ENERGY TRANSFER I N THERMAL METHYL ISOCYANIDE
2055
ISOMERIZATION
Energy Transfer in Thermal Methyl Isocyanide Isomerization. Dependence of Relative Efficiency of Helium on Temperature'"
by S. C. Chan,lb J. T. Bryant, and B. S. Rabinovitch Department of Chemistry, University of Washington, Seattle, Washington 98106
(Received January 6 , 1970)
The thermal methyl isocyanide isomerization system was studied with helium as the added inert bath gas at five different temperatures over a range of 115". A lowering of the apparent activation energy by 1.5 kcal mol-' was observed. The dependence of observed activation energy on cross-sectional changes with temperature is discussed. While the direction of change is in accordance with predictions from theoretical calculations, the actual variation is small and a much wider variation of temperature is required for appreciable effects.
Introduction Vibrational energy transfer at the high levels of excitation in thermal reaction systems has now been extensively documented in the methyl isocyanide isomerization system at 280.5°.2 What is still little studied in thermal systems is the variation of the relative collisiona,l efficiency Po with temperature. The literature doea afford an interesting difference. I n the thermal decomposition of hydrogen peroxide, a large decrease in activation energy upon the addition of helium to a mbstrate system was ~ b s e r v e d ;on ~ the other hand, in the thermal decomposition of nitrous oxide, a significant activation energy increase upon adding CF,, COz, or S02, respectively, was found.4 Based on some theoretical assumptions which accord with much of the data on the temperature dependence of vibrational energy transfer in chemical activation systems,6 it is expected that in thermal systems the observed activation energy should decrease on the introduction of weak collider bath molecules.6 In the present paper, a study of the variation of Po with temperature in the thermal methyl isocyanide isomerization system is reported for helium as the inert bath molecule. Helium has been shown to be the weakest activation-deactivation collider in the system2 and is expected to demonstrate a maximum temperature variation. The reaction rate was studied over a variation of 115" at temperatures from 210 to 326".
Experimental Section The sources and purification of methyl isocyanide and helium have been described e l ~ e w h e r e . ~ ~ ~ The apparatus, procedure, and chemica lanalysis have been discussed in detail elsewhere. A static method was used; a 12-1. Pyrex flask served as the reactor and a salt bath as thermostat.
In each run, a roughly constant amount (8 X mm) of methyl isocyanide was expanded into the reactor together with a known amount of He. Reaction was carried to 2-50% conversion; the lower percentage was used for low temperature runs, while the upper amount was convenient for high temperature. The product of the reaction was analysed by gas chromatography with a 14-ft column of 1% tetraglyme on Fluoropak-80.
Results Measurements of the pumping rate of He a t 315" were made, and it was found that the pumping-down correction to the reaction time was negligible. The measured unimolecular rate constants (ko) at 210, 220, 315, and 326" are summarized in Table I ; those at 280.5' are given elsewhere.2 The second-order activation rate constants, ka, were evaluated from the slope of the plots of ko vs. p , the pressure of added helium. These quantities are also listed in Table I. The Arrhenius activation energy, E,, was obtained from these (Figure 1) and is 35.2 kcal mol-l. (1) (a) This work was supported by the National Science Foundation; (b) Ph.D. Thesis, 1970. (2) S. C. Chan, B. S. Rabinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto, Y. N. Lin, and 5.Pavlou, submitted for publication,
(3) W. Forst, Can. J . Chem., 36, 1308 (1958). (4) T. N. Bell, P. L. Robinson, and A. B. Trenwith, J . Chem. Soc., 1440 (1955) ; 1474 (1957). (5) (a) G. H. Kohlmaier and B. S. Rabinovitch, J . Chem. Phys., 38, 1692, 1709 (1963); (b) D. W. Setser, B. S . Rabinovitch, and J. W. Simons, ibid., 40, 1751 (1964); 41, 800 (1965). (6) D. C. Tardy and B. S. Rabinovitch, ibid., 45, 3720 (1966); 48, 1282 (1962). (7) F. J. Fletcher, B. 5. Rabinovitch, K. W. Watkins, and D. J. Locker, J . Phys. Chem., 70, 2823 (1966). (8) 5. C. Chan, J. T. Bryant, L. D. Spicer, and B. 5. Rabinovitch, ibid., 74, 2058 (1970).
Volume 74, Number 10 M a y 1 4 , 1970
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S. C. CHAN,J. T. BRYANT, AND B. S. RABINOVITCH
Table I : Measured Rates of Isomerization at Different Temperatures Temp, OC
210
220
280.P 315
326
ko, 10-6
sec-1
0.0396 0.0548 0.0735 0.0844 0 . IO6 0.0544 0.0819 0.134 0.131 0,187 0.236 0.220 39.7 66.0 89.3 121 147 57.9 108 141 170 190
P, 10-2
mm
16.5 27.9 43.1 53.9 61.6 12.9 20.0 35.9 46.7 63.5 75.2 79.5 25.6 51.4 73.6 110 136 25.9 53.9 78.9 98.9 114
0.138 A 0.0125
10’/T (DEG:’)
Figure 1. Arrhenius plot for the thermal CHaNC-He system.
0.257 f 0 . 0 2 1 16.4 f- 0.2
96.3 f- 1.8
148 f- 5
a Standard deviation of the slope of the least-squares line. I,Rate data given in ref 2.
Discussion Now Pc is given by the expression
where the p’s and u’s are reduced masses and LennardJones force constants, respectively, for the appropriate isocyanide, NI 5 helium). Here collision pairs (A F = ( ~ A A ( ~ ’ ~ ) * ) / ~ A M ( ~ ’ where ~)*, the numerator is a = tabulated functiong of T*(lcT/e~) and of ,,6 pA2/2eAUA3; EA is the force constant and ,LLA is the dipole moment of A; the denominator is a tabulated function of T*((~T/EAM).Equation 1 is simply the ratio of ICa values corrected for collision frequency. On differentiation of the logarithm of pc with respect to 1/T, eq I becomes
This affords an estimate of the temperature variation of P o . The fall-off behavior of the pure substrate system has already been studied.’,l0 The Arrhenius activation energy EaA= 36.3 kcal was measured for the low pressure region. It remains to evaluate the differential d In f/d(l/T) in eq 2 in order to estimate the change of pc. There is no simple functional relationship between Q ( 2 , 2 ) * and T, and this differential cannot be evaluated analytically.ll A plot of In 5 us. 1/T, however, reveals The Journal of Physical Chemistry
the existence of a linear relationship in this temperature range. d In t/d(l/T) was estimated from the slope of this straight line and is assumed to be independent of temperature. The quantity is equal to 222°K and produces a decrease of 0.44 lical mol-‘ in the observed activation energy in the CH3NC-He system. The significance of eq 2 is thus the following. The observed variation with temperature of the relative rate at constant pressure is not the true variation of Po which should be based on a constant ratio of collision cross sections. Accompanying the change in temperature is a relative variation of collision cross sections of the substrate and the bath molecules in the form of the dependence of f on T. The observed change in activation energy must be corrected by this in order to find the true temperature dependence of Po. I n general, this correction will tend to be larger when EA/^ and e ~ / kdiffer widely or when the collisional behavior of pure A and of A with ;\il follow different potential laws. Thus d In Pc/d(l/T) is equal to lOOO(1.1 0.4)/R for this system, where R is in cal mol-’ deg-’. Equation 2 can then be easily integrated. The value Pc = 0.24 has already been measured for helium a t 280.5°;2 then Pc can be estimated for other temperatures (Table 11). It has been previously shown6 that pc is a function of E’, i.e., Pc = @,(E’),where E f is a dimensionless parameter defined as, E’ = (AE)/(E+); (AE) is the average amount of energy removed per collision from the excited species by a bath molecule, and (E+) is the equilibrium value of the average excess energy of the substrate molecules above the critical threshold. The differential in eq 2 can formally be expressed as
+
b_ In _ pc _ d(AE) d In _ _Po _-_ _ d(l/T)
b(AE) b(l/T)
b In pc ?)(E+) +--b ( E + ) b(l/T) (EaA - Ea‘)/R
(3)
(9) L. Monchick and E. A. Mason, J . Chem. Phys., 36, 2746 (1961). (10) F. W. Schneider and B. S. Rabinovitch, J . Amer. Chem. Soc., 84,4215 (1962). (11) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,” John Wiley and Sons, Ino., New York, N. Y., 1934,p 1126.
ENERGY TRANSFER IN THERMAL METHYLISOCYANIDE ISOMERIZATION Table 11: Summary Values of Po, (Et),and (AE) at Different Tem.peratures Temp, O C
POW)
210 220 280.5 315 326
0.29 0.28 0.24 0.22 0.21
(E+),
om-1
(AE),. cm-1
400 410 470 510 500
460 460 450 450 447
a Values are based on t h e exponential form for t h e collisional transition probability distribution (ref 6); t h e change with temperature has only qualitative significance.
if $, is independent of temperature. Based on a particular statistical model for the collisional transition probability diskribution, it has been shown that both terms on the right-hand side of eq 3 are either greater than or equal to zero, depending on whether the bath molecule is a weak collider or a strong collider, respectively. Universal plots of Po vs. E’ have been given.6 For weak colliders, it appears that the exponential model is more appropriate.6*12The variation of (E+) with temperature for the thermal methyl isocyanide system may be readily evaluated, and the value of (AE) for helium inert gas at different temperatures can thus be estimated (Table 11). The observed activation energy in the present system decreases in the presence of a weak collider bath molecule. This change is in the opposite direction to that found in the work of Trenwith, et aL4 Over a temperature range from 650 to 750’, they observed an increase in the activation energy for pure substrate (-55 kcal mol-’) of 14, 3.6, and 2.3 kcal mol-’ upon adding SO2, CF4, and COz, respectively. The first increase is suspiciously large as the authors themselves have suggested. The data are suspect for the two remaining smaller activation energies, also, since the system is complex and, in addition, substrate-inert gas dilution effectse may be prominent. But if the direction of the change is correct in general, this suggests that the thermal decomposition of nitrous oxide, which is a small molecule, cannot be described by a
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quasistatistical model of vibrational energy transfer which seems appropriate for large molecules a t high levels of excitation and which predicts a decrease in activation energy.6 A qualitative criterion of the expected behavior is the relative collisional efficiencies of noble gases in this system; helium was found to be the most efficient of these. This is in accord with experimental findings13 at low energy levels for small molecules and also with general predictions derived from the Landau-Teller theory. l4 Indeed, Nikitin claimed to find a good fit16between the experimental rate constant and that calculated via the SchwartzHerzfeld equation14for the pure substrate system. We hope that further experimental confirmation will be sought. In the hydrogen peroxide system3 an ostensible lourering of 5.6 kcal mol-‘ (48.1 to 42.5 kcal mol-’) in activation energy upon adding helium was found, which is surprisingly large. The temperature was only varied over a range of 40” (431-470”)) and the Arrhenius plots show very bad scatter; we believe that this alleged activation energy decrease is not reliable. In the methyl isocyanide system, the true activation energy decrease is only 1.1 0.4 = 1.5 kcal mol-l in the presence of helium over a 115’ range. The activation energy estimated from the Arrhenius plot is very sensitive to experimental error in rate constants, and our results should be considered as only qualitative; they give an indication that collisional efficiency may decrease slowly with rise in temperature for this system. But no marked effects are to be expected for small temperature changes in thermal systems on the basis of the present results a t not very highly elevated temperatures.
+
(12) Y. N. Lin and B. S. Rabinovitch, J. Phys. Chem., 7 2 , 1726 (1968). (13) R. A. Walker, T . D. Lossing, and S. Legvold, National Advisory Committee Aeronautical Technical Notes, 1954, p 3210. (14) For comprehensive reviews, see (a) T . L. Cottrell and J. C. McCoubrey, “Molecular Energy Transfer in Gases,” Butterworth and Co. (Publishers) Ltd., London, 1969; (b) K. F. Herzfeld and T. A . Litovitz, “Absorption and Dispersion of Ultrasonic Waves,” Academic Press, Inc., New York, N. Y., 1959. (15) E. E. Nikitin, Dokl. Phys. Chem., 129, 921 (1959).
Volume 74, Number 10 M a y 14, 1970
