D. W. SETSERAND J. C. HASSLER
1364
Collisional Deactivation of 1,Z-Dichloroethane Molecules Containing 89 Kcal Mole-1 of Vibrational Energy
by D. W. Setser and J. C. Hassler Chemistry Department, Kansas State University, Manhattan, Kansas 66602 (Received October 8,1966)
The combination reaction of chloromethyl radicals WBS used to generate 1,2-dichloroethane molecules with an average energy of 89 kcal mole-' dilutely dispersed in an inert gas bath at 25'. By measuring the ratio of decomposition product (vinyl chloride) to stabilization product (1,2-dichloroethane) at low pressures, the vibrational collisional transition probabilities were estimated for CH3C1,CH2Clz,CF4, N2, and Ar with the highly energized CzH4C12molecules. Based upon a simple stepladder deactivation model, the average increment of energy transferred per gas kinetic collision is -10 kcal mole-' for CH3Cl, CH2C12,and CF4 and -6 kcal mole-' for Nz and Ar. These data concur with previous work which emphasized that highly vibrationally excited polyatomic molecules rapidly lose vibrational energy in collisions. The similar, but probably not equal, deactivation efficiency of CF4 compared to CH3C1 or CHzClz with 1,2-dichloroethane suggests that dipole-dipole type interactions are not unduly important for vibrational energy transfer from highly excited polyatomic molecules, at least not for these examples.
Introduction Chemically activated' ground electronic state 1,2dichloroethane molecules can be produced2 with an average internal energy level of 89 kcal mole-', but with a narrow dispersion, a t a bath temperature of 300°K. I n the gas phase two important kinetic processes are possible: unimolecular reaction via HC1 elimination and loss of active energy by collisions with heat bath molecules. A third process, infrared chemiluminescence, is an interesting possibility but it is too slow3 to compete with the two processes mentioned above at the pressures used in this work. The unimolecular HC1 elimination reactions of chloroethanes have been previously reported and the data have been adequately interpreted according t o an RRKRI calculation based upon a four-centered transition statea4 A small systematic programming error in the calculation of the moments of inertia tabulated in Table VI11 in ref 4 has been discovered. The values are high by 10-20%. Corrected values will soon be published; conclusions reached in this paper remain unaffected. I n this paper, the vibrational collisional transition probabilities for CH3C1, CH2C12, CF4, Nz, and Ar with chemically activated 1,2-C2H4C12 are reported. The Journal of Physical Chemistry
They were measured by comparing the competition between unimolecular reaction and collisional deactivation at low pressure^.^ Since the critical energy for HC1 elimination is about 55 kcal mole-', the energy region of interest, which will be referred to as the active region, spans from 94 to a few kcal mole-' above the critical energy. The literature dealing with vibrational energy
(1) B. S. Rabinovitch and M. C. Flowers, Quart. Rev. (London), 18, 122 (1964). (2) (a) D. W. Setser, R. L. Littrell, and J. C. Hassler, J . Am. Chem. Soe., 87, 2062 (1965); (b) J. C. Hassler, D. W. Setser, and R. L. Johnson, J. Chem. Phys., 45, 3231 (1966); (c) J. C. Hassler and D. W. Setser, ibid., 45, 3237 (1966). (3) From abaolute absorption intensity measurements, the infrared emission lifetimes of methane, R. C. Millikan, J. Chem. Phys., 43, 1439 (1965), and methylamine, G . T. Tiedeman, R. Ingalls, and J. S. Margolis, ibid., 42, 2627 (1965), have been shown t o be considerably longer than the time between collisions even a t the lowest pressures used here. (4) J. C. Hassler and D. W. Setser, ibid., 45, 3246 (1966). (5) Descriptive application of this method can be found in (a) R. E. Uarrington, B. 9. Rabinovitch, and M. R. Hoare, ibid., 33, 744 (1960); (b) G. H. Kohlmaier and B. 9. Rabinovitch, ibid., 38, 1962 (1963); (c) D. W. Setser, B. S. Rabinovitch, and J. W. Simons, ibid., 40, 1751 (1964).
COLLISIONAL
DEACTIVATION O F l,%DICHLOROETHANE hfOLECULES
transfer is volumin~us.~JVibrational-translational, vibrational-rotational, and vibrational-vibrational exchange and various combinations of these possibilities have received study both experimentally and theoretically. However, the majority of the work for both diatomic and polyatomic molecules deals with the lowest transition probability, Pol, for which usually hv > kT. A significant exception to this statement is the recent work of Steinfeld and Klemperel.8 in which vibrational energy transfer from the twenty-fifth level of the B3a electronic state of 1 2 was measured for a variety of gases. Similar quantitative or even semiquantitative data for polyatomic molecules containing large amounts of vibrational excitation are very scarce. The situation has been adequately summarized by Rabinovitch.6b The more useful data have been derived from systems in which the molecules were activated by means other than collisions; they include fluorescence studies of 0-naphthylamine and similar molecule^,^ quantum yield work for ketene’O* and hexafluoroacetone,lOb and chemical activation studies of butyl radicalssb#’‘ and cyclopropanes.6cJ2 All these results are in qualitative agreement; that is, relatively large quantities of energy are removed from the vibrationally excited molecule upon each collision. For example, helium and butene remove at least 1.5 and 9 kcal mole-’, respectively, from sec-butyl radicals which are at an energy of -40 kea1 mole-’. The data contained in this paper, which are for a completely new chemical activation system, support this trend of efficient collisional removal of vibrational energy from highly activated polyatomic molecules. Some of the finer points, such as the role of rotational degrees of freedom, influence of dipole moments upon the transition probabilities, etc., will be discussed. I n view of the results summarized above, it would seem a,gpropriate to question the validity of the occasionally measured13 and/or assumed14 low-collisional efficiencies for inert gases with vibrationally excited polyatomic molecules in various systems, usually photochemical in nature. The measured values, as the authors themselves sometimes point out, may result from an incomplete mechanistic understanding of the reactions taking place or from some direct chemical interactions of the “inert” gas with some component of the system rather than just mere physical energy transfer by the inert gas. The work of Rabinovitch and co-workers dealing with highly vibrationally excited polyatomic molecules has strongly suggested that the collisional efficiency decreases” with increasing temperatures in contradistinction to the Pol transition probabilities. This has been interpreted as manifestation of the im-
1365
portance of the attractive potential for the interaction of the collision partners. The 1,2-di~hloroethane’~ system with CHG1 and CH2C12,as contrasted with CF4, as collision partners affords the possibility of observing the influence of attractive dipole-dipole interaction upon the magnitude of the collisional transition probabilities. The vibrational collisional transition probabilities of 12*(B3T, Y = 25) and butyl radicals (E) = 40 kcal mole-’ with molecules having permanent dipoles showed no special features ; however, the interaction of two permanent dipoles has not been investigated until now.
The Experimental System Chemical Reactions. The chemically activated 1,2C2H4C12molecules with average energy of 89 kcal mole-’ were produced by the combination of CH2Cl radicals which in turn were generated by the C1- and/or H-atom abstraction reactions of CH2 from CH3C1 or CH2C12.2g16The over-all features of these chemical activation systems, including evaluation of the pertinent (6) T. L. Cottrell and J. C. McCoubrey, “Molecular Energy Transfer in Gases,” Butterworth and Co. Ltd., London, 1961. (7) For recent reviews see (a) A. W. Read, P r o p . Reaction Kinetics, 3, 203 (1965), (b) A. B. Callear, Chem. SOC. Ann. Rept., 51,48 (1964); (c) K. Takayanagi, “Advances in Atomic and Molecular Physics,” Vol. I , Academic Press, Inc. New York, N. Y., 1965. (8) J. I. Steinfeld and W. Klemperer, J . Chem. Phys., 42, 3475 (1965). (9) B. S. Neporent and S. 0. Mirumyants, Opt. Spectry. (USSR) English Transl., 8, 336 (1960); M. Boudayt and J. T. Dubois, J . Chem. Phys., 28, 223 (1955); B.Stevens, Mol. Phys., 3, 589 (1960); B. Stevens and M. Boudart, Ann. N . Y . Acad. Sci., 67, 570 (1957). (10) (a) G. A. Taylor and G. B. Porter, J . C h m . Phys., 36, 1353 (1962); (b) P. G. Bowers and G. B. Porter, J . Phys. Chem., 70, 1622 (1966). (11) G. H. Kohlmaier and B. S. Rabinovitch, J. Chem. Phys., 38, 1709 (1963). (12) J. W. Simons, B. S. Rabinovitch, and D. W. Setser, ibid., 41, 800 (1964). (13) For example, (a) S. Toby and B. H. Weiss, J . Phys. Chem., 68, 2492 (1964), find relative deactivation efficiencies for ethane formed from 2CHs -L CZH8 of 2.0, 1.0, 0.3, and 0.06 for acetone, azomethane, sulfur hexafluoride, and carbon dioxide, respectively; (b) R. D. Giles and E. Whittle, Trans. Faaraday Soc., 61, 425 (1965), report relative collision efficiencies of vibrationally excited CHsCFa with c-CeF12, hexafluoroacetone, acetone, and nitrogen of 1.0, 0.75, 0.39, and 0.075, respectively. These efficiency factors are usually obtained from high-pressure measurements. Therefore, they are combined effects of cascade through an active energy region and/or a reduced effective collision cross section (see ref 3b and text). For even both combined effects, the numbers quoted by these authors appear t o be too small especially for Nz and COz. (14) 8. W. Benson and G. Haugen, J . Phys. C h a . , 69, 3898 (1965). The efficiency factors of 0.1-0.2 used by these authors for vibrationally excited fluorinated ethanes seems much too low. (15) Since the period for internal rotation is short, S. W. Bensonr K. W. Egger, and D. M. Golden, J. Am. Chem. Soc., 87, 468 (1965), compared t o the lifetime of the activated molecule (10“ sec), it is apparent that the average conformation of the vibrationally excited ~ , ~ - C Z H Iwill C Zhave a dipole movement. (16) C. H. Bamford, J. E. Casson, and R. P. Wayne, PTOC.Roy. SOC. (London), A289, 287 (1966).
Volume 71, Number 6 April 1967
D. W. SETSERAND J. C. HASSLER
1366
energies and calculation of specific rate constants, have been previously p r e ~ e n t e d . ~An , ~ obvious practical advantage of the 1,2-C2H4C12 molecule for study of energy transfer is the convenient pressure range, 0.5-5 cm, in which unimolecular reaction effectively competes with collisional deactivation. For unit deactivation efficiency, the system is described by eq 1 and 2.17 The experimental nonequilibrium rate constant has been defined as k a = w(D/S) CH&1
+ CH&l+
CH&l-CH&l*
(1)
ka
CH&l-CHzCl* + HCl C2H3C1(decomposition, D ) (2a)
+
CH2Cl-CH2C1* 5 CH2C1-CH2C1(stabilization, S ) (2b) where w is the gas kinetic collision frequency. It was compared to the calculated unit efficiency rate constant, which equals wi:(ke/ke
+ w)f(e)de/Sm(w/ke + w)fCO
(€)de,where ke is the specific reaction rate constant and f(e) is the distribution function of the formed molecules. Due to the small energy spread of f(e), the magnitude of k. would show a small monotonic decline with decreasing pressure for this unit deactivation model. For 1,2-C2H4C12 formed at 300°K this is a small effect, about a factor of 1.1,and we will give it no further consideration. If collisional inefficiency is introduced, see Figure 1, eq 2b is no longer sufficient and the model that we will utilize in this work is formulated in the next section. However, the definition of the experimental apparent rate constant is retained. It should be emphasized that the conclusions previously reached214concerning the nonequilibrium reactions of chloroethanes are not changed in any way by the introduction of collisional inefficiency. The previous data included the higher pressure region, ie., S / D > 0.7, and in the high-pressure region the magnitude of k, is quite insensitive to the exact collision mechanism5J7 and, a t any rate, appropriate allowance was made for the small effect upon kaa. In the present paper, the low-pressure region is of interest and new low-pressure data will be presented for CH2C12, CF4, and CH3C1 as collision partners. Also data covering the entire pressure region for N2 and Ar as the bath molecules will be shown. The most important experimental measurements for the determination of collisional transition probabilities are the values of k, (as defined above) a t very low pressures, ie., low S / D ratios. Since the stabilization product is present in only small quantities, the critical measurement is the quantity of stabilization product, The Journal of Physical Chemistry
which is 1,2-C2H4C12. The HC1 reacts with either ketene or diazomethane (the CH2 precursors) to give acetyl chloride or methyl chloride, respectively, and the only measurable decomposition product is vinyl chloride. For both the butyl radical and the cyclopropane chemical activation cases,5,11,12 the intrinsic usefulness of the systems was never fully realized because of mechanistic complications, such as side reactions, which required that corrections be applied to the data, especially to the measured quantity of stabilization product. For 1,2-C2H4C12 the situation appears to be somewhat better, and as far as is known the measured quantity of 1,2-C2H4C12 corresponds directly to the stabilized product. However, for the chloroethanes other problems arise. Due to the high boiling points of the products, glpc analysis must be done a t elevated temperatures and inevitable scatter of the data seems to occur with our apparatus. The situation for measuring vinyl chloride, the decomposition product, is not quite as good as for 1,2-CzH4C12,the stabilization product, although fortunately the yields of the decomposition product are large at low pressure and the corrections which will be mentioned below are not critical. It is thermodynamically possible for the vibrationally excited vinyl chloride formed in eq 2a to undergo further HC1 elimination to form acetylene. This was, however, shown not to happen a t the lowest pressure used in this work. For the system employing the reaction of CH2 with CH3Cl, the measured yield of vinyl chloride corresponds directly to the decomposition product. Unfortunately, this is not true for the reaction of CH2 with CH2C12, although the glpc analysis is easier than for the CHIC1 case. As has been previously discussed2c for the CH2C12 system, there are three sources of vinyl chloride: (1) decomposition of 1,2-CzH4C12,which is the appropriate decomposition product in eq 2a; (2) decomposition of 1,1-C2H4C12;and (3) a pressure-independent source which has been attributed to the direct disproportionation reaction of CH3 with CHC12. The CHCl2 and CH3 radicals arise from H abstraction by CH2 from CH2Clz and are present in smaller steady-state concentrations than the CH2Cl radical; therefore, the quantities from eq 2 and 3 are smaller than from eq 1. The method of subtracting out the contributions of eq 2 and 3 to the vinyl chloride yields is explained in the results section. The point to be made at the present time is that for the CH2Clzsystem the values for k, at high pressure cannot be obtained with high accuracy due to these correction factors. However, since the (17) B. 8. Rabinovitch and D. W. Setser, Advan. Photochem., 3 , 1 ( 1964).
1367
COLLISIONAL DEACTIVATION OF l,%DICHLOROETHANE MOLECULES
low-pressure data are the more important, this is not necessarily a serious limitation for deactivation efficiency studies. Collisional Deactivation Model and Steady-State Formulation. Description of the relaxation of vibrationally excited polyatomic molecules dilutely dispersed in an inert gas and undergoing unimolecular reaction has been thoroughly discussed.ss11s12J8 Primarily for reasons of convenience of comparison, we will use the formulation and notation of Rabinovitch and coworkems The energy region and the microscopic kinetic processes are depicted in Figure 1. Obviously the problem is a many-leveled one and requires the microscopic collision and unimolecular reaction probabilities for each level. The active energy region must be divided into levels which are sufficiently narrow so that the appropriate energy dependence of the collision and reaction probabilities can be adequately represented. It has been found that levels of 1 kcal mole-' width are sufficiently fine grained for this p u r p o ~ e . ~As a simplification we will take the collisional transition probabilities in the active region to be independent of the energy. This is reasonable in our case because the energy changes by less than a factor of 2 in the active region and because only the top half of the active range is really significant. The steady-state transport equation which describes each level has the form
dnz -- wZ5Ptjnj- wcP5tn$- kfin, + Wet= 0 dt
(1)
j
The nr is the steady-state population of the ith state; k f r is the specific rate constant at energy ~ i ; P j r is the probability per collision that a molecule in state i will undergo a transition to state j , z P j r= 1; R is the i
total chemical activation formation rate of 1,2-C2H4C12; and Rferis the fraction of the formation rate into the energy region i, or stated another way, fci is the fraction of the normalized distribution function of formed molecules for region i. From these definitions it also follows that the rates of formation of decomposition and stabilization products are given by D = zICfiniand S = R - C k e i n i , respectively. Since the i
i
experimental rate constant is defined as k, = wD/S, the calculated rate constant has the analogous form k, = w ( C k , m t ) / ( R - Ckeinc> i
i
(11)
These equations can also be cast into a compact matrix formulation. l 9 The values for fer and IC,, have been previously pre~ e n t e d . ~The computed kel for 1,2-CzH4C12 did not
)ECOhPOSED PRODUCT CLYCl
+
k d
HCI
0
Figure 1. Schematic representation of kinetic processes occurring in the active energy region for 1,2-CzH<. The 6 factor has been considered to be equal to unity.
quite match the observed experimental value. Some reasons for this have been previously discussed and it was concluded that a major factor was the uncertainty in our knowledge of the critical energy of the reaction. The calculated values for chloroethane and 1,l-dichloroethane matched the experimental values reasonably well. Therefore, the discrepancy between the calculated ICft from the model and the experimentally determined rate constants for 1,2-C2H4C12is not due to some complicated deactivation scheme, because the same discrepancies would have been expected for the other two chloroethanes if that were the case. Furthermore, the experimental value is lower, not higher, than the calculated value. The energy dependence of the computed rate constants for 1,2C2H4CI2has been shown4 to be nearly correct and for these present calculations the values of ICft were decreased uniformly by a factor of 4 so that the calculated magnitude of IC, at high pressure agreed in a reasonable way with the experimental values that had been adjusted to unit deactivation efficiency. Reducing the magnitudes of ICfi has little significance for determining the collisional transition probabilities and was really unnecessary (see Figure 11 of ref 5c). The primary advantage is convenience. These adjusted rate constants and the distribution function are shown in Figure 2. If the transition probabilities could be calculated from basic theory, then using f f r and ICft would permit eq I t o be solved for the ni. This is not possible, and (18) R. V. Serauskas and E. W. Schlag, J. Chem. Phys., 42, 3009 (1965); 43, 898 (1965). These authors describe. the "Many-Shot Expansion" technique for calculating D and S. This method has been extensively employed by Rabinovitch and cc-workers, see especially, ref 5b. (19) M. R. Hoare, ibid., 38, 1630 (1963).
Volume 71, Number 6 Aptill087
D. W. SETSER AND J. C. HASSLER
1368
lo’
Pt,=l
j - i = s
Pij=O
j - i f s
This assumes that Pi, = 0; if not, then the value of P,-a,j is replaced by P where p = 1 - P f tand the model becomes a very simple bimodal transition model which includes elastic collisions. Results of computations using the fcl and k,! of Figure 2 for various values of s with P i t = 0 are presented in Figure 3.
--lo8 I
0
w
”
Y
2 2 30’ v)
z
0 0 W I-
a
K
106
Id ad
I 65 7s 85 ENERGY ( k c a l mole-I)
95
Figure 2. Specific rate constants, ke, and distribution function, f ( ~ ) for , ~,P-C~HICL.The rate constants have been adjusted (see text) by a factor of 4 relative to the calculated RRKM rate constants of ref 4.
the purpose of this work is to use the experimentally determined S and D values at various pressures together with k,, and .fet in order to deduce some knowledge about the Pij. We will assume simple deactivation models and compare the calculated result with experiment. The numerical computations were done with the IBM 1410 using the technique that has recently been formalized and named the “Many-Shot Expansion.”ls This same computational technique was also previously utilized in the chemical activation c a l ~ u l a t i o nby~ Rabinovitch ~ ~ ~ ~ ~ ~ and co-workers. Previous computations for cyclopropane and butyl radicals have encompassed deactivation models which used stepladder, gaussian, and exponential distribution probabilities, including transitions Pi, with i > j. In general, the experimental data were not sufficiently good to delineate decisively between the various cases. The present data are little better and there is no point in attempting to match the experimental behavior to anything but the model employing the simple stepladder cascade through the active energy region. For such a model, energy decrements, A€ = s kcal mole-’, are of constant size and up transitions are not allowed. The collision probabilities are given by the following relations. The Journal of Physical Chemistry
02-
L
I 0.2
0.0
I 0.4
1
I
0.8
1.0
I
0.6 PRESSURE
(cm)
I
Figure 3. Calculated apparent rate constants, k., from the simple stepladder deactivation model (0 = 1) plotted rn a function of pressure.
The features of the multistep cascade deactivation model have been thoroughly discussed by Kohlmaier and Rabi~iovitch.~~ Some of this discussion is reviewed below for the particular case of activation to a single level (a monoenergetic distribution function) in order to clarify the basis for the comparison of the experimental and calculated results. The notation applies to Figure 1. Let n be the number of levels in the active region and T the number of transitions necessary for the molecules to cascade from n to below eo. The values for S, D, and k, are given by the expressions
The high- and low-pressure limiting forms of kaT are of interest. At high pressure w > k,,, and by expandk,J and dropping terms of kcz2and higher ing n(pw
+
T
DT/ST = ( 1 / @ ~ ) ~ [
+ < P w ) ~k-.,~] C- 1 t=l
c
(IV)
I
hamT= 1/P
t=l
k,t
COLLISIONAL
DEACTIVATION O F l,%DICHLOROETHANE MOLECULES
At low pressures w < k e , , arid from the expansion of eq I11 it can be seen that k,oT
=
w(l/pw)TiIk,r t=l
Consider a comparison of calculated and experimental rate constants in the high-pressure region, i.e., S / D > 0.7 for ll2-C2H4C12. Equation IV and Figure 3 show that little pressure dependence of ka can be expected and only comparison of absolute magnitudes of ka from one gas to another can have significance. The rate constant ratio for gas A and B has the form
-t-1
t=l
and obviously depends upon T A , T B , PA, and OB. As pointed out by Kohlmaier and Rabinovitch, uncertainties in the P ratio are equivalent to uncertainties in the collision cross sections uA2 and ug2. If gas B has unit efficiency, then the comparison in eq VI can be used as an assignment for two possible extremes-a maximum value for T A , which is equivalent to a minimum s, if the @ ratio is taken as unity, or alternatively a minimum p ratio, if T A is taken as one. Fortunately, consideration of the low-pressure region can help to remove some of the ambiguity13 of the high-pressure comparison. At low pressures, Figure 3 shows that k , is strongly dependent upon the pressure. If cascade occurs, k , a ( l / ~ ) ~ -according l to eq V and a reasonably good measure of T can be obtained from this pressure dependence, An additional advantage is that the “turnup” behavior of k a is independent of @ or u2. It is apparent that if sufficiently reliable data could be obtained in the low-pressure region, then good assignment of the collision transition probabilities could be made. After examination of the low-pressure region and assignment of an s value, then the high-pressure region can be used to evaluate the P ratio. I n actual practice it is easier to match experimental data to calculated curves on a plot of kaT/kamT us. S I D rather than on a plot of just kaT us. pressure.
1369
present in the sample. Analysis for the CH2Cl2 system was done in a single pass through an octoil column; for the CH&1 system, the 1,2-C2H4C12analysis was done with an octoil column, the sample was trapped, and C2H3Clanalysis obtained with a Porapak column. The data consist of measurements of the quantities of vinyl chloride and 1,Zdichloroethane at various pressures. The results are summarized in Figures 4 and 5 . The data for the high-pressure region ( S / D 2 0.6) have already been published2bgcfor the CH3C1, CH2C1, and CHzClz CF4 systems; therefore, only the low-pressure data are shown. Both the highand low-pressure data for Ar and N2 are displayed in Figure 4. For the ideally behaved 1,2-C2H4C12chemically activated system, which we define as one with no source of either 1,2-C2H4C12or C2H3Cl other than stabilization or decomposition of hot 1,2-C2H4C12, and P vs. 1,2both the 1/P vs. C2H3C1/1,2-C2H4Cl2 C2H4C12/C2H3C1plots (see Figure 4) should go through the origin. This is the case for the reaction of CH2 with CH3C1,but it is not the case for the plot of CzH3C1/C2H4C12vs. 1/P for the reaction of CH2with CH2C12. The cause of this intercept has been previously discussedzcand a brief summary was given in the previous section. Treatment of Experimental Data. The linear intercept of the 1/P vs. CzH3C1/1,2-C2H4Cl2 plots, which arises from two sources of vinyl chloride other than reaction 2a, must be used to convert the measured yields of vinyl chloride to the true quantity of decomposition product. The additional sources of C2H3C1 arise from the CHI and CHC12 radicals which are produced by hydrogen abstraction of CH2 with CHZC12.
+
Results Experimental Procedure. The details of the experiments have been previously presented.2bsc Briefly stated, the experiments consisted of photolyzing mixtures (1-2 : 10 : 100) of diazomethane or ketene with CHzC12 or CH3C1 with inert gas. After photolysis, the inert gas was removed by pumping the sample through traps a t the appropriate temperatures and the sample was analyzed by glpc. For CH2C12or CH3C1 as the deactivating gas, of course, no additional inert gas was
IIPRESSURE
(cm-’)
Figure 4. Experimental data a t high and low pressures for photolysis of ketene with CH2Cl2 using Ar and Nz as the deactivating gas: A, high-pressure region; B, low-pressure region; see also the legend of Figure 5 .
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D. w. SETSERAND J. c. HASSLER
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Table I : High-pressure Rate Constants for 1,2-C2H4C12
:",e
A cyci
Deactivating
0
-
U
A*
I " f04-
CHaCl' CHZClz CF4 Nz Ar
0
ooo e.
A 02-
gas
0 0
A
06-
0
8 oo
&AQ@ 00.
I
I
I
I
I
Figure 5. Low-pressure experimental data for photolysis of CH2N2with CH2C12 (high-pressure intercept of 0.16), the photolysis of CHZNZwith CHzClz using CF4 as principal bath gas (high-pressure intercept = 0.45), and the photolysis of ketene with CH&1 (no high-pressure intercept). For these data and those of Figure 4B, some curvature is expected a t the low pressures. Such curvature is present, although it is hardly apparent on the scale shown. For this reason, straight lines are not drawn through these data.
k,,a cm
1.6 1.8 2.3 2.5 3.3
1.81 X 1.96 X 2.46 X 3.31 X 3.48 X
108 108 108 108 108
a Pressure a t which S/D = 1.0. The collision diameters used21 in converting the numbers in column 2 into rate constants were 6.0, 4.15, 4.75, 4.70, 3.85, and 3.40 A for 1,2-C2H4Clz, CH3Cl, CH&12, CFd, N2, and Ar, respectively. These are the conventional LennardJones diameters.21 At the same pressure the collision rates of these various gases with CzH4Clz differ by less than 10%. For this reason the calculation of w was done as if the gas mixture consisted of only the principal component gas. e There is no high-pressure intercept in this system and IC. is just the slope of the 1/P vs. C2H3Cl/l,2-C2H4C12 plot a t high pressures.ab Within our experimental error, 1.81 X 108 should be considered equivalent to 1.96 X los.
purposes these details are not important, providing the yields of vinyl chloride are corrected in the apSince the amount of hydrogen abstraction depends propriate way. It is sufficient to use the linear exupon the energy state of the reacting CH2, which trapolations obtained from graphs such as Figure 4 varies with the source of methylene and the nature of in order to correct each vinyl chloride yield to the true the inert gas,2othe value of the intercept must be dedecomposition yield of eq 2 . The uncorrected lowtermined for each deactivating gas. At the pressures pressure energy transfer data are shown in Figures 4 and used in this work, the two additional CzH3Cl sources 5 as plots of pressure vs. 1,2-C2H4ClZ/C2H3C1. The may be considered together, and the experimental situaexcess vinyl chloride was subtracted from each of tion can be summarized as the ideal chemical activation these points and the value for k , calculated on the system plus a pressure-independent reaction which basis of k . = w ( D / S ) ; these values were divided by gives the decomposition product. Equation 3 dek,, for the inert gas in question and the results are scribes the pressure dependence of the ratio of vinyl plotted in Figures 6 and 7. chloride to dichloroethane (see Appendix of ref 2c); Matching of Deactivation Models to Low-Pressure 6, which is obtained from plots such as Figure 4,is the Experimentul Data. The calculated k,"/lc.,* curves ratio of CzH3C1 that arises from the "pressure-independent" source relative t o the total yields of C2H3C1 for different step size are superimposed upon the experimental data in Figures 6 and 7. Since the deactivating efficiency of CH2Clz is roughly similar to Ar or Nz, the calculated rate constants for the 1O:l mixture of inert gas with CHzClz were obtained by asplus 1,2-C2H4C12that are produced by reaction 2. The suming that all collisions, whether with CH2Clz or inert high-pressure rate constant for each gas was obtained gas, were identical. The data are badly scattered, but from graphs of the above function; Le., k a = slope/ it is certainly apparent that some collisional ineffi(1 a), and the values are summarized in Table I.21 ciency is present. Since the data are quite scattered, Actually, at even higher pressures (see Figure 1 of ref 2c) the linear curve of Figure 4 would show down(20) For CHZCO and CHZNZas methylene precursors with CH&lz, ward curvature due to the onset of stabilization of the ratio of ka/kcl was estimated as 0.2 and 0.4. respectively. Adding inert gas increases the hydrogen abstraction; for CF4 with CHZNZ l,l-CzH4C12. Even after all the l,l-CzH4C12is stabithe ratio was -0.8 and for NZ with CHnCO -0.6. Some factors lized, however, residual vinyl chloride was found2" to which influence the chlorine and abstraction ratio have been summarized in ref 2c. be present. This CzH3Cl was tentatively associated (21) J. 0. Hirschfelder, C. F. Curtis, and R. B. Bird, "Molecular with the direct, pressure-independent dis&oportionaTheory of Gases and Liquids," John Wiley and Sons, Inc., New tion of CHI and CHC12 radicals. For our present York, N. Y., 19134, 1212.
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The Journal of Phyeical Chemistry
COLLISIONAL DEACTIVATION O F 1,2-DICHLOROETHANE MOLECULES
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Table 11: Energy Transfer Increments for Cascade Deactivation Model Deactivating
Energy increment,
gas
8
CHzClz CHIC1 CF4 NzcDd ATCsd
I
0.0
I
0.2
I
0.4
I
0.6
S/D
I
I
0.8
1.0
I.2
Figure 6. Plot of k J k , us. S/D for CHzC12, CFd, and CH&l as deactivating gases. The curves are calculated from the simple stepladder model with values for the stepsize as indicated. Each calculated curve was drawn by using its own k,," value, see Table 11.
0-b -Ar
I
00
I
02
I 04
I
06
510
I
08
I 10
I2
Figure 7. Plot of k,/k., us. S/D for NZand Ar as deactivating gases. The curves are calculated from the simple stepladder model with values for step size as indicated. Each calculated curve was drawn by using its own k,,* value, see Table 11.
we will adopt the point of view of choosing reasonable lower limits to the jump size that fit the data. These energy increments are tabulated in Table I1 along with the value of kame that accompanies that particular s value. Although the scatter of the data prevents detailed selection of a collisional deactivation model, some discussion of the individual gases is worthwhile. Consider first the more efficient deactivators, CHSC1 and CH2C12. A general feature of these data, as well as for CF, and for nT2, is that for S / D > 0.3 a larger jump size is needed than for the data with S / D < 0.3. The result is that the calculated curve which fits the larger S / D data and corresponds to a larger s value tends to
>12 >10
>8 ~6 -6
CalodO kame, 8eo -1
2.66 X 2.84 X 3.14 X 3.65 X 3.65 X
108 108 108
108 lo8
Relative km ratiob Calod Exptl
1.0 1.08 1.18 1.37 1.37
1.0 1.0 1.29 1.74 1.83
' For unit deactivation, the value of k,, is 2.30 X 108 for the Since the values of k,i specific rate constants of Figure 2. do not perfectly match the unit efficiency experimental rate constant, comparison of calculated and experimental values of k,, have no validity (see also the text for limitations of such comparison under ideal circumstances) and only relative values can be compared. For a jump size of 4 kcal mole, k,,* = 4.75 X 108 and the calculated k,, ratio relative to s = 12 would See text for discussion of these selections of s. be 1.78.
cut through the lower S / D points. One possible solution may be that the k,, values derived from the higher pressure data ( D / S vs. 1/P plots discussed earlier) may be too large by 10-30%. If that were the case, the points for the CHzClz systems would all be elevated on the graphs (but the higher S / D points more so) and would better fit a stepladder model. The results at S / D < 0.5 for CH3C1 seem to fall only slightly below the s = 10 curve. There is little scatter, but there is an apparent tendency again for the higher S / D points t o fall on larger s curves than do the lower S / D points. The accuracy of the data at the present time is not sufficient to warrant criticism of stepladder cascade as an appropriate deactivation model. However, these data would seem to argue against a model having an exponential distributions of jump sizes which gives even flatter k,/ka, vs. S / D curves than does the stepladder model. The results for the less efficient deactivators, Ar and N2, are clearly different than for CH3Cl or CH2Cl2. A value of 6 for s fits the N2 data reasonably well; although the Ar results are badly scattered, the s = 6 curve passes through the center of the range of points. The points at S / D > 0.6 again fall below the s = 6 calculated curve. If a lower experimental value of kam were selected (to bring the high S / D points into agreement with the stepladder predictions), then s = 4-5 would perhaps be a better representation of the data. If such a choice for the experimental k,, were made, then the experimental ( k a m ) A r or NJ(kam)CHzC1, ratio would be less than 1.75; this would be below the calculated kam8=4/kam8=12 = 1.78 value. Thus, s = 4 Volume 71,Number 6 April 1.967
D. W. SETSERAND J. C. HASSLER
1372
would appear to be an absolute minimum and s = 6 a more likely possibility; s = 8 is certainly too large. The CF4 data are of particular interest because the comparison with CH2C12matches gases with the same reduced mass, but one has a dipole moment and the other does not. Unfortunately, interpretation of the CF, data is somewhat ambiguous. For these reasons the CF4 data are discussed separately. The data are depicted in Figure 6 using the k a m value of 2.46 X lo8 sec-1 obtained2c from a 1 / P us. GH&1/1,2-CzH4C12 plot. This value best fits that plot. However, examination of Figure 6 shows that most points with S / D > 0.4 lie below the curve for s = 12, but that the three points below S / D = 0.4 tend to lie above even s = 10. This is the same problem as for the other gases but is much worse in this case. The shape of the data can be improved relative to the stepladder curves if the magnitude of the experimental k,, is reduced. If k,, is lowered to 2.10 X 108 sec-', the experimental ( k a m ) C F 4 / ( k a m ) ~ H 2is ~ ~ 1.16 2 and would correspond to the calculated ratio of ka-8=8/k,ma-12. Also, reasonably good fit to the s = 8 curve is obtained for all points in a plot such as Figure 6 except for the very lowest S / D point. Further improved data are obviously needed but for the present s > 8 seems to be a reasonable conclusion. Deactivation Model and High-pressure Data. After fitting the low-pressure turn-up data, the high-pressure rate constants may be compared to the calculated results from the model. The calculated kam8values relative to CH2C12for each gas are shown in Table 11; comparison with the experimental values indicates that a very small p factor might be present for CF4, N2, and Ar, although the effect is within our experimental error. A slightly smaller jump size for Ar and N, or a somewhat smaller IC,, (both factors are encompassed by our experimental error as discussed in the previous section) would reduce the 0factor to unity. The conclusions of the preceding paragraph are based upon the assumption that 0for CHzC12and CH&1 is unity. If it is not, then the above conclusions would be reduced to the statement that the p for the remaining gases is the same as for CH2Clz and CH3C1. There is no way of finding for CH&1 or CH2C12 from our data. However, based upon the efficiency of CH3Cl with vibrationally excited butyl radicals and on efficiencies usually found between similar type molecules in low-pressure thermal unimolecular reaction rate studies,22the p factor collisional efficiency must be close to unity. Nevertheless, this point needs further attention and experiments employing inert gases with potentially larger energy transfer probabilities are being planned. The Journal of Phy8icaE C h m i e t r y
Discussion The most important aspect of this work is the further support that it provides for the efficient deactivation of highly vibrationally excited polyatomic molecules5J0,11by even monoatomic and diatomic collision partners. Correspondingly more efficient deactivation was found for collision partners of increasing molecular complexity, as would have been e ~ p e c t e d . ~ The strong collision limit was not found between CzH4Cl2and even the most efficient gases, and considerable further work is needed to pinpoint the exact deactivation model. Interesting comparisons can be made between the collisional deactivation results from chemically activated cyclopropane12 and 1,2-C2H4C12. They both have about the same quantity of excitation energy and the same number of degrees of freedom. Based upon a stepladder model, the average loss of energy per collision of cyclopropane with C2H4 and Ar or N2 at 25' was found to be 10-15 and 6 kcal mole-', respectively. Considering the limited quality of the data for both cyclopropane and 1,2-dichloroethane this is remarkable agreement with the step sizes of -12 and 6 kcal mole-' found for CHzCl2 or CHsC1 and N2or Ar, respectively, with 1,2-CzH&12. Sound-dispersion studies23 with CzHsCl, CHICHF2, CClF2CClF2,and CH3CC1F2have shown that between six and ten self-collisions are required to remove 1 quantum of energy from the lowest vibration. Dichloroethane would be expected to behave in a similar manner. Based upon the results of this work, the collisional removal of vibrational energy from 1,2-C2H&12 excited to 89 kcal mole-' is certainly much faster than the Pol process. The energy transfer probabilities at the higher energies must involve multiple quantum transitions, but it should be noted that the density of energy levels is very high, 210'O states/kcal mole-', in the active energy region. Recent measurements of the vibrational energy transfer from I2 (B37r, v = 25) for which the vibrational energy level spacing is small (0.2 kcal mole-') showed that for such small spacings the vibrational-translational energy transfer (Av = 1 or 2 with reduced probability for the latter) occurred with nearly every gas kinetic collision with polyatomic molecules. Also, the transfer probabilities showed a dependence upon reduced mass that was much different from that normally found for gases which follow the Landau-Teller deactivation scheme.6J In fact, the trend resembled the reduced mass effect found for collisional deactivation of highly vibration(22) F. J. Fletcher, B. S. Rabinovitch, K. W. Watkins, and D. J. Locker, J . Phys. Chem., 70, 2823 (1966). (23) L. M. Valley and S. Legvold, J . Chem. Phya., 36, 481 (1962).
COLLISIONAL DEACTIVATION O F l,%DICHLOROETHANE MOLECULES
1373
has the lower vibrational frequencies. It would ally excited polyatomic molecules, aa can be seen by appear that the combined effects of the lower frecomparison to the butyl radicaP work, i.e., increasing quencies of CH2Cl2 and its dipole moment do cause efficiency with increasing reduced mass. it to be somewhat more efficient, but the effect is not The degrees of freedom of the collision partners that large. The Lennard-Jones interaction energies (@) may be effective in the vibrational energy transfer of polyatomic molecules have been d i s c ~ s s e d , ~ for ~ ~ CF4 ~ and CH2Cl2 with CzH4ClZ were estimated to be 250 and 398O, respectively.26 Apparently this inbut no firm conclusions have been reached. The crease in interaction energy, which is a reflection of the equivalence of our results for Ar and Nz as deactivators dipole-dipole forces, is insufficient to greatly affect would tend to suggest that the rotational degrees of the mechanism of energy transfer. Although more exfreedom of the inert gas (the possibile participation of amples are needed, we conclude on the basis of these the rotational degrees of freedom of the vibrationally data that the interaction between permanent dipoles excited molecule must be remembered) are not very appears not to be crucial for facilitating the transfer of important and that very high vibrational frequencies, vibrational energy during a collision. such as in Nz, probably do not accept significant Attempts are currently being made to improve our amounts of energy from the vibrationally excited analytical techniques, which should lead to data of immolecule. The similarity of the collisional efficiencies of H2, Dz, and He5b311with excited sec-butyl radicals proved quality. When this is achieved, further work [and recent studiesz2of energy transfer in low-pressure for a variety of inert gases will be reported. It is evident that the 1,2-CzH4C1z chemical activation systhermal unimolecular reaction systems] have also been tem still holds considerable potential for deducing deused to support such a claim. If, as has been sugtails of energy transfer from highly vibrationall-y exg e ~ t e dthree , ~ ~ translational modes become three loose cited polyatomic molecules. vibrations in the collision complex and the energy is equilibrated between these three and the vibrational Acknowledgments. We wish to thank Mr. Ken Dees degrees of freedom of the excited molecule, then the for doing the experimental work with CH3C1. Grateful 18 = energy increment would be AE = (89)3/3 acknowledgment is made to the Division of Air Pollu13 kcal mole-'. Evidently, such complete coupling tion, Bureau of State Services, Public Health Service, does not occur for collisions with CzH4Cl2,at least with for financial support of this research. Ar and N2. It seems likely that some vibrationalvibration transfer is important for CH3C1, CH2C12, and C R . (24) B. Stevens, Mol. Physics, 3, 589 (1960). A new finding of this work was the r e l a t i ~ e l ysmall ~~ (25) The measured difference between CF4 and CHzClz was small, about 30% in the ratio of stabilization product t o decomposition difference between vibrational deactivation efficiency product, over the major part of the pressure range. In kinetic for molecules with (CH3C1 or CHZClz) or without studies employing these types of measurements, similar effects of (CR) permanent dipole moments toward 1,2-C2H4C12, dipole-dipole interactions could be expected. We do not mean that all details of the collision event for CF4 as compared t o CHZClz which also has a permanent dip01e.l~ The reduced are identical, but rather that for these types of macroscopic experimasses for collision of CF4 and CHzC12with CzH4ClZ mental measurement, there is not much effective difference. (26) The s / k value for CzH4Clz was taken to be the same as that for are virtually identical, 46.6 os. 45.8 and the number CHzClz. The mixed interaction e n e r a was calculated according t o of degrees of freedom are the same, although CH2Cl2 (tln)l/z for the values of ref 21.
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Volume '71, Number 6 April 1967
