6549
Nitrogen Dioxide Catalyzed Geometric Isomerization of Olefins. Isomerization Kinetics of the 2-Butenes and the 2-Pentenes J. L. Sprung, H. Akimoto,' and J. N. Pitts, Jr.* Contribution from the Department of Chemistry, University of California, Riverside, California 92502. Received February 21, 1974 Abstract: Arrhenius parameters have been determined for the NO2 catalyzed geometric isomerization of the 2-butenes and the 2-pentenes. For cis-2-butene, trans-2-butene, cis-2-pentene, and trans-2-pentene respectively E, kcal mol-' = 11.8, 12.2, 11.2, and 12.5 and log A , 1. mol-' sec-l = 7.86, 7.65, 7.49, and 7.72 over the temperature ranges 298-366, 297-370, 298-381, and 298-382°K. Combination of these results with the results of thermochemical calculations permits calculation of 298 OK rate constants for NO? addition to the double bond of ten simple olefins. These rate constants suggest that this reaction is unimportant in the bulk consumption of atmospheric olefin pollutants.
P
reviously we reported that NO2 catalyzes the thermal geometric isomerization of the 2-butenes and the 2-pentenes. * By analogy to previous studies of radical catalyzed geometric olefin isomerizations, we suggested that the isomerization proceeded by NO, addition to the olefin double bond to form a nitroalkyl radical, followed by bond rotation and loss of NOz to form the isomeric olefin.,& We also noted that in a polluted urban atmosphere capture of the intermediate nitroalkyl radical by molecular oxygen would constitute a thermal pathway for the atmospheric oxidation of olefin pollutants which, if fast enough, could be of considerable significance for the formation of smog. In this paper we described the results of detailed studies of the kinetics of geometric isomerization of the 2-butenes and the 2-pentenes and the use of these results to estimate the importance for the consumption of atmospheric olefin pollutants of processes initiated by NOz addition to an olefin double bond.
subscripts denote initial concentrations. This expression may also be written [Tlt/[Cl~= kcis[N0210t
(3)
+
Since [T],/[C], = (1 [C],/[T],)-' by measuring [C],/ [TI, as a function of time (t), the observed rate constant, kcis,can be determined easily and precisely. All experiments were run to conversions of less than 5 % . As expected for such low conversions, the observed dependence of [C],/[T], on t was always linear. Figure 1 illustrates the precision of the linearity routinely obtained. Nevertheless, this apparent linearity must mask the perturbing effects of some reverse isomerization. Normal kinetic treatment of the following reaction scheme cis-olefin
+ NOz
kcm
NO2
+ rrarzs-olefin
(4)
ktms
Experimental Section The chemicals, apparatus, and analytical methods used in this
yields eq 5, where KTC = ktrans/kois. Iterative use of
study have been described in two previous papers.?
Results
The equations used to develop the experimental data were identical for all four olefins. They will be described only as they apply to cis-olefin. Exchanging the symbols C and T will yield the corresponding equations for trans-olefin. For the reaction NO?
cis-olefin ---f trans-olefin
(1)
the initial rate of isomerization at low conversion may be writtenza d[Tl/dt
=
kcl~[NOnlo[Clo
(2)
where kcis is the experimentally determined rate constant, T and C denote trans- and cis-olefin and the zero (1) National Institute for Environment, Yatabe, Ibaraki, Japan. (2) (a) J. L. Sprung, H. Akimoto, and J. N. Pitts, Jr., J . Amer. Chem. Soc., 93, 4358 (1971); (b) H. Akimoto, J. L. Sprung, and J. N. Pitts, Jr., ibid., 94,4850 (1972). (3) (a) M. H. Back and R. J. Cvetanovic, Can. J . Chem., 41, 1396 (1963); (b) S . W. Benson, K. W. Egger, and D. M. Golden, J. Amer. Chem. Soc., 87,468 (1965).
}
IT], [CIO [TI0
+
(5)
eq 5 allowed the raw rate constants (kcis or ktrans)calculated using eq 3 to be corrected for the perturbing effects of reverse isomerization. To do this the raw values for koisand ktranswere used to calculate an initial set of Arrhenius parameters for these rate constants. An initial value of KTC(or KcT) was then calculated from these Arrhenius parameters. Substitution of this value into eq 5 now allowed a new set of values for kois (or ktrans)to be calculated. This process was repeated until a consistent set of values was obtained for koisand ktrans. These values and our experimental conditions are tabulated in a supplemental table presented in the microfilm edition of this journal. Arrhenius Parameters Figures 2 and 3 present plots of log k us. 8-' where 8 = 2.3RT. The lines are the least-squares lines calculated from the data presented in the microfilm edition.
Sprung, Akimoto, Pitts 1 NOz Catalyzed Geometric Isomerization of Olefins
6550 TEMPERATURE
( O K )
I,o
TIME
(min)
I
Figure 1. Plot of the mole fraction of trans-2-butene US. time for the cis- to trans-NO2 catalyzed geometric isomerization of cis-2butene. The least-squares slope of the plot is 2.64 f 0.03 X lo-' min-1. Reaction conditions were 9.00 Torr of cis-2-butene, 0.100 Torr of NO,, and 54.4 0.2". The nonzero intercept is due to the presence of a trace of trans-Zbutene impurity in the starting cis-2butene.
-1.0
1
*
TEMPERATURE
(OK)
380
360
340
320
300
I
I
I
I
I
I
I
I
I
I
I
I
I
io,ooo/e Figure 3. Arrhenius parameters for the NO2 catalyzed geometric isomerization of cis- or trans-2-pentene. Plot of log k cs. 8-I where 8 = 2.3RT: (0)cis-Zpentene; ( 0 ) trans-2-pentene.
I
summarizes these results. For reasons presented in the Discussion, we believe that the E value for trans-2butene is about 0.6 kcal too low which would make the value of log A low by about 0.3 log units. Discussion The reaction of NO2 with simple olefins is mechanistically and kinetically quite ~ o m p l e x .Because ~ of this, the easiest way to determine an upper limit for the rates of processes initiated by NO2 addition to an olefin double bond is to determine the rate constant for the initial addition step. As is described below, this can be conveniently done by combining our present experimental results with the results of a number of thermochemical calculations. Rate Constants. For the reaction NO, -1.51
'
'
6.0
I 6.4
'
'
6.8
'
7.2
I
'
T+
10,000/ 6
Figure 2. Arrhenius parameters for the NOz catalyzed geometric isomerization of cis- or trans-2-butene. Plot of log k us. 8-I where 0 = 2.3RT: (0)cis-2-butene; ( 0 )trans-2-butene.
The slope and intercept of each least-squares line give the Arrhenius parameters of that reaction. Table I Table I. Arrhenius Parameters for the NO2 Catalyzed Geometric Isomerization of the 2-Butenes and the 2-Pentenes Olefin
E. kcal mol-'
Log A , 1. mol-' sec-I
cis-2-Butene trans-2-Butene cis-2-Pentene trans-2-Pentene
11.81 i 0.083 12.19 I-t 0.118 11.23 i 0.092 12.48 f 0.088
7.861 i 0.058 7.652 i 0.081 7.494 i 0.062 7.720 i 0.059
Journal of the American Chemical Society
/ 96:21 1
1
2
the rate constants, k , and kb, may be expressed in Arrhenius form as follows k a - A --E,/RT and kb = Abe-EblRT (7) (4) (a) J. H. Thomas, Trans. Faraday Soc., 48, 1142 (1952); (b) T. L. Cottrell and T. E. Graham, J. Chem. Soc., London, 556 (1953); (c) ibid., 3644 (1954); (d) S. Jaffe in "Chemical Reactions in Urban Atmospheres," C. S. Tuesday, Ed., Elsevier, New York, N. Y., 1971; (e) S. C. Chao and S . Jaffe, J. Chem. Phys., 56, 1987 (1972);. (f) B. V. Ashmead and J. H. Thomas, 14th Symposium on Combustion, The Combustion Institute, 1973, p 493.
October 16, 1974
6551
where k,/kb = Knb and -RT In Ksb = AHaborCTASabo~c.But Ea = AHab0sC E b , A , = A b e A S ~ b 0 " l R , and A b = (ekT/h)eASb*IR. SO, if AHab'", E b , ASabo'c, and A&* are known, k, may be calculated. As is described in the Appendix, AHabo'c, ASab'", and A&* can be calculated or estimated for a number of simple olefins by thermochemical or incremental meth0ds.j Therefore, if Et, can be determined, k, can be calculated. Two facts permit Eb to be determined. First, for simple olefins EL,is unlikely to be very sensitive to either the nature of the substituents (R], Rz, R3,and R,) or the conformation (cis or trans) of the nitroalkyl radical 2 . Therefore, E b ought to have nearly the same value for most simple olefins. Second, as is shown below, the rate constants (kcis or ktrans)for the NO, catalyzed geometric isomerization of cis- or trans-2-butene or -2pentene may be expressed as functions of only Eb and several fundamental constants (e, k , hj and calculable thermodynamic quantities (A& A S a b ' AHabozC,and AHI',~,which is defined below). Therefore, our experimental rate constants may be used to calculate a value for Eb which will be applicable to most other simple __ olefins. The NOz catalyzed geometric isomerization of 2butene or 2-pentene most likely proceeds2a,3by the following mechanism
*,
mC,
1
I
+
I
I
COO R DI N AT E
R E ACT1 ON
Figure 4. Schematic energy surface for the NOz catalyzed geometric isomerization of a simple olefin, illustrating the relations between the various thermochemical energy parameters used in this paper.
Because Kcb = Kc(t,t >> 1, for low conversions where
