2171
ENERGY TRANSFER IN THERMAL ISOCYANIDE ISOMERIZATION were used. On the other hand, it would be quite naive not to maintain reservations concerning the reliability of such details of the experimental results, and refinement of the calculations is not worth pursuing at this stage. Other related experiments are under way.
Appendix Rates of H B C and T C Decomposition. The following parameters and frequencies were used to calculate the kE for HBC: EO = 15, 556; I+/I = 2.1 H B C Frequencies. 364,865,547,250,505, 1300,590, 367, 1100, 450, 500, 1280, 1275, 367, 3025, 1475, 1028, 3101, 1100, 739,865,364, 865, 547, 250, 505, 1300, 590, 367, 125, 450, 300, 1280, 1275, 367, 2211, 1074, 887, 2329,928,528,720. H B C Complex Frequencies. 544, 365, 367, 261, 171,
1500, 100, 200, 1100, 450, 500, 1280, 1275, 367, 3025, 1475, 1028, 3101, 1100, 739, 720, 364, 865, 547, 250, 505,1300,590,367,125,450,300,1280,1275,367,2211, 1074,887,2329,928,528. The following parameters and frequencies were used to calculate the ICE for tetrafluorocyclopropane (TC) : Eo = 15,556; I+/I = 2.20. T C Molecular Frequencies. 364, 865, 547, 250, 505, 1300, 590, 367, 1000, 450, 202, 1280, 1275, 367, 3025, 1475,1028,3101,1100,739,865. T C Complex Frequencies. 644, 365, 397, 261, 171, 1500, 100, 200, 1000, 450, 202, 1280, 1275, 367, 3025, 1475,1028,3101,1100,739. Collision Frequency. For effective collision diameters taken as 3.8 and 7.5 A for CO and HBC, respectively, o = 1.65 X lo7sec-l per mm of CO.
Energy Transfer in Thermal Isocyanide Isomerization. n-Alkanes and n-Alkenes in the Ethyl Isocyanide System' by S. P. Pavlou and B. S. Rabinovitch* Depdirtment of Chemistry, University of Washington, Seattle, Washington 98106
(Received February 8, 1971)
Publication costs assisted by the National Science Foundation
The effect of n-alkane and n-alkene bath molecules on the thermal isomeri~ationof ethyl isocyanide has been studied at 231" in the lower region of falloff. Members of the respective homologous series up to Ce were investigated. Relative activation-deactivation efficiencies, pu'(D)and pu(D), were determined with use of inert molecule cross sections appropriate for this system. The measured incremental collision diameters, ASAM, were compared with earlier values obtained from energy-transfer studies with the simpler CH3NC homolog. In the C2HsNC system, the critical molecule complexity (C2 member), beyond which increasing chain length induces no enhancement of intrinsic collisional efficiency, is reduced for both homologous series relative to the methyl system. This effect is discussed in terms of the structural and internal parameter changes of the substrate molecule,
Introduction The collisional efficiencies of a large number of inert bath gases for the thermal isomerization of CHaNC in the second-order region has been s t ~ d i e d . ~The , ~ behavior of homologous series of n-alkanes, l-alkenes, 1alkynes, n-perfluoroalkanes, and n-nitriles was investigated at infinite dilution of s u b ~ t r a t e . ~These ? ~ studies revealed that the relative activation-deactivation efficiencies increase with chain length of the members of a homologous series; however, constant efficiency is achieved a t some critical chain length, no; apparent further increase in collisional efficiency for n > no is merely a display of the increase in the effective colli-
sional diameter, SAM,, for larger bath gases and does not represent an increase in intrinsic efficiency per collision. (1) (a) This work was supported by the National Science Found& tion; (b) From the Ph.D. Thesis of S. P. Pavlou, University of Washington, Seattle, Wash. 1970. (2) F. J. Fletcher, B. S. Rabinovitch, K . W. Watkins, and D. J. Locker, J. Phys. Chem., 70, 2823 (1966). (3) S. C. Chan, B. S. Rabinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto, Y . N. Lin, and 8. P. Pavlou, ibid., 74, 3160 (1970). (4) Y . N. Lin, S. C. Chan, and B. 8. Rabinovitch, ibid., 72, 1932 (1968).
S. C. Chan, J. T. Bryant, L. D. Spicer, and B. S. Rabinovitch, ibid., 74, 2058 (1970). (5)
The Journal of Physical Chemistry, Vol. 76, No. 1.4, 1971
S. P. PAVLOU AND B. S. RABINOVITCH
2172 To investigate this phenomenon further, similar studies have been pursued in the CzHsNC system. The advantages of extending the experimental work on bath gas behavior to higher isocyanide homologs have been pointed out.2*6
Experimental Section Materials. The sources and purification of ethyl iso-. cyanide have been described in Le Methane, ethylene, propylene, and 1-butene (all research grade from Phillips Petroleum Co.) were used without purification. Ethane, propane, and n-butane (Matheson Co., CP grade) were analyzed chromatographically; only 2% hydrocarbon impurities were present. n-1-Pentene, 1-hexene, n-pentane, and n-hexane (Chemical Samples Co., 99.501,) required no purification. Condensible gases were deoxygenated by the freeze-pump method. Apparatus and Procedure. The experimental setup and procedure were the same as those described in I. Rate determinations were made in a static system. The reaction vessel was a 229-1. Pyrex flask heated in a stirred furnace. The temperature was controlled by a proportional controller and was measured by using eight calibrated chromel-alumel thermocouples placed in good thermal contact with various points of the reaction vessel. During a run the temperature was constant to *0.3" and the agreement between all thermocouple readings was ~ 0 . 2 " . Various amounts of inert gases were added to a constant amount of substrate (-3 X mm) such that the dilution, D, varied on a collision basis from approximately 20 to 200 throughout the series of runs, depending on the gas. The lower range corresponded to the more efficient (strong) colliders so that dilution was near-infinite in all cases. Isomerization was carried to between 8 and 35% reaction. Analysis. The analytical technique was similar to that employed in I. All analyses were made by gas chromatography. Two different columns were used to optimize separation of the propionitrile product peak from the inert gas peak: these were a 12-ft column of 5% tricresyl phosphate on acid-washed Chromosorb G, for runs with hydrocarbon bath gases up to CI, and a 25-ft column of 1% squalane on Fluoropak-80, for the C6 and Ce homologs. Calibrations of the columns were made before and after each series of analyses. I n a few cases, rate constants were obtained on both an "absolute" and "internal" standard basis as in I; good reproducibility between internal and absolute values was achieved. Some inert gas interference with the acetonitrile peak occurred, and only absolute values were obtained in most cases. Results and Discussion Treatment of the Data. The experimental corrections described in I were applied to the present data. All rate data were brought to a standard temperature of 231". The Journal
of
Phyaical Chembtry, Vol. 76,No. 14,1971
Time correction for sample removal averaged 8.5, 3, and 5% for CH,, CzHa, and C Z H ~respectively. , For all other members in both series, pump-out time corrections were usually less than 2%, depending on the total pressure and the reaction time. Rates of isomerization were obtained in a region of falloff, k / k , 2 0.03, where wall effects were small. (The observed rate constants are summarized in the Table VI.) Collisional Eficiencies. A detailed discussion of the experimental relative collisional efficiency quantities appropriate for these studies and their dependence on reaction order and dilution (D) of substrate has been given in I. Relative efficiencies on a pressure-to-pressure basis, 8,'(D) and Dp(D), and on a reduced masscorrected basis, &'(D) and &(D), were obtained from the relations described there. For an appropriate narrow range of dilution, and for a narrow range of falloff, the dependence of ,8 quantities on D and reaction order, 4, is small. The width of these ranges depends on the efficiency of the bath gas. All members of both homologous series, except CHI, exhibit nearstrong collider behavior and averaging of the ,f3 quantities is appropriate, in principle, for the dilution range (200 > D > 20) and falloff range (0.03 < k / k , < 0.13) used here. For some gases, a trend in the p values with pressure seems to exist. Its origin, if real, is not known and values were averaged. (All ,8 quantities are gathered in the Table VI.) Extrapolation of the high dilution A'( ) and B,( 03 ) quantities to their second-order limit Po,( 00 ) was made for each bath gas in the same manner as described in I ; their values are shown in Table I and the simplified designation /?, will be used in the future. Incremental Cross Sections. I n most work in chemical kinetics, collision diameters have conventionally been selected by fiat or calculated with the use of hardTable I : Low-Pressure Mass-Corrected Relative Efficiencies (D =
co
)
&Ll'(m)
&(-)
n-Alkanes CH4 CzHe CaHs C4H10 CE"z C8H14
0.38 0.62 0.71 0.85 0.94 1.01
0.25 0.50 0.62 0.78 0.90 1.02
0.32 0.56 0.67 0.82 0.92 1.01
0.51 0.57 0.73 0.82 0.92
0.57 0.62 0.76 0.85 0.93
n-Alkenes CzH4 CaHe CdHs CaHio CeHiz
0.62 0.66 0.78 0.87 0.93
(6) 8. P. Pavlou and B. S. Rabmovitch, J . Phya. C h m . , 75,1366 (1971).
2173
ENERGY TRANSFER IN THERMAL ISOCYANIDE ISOMERIZATION Table 11: Incremental Collision Diameters in the EtNC System, A n-Alkanes
n-1-Alkenes
4.81apb 5.280
0,089i~0.01 0.43 0.47
4 . 8 5 4 5.130 0.074f 0.02 0.36 0.38
Mean = 0.395
0.61 0.57 a Internally consistent value, based on PO(m ) = 1 for Ma (see Table 111). b Preferred values in bold face. 0 Viscosityderived value, ref 5.
Table 111: Effective Collision Diameters, I"
%I, for Hydrocarbons
(SAA
sphere cross sections evaluated from transport data. In earlier work on isocyanide isomerization the desirability of determining a self-consistent set of molecular cross sections appropriate for the energy-transfer system under investigation was pointed out. Values of relative collision diameters for several homologous series, including n-alkanes and n-alkenes, have been obtained from measurements of incremental collision diameters, ASAM,in the CHaNC ~ y s t e m . ~Determination of these quantities in the CzHsNC system is based on the same considerations. The postulate is made, as was confirmed experimentally4~6 for CHaNC, that at and above some critical chain length, n,, the relative low-pressure limiting
=
6.43%I)
-I1
SAMs
UMn
1
4.31d 4.81 5.24 5.67 6.10 6.53
2.42 3.58 4.28 4.78 5.52 6.26
4.85 5.21 5.57 5.93 6.29
3.74 4.06 4.60 5.22 5.84
-.
~-1110
AN^)
n
CMn
mI./h
SAkin
"M*
OK
4.74 5.28 5.69 5.93 6.22 6.52
3.80 4.42 5.06 5.20 5.70 6.20
144 230 254 325 325 325
1.16 1.26 1.28 1.35 1.35 1.35
5-13 5.60 5.96
4.23 4.67 5.31
205 303 310 310 310
1.23 1.33 1.34 1.34 1.34
oA&fn(l!2)
*
n-Alkanes 2
3 4 5 6
5.95 6.26 6.58
5.23 5.77 6.31 n-1-Alkenes
2
3
4 5 6
5.85 6.18 6.50
5.09 5.65 6.21
a Values based on ASAM (Table 11)with SAM$ determined by Bo( m ) = 1 for nc = 2. b From collision diameters, u~M,, determined in the CHaNC system for which BO( co ) = 1 a t n, 2 4. c From viscosity values of UM, (ref 4 and 5). d Value on the basis of the internally consistent SAM%value in set I relative to its value in set 111.
efficiency on a collision-per-collision basis Po( 00 ) reaches a constant value (unity) for higher members in the series. Then for all members of the homologous series for which n 2 n,
Table IV : PO(m ) Values of Hydrocarbons for the C2HbNC and CHaNC Systems r-CiHsN Ia
-C 111"
CHaNC
0.59 0.83 0.85 0.91 0.96 1.0
0.61 0.76 0.79 1.00 1.01 0.99
where i is the increment in carbon number of the chain and SAM, is the effective collision diameter of the colliding partners, A-M,. A s A ~may ~ be treated as constant with each CH2 increment, for a small number of increments, i. Thus
0.60 0.80
A plot of R,, us i should display linear behavior. ASAM can be calculated directly from the slope and the value
n-Alkanes
1 2 3
4 5 6
0.70 1 .o 0.99 0.95 0.98 1.02
n-1-Alkenes 2 3
4 5 6 a
1.0 1.06 0.99 1.0 1.03
As in Table 111.
0.87 0.86 0.90 0.92 0.94
1.00
0.99 1.01
SAM,.
From the plots of Rnzus. i (Figure 1) with trial values of n, = 1 and n, = 2 for alkanes and n, = 2 for alkenes, one observes that n, = 2 is the critical value for both The Journal of Physical ChemGtry, Vola76,No. 14, 1071
S. P. PAVLOU AND B. S. RABINOVITCH
2174 ~-
~~~
~~
Table V : Summary of Rate Data and Relative Collisional Efficiencies P(Mix), 10-2 mm
26 38 52 75 100 185
0.86" 1.43 2.09 3.18 4.10 6.61
k(Mix) , 10-6 sec-1
PP'W
(BM/CAM)
3.23 i O.lgd 4.78 rt 0.38 5.97 =!c 0.37 7.71 i 0.64 8.65 11.0 i O . 5 1
CHn 0.52 0.54 0.51 0.49 0.46 0.43
0.40 0.42 0.40 0.37 0.34 0.30
0.40 0.41 0.39 0.37 0.35 0.33
0.27 0.28 0.27 0.26 0.23 0.20
1.49
0.59 0.61 0.62 0.64 0.60 0.58 0.54 0.55 0.57 0.47
0.62 0.63 0.64 0.65 0.63 0.60 0.57 0.59 0.63 0.55
0.50 0.58 0.52 0.53 0.51 0.49 0.46 0.47 0.48 0.42
1.19
0.68 0.80 0.70 0.68 0.59 0.60 0.53
0.74 0.82 0.74 0.72 0.66 0.68 0.64
0.64 0.76 0.60 0.64 0.56 0.57 0.50
1.06
0.59 0.98 0.83 0.85 0.79 0.80 0.76 0.65 0.62
0.71 1.00 0.90 0.90 0.86 0.87 0.89 0.74 0.75
0.60 1.00 0.84 0.87 0.81 0.82 0.77 0.67 0.64
0.98
0.83 1.01 0.99 0.87 0.66 0.78 0.78
0.91 0.96 1.03 0.97 0.96 0.87 0.88
0.88 1.07 1.05 0.92 0.70 0.82 0.83
0.93
0.86 0.90 0.90 0.84 1.00
1.02 1.06 1.00 1.00 0.97
1.03 1.08 1.00 1.00 0.96
0.90
0.76 0.64 0.63 0.55 0.53
0.73 0.64 0.62 0.56 0.55
0.63 0.53 0.52 0.45 0.43
1.22
25 23 25 30 58 73 70 105 180 206
1.02 1.06 1.07 1.46 2.06 2.60 2.79 3.81 6.07 9.96
4.80 5.03 5.11 6.47 7.93 9.19 i 0.12 9.15 rt 0.38 11.7 r t 0 . 0 2 16.9 i 0 . 1 8 20.7
CzHe 0.69 0.71 0.71 0.72 0.68 0.67 0.64 0.65 0.69 0.61
24 41 64 71 80 145 185
0.91 1.54 2.63 2.77 3.34 5.47 6.53
4.89 7.91 10.6 10.7 11.2 16.2 16.9
CaHa 0.77 0.85 0.77 0.75 0.69 0.71 0.66
20 21 29 30 46 65 78 83 206
0.86 0.78 1.15 1.27 1.80 2.58 2.81 3.44 7.36
4.25 5.59 6.65 7.14 8.84 11.6 11.8 12.3 20.3
0.69 0.98 0.88 0.89 0.85 0.85 0.82 0.73 0.74
4HlO
CsHn 28 39 48 80 98 109 140
1.01 1.40 0.88 2.69 2.74 3.44 5.03
6.01 8.74 6.19 10.4 12.8 14.0 18.3
0.88 1.00 0.99 0.91 0.74 0.83 0.85 C6Hl4
27 51 67 117 124
0.87 1.48 1.95 3.80 4.70
6.19 8.00 10.3 16.6 18.8
0.91 0.92 0.92 0.89 1.00 CzH4
12 19 32 41 60
0 609 1.07 2.02 2.17 3.43 I
4.04 5.46 8.52 8.11 10.8
The Journal of Physical Chemistry, Vol. 76,No.14, 1971
0.83 0.74 0.72 0.65 0.62
ENERGY TRANSFER IN THERMAL ISOCYANIDE ISOMERIZATION
2175
-~
Table V. (Continued) k(Mix)
P (Mix), D“
10-2 m m
Bp@)
BN‘CD)
BP@)
(NAA/NAY)
0.76 0.71 0.67 0.69 0.63
0.67 0.62 0.58 0.54 0.61
0.72 0.67 0.63 0.61 0.66
0.63 0.58 0.54 0.50 0.57
1.07
4.42 4.69 5.47 8.82
C4Hs 0.89 0.71 0.74 0.78
0.85 0.69 0.65 0.71
0.89 0.71 0.74 0.78
0.85 0.69 0.65 0.71
1.00
1.03 0.81 0.61 0.71
1.09 0.86 0.72 0.82
1.05 0.85 0.64 0.76
0.94
0.87 0.84 0.93 0.82 0.70
0.96 0.95 1.01 0.93 0.82
0.95 0.92 1.02 0.90 0.78
Bp‘(D)
10-8 sec-1
CsHe 20 45
0.894 1.39 2.01 3.13 3.40
46
90 76 16 20 32 55
4.76 6.11 7.55 10.8 10.5
0.64 0.85 1.13 2.01
18 36 95 77
0.61 1.35 1.42 2.54
4.91 7.00 7.57 10.4
C6H10 1.02 0.82 0.69 0.78
16 38 40 52 73
0.504 1.09 1.30 1.69 2.55
3.84 6.44 7.82 8.64 10.3
CsHia 0.91 0.89 0.95 0.86 0.77
+
a Dilution, D,is on a collision basis where w = w(A,D) w(M,D) = 1.59 X lo7P(A,D) $. 1.97 X 106 ( s A M ) / ~ A M ~ / ~ P(M,D); ) the sec’l. Lower collision cross sections, SAM”, used are the values given in set 1, Table I11 with SAA = 6.43 A. a k, = 1.56 X falloff value which was excluded in averaging. d Average deviation of absolute and internal standard values from the mean.
“
O
0
1
2
d
3
4
5
6
i Figure 1. Plots of R,; vs. i for n-alkanes, 0,with: a, n, = 1; and b, n, = 2; and for n-l-alkenes, 8, with n, = 2.
series (Figure 1, curves a and b). A least-squares treatment of the data for n, = 2 gives values for the slope of the lines, ASaM/SAMdn, and SAM, is then fixed once the value of SAM^ is assigned. Two different bases may be used to assign SAM2. Conventionally, these quantities have been obtained from other sources, principa$y viscosity measurements. On this basis,6 UA = 5.$0 A,, , ,a = 1.12, Q A A ( ~ ~ ~= )* 1.65, and SAA = 6.43 A; also uM2 was taken as 3-6 4.42 and 4.23 A, with e ~ / k= 230 and 205”K, for
CzHa and CzH4, respectively, with values of Q A M ( ~ ’ Q * of 1.26 and 1.23. The standard combining rules are used. A second, internally consistent set of SAM, values appropriate to the present phenomenon may be calculated by adopting the value Po( ) = 1 for the critical member of each series (no = 2 for both), and using this condition to evaluate SAM^. All higher SAM, were obtained from ASAM,&AM*, and eq 1 or 2. The results are tabulated in Tables I1 and 111. For the n-alkane series, the agreement of these values (set I, Table 111) with those based on viscosity data (set 111)is also good. Similar concordance has been previously found in the CHINC system.4*5 Values of UM,, have been computed from the relation, SAM, = UAM,[~(2’2)*]1’2, and the combining rules for (TAM, and CAM,, and are given in Table 111. Comparison with the CHaNC System. From energytransfer results in the CH3NC system, a mean value of ASAM = 0.31 8 was determined for the present two homologous series and a mean of 0.33 A if values for the related n-alkyne series are also included. The latter value corresponds to AUM = 0.57 per CH2 group in the hydrocarbon chaine5 I n the present studies, the value AUM = 0.64 is deduced from the mean value of ASAM = 0.395 (Table 11). All values are encomT?MJ O U Tof ~Phyeieal ChembtTy, Vol. 76, No. 1.4, 1971
S. P. PAVLOU AND B. S. RABINOVITCH
2176 passed by AUM = 0.60 f 0.04 A. Good agreement of these s values with earlier results from CHaNC is found (cf. I and 11,Table 111). The relative collisional efficiencies on a collision-percollision basis, PO(00 ) , calculated from the deduced SAM^ values are gathered in Table IV; the corresponding quantities determined in the CHaNC system are also given. Constancy of Po(..), near unity for n 2 2 was noted above when the internally consistent SAY^ values for ethane were used (set I). The viscosity-based values (set 111)are less consistent and show an increase. The enhanced collisional efficiencies of CzHs and CZH4 for C2H6NC,relative to their efficiencies for CHaNC, can be rationalized in terms of similar arguments presented in I. A summary of data and collisional efficiencies is given in Table V. 1. Angular Momentum Conservation.7 These restrictions may be less severe for the C&bI\TC case since the orbital moment of inertia value for RNC collisions with CzHs or CzH4, IL, is closer in magnitude to the principal moments, I B and IC of C2HbNC than of CHaNC, e.g., I L C z H 4 ‘v 420; I B ’v~ 97, IcA ‘v 110, amu for EtNC; and 1 ~ 0 2 ~’v 4 370, ICA ‘v 50 amu A t , for CHaNC. More effective coupling of these moments via the collision complex occurs in the C2H6NC case, such
Az,
Table VI: Moments of Inertia, amu Aj2
IA
IB IC
CaHP
CZHB’
CHsNC‘
CsJ3&JCc
3.0 17.0 20.0
6.5 25.3 25.3
3.2 50.3 50.3
12.6 97.8 110.4
a Reference 7. Ir B. 8. Rabinovitch and D. W. Setser, Advan. Photochem., 3, 1 (1964). c K. M. Maloney and B. S. Rabinovitch, J . Phys. Chem., 73, 1652 (1969).
The Journal of Physical Chemistry, Vol. 76, No. 14, 1071
that obedience to conservation of total angular momentum is more favorable, relative t o the CHaNC case, for collision with energy transfer. On the other hand, the values of the moments of inertia, I A , I B ,IC,for C2H4 and CzHa (Table VI) which contribute to the total rotational angular momentum are more comparable with the IcA values of CHaNC than with I B , cof ~ CzHsNC, and rotational coupling is, on this basis, expected to be more enhanced, especially for CzH4, in the CHaNC case. 2. Ej’ective Number of Transitional Modes of the Collision Complex. The molecule figure axis rotation may be taken active for intermolecular energy exchange for C2H6NC,in contrast to its role as an ineffective heat reservoir for transfer of internal energy from CH8NC.7J Thus the effective number of transition modes is larger for CZH6NC and results in an increase of energy-transfer efficiency. 3. Substrate Complexity. The change in complexity of the substrate molecule provides a counterbalancing factor to the observed trend; CzHsNC is a larger energy sink than CHaNC and the removal of energy is expected t o be a less efficient process in the former case. 4. Chemical Similarity. It was pointed out earliera*’ that for efficient complex deactivators, such as higher members of hydrocarbon series, some of the internal modes are probably active for intermolecular energy exchange. Since the alkyl moiety of the C2H6NC molecule resembles the hydrocarbon bath molecule more than that of CH3NC, some internal modes in this group of the substrate molecule might provide an energy removal path that is not as favored for the CHaNC homolog with its smaller and tighter methyl alkyl group. (7) Y. N. Lin and B. 5.Rabinovitch, J . Phya. Cham., 74,3161 (1970). (8) K.M.Maloney and B.J. Rabinovitch, ibid., 73, 1862 (1969).
