1230
Journal of the American Chemical Society
(14) At every temperature the calibration factor a/ in /I= alk?/[jlss, where j is m/e 67, 54 (1.5hexadiene), and 44 (CO?),was determined by at least two different flow rates k e / [ j l S s= 5'.p, relates mass spectrometric intensities (//) to stead state concentrations of a molecule ([jlSs). (15) In (K,,d/M') = [ASg AnR(1 t In (R'T))]/R AF'IRT, where the superscript refers to a standard state of 1 atm and R' distinguishes the gas constant in units of L atm/mol K from units of cal/mol K. (16) Defining z, = yskeBA(s), zB = yBkeBA(B),and Kr.d = k,/kd, the propagation Of errors yields for the relative error of K,.d the following expression:
101:5
/ February 28, 1979
r+/ro = (SDO/RT)'/~This rotational maximum of the effective potential, including rotation, is not very sensitive to either Tor the precise value of DO,and for most common values of both occurs in the range p+ = 2.53.0. (27) For any reaction A B ra A t B
APO = P Erd
d
E Ae7.d
 Eo, = F ' d =
[email protected],,& critical energy + RT= AE*o,d t (AC*v,d)roTt RT
Erd = A P o
. . (17) S. W. Benson, "Thermochemical Kinetics", 2nd ed., Wiley, New York, 1976. (18) H. E. O'Neal and S. W. Benson, Int. J. Chem. Kinet., 1, 217 (1969). (19) The uncertainty in AH' from the equilibrium measurements (2) is estimated to be f l kcal/mol. Together with the uncertainty in AHOf(BA) of f 0 . 5 kcal/mol, the combined uncertainty for AHOt(allyl,g) amounts to f 1 . 5 kcal/mol. (20) M. Rossi and D. M. Golden, J. Am. Chem. SOC.,following paper in this issue. (21) K. Y. Choo. P. C. Beadle, L. W.Piszkiewicz, and D. M. Golden, Int. J. Chern. Kinet., 8, 45 (1976). = ~~,k,~~[N2],,= a N Z P N 2 = a N 2 F i N 2 . For explanation of symbols, see (22) ref 14. (23) Experiment no. 1 in Table Ill was performed at an earlier stage of the recombination series than no. 2 and 3, indicating variable wall conditions of the reaction vessel within the series of experiments. (24) P. J. Robinson and K. A. Holbrook, "Unimolecular Reactions", Wileylnterscience, New York, 1972. (25) (a) G. P. Smith, M. LevOn, and D. M. Golden, submitted for publication; (b) A. C. Baidwin and D. M. Golden, J. Phys. Chem., 82,644 (1978); (c) A. C. Baldwin, K. E. Lewis, and D. M. Golden, Int. J. Chern. Kinet., submitted. (26) The separation distance along the bond axis was chosen in such a way that it corresponded to the top of the centrifugal barrier in a model for a LennardJones potential of the CC bond connecting both C3H5 units: pf =
/
+ (
[email protected],d)roTf
RT
since
A P o = A P T  ( ACv)roT E r d = A P T  (AC,)'oTt (AC*v,d)roTt RT i?d = A P T t (Ac*,,)ror
7
(28) Given and /A/B/C for a rotational model transition state, changing /A/& to C ' I B lc' results in a different hindrance parameter (v')to yield the same Arrhenius A factor through the following relation: a' = 100  (100  a) I*' /B'/C'

If
[
/A'/B'/C'
> IA$/C,it then follows that q"<
/A/B/C
9.
(29) W. L. Hase, J. Chem. Phys., 64,2442 (1975); W.L. Hase in "Dynamics of Molecular Collisions", W. H. Miller, Ed., Plenum Press, New York, 1976. (30) k,(exp) = A,e3.3'2 at T = 1000 K with E, = 3.3 kcal/mol from Ed = 59.3 kcal/mol, and A€ = 56.0 kcal/mol. (31) See references in ref 22a; S. W. Benson and H. E. O'Neal, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 21 (1970). (32) G. McKay and I. M. C. Turner, Int. J. Chem. Kinet., 10, 89 (1978). (33) D. A. Parkes and C. R. Quinn, J. Chern. SOC.,Faraday Trans. 1, 72, 1952 (1976).
Absolute Rate Constants for Metathesis Reactions of Allyl and Benzyl Radicals with HI (DI). Heat of Formation of Allyl and Benzyl Radicals M. Rossit and D. M. Golden" Contribution from the Thermochemistry and Chemical Kinetics Group, S R I International, Menlo Park, California 94025. Receiued May 4, I978
+

+
Abstract: The metathesis reaction C3H5. HI (DI) C3H6 (C3HsD) I. (k3) has been studied in the gas phase using the VLPP technique. The result with DI, using diallyl oxalate as a radical source, is log (k3D/M' SI) = (10.1 1 f 0.30)  (5.7 f l.5)/0 a t T = 1000 K. The result using 3,3'azopropene as a radical source is log (k3,'MI sI) = 8.93 f 0.18 a t T = 1000 K, where L9 = 2.303RT in kcal mol'. For the metathesis reaction C6HsCHz. DI CbHsCHzD I. (k3). log (k3D/M1 sI) = (10.46 f 0.30)  (6.3 f 1.5)/0 at T = 1000 K. These rate expressions were extrapolated to lower temperatures using a transitionstate model in order to compute the equilibrium constants for the above metathesis reactions using the rate constants for the reverse metathesis from iodination studies. The equilibrium constants yield Mi"f(allyl) = 39.4 f 1.5 kcal/mol and SHOf(benzy1) = 47.80 f 1.5 kcal/mol a t T = 300 K . These values correspond to stabilization energies of 11.4 f 1.5 and 10.1 f 2.0 kcal/mol, respectively (i.e., DH(ally1H) = 86.6 f 1.5 kcal/mol and DH(C6HsCH2H) = 87.9 f 1.5 kcal/mol).
+

+
with the following overall equilibrium:
1. Introduction
RI
A large number of values for freeradical heats of formation (AHOf (Re)) have been obtained by the spectrophotometric
iodination technique which is well documented in the literature.' The pertinent reactions are I1
+ M * 21 + M
t Postdoctoral Research Associate.
KI,
(1)
+ HI s R H + 12
(4)
In general, the temperaturedependent values of kl and k2/k3 (starting with R I HI) or kq and K3.4 (starting with R H 12) can be obtained. The usual method of extracting AH"f(R.) from these studies is to assume that E2 = 0.0 f 1 .O kcal/mol and/or E3 = 1.0 f 1.0 kcal/mol. (The measured values of E2  E3 are not inconsistent with these assumptions). Thus, a measurement of E4 will yield a value for AH"3.4 and AH"f(R.) will follow since the appropriate values for HI, Iand R H are known.2 Very lowpressure pyrolysis (VLPP) allows the measurement of fast bimolecular reactions such as (5) in the gas phase.
+
+
0 1979 American Chemical Society
/
Rossi, Golden 8.0
,
1231
Metathesis Reactions of Allyl and Benzyl Radicals with HI I
I
I
I
I
A E X T R A P O L A T E D FROM TABLE I l l log Ik:/M.'
5.')
8.2
0
10
20
30
F;,.'
ilmolec s111
40
50
60
70
8.1 8.0 E
EO
R.+HI%RH+I.
(5)
We take advantage of the fact that the measured rate constants k3 are unencumbered by competitive radicalradical recombinations relative to which the overwhelming majority of fast bimolecular radicalmolecule reactions have been m e a ~ u r e d . ~ The availability of Arrhenius parameters for forward and back reaction rate constants provides.values for AH"f(R) and entropies of radicals (S"(R.)). Accordingly, we report in this work the rates of the reactions C3H5C6H5CH2
+ HI (DI) +C3H6
(C3HsD)
+ I*
+ HI (DI) 2C6HsCH3 ( C ~ H S C H ~ D+ )I*
(6) (7)
together with their Arrhenius parameters over an extended temperature range, thereby obtaining values for AH"f(R.) of allyl (C3Hs.) and benzyl (C6HsCH2) radicals by using the results of previously published determinations of k4, A4, and E4 from iodination studies of propylene4 and t o l ~ e n e . ~ 11. Experimental Section The description of the VLPP molecular beam sampling apparatus, together with the allquartz reaction vessel (Knudsen cell), has been presented in the preceding publication.6 The twoaperture Knudsen cell was characterized by the following parameters: V = 0. I34 L, o = 4982(T/M)1/2 sl, keM(B) = 2.5571(T/M)'/2 sl, keM(S)= 0.2088(T/M)1/2sl, B referring to the large and S to the small reactor escape aperture. The source and purification of the radical precursors diallyl oxalate ( C ~ H I O O 3,3'azolpropene ~), ( C ~ H I O N and ~ ) , bibenzyl (Cl4H14) have also been described.6 Benzyl vinyl ether (CgHlo0) was synthesized according to literature methods.' GCMS analysis showed a 2% impurity of benzaldehyde (C7H6O), which did not interfere with our measurements. The standard gashandling system was heated in order to increase the vapor pressure of diallyl oxalate, bibenzyl, and benzyl vinyl ether, such that suitable flow rates of the radical precursors into the heated Knudsen cell could be obtained. Hydrogen iodide (Linde Air Products, Inc.) and deuterium iodide (99 atom %, Merck Sharp and Dohme, Ltd., Canada) were used without further purification. The experiments were carried out by setting the flow of the radical precursor to a low and constant value and monitoring m/e 43 (CjH5D) and 92 (C7H8) or 93 (C7H7D) as a function of flow rate of H I or DI. The reaction vessel had two inlet (capillary or needle valve) systems from two independent gashandling systems so that the components met for the first time in the hot reactor.
111. Results and Discussion
+
'
11
12
'
13
T
loo0 K
=
_AI 14
I
'
15 16 17
I 18
L
20
19
lod KIT

k3
9
I 10
5iy05m;A
[10171
Experimental determination of k j (see eq 8) for the metathesis reaction allyl. + DI propylened, + I. at 1014 K. Representative example from Table I .
Figure 1.
'
301 
= 110 11 i
A. Allyl Radical HI (DI). Diallyl oxalate (CxH1004)was used as a precursor for allyl radicals at (7')= 1000 K and
.
Arrhenius plot of rate constants from Table I : least squares analysis of Arrheniua plot with rate constants k 3 D for the reaction CjHy DI CjHsD I.;   , predicted rate constants k j H for the reaction CsH5. + H I * C3H6 I.taking intoaccount the primary isotope cffect when DI is replaced by HI. Figure 2.
+

+
+
3,3'azolpropene ( C ~ H I O Nat~ () T ) = 750 K. By using two different precursors for allyl radical it was possible to cover a range of 380 K in the study of the metathesis (6). Application of the steadystate assumption to reaction 6 in a lowpressure stirred flow reactor results in the following relationx (see Appendix for details of the derivation):
where f is the fraction of radicals "titrated" at a certain steadystate concentration ( H I ) / M or specific flow of HI into the reactor (RIHl/molecules s  I LI), and k,C3H5. and k," are the escape rate constants (sl) of allyl radical and HI out of the reactor. f is defined as (C3H6)/(C,H,),, where (C3H6) is the steadystate concentration of C3H6 at a certain (HI), and (C3H6)m is the same concentration at (HI) = a,where essentially all radicals have reacted with HI. In the case of diallyl oxalate as precursor for allyl radical, (COz) could be taken as representative of the amount of the allyl radicals present in the reaction system, so that l/f could be equated to (
[email protected])/(C3H6) or R " C O ~ / R " C ~This H ~ . method proved to be valid because plots of l/f vs. R O C ~ ~ / R O C yielded ~ H ~ straight lines with unit intercepts, confirming that the amount of COz present w a s indeed representative of the amount of allyl radical in the system. We believe that use of COz as a marker for the production of allyl radicals in the system diallyl oxalate DI renders the determination of the rate constant k3D more reliable than k3H for the system 3,3'azo( I)propene HI, where the contribution of N l had to be evaluated by subtraction of mass spectrometric signals at m/e 28. The following assumptions have been made in deriving eq 8: ( H I ) >> (C3Hs.) and R ' H I= R'HI, where R ' His~the flow of H I in and R'HI is the flow out of the reactor. Under our experimental conditions both assumptions were found to be justified, so that a plot of l/f vs. 1 /( R ' H I )gave a straight. line with unit intercept (within experimental error) and (keCjH5.keH1)/k3 as slope, from which k3 was readily obtained, given the reactor parameters6 Special attention was paid to the requirement of carrying out the titration at the lowest possible concentration of C3H5. in order to suppress the bimolecular recombination reaction. Figure 1 displays a typical plot of l/f vs. 1 /(F'DI) and Table I lists the rate constants k3/Ml sl as a function of temperature. These are plotted in the usual Arrhenius form in Figure 2. The results from Table I are
+
+
k3D
= 7.2 X I O s MI
k3H
at (7')= 1000 K
sI
= 3.6 X IOx M'
sI
at T = 635 K
Journal of the American Chemical Society
I232
Table I. Rate Constants for Metathesis Reactions as a Function of Temperature T,K
k3/M'

1 101:5 /
February 28, 1979
Table 11. Estimated Entropy of Activation for the Metathesis C3Hy H I (Standard State: 1 atm) Reaction C3H6 1.
+
+
sI
& + D I k , D  w D + I
884 907 91 1 929 929 962 1007 1014 &
+
H
I
L
635 697 76 1 878 982
4.30 X 4.80 X 4.90 X 6.68 X 6.99 X 6.37 X 8.06 X 6.76 X A +I 3.57 x 5.50 x 4.83 X 7.24 X 8.54 X
IO8 IO8 a lo8 IO8 IO8 IO8 IO8 a IO8
3 0 0 K 5 3 0 K IOOOK
1 stretch 108 b.c 108 b
[c'
IO8 IO8 lo8
*.I)
(9)
taking allyl iodide (C3HjI) as a model, adding two C H I bending and one (CH)I stretching (= reaction coordinate) mode to C3Hj1, and including other minor corrections due to the presence of the extra H atom in ( 9 ) .Table I1 demonstrates the method and summarizes the result for the entropy of activation L L S ~ O * of the reverse of reaction 6. Using the ( value listed in Table I11 and the relation AT = T2  T I (10)
for the change in Arrhenius activation energies of rate constants expressed in molar units (M) one obtains the following

ASdO' ~~
2 x
1.39 2.1 1 2 x
1.39 2.1 1
2x
1.40 2.40 3.60 reaction coordinate
 
Owing to the better quality of the DI data compared to the H I data (smaller uncertainty limits, pure sample, more points over a certain temperature range (see above)), the following approach was taken in this paper. The Arrhenius expression for the DI data, given by log k3D/Ml sl = (10.1 1 f 0.30) (5.7 f 1.5)/0 at T = 1000 K, where 0 = 2.303RT in kcal/mol, was transformed to an Arrhenius expression for the H I data by means of the experimentally derived ratio k3H/k3D= 1.18 a t T = 1000 K (Figure 2). The isotope effect was accounted for by setting A3D/A3H = 1.26 and choosing E3D  E3H = 0.80 kcal/mol, so that k3H/k3D = 1.18, resulting in the following Arrhenius expression for the H I system: log (k3H/M1 sI) = (10.01 f 0.30)  (4.9 f l.5)/6 a t 1000 K. This small isotope effect is in line with expectations from an extensive body of data, indicating k H / k D = 1.5 f 0.59 a t temperatures around 500 K. The data for the H I system (Figure 2 ) suggest slight curvature of the corresponding Arrhenius plot. In the following paragraph a transition state model for reaction 6 or its reverse (with H I as reagent) will be developed, which will result in temperaturedependent Arrhenius parameters and therefore will be compatible with a curved Arrhenius plot of k3H. Golden et aL4 found the following rate expression a t ( T ) = 530 K: log (k4/MI sl) = 10.25  18.04/19, where 0 = 2.303RT in kcal mol'. I n order to provide a value a t 1000 K for the equilibrium constant K4,3 = k4/k3 (3), where R. = C3Hj., a transitionstate model, which has been shown by Benson and coworkers to be appropriate* in cases of metathesis reactions, such as (6) and (7), was used to extrapolate the measured rate constant k4 from 530 to 1000 K. The transition state ( 9 ) for reaction 6 or its reverse was approximated by ,HI
+
,H
resonance stiffening of internal rotation Vo = 2 13 kcal/mol C=C, 1650 cm' CC, 1400 cm' CC, 1000 cmI CC, 1400 cmI 420 cmI 635 cm'
Radical source: diallyl oxalate (C8H1004). Radical source: 3,3'azo Ipropene ( C ~ H S K Z C ~ H S Average ). value of three experiments.
AE, = A T ( A C , * ) T , ~ ~2 R A T ,
1.39 2.11
2 bending (Ca*,H'.*~) 300 cmI
a
e'
28.42 29.30 30.56
A S 40*' corrections: spin ( R In 2) rotationo
2.30
2.10
 1.67
0.0 +O. I O 0.0 0.10 0.30 0.50 0.52 1.00 0.90 25.04 24.40 22.63
~
Adjusted to give experimental A4 a t ( T ) = 530 K log (A4IMI sI) = 10.25.
Arrhenius expression for k4 a t T = 1000 K: log (k4/M' sl) = 11.15  21.22/0 (see Table 111, column 3 ) . K4,3 at T = 1000 K then turns out to be 3.98 X which, together with a n estimate for So(allyl)loand C , data2.I0 (Table 111, column 7), yields a "third law" standard heat of formation AHof(allyl) = 39.4 f 1.5 kcal/mol a t T = 300 K.I4 Table 111, column 3 , also shows the Arrhenius expression for k4 at 300 K deduced as before by means of (AC*,,4). Furthermore, the Arrhenius expression for k3 was extrapolated to lower temperature (see Table 111, column 2) with AS4O*, and the estimated overall entropy change ASO4.3 for reaction 62 resulting in an Arrhenius activation energy of 2. I kcal/mol for k3 a t T = 530 K, a value slightly different from the "usual" assumed value of 1.O f 1 .O kcal/mol used throughout the 1iterature.l Table 111 thus provides a good example of an internally consistent set of Arrhenius and thermochemical parameters. 'The allyl radical heat of formation derived above from two separate experiments is in excellent agreement with a recent equilibrium study and other determinations of AHof(allyl).6 The present value for AH"f(allyl) provides an allyl resonance stabilization energy (ARE) of 11.4 f 1.5 kcal/mol (see, e.g., ref 1 1 for the definition of ARE). The large variation of A3 and A4 with temperature (Table 111) is noteworthy; this brings about a concomitant change in E3 and E4 which tends to partially cancel the increase in the A factor. Obviously, this cancellation of log A vs. E is only partial, so that the suggested slight curvature in the Arrhenius plot in Figure 2 results. It has repeatedly been pointed out in the literature3 that the Arrhenius A factor for the reaction of I with an alkane or olefin is quite high (log A4 = 10.3 at 550 K). Such a behavior is obvious from Table 111 in the present case as well. B. Benzyl Radical HI (DI). At ( T ) = 880 K benzyl radicals were generated by unimolecular decomposition of benzyl vinyl ether (C7H7OC2H3) and a t ( T ) = 1060 K by the bondbreaking process in bibenzyl (C,H7C7H7). The evaluation of the rate constant k3 (7) follows the same lines as in the case of allyl radical. Figure 3 displays a typical l/fvs. l / ( F ' ~ l )plot (eq 8), wherefrepresents, by analogy with the definition given in section A, the fraction of radicals titrated a t a certain steadystate concentration of HI with respect to the total concentration of radicals present in the absence of HI; Table IV lists the resulting rate constants k3,'Ml sI as a function of temperature, and Figure 4 shows the corresponding Arrhenius plot. By using two different benzyl radical precur
+
Rossi, Golden
/
1233
Metathesis Reactions of Allyl and Benzyl Radicals with H I
Table 111. Kinetic and Thermochemical Parameters for the Equilibriume
propylene
T/K
1%
1% (k3/Ml
SI)
(k4/M'
1000 logk3D 10.11  5.718
eu
eu
AH04,3, kcal mol]
5.25
5.94
16.30
ASO4.3,'
s')
11.15  21.22/6'
1000 log k 3 H 10.01  4.9/6'
+ I 3 allyl. + HI k3 aS04%3,b
530 9.03  2.12/6'
10.25
 18.04/8
5.62
5.40
15.90
 1.31/6'
9.60
 16.86/6'
4.65
4.50
15.53?
300 8.59
(LC,,,)
(AC*,,P'
0.85
2.79
1.60
1.12
From Arrhenius expressions using In (A4/A3) = AS04,3/R. Thermochemical estimate, ref 2 and I O . Yields AHof(allyl) = 39.40 f 1.50 kcal/mol at 300K. Calculated from S q o * of transitionstate model in Table 11. e Italicized values represent experimental results; others are extrapolated Arrhenius parameters using transitionstate model (9) from Table I1 (6' = 2.303RT in kcal/mol), and estimated values for AS04 (column 5 of Table 111).
Table IV. Rate Constants for the Metathesis Reaction as a Function of Temperature
cn+
7
I
I
b
&OO
CH,D
D
I
C
&
+ I l l f 3.00
7.08 X 5.78 X 9.03 X 6.99 X 9.35 x 1.35 X 1.23 x
81 1 85 1
856 922 963 986 1004 IO07
1.40 ~~
x
IO8 IO8
1038 1049 I050 1088 1090 1109 1126
a a
lo8 a IO8 a 108 lo9 109 b 109 b
1.51 x 1.27 x 1.70 x 1.37 x 1.32 x 1.72 x 2.30 x
109 b 109 b 109 b 109 b 109 b 109 b 109 b
~~
1
1 1
0'
I 20
10 F';
40
[10'71
timoiec s  1 1  1

I
1 30
Figure 3. Experimental deterniination o f A.3 (see eq AIO) for the metathesis reaction benzyl. DI toluenedl I. at 989 K. Representative example from Table I V .
+
+
a Radical source: benzyl vinyl ether (C6H5CH20C2H3). Radical source: bibenzyl (1,2diphenylethane).
sors, which decompose a t different temperatures, it was possible to study the metathesis reaction 7 over a range of 315
K. The rate constant k3D was found to be 1.23 X lo9 Ml sl a t ( T ) = 1000 K. The activation energy E3Dat 1000 K is 6.3 f 1.5 kcal/mol as found by a leastsquares analysis log (A3D/M' sl) = 10.46 f 0.30), in remarkable agreement with the parameters found for allyl radical. The Arrhenius plot in Figure 4 suggests, by analogy with the allyl case, slight curvature at higher temperatures and a possible small systematic error between the two series of different precursors for benzyl radical, but it is obvious as well that the straight line, corresponding to E3 = 6.3 f 1.5 kcal/mol, does not do violence to the present data. In close analogy to the allyl case discussed in part A, the experimental Arrhenius expression for k l D a t 1000 K was transformed into an Arrhenius expression for k3H to account for the primary isotope effect, replacing DI by HI as reagent. The result is log ( k 3 / M  l s  I ) = (10.36 f 0.30)  (5.5 f 1.5)/0, where 0 = 2.303RT in kcal/mol, and the condition k 3 H / k 3 D= 1.18, as measured experimentally in the allyl case, holds. Owing to the more preliminary nature of the iodination study of t o l ~ e n ethe , ~ experimental rate of the reverse of reaction 7 at T = 500 K was assumed to be correct (1.41 X lo2 M' sI) rather than using the published Arrhenius parameters, since A4IMI s  I seems to be too low by a t least two orders of magnitude (log ( A 4 I M  I s') = 8.75, E4 = 15.20 kcal/mol). In order to derive a value for the equilibrium constant K4,3 = k 4 / k 3 a t T = 500 K ( 3 ) , where R. = C ~ H ~the S ,transitionstate model (1 1 ) was used by analogy with the allyl case, discussed above. Benzyl iodide ( C ~ H T Iwas )
T = 1000 K
51 9.10 8.90 8.70 1
8 8.50 8.50 9.W
9.50 10.00 10.50 11.00 11.50 12.00 12.50 104 K n

..
Figure 4. Lcaatsquares .Arrhcniua plot ol' r;ite const;ints l'roni Table IV for the reaction C7H7. DI C7H7D I.: bibcnryl ;IS precursor: 0 bcniql v i n y l cthcr LIS prccuraor f o r ben7yl radic:ils.
+
+
taken as a model and corrected for the transition state ( I O ) as before. Table V shows the detailed corrections and the computed entropy of activation AS3O* for reaction 7. Using the ( A C * , 3 ) value listed in Table VI, as computed from the temperaturedependent A S 3 O * values of Table V and relation I O for the change in Arrhenius activation energy with temperature, one obtains the following Arrhenius expression for
1234
Journal of the American Chemical Society

Table V. Estimated Entropy of Activation for the Metathesis Reaction C7H7.
+ HI
C7HgH
AS,O*' = SO(C,H,I)
+ I. (Standard State: 1 atm)
 SO(HI)  sO(C,H,.) 300 K 500 K 1000 K 33.23 35.22 37.44
AS30*'
corrections: spin ( R In 2) rotationa
1.39 2.94
2 bending ( C  ' * H * ' ~ :~200 ) cmI 1 stretch
c**~''I):
 
resonance stiffening of internal rotation, VO= 3 13.0 kcal/,mol CC, 1000 cm1 CC, 1200 cm' AS30*
1.39 2.94
1.39 2.94
2 x 2 x 2 x 2.20 3.10 4.40 reaction coordinate 1.86
1.72
1.53
0.10 0.20 0.38 26.46 26.61 26.22
a Adjusted to give experimental A3H at ( T ) = 1000 K (log (A3H/M' S  I ) = 10.36).
a t 500 K: log (k3/MI sl) = (9.67 f 0.30)  (3.20 f K 4 , 3 at T = 500 K is then computed to be 7.54 X which yields a standard heat of formation AH'f(benzy1) = 47.80 f 1.50 kcal/mol at 300 K, using an estimate for So(benzyl)Ioand C, data2,l0listed in Table VI. The comparative rate shocktube decomposition of isobutylbenzene at ( T ) = 1100 K yields AH'f(benzy1) = 48.0 f 2.0 kcal/molI2 a t 300 K under the assumption of zero activation energy (in pressure units) for the reverse reaction a t reaction temperature (Arrhenius activation energy for decomposition Ed = AH'), a value markedly higher than the currently accepted value from iodination studies and related evidence' of 45.00 f 1.5 kcal/rnol. However, if one converts the measured Arrhenius activation energy for the decomposition of isobutylbenzene of 69.6 kcal/molI2 into the thermodynamic function A H 0 3 0 0 by making the convenient assumption6 that the activation energy for recombination a t 0 K is zero,I5 one deduces AH'f(benzy1) = 46.40 kcal/mol a t 300 K. This method, however, necessitates the use of an appropriate model for the transition state. In this example, we used a rotational transition stateI3 to deduce (AC,*)in order to obtain the critical energy Ed,O from the activation energy a t 1100 K. Thus, the total spread in AH'f(C7H7.) amounts to 3 kcal; there are two points which are noteworthy when discussing this discrepancy. First, the accepted value of 45 f 1 kcal/mol is based on an estimated rate for reaction 6 that is consistent with a n activation energy of 1.O f 1 kcal/mol. In the present work, k3
1.50)/0.
/
1015
1 February 28, 1979
we have measured the rate and the activation energy for reaction 6, although for the deuterium system and a t higher temperatures. Use of a reasonable transitionstate model together with the measured isotope effect for the analogous allyl system leads to AHOf(C7H7.) of 47.8 f 1.5 kcal/mol. Secondly, as stated above, the "high" heat of formation of 48.0 kcal/mol from the singlepulse shock tube decomposition of isobutylbenzeneI2 reduces to 46.40 kcal/mol if one makes a different assumption regarding the activation energy for the recombination reaction. To summarize, it seems to us that the best value for AH'f(C7H7.) is around 47.0 f 1 .O kcal/mol on the basis of experimental evidence. A consistency check on A S 0 4 , 3 and thus on the standard entropy of benzyl radical using the Arrhenius parameters A 3 and A 4 (2.30R log A 4 / A 3 = A S 0 4 , 3 ) could not be performed because of the lack of reliable Arrhenius parameters for the reverse of (7).5 Instead, Arrhenius parameters were calculated for the reverse of (7), log A d , E d , using an estimate for A S 0 4 , 3 (ref 2 and 10) at 500 K, the extrapolated rate constant k 3 (through transitionstate model displayed in Table V), and the experimental rate for the reverse of (7) from the iodination study of t o l ~ e n eThis . ~ method, that is described in some detail in part A dealing with allyl radical, yielded the rate parameters for k 4 at T = 300, 500, and 1000 K, listed in Table VI. The same observations can be made as in the allyl case when considering the magnitude of log A 4 and log A 3 , respectively. Acknowledgment. This work was supported, in part, by Contract F4462075C0067 with the Air Force Office of Scientific Research. Appendix For a radical titration (metathesis) with HX, where X = I, Br, the pertinent reaction system is
R.
+ HX ~
R
+ X.H
(A 1 )
Under steadystate conditions, the following expressions for the concentration of the involved species result d(RH)/dt = ka(R*)(HX)  keRH(RH) 0 d(R.)/dt = R R i  keR.(R.)  k,(R)(HX)
(A4)
=0
d(HX)/dt = R i ~ x keHX(HX) ka(R.)(HX)
E
(A5) 0 (46)
where k,P is the escape rate constant of species P and R p i is the
Table VI. Measured and Calculated Rate Parameters and Thermochemical Parameters for the Equilibriumd toluene + I.
3benzyl + HI k3
TIK 1000
log (k3/M'
ASo4,3/eua
AHO4.3, kcal/mol
6.46
17.30
1% SI)
log k j D
(k4/M'
SI)
1 1.77  23.6018
500
10.46  6.310 logk3H 10.36  5.518 9.61  3.2018
1 1.02  20.30/0
6.16
1 7.08
300
9.26  2.5010
10.36  19.10/8
5.0
16.62
1000
(.IC,,
da
0.43 2.28
(AC*P,
)C
0.56 0.30
Thermochemical estimate, ref 2 and IO. From K4,3 = k4/k3 and 6SO4.3. Values for 6HO4.3 at 300 and 1000 K computed with (6Cp,4,3). Calculated from 6 S 3 O * of transitionstate model in Table V. d Italicized values represent experimental results; others are calculated Arrhenius parameters (using transitionstate model ( I O ) from Table V, (0 = 2.303RT in kcal/mol).
Wong
/ Absolute Rates of Hydrogen Abstraction
1235
flow rate of P into the VLPP reactor (in units of molecules sl LI). With the use of (A4)(A6), (RH) can be expressed as a function of (HX): k ka RR'( R H ) = %(R*)(HX) = ke keRHkeR* k,(HX) R i ~ ~ X (A7) keHX ka(R)
+
+
(A7) is simplified to give (A8) under the condition (HX)
>>
(R.): k, R R ~R i ~ x (RH), = ~~ (A8) keRHk,(HX) keHX With the definition l/f = ( R H ) m / ( R H ) , the following expression is obtained, where ROHX= keHX(HX):
In the limit of high (HX), where R i ~ =x R'HXholds to a good approximation and where R R is~ negligible with respect to R'HX and R i ~ xrespectively, , (A9) can be simplified to expression (Alo), which relates the experimental quantities l/f and R i H x to the desired rate constant k, if the escape rate constants keR.and keHXare known
+ keRkeHX kaRiHx
l/f = 1
(A10)
References and Notes (1)D. M. Golden and S.W. Benson, Chem. Rev., 69, 125 (1969). (2)S. W. Benson, "Thermochemical Kinetics", 2nd ed., Wiley, New York, 1976. (3)J. A. Kerr in "Free Radicals", Vol. 1, J. K. Kochi, Ed., Wiley, New York, 1973. (4) . . D. M. Golden, A. S.Rodgers, and S.W. Benson, J. Am. Chem. Soc., 88, 3196 (1966). (5)R. Walsh, D. M. Golden, and S. W. Benson, J. Am. Chem. SOC., 88,650 (1966). (6)M. Rossi, K. D. King, and D. M. Golden, J. Am. Chem. Soc.,preceding paper in this issue. (7) W. H. Watanabe and L. E. Coulson, J. Am. Chem. Soc., 79,2828 (1957); H. Yuke, K. Hatada, K. Nagata, and K. Kaiiyama, Bull. Chem. SOC.Jpn., 42,
3546 (1969). (8)N. A. Gac, D. M. Golden, and S.W. Benson, J. Am. Chem. SOC.,91,3091 (1969). (9)A. F. TrotmanDickenson and G. S.Milne, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 9 (1967). (IO) H. E. O'Neal and S.W. Benson, lnt. J. Chem. Kinet., 1, 217 (1969). (1 1) D. M. Golden, N. A. Gac, and S. W. Benson, J. Am. Chem. Soc., 91,2136 (1969). (12)W. Tsang, Int. J. Chem. Klnet., 1, 245 (1969);IO, 41 (1978). (13)D. F McMillen, P. L. Trevor, and D. M. Golden, in preparation. (14)The combined error limits have been estimated to be f 1.5kcal/moi in view of the highprecision determinations of k4 (ref 4). (15)This assumption results in the following relations:6Ed.0 = AP,,; AEor=
AF0
+ T( AC"),where
Ed.0
is the critical energy for the bondbreaking
reaction.
Direct Measurement of Absolute Rates of Hydrogen Abstraction by tertButoxy Radicals. A Flash Photolysis Electron Spin Resonance Study S. King Wong Contribution from the Photochemistry Unit, Department of Chemistry, The Uniuersity of Western Ontario, London, Ontario, N6A 5B7 Canada. Receiced March 13, 1978
Abstract: The flash photolysis electron spin resonance spectroscopy is applied to direct monitoring of the growth of the product radicals from the hydrogen abstraction reaction to obtain the rate constant. Photolysis of ditertbutyl peroxide is the source of tertbutoxy radicals. Cyclopentane, anisole, methyl rertbutyl ether, and methanol as hydrogen atom donors have been studied: the Arrhenius parameters log A (M' s') and activation energy E , (kcal/mol) per active hydrogen have been determined to be 9.1 and 6.1, 8.8 and 5.9, 8.8 and 5.2, and 8.6 and 5.3, respectively. The absolute rates (20 "C) are about a factor of 1.5 higher than the previous (indirect) estimates, but about a factor of 2 lower t h a n a recent study by Scaiano et al. using optical laser flash photolysis.
This work was initiated for two major goals: (1) the production of radicals for CIDEP (chemically induced dynamic electron polarization) studies],' by the photochemical decomposition of ditertbutyl peroxide3 (BOOB) and (2) the measurement of absolute rate constant of hydrogen abstraction reaction by tertbutoxy radicals (BO.). We failed to observe any CIDEP effect in the systems studied, but we wece fortunate enough to be able to measure the absolute rate constants of some of the hydrogen abstraction reactions of BO.Our method represents a more direct way than previously reported to measure these rate constants, which are still hard to come by.435 In 1960 Walling started reporting a series of a wellplanned and elegant investigations on the rate of hydrogen abstraction reactions by tertbutoxy radicak6 A very large amount of relative rate constants have since been determined. The basic reaction used was the wellknown radical chlorination of hy
drocarbons by tertbutyl hypochlorite (BOCI). Relative reactivities of organic compounds toward BO. ( k l / k ~ ' )may be measured in competitive experiments where two substances ( R H and R'H) react with BO. and the product radicals then form products such as organic chlorides by reaction with hypochloride (or carbon tetrachloride if other initiators of BO. are used). See eq 1, ,'l and 2.The ratio of rate constants kl/kl' may be determined by estimating the relative yields of RCI and R'CI or the consumption of reactants in competitive experi
BO *
BOH
+
R e
8OCl
BOH
+
R'.
BOCI o r C$lr
o r CtI4 RC,
R'CI
(1)
(1')
R H (CH3)zCsO + C H 3 .
0 1979 American Chemical Society
(2)