(‘Pul) atoms. It has been shown in ref. [l] that the ratio of the reaction rate to the total concentration of CH,F + Br, is a linear function of this concentration. The tangent of the slope of the straight line obtained is proportional to the rrtte constant of Br(‘P,,,) + CH,F reaction, and the intercept is proportional to the rate constant of the reaction Br(‘P& + CH,F. Experimental results obtained at i6O’C (fig. 3) show that the tangent of the slope increases under vibrational CH,F excitation, whereas the intercept does not vary within the experimental accuracy. This means that at pressures 0.04-0.2 Torr vibrational CHLIF excitation appreciably accelerates the reaction with Br(‘P,,,) and influences negligibly that with Br(‘P,,,). The low accuracy of such experiments did not allow us to evaluate quantitatively the acceleration of the reaction Br(‘P,,,) + CH,F at vibrational excitation. Much more accurate are experiments dealing with the comparison of the reaction rates under infrared irradiation and light with wavelengths 3650 and 4360 A at lower temperatures when the equilibrium reaction rate at 4360 A wavelength is determined entirely by the reaction of the excited bromine atoms. The reaction rate under infrared irradiation is proportional to the product of the light intensity

L.N. Kruwopyoroc

34x

0

et ul./Activution cwgy

I

I 4

2 r+_

6 &~-!0-%~-~J

Fig. 3. Plots of kV/nand I+$/II versus ~~~~~~~~~~~~ [CH,F] : [Br?] F I : 1, [Ar] = 2.3 x IO” cmw3,

t = 160’. P = 21 W, i = 4360A. and the Br, absorption coefficient at the corresponding wavelength. It fohows that at 80°C the acceleration of rhe reaction Br(‘P,,,) + CH,F under vibrational excitation does not exceed 3% of that for the reaction Br(‘P,,,) + CH,F. 3

0

P-O

0

p-2iw

3 e?

1 -

2.0

25

IOj/T

3.0

(K-‘1

Fig. 4. Plots of log W versus I/Tunder COJaser irradiation with 21 W power acd without it. [CH,F] = 4 x 1015 cmM3, [Br,] = 8 x 10’5cm-3, [IAr] = 2.3 x 10” cmw3-

ofthe reuctiorl Br (‘P,,2)

+ CH,F

Below’we give experimental results on studies of vibrational excitation effects on the reaction between CH,F and Br[‘P,,2). The Br2 dissociation was induced by light with 3650 A wavelength which produced only nonexcited atoms. Fig. 4 presents plots of the equilibrium CH,F bromination rate under light with 3650 A wavelength and the bromination rate under COJaser radiation with 21 W power in the Arrhenius coordinates. It is seen that under infrared irradiation the reaction rate becomes ten to one hundred times higher. This acceleration cannot be attributed only to the vibrationally excited CH,F molecules resulting from the laser radiation. Indeed, if the reaction activation energy decreases by the value of the vibrational quantum (3 kca) mole- ‘), the maximum reaction rate acceleration cannot exceed $exp (hv/lrT) which is 60 at 40%. Greater accelerations may result from participation of highly excited molecules generated by V-V relaxation. Therefore, under such conditions one cannot determine the reactivity ofconcrete vibrationally excited states but associate it with the total concentration of the vibrationally excited molecules which is characterized by a vibrational temperature, different from the translational one. A weaker temperature dependence of the reaction rate under infrared irradiation (Iig. 4) as compared with the equilibrium reaction shows that the translational energy is not a basic Iactor in surmounting the activation hurrier of this reaction. However, the translational activation energy cannot be determined from this dependence since the vibrational temperature depends not only on the laser power which, in our experiments, was constant at various temperatures, but also on the absorption coefficient and the V-T relaxation rate which are temperature-dependent. The investigation of the reaction rate under the laser radiation, Iv, and without it, lV,, versus CH,F concentration (fig. 5) has shown that this dependence is rather weak over the concentration range (2-8) x 10” cme3. This is evidence for the fact that the acceleration resulting from the thermal heating is negligible. At such CH,F pressures the V-V relaxation is much faster than the V-T relaxation (which depends mainly on the relaxation with argon). Thus, there is a stationary distribution of CHJF molecules among vibrational levels which

40-

600

P(W) 0

Fig. 6. Plots of Wversus the laser power at vsrious temperatures. [CH,F] = 4 x 10” cm-‘,

2

[Brl] = 8 x 10” cm-‘, [Ar] = 2.3 x IO” cmm3. Fig. 5. Plots of IV/W0versus CH,F concentration various temperatures. [Br2] = 8 x lOI cme3, [Ar] = 2.3 x IO” cmb3, P = 21 W.

at

of CH,F pressure. The decrease of the i,v/W, ratio at CH,F concentrations below 2 x 10” cme3 must be associated with violation of this distribution on high reactive levels due to the competition of V-V and V-T relaxations. Fig. 6 presents plots of the reaction rates versus the CO,-laser power at various temperatures. This nonlinear dependence is also evidence for the fact that molecules with higher vibrational excitation, as those initially formed by the laser radiation, participate in the reaction. In fact, these data can he used to determine the vibrational temperature dependence of the reaction rate at Fixed translational temperatures. For that purpose one needs the absorption coefficients and the V-T relaxation rates (including the relaxation by the walls) at various temperatures. Since experimental determinations of these values are inaccurate, the vibrational temperature obtained in this way would not be accurate either. Therefore, to calculate the vibrational temperature we measured experimentally the total is independent

10

PWJ Fig. 7. Plots of n*/rzOversus the laser power. $ experiment; -----calculation for E = 11.0; 12.2; 13.0 kcal mole- ‘.

concentration of the vibrationally excited molecules at room temperature. Plots of IZ*/II, versus the !aser power are given in Jig. 7. A pronounced bend of the

350

L.N. Krasnoproroo et uf./Actiscrtion energy of the reaction Br (‘P,,?)

+ CH,F

curve in the region of 3 W is attributed to the strong dependence of CH,F V-T relaxation on the vibrational temperature [9]_ At high temperatures such measurements are very inaccurate because it is very difficult to stabilize the temperature of the cell all along the vessel including the NaCl windows. Besides, the kinetic measurements are impossible at room temperature since the reaction is too slow. A minimum temperature at which the ratio I.+‘/IV, can be reliably measured is SO’C. Therefore, to compare n*/nO measurements at room temperature with the kinetic data (lig. 6) obtained at various temperatures, we extrapolated the latter to room temperature. The dependence of Won the laser power can be represented by the empirical formula

among vibrational levels independently of CH,F pressure (see lig. 5), we represent this as a Boltzmann distribution with the effective vibrational temperature TV. In general, due to a fast intramode exchange each vibrational mode vi can have its own Boltzmann distribution. Its vibrational temperature T;.; can be calculated providing the mechanism of energy distribution between the modes is known [12]. The scheme of the vibrational modes for CH,F molecules is given in fig. 9. Assuming the following energy distribution mechanism for CH,F modes [ 121

rye-6 = I$-“( 1 + p).

one can estimate the difference between the vibrational temperatures of the modes. If we set the vibrational temperature of the vj mode equal to 600 K (maximum effective vibrational temperature in our experiments) then, using relations from refs. [12, 133, we have

(4)

Fig. 8 shows the plot of Ip-6 versus the infraredirradiation. The extrapoIation offl va!ues determined from this dependence in coordinates In /I- I/T, yeald the value 5.7 f I for room temperature.

CH,F(v,) Z$ CH,F(v,) + CH,F&,

=+ CH,F(2v2, 2v,) Z$ CH3F(v1, v.J,

E,ilT.i - -%,& 4. Discussion Suppose at CH,F concentrations exceeding 2 x IOl5 cm- 3 there is a stationary distribution

Fig. 8. Plots of I+“‘.6versus P. Conditions are the same as in lig. 6.

vg)

= (& - E,,Y?

(51

(6)

where T is the translational temperature, E,i and E,, are the energies of the levels involved into the energy transfer. Hence T., = 550 K, ?;.. = ?;., = 470 K, TV, = ‘T;, = 470 K. Note, however, that the above scheme of energy distribution in CH3F cannot

Fig. 9. Scheme of CH3F vibrational modes.

L.N. Krcmopyorou rt ol./Actiultiotl etlrrgp o/f/~ reacriorr Br (‘P,,,) + CHJ

be approved in full. For example, in ref. [ 141 it was shown that under pulse excitation of the 19~CH,F mode the v, mode begins to luminescence earlier than the vz mode. This means that the v1 modes may get populated during the process CH,F(3r,)

+CH3F(s,).

(7)

If account is taken of this process, the temperature of the V, mode will be higher than that of the 11~ mode. If both processes are taken into account we obtain an average value of the vibrational temperature. Thus, there are at present no reliable data for the calculation of vibrational temperatures of CH,F modes under laser irradiation. The above calculations show the accuracy of using the concept of an effective vibrational temperature. Having accepted

the effective vibrational

model, we can determine the vibrational activation energy E, by the formula temperature

E, = R?;.’ 6 In W(T,, ?;.)/a?;.

(8)

Here E,, in general, can be dependent

on translational temperature. Then, over a not very wide range of vibrational temperatures, iV(?;, K.) = I+$(?;)exp[E,R-‘(I/T where &(?;)

-

l/T.)],

(9)

= lV(T, ?;).

The vibrational activation energy calculations by this equation are hampered since the concentration of the excited molecules II*, and thus the vibrational temperature T,, are not constant along the radius of the reaction vessel. In case of large lV,/!V, values one can use an approximation similar to that employed to study kinetic characteristics of the reaction under laser heating [15-171. Setting <(r) = l/RT, -

l/RT,(r),

(10)

we obtain

IV =

3 nR’

Rexp [c(r)E v-] hr dr s

(11)

0

In the case of large exp (CEJ values the basic contribution to the reaction rate acceleration under laser irradiation is made by the region in the vicinity of maximum <. Hence, by expanding t(r) in il series using only the quadratic term we get

351

R

-$

exp {l<(O) - ar’] E,} 2nr dr sn = IV, exp [E,<(O)] [I - exp ( -aR’E,)]/zR’E,.

IV =

(12) Considering the whole <(r) prolile to be parabolic, c(r) = c(O) - a?, we have c(R) = 0 = <(O) - aR2, i.e.. u = <(0)/R”, hence W/IV, = {exp C<(O)&] - I }/<(O)E,,

(13)

Depending on the laser radiation power, the ratio W/IV, is determined by the empirical formula (4) with j = 5.7 extrapolated to room temperature, i.e.,

1 =1+

exp [E,R- ‘(l/T - I/?;) - I] ‘A E,R_‘(I/?; - l/?J With the vibrational from the formula

temperature

fl*/lIo 5 11*/1z= l/Z(T)

-

5.7P. (14)

T, determined

l/Z(7J,

(15)

where 1zis the total concentration of CH3F, I:* is the increase in the vibrationally excited molecules concentration under laser irradiation, and Z(T) is the partition function of the CH,F molecules, we cdn calculate the vibrational activation energy E, by formula (14). E, was selected such that the best lit of the dependence of fz*/tzOon the laser radiation power calculated by eqs. (14) and (15) to the experimental

dependence could be obtained. Z(T) was calculated in harmonic approximation using the normal vibrational frequencies of CH,F given in ref. [IS]. Fig. 7 presents such a dependence (the middle dashed line) at E, = 12.2 kcal mole- ‘. The dependences calculated for E, = 11.0 and 13.0 kcal mole- ‘ are shown for comparison. It is shown that the vibrational activation energy for the reaction Br(‘P,,?) + CH,F - HBr + CHtF obtained with the-assumption of average vibrational temperature and the above approximations, is 12.2 f 0.5 kcal mole- ’ . The vibrational activation energy calculated by two different energy distribution mechanisms (5) and (7) and by three different mechanisms of the vibrational energy influence on the reactivity [(l) every state with the same vibrational energy has the same reactivity; (2) only molecules with the

352

L.N. Krasnopyoroc et al./Actiuation energy of the reaction Br (‘P,,,)

+ CH,F

stretch C-H vib:ation Yeand v&react; (3) only molecules with the stretch and bend C-H vibration v1_4+ vLe5react] ranges rrom 10 to 15 kcal mole-‘. Thus, E, = 12.5 + 2.5 kcal mole- ‘_The equilibrium activation energy of this reaction is 14.6-16.1 kcal mole-’ [l, 191. Ana!ysis of the experimental data regarding the influence of Br electronic excitation [ 1] and CHSF vibrational excitation on the rate of the reaction

Then

~3,#,.

EJ > 0

at E, > EF, E, > Ef,

Br + CH,F yealds the following qualitative picture of the process. The diagram of the reaction profile

CT@,,

E,) = 0

at E, d Ef, E, < Et,

is given in fig. IO. This shape of potential curves results from qualitative quantum-mechanical considerations [20] and is corroborated by calculations on the F + Hz system [21]. In this case the reaction of electronically excited bromine atoms is possible only by a nonadiabatic transition to a lower potential surface which correlates with the reaction products in their ground electronic states. Let G&E~, E,) be the cross section of the reaction Br(‘P,,,) + CH,F, o&5,, E,) be that of Br(‘P,,J + CH,E Suppose (cf. ref. [21]) that after the nonadiabatic transition the probability of the reaction is the same as if the system were initially in

the lower potential surface with energies E; = .E, i (1 - y)E,, E:. = E, + yE, (where Es is the

spin-orbital splitting energy of Br atoms, 10.54 kcal mole- I, y the portion of this energy converted into vibrational energy at the nonadiabatic transition).

reaction

coordinate

Fig. IO. Prolile of the reaction Br + CHI,F.

a,,&% EJ = P(E,, E,) x

Q3/2

I.&

+

(1 -YULE,

+

YE*13

(161

where P(E,, E,) is the probability of nonadiabatic transition.

If the dependence of c3,2 on E, and E, is

of a threshold character, i.e.,

(17)

then the rate constants for the reactions of Br(*P,J and Br(‘P,,,) with CH,F can be written in the form k3,L

=

Aexp(-

Ef/R’I; - EffRT,),

k 1,2 = I’(Ef’, EF)A exp ( - E;JR’I; - E;/RTJ, where E;=Ey-(I-y)E,,

ifEfz=-(l-y)E,; if EF < (1 - y)E,,

=o , E: = Et - yE,, = 0,

W)

if

(1%

Ef > YE,;

if ~5: f YE,.

(20)

In the case of bromine atoms the conversion of the energy of spin-orbital interactions into that of translational motion is hardly probable [22], whereas the quasi-resonance energy transfer to vibrational degrees of freedom can proceed with an appreciable rate [23-271. Thus, in our case it is y z 1 and we can expect the reaction activation energy of the electronically excited Br atoms to decrease by the value of ES since I$? (12.2 kcal mole-‘) > ES (10.5 kcdl mole- ‘) which is observed experimentally. In this case the decrease in the pre-exponential factor must be attributed to a small probability of the nonadiabatic transition P(EF, Et). On the other hand, at CH,F vibrational excitation the reaction of electronically excited Br atoms can be accelerated to the degree allowed by the rest of vibrational activation energy, Ef - ES = l-2 kcal mole-‘. Estimates show that at ‘T;= 300 K, TV= 600 K (maximum vibrational temperature achieved in our experiments) we can expect only a tenfold acceleration of CH,F reaction with Br(‘P,J. This is more than two orders of magnitude less than the acceleration of the reaction Br(2P,,2) + CH,F and agrees with experiment.

L.N. Krmnopyorov et al.jActi~ufion wrgy

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[4]

[5] [6] [7] [8] [9] [IO] [I-i] [12] [13]

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of the wuctiort Br (2Pa,2) + CH,F

353

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