and SixXenter Unimolecular Reactionsla

ARRHENIUSA FACTORS FOR UNIMOLECULAR REACTIONS

2903

A Method for Estimating the Arrhenius A Factors for Four- and SixXenter Unimolecular Reactionsla

by H. E. O’Neal and S. W. Bensonlb Department of Thermochemivtry and Chemical Kinetics, Stanford Research Institute, Menlo Park, California 94026 (Received March 2,1967)

The Arrhenius A factors for gas-phase, unimolecular reactions which proceed through a cyclic transition state are examined from the point of view of transition-state theory and are shown to be compatible with a structure which is looser than the ring prototypes. On the basis of a few simple rules for assigning bending, stretching, and torsion frequencies it is shown that quantitative estimates of these A factors can be made to within the average experimental uncertainty of +0.3 unit in log A (units of sec-I). The extreme range of A values extends over 6.0 log units. I n a few isolated cases the discrepancy between estimated and observed A factors exceeds 1.0 log unit and the weight of evidence suggests that the experimental values may not be reliable. The reactions include dehydrohalogenations which go through four-center transition states, ester pyrolyses, “Ene” reactions, which go through six-center transition states, and Cope rearrangements which do the same. The dnalysis confirms previous suggestions that the most important contributions to AS* come from losses in hindered internal rotations (about -4.0 gibbs/mole per rotor) in forming the loose cyclic structure. However, other coupled changes in structure can also be important.

Introduction A large fraction of the gas-phase unimolecular reactions which have been studied appear to take place by way of four-center and six-center cyclic activated complexes.2 The vast majority of the four-center reactions are hydrogen halide eliminations from the alkyl halides t o produce olefins. Losses of water, ammonia, and hydrogen sulfide from tertiary alcohols, amines, and mercaptans have been observed in only a few cases. The majority of the six-center reactions involve the cleavage of esters into carboxylic acids and olefins. A fairly large and related category of cleavages is reported for 2-hydroxy 4-olefins into olefins and aldehydes (or ketones). The last large group are allylic (Cope) rearrangements. The Arrhenius parameters for these reactions are consistent with the transition states proposed. Activation energies are always lower than the bond dissociatiOn energies Of the weakest bonds in the molecule (indicative of concerted, bond-breaking, bond-forming processes) and activation entropies are either very

small or negative (indicative of the restrictions in motion resulting from the formation of the cyclic transition states). Reported A factors for these reactions exhibit considerable spread (e.g., four-center, 1010.*-1014Jsec-’ ; six-center, 109.0-1015.2 sec-I). The vast majority, however, fall within a rather narrow range, e.g., foursec-’; 6-center, * 1.5 sec-’. center, 1013J* No general methods presently exist for evaluating how “reasonable” the reported A factors are for these reactions. Lower limits have been suggestedzaby assuming that the entropy of activation is about -4 gibbs/mole for each hindered rotation that is tied up in going to a ring compound. This was based on the known intrinsic (Le., symmetry-corrected) entropy differences ‘so

(1) This project has been supported in part by a contract with the Office of Standard Reference Data, National Bureau of Standards; (b) T~ whom reprint requests should be addressed. (2) (a) A. F. Trotman-Dickenson, “Gas Kinetics,” Butterworth and CO.Ltd., London, 1955, PP 126-127; (b) S. W.Benson, “Foundation of Chemical Kinetics,” McGraw-Hill Book Co., Inc., New York, N. Y., 1960, pp 225-264.

Volume 71, Number 9 August 1967

H. E. O'NEALAND S.W. BENSON

2904

Table I : Frequencies Assigned to Normal and Partial Bond Bending and Stretching Motions

C=O

c-0

C-0 ethers C-0 acids. esters

c.0 c=c c-c c-c c-c

C

1700 1400 1100 1200 710

675 3000 2200 1100

C-H C.H C-F C*F c-el C.Cl

1450

700

1000

700

1150

400

800

c/

1200

C

840

C

1150

c/

800

C

420

d C C\ C

420

290

c/ ' c

300

420

c/ \c

400

420

c/ ' c

280

420 850

c/ \o

400

c/

280

820 650 490 500 375 560 420

c-I c.1

C-Br C.Br

C

C

/ \c C

\c

C

C

c/ ? \ c C / \o 0 C

A \

0

0

c=c=c

635 700

*c1

/ \ C /

280

C

*

Br

360

Br

250

C

/

\I

320

C *

I

220

0 0 C C

'0

o/c\o

400

Note that bending frequencies are surprisingly consistent with the relation, w1/wz = (p2/pl)'l2. Deviations from this relation seldom exceed 50 cm-l. Here the reduced mass is p = ( M A M B / M A M B )for the bend (A-R-B). b Methyl and methylene wags

+

( "' e )

t , w bends and have been asand twists, whose frequencies range from 1000 to 1300 cm-1, have been equated with H' signed a mean value of 1150 cm-l. Methylene rocks have lower frequencies (Le., ~ 7 0 0cm-1) which correspond closely to the

out-of-plane (H/"C)

bends in olefins.

between the cyclic and open-chain paraffins. Thus 8"int(cyclobutane) - 8"i,t(n-butane) = - 12.1 gibbs/ mole or 4.0 per rotation while the cyclohexane-nhexane pair give -4.7 per rotation. Since in the vast majority of four- and six-centered react'ions, one and three internal hindered rotations are lost, respectively, one estimates lower limits of: four-center, AS*(4) 2 -4.0 eu, A.(4) 2 1012-6 sec-I; six-center, Ah'*(6) 2 -14.1 eu, Acn 2 lO1O.*sec-'. The Journal of Physical Chemistry

Since the observed A factors are invariably much higher, transition states looser than the four- and sixatom ring prototypes are implied. By considering in more detail the entropy changes taking place in the four- and six-center activation processes, we have developed a simple, general method by which fairly reliable a priori estimates of the A factors for such reactions can be made. This method is presented in the following paper.

2905

ARRHENIUS A FACTORS FOR UNIMOLECULAR REACTIONS

state theory, is given by ekT A = exp{ AS*JR} h

sume that there is no change in electronic degeneracy and that we can neglect the demonst,rably small changes in the rotational entropy. The only important contribution to AS* must then come from symmetry changes and changes in the vibrational frequencies and internal rotations. For calculational p u r p o ~ e s ,four~

Calculation of A factors requires estimates of AS*, the entropy of activation. For a unimolecular reaction, the translational entropy is, of course, unchanged in passage t o the transition state. We shall also as-

(3) Present evidence is reasonably convincing to the effect that there is considerable polar character to these states. See S. W. Benson and G. R. Haugen, J . A m . Chem. Soc., 87, 4036 (1966); J . Phys. Chem., 70, 3336 (1966).

Calculation Procedures The Arrhenius A factor, according to transition-

_ 1

Table I1 A. Internal Rotations-Barriers, Partition Functions, and Entropies

Groups

Barrier, kcal/mole

Partition function,"Sc Qr,? (800'K)

300

400

Methyl (Me) Ethyl (Et) Isopropyl (i-Pr) t-Butyl (t-Bu) Phenyl (Ph) Benzyl (Bz) Hydroxyl (OH)

3.0 3.5 4.0 4.5 4.0 4.0 2.0

15.6 52 65 72 63 92.5 8.8

5.8 8.2 8.6 8.8 8.6 9.4 4.6

6.1 8.5 8.9 9.1 8.8 9.6 4.9

S o f , r ,gibbs/mole b a t TOK 600

6.5 8.9 9.3 9.5 9.3 10.0 5.3

800

1000

6.8 9.2 9.6 9.8 9.5 10.3 5.7

7.0 9.4 9.8 10.0 9.8 10.5 5.8

B. Torsion Frequencies for Methyl-Substituted Ethylenes U,d

em-1

Ethylene (C2H4) (E)t = CH2zCHz Propylene (CaHa) (P)t = CHZ-CHCHa Isobutene (CIHB) (i-B)t = (CH3)tC-CHz cis-2-Butene (C4Hg) (cis-2-B)t = ';>CA-CC~C

1450

kc

H

1.15

800

1.0

1000

0.65

1450

0.56

280 3000 2200 1300

2.8 0 0.05 0.38

1150

2.1

700 400

1.2 2.1 0.0

gibbs/mole

C H ’ \H

C

C

c/ - c 1 4(C-H) C.H

c/ \Cl 5(C-H)

400 3000

2.1 0

c-c

1000

0.65

c-c

1150

2.1

4 H C

700

1.2 5.8 1.3

H I ‘C1 (CH~ACH~CH~)~ .-+ (reaction coordinate)

4(H/C

S o (BOO’K),

C

C 4(H/

Freq, o,om-’

C

( A c)

.O>,.t

H’ \Cl CHs(ir, 3 . 5 kcal) c-Cl

650

S O T = $14.3

ASoSu*‘u 10.8

-

w It

SOT*

= 10.8

14.3 = -3.5 gibbs/mole

reacting ends), the internal rotations of the reactants transform to out-of-plane ring vibrations involving all of the atoms of the ring. The ring vibrations in this latter case become not only diffcult to visualize but also impossible to assign in any simple fashion. The loose cyclic transition state proposed, then, is energetically reasonable, operationally convenient, and, as we intend to show, gratifyingly consistent with the data. Its use, if anything, should provide an upper limit to the Arrhenius A factor since a more fully developed ring would mean a “tighter” structure and, therefore, a larger entropy loss. Vibrational assignments used for the ground states and for the “loose” cyclic transition states were based on existing frequency4 assignments for normal bond bends and stretches. Frequency assignments for the partial (1/2 and 3//z bond order) bond stretches and bends were estimated from the single-bond frequencies using Badger’s rule and Pauling’s equations relating bond orders and bond length^.^ Frequencies so adopted are shown in Table I. Internal rotation entropies (Table IIA) were obtained from the appropriate free-rotor partition functions with corrections for “average” reduced mass effects6 (see Table I1 and footnotes). Since entropies of internal rotations are large relative to vibrational entropies, restrictions in the former will result in the

most significant entropy losses in the activation processes. Assignments of the frequencies of the torsions replacing these internal rotations were made with the help of frequency assignments for the methyl-substituted ethylenes’ (see Table IIB) . Torsion frequencies of the a/2-order bonds were taken as half the torsion frequency of the corresponding olefin. This is roughly the average of the single- (free rotation) and doublebond frequencies. Torsion entropies about one-electron bonds (e.g., the torsion around the 0 . C bond in the ethyl acetate transition state) were estimated from the partition functions for free rotation and the estimated end interactions of the transition states. The latter were taken to be the barriers t o free rotation about the one-electron bonds. These end interactions were in most cases about 10-15 kcal/mole. To illustrate, the vibrational assignments for the ground and transition states of ethyl chloride, with their (4) R. M. Silverstein and G. C. Bassler, “Spectrometric Identification of Organic Molecules,” John Wiley and Sons, Inc., New York, N. Y., 1963. ( 5 ) L. Pauling, “The Nature of the Chemical Bond,” 3rd ed, Cornel1 University Press, Ithaca, N. Y., 1960, pp 221-264. (6) K. 5. Pitzer and L. Brewer, “Thermodynamics,” G. N. Lewis and M. Randall, Ed., revised ed, McGraw-Hill Book Co., Inc., New York, N. Y., 1961, pp 439-446. (7) D. W. Scott, G. Waddington, J. C. Smith, and H. M. Huffman, J. A m . Chem. Soc., 71, 2769 (1949).


H.E. O'NEALAND S. W, BENSON

2908

Table IV O H

Bends

\c

-C //

Basic ring skeletons Esters

\

0-c

AS +ring =

/

+ + + + + + ++

so Stretches so

2 . 0 2.0 2.0 0.6 (Cd) (C--O)e (C-C) 0.17 0.45 0.65 0 . 0

Bends

(oJC\o) + (do. c) + (o - c\c)

so Stretches so

+ ++ + +

+1.9 gibbs/mole

+ (C-0) ++0 .(C-H) 6

++

+

(H*

c\

2.0 2.8 2.8 0.65 1.0 ~ ( C A O ) (C-LC) (C.H) (C*O)ro 0 . 6 0.4 0.07

+

H

)(

H

*

"Ac)

-,-Unsaturated alcohols

Bends

so Stretches so

+ + ++0.25 (C-0) + (0-H) + + + 0.0 0. H C. H / . A C 0 or C 0

2.0 2.0 2.1 (C=O) +2(C-C) 0.17 1 . 3 0.6

\;.c*cY

hC.J

C Bends

so Stretches so

Cope rearrangements

/ C \

Bends

so so

Stretches

c c c-c

7 O r C

Stretches

So

The Journal of Physical Chemistry

b l \ c \ /

=

0-c

+ + +

4.0 4.0 2(C=C) 3(C-C) 0.4 1.95

c. c

C

so

+ (C-C),,

c c

\

/

Bends

.

+ + + +

2.0 2.8-+ 2 . 8 4- 1.0 2(CLO) (C-LC)'+ ( 0 . H ) 0.6 0 . 4 0.07 4- 0.0

\

c. c

/ ' I C or C

\

C

( 7.c) ( AC)

2 c

+ 2 c

+ +

5.6 4.0 4(bC) (C.C)ro 1.6

0.8 gibbs/mole

2909


// C \

H atom transfers

Bends

C

6.0 0.5 (C-H) 2(C=C) 0.0 0.4 1.3

Bends S" Stretches

2 C

\c

+

- 1 . 0 gibbs/mole

=

c=c

+ 2(C-C)

( A) ( C

A S *ring

/

+ + + +

so

Stretches S"

H

H

C

) ( +

H

\

H

e C

) ( AC) +

C

rc

so

\ / -c-c-

Alkyl halides

I

AS*ring = $0.3 gibbs/mole

I

H X Bends

So Stretches

so

+

2(H'"\H) (C/'\X) 0.5 2 . 1 0.5 (C-C) (C-X) (C-H) 0 0.65 1.35

+

+ + + +

S"

(H

*

/

+ (€3 ' '\H)

"C)

(X = C1)

+

\ -c-c-

Bends S" Stretches

+ (H/'\X)

+ 0.65 + 2 . 8 + 0.5 ( C * H )+ (C-C) + (C*X)rc 0.05 + 0.4

(Cy'

*

X)

+ (H"

*

X)

1.0

Special systems Basic ring skeletons 1,3,5-Hexatriene

Bends So Stretches So

c c // \c C \

c=c

/

AS%ing =

- 1 . 6 gibbs/mole

8.0 3(C=C) 2(C-C) 0.6 1.3

+ +

Bends

so

Stretches So

6.0 ~(CAC) 2.3


H.E.O'NEALAND S. W. BENSON

2910

Table IV (Continued)

Iliacetatesa

\

O-C-

AS* ring

/

=

1 . 2 gibbs/mole

I

Bends

so

Stretches

so

2.0

+ + + ++

4.0 2.0 2(C=O) 2(C-O). 0.35 0.9 1.2

+ 2(C-0)

\ o

0. CY

0

-C

\

i

/

0.cI

Bends

so so

Stretches

+ ++ + +

++

2.0 2.8 2.8 2.0 4(C-O) (C-L-O) (C.O),, 1.2 0.8 0.0

a Note that a carbonyl conjugation with the polarized ring is proposed. The resulting stiffening of the ring and torsion is required to approach by calculation the abnormally low A factors for these reactions. The same interaction has been assumed in the acetic anhydride, Sbutenoic acid, and trichloromethyl formate reactions.

corresponding entropy contributions to those states, a t 600"K, are shown in Table 111. Entropies have been calculated from the vibrational frequencies using the harmonic oscillator tables of ref 6.

Ground State Motions of the heavy groups are here represented C by a C-C and a C-C1 stretch and by a C / \C1 bend. Hydrogen motions relative to each other are described C ' bends (three in the CH3group and one by four H/ H in the CH~group). The four (H/TC)w,,bendsaccount for the methyl and methylene wags and twists, and the C (H' \Cl), bend accounts for the methylene rock. The barrier to the methyl rock is very low (ie., -3.5 kcal/mole). Therefore, this motion is the hindered internal rotation.

only +0.3 gibbs/mole (see Table IV). The reaction coordinate has been taken as the (C-Cl) stretch. The intrinsic (or symmetry-uncorrected) entropy of activation is obtained as the difference between the vibrational entropies of the activated complex and ground state

AS*i,,

=

So

* - So = -3.5 gibbs/mole

The reaction path degeneracy for ethyl chloride is three.8 Thus, one obtains a total entropy of activation of A S * = -1.3 gibbs/mole and an estimated A factor a t 600°K of A = 101a.3 sec-' (observed, Table V, 1018.6 f 0.5). Similar considerations for the ethyl acetate reaction have led to the frequency and entropy assignments shown in Table VI. One should particularly note the identification of the reactant internal rotations and the transition-state torsions with the corresponding motions of the hydrocarbons of similar mass. Thus, the

Transition State The changes in ground-state vibrations to those of the transition state may be followed in the above tabulation. It is seen that the major entropy loss comes from the restriction of the methyl rotation ( L e . , - 3.7 gibbs/mole). All other vibrations contribute N


(8) The reaction path degeneracy corresponds to the number of ways the H-Cl elimination can occur and is always given by the ratio of the over-all symmetry numbers of the ground state ( a ) and activated complex ( a * ) . Thus, AS*(total) = AS*., 4- R In ( a / u . * ) . If optical activity exists, the reaction path degeneracy is given by (n* u l n a *),where n and n are the number of optical isomers of the ground and transition states, respectively.

*

2911

ARRHENIUSA FACTORS FOR UNIMOLECULAR REACTIONS

Table V:

Fcw-Center Elimination Reactions (RX -W Olefin

7 Ethyl-X

n-Propyl-X n-Butyl-X n-Pen tyl-X n-Hexyl-X Isopropyl-X

sec-Bu t yl-Xb

t-Butyl-X

t-Amyl-X" Isobutyl-X Cyclohexyl-X Cyclopentyl-Xd 1,1,l-Trichloropropane 2,2-Dichloropropane 1,2-Dichloropropanee 1,l-Dichloropropane 1-Chloroethyl methyl ether' Bornyl chloride Isobornyl chloride 1,l-Dichloroethane

x

=

c1-

LogA

E

13.16 14.2 14.6 13.51

56.46 59.5 60.8 56.61

13.45 13.50 14.5 14.0 13.63 14.61 13.81

55.0 55.08 57.9 57.0 55.15 58.3 55.33

13.40 50.5 13.40 50.5 13.64 51.1 13.62 14.0 14.07 13.9 13.74 13.77 12.4 14.2 13.7 14.65 14.02 13.77 13.88 13.47

49.6 50.6 50.75 46.2 44.69 45.0 41.4 46.0 44.9 46.0 56.85 50.0 50.2 48.3

14.07 11.9 13.8 12.76 11.46 13.99 14.78 12.08 11.65 13.45

54.2 43.9 54.9 51.2 33.3 50.55 49.7 49.5 48.3 53.5

Ref

j k 1

m n m o n m p

+ HX)

-X Log A

-

BE

x-

-

I-

E

Ref

Log A

52.3 53.9 52.2 52.0 53.7 50.7 50.7 50.9

jj kk 11

14.1 52.8 13.36 50.8

13.09 50.5

00

12.86 13.45 12.95 12.85 13.19 13.0 12.9 13.18

Calod----7

E1

Ref

LogA

ECI

bbb

13.3

56.5 53.5 50.6

13.2

54.2 51.5

13.2

54.2

13.2

54.2

13.2 13.66

54.2 51.2 47.8 45.0

EBr

a,ccc

mm j jj nn nn

m 1 q j

r s

13.14 50.5 00 13.6 47.7 j j 13.62 47.8 pp 12.63 43.8 qq 13.53 46.47 rr

14.46 14.79 12.96 12.90 13.67 15.2

48.2 47.96 43.5 42.9 45.07 47.9

ddd eee

jfj ggg

j

jjf

13.4, 13.1

t

u u

w

13.3 14.0 13.5

40.5 ss 42.0 tt 41.5 u

13.73 38.03 j

13.83

45.2 41.8 38.4

x y z

y aa

bb cc dd

13.6 40.5 uu 13.05 50.4 vu 13.52 46.1 ww 11.9 41.4 22 12.84 43.7 yy

13.1, 13.7 12.9 53.2 50.1 13.5 49.2 46.0 12.8 13.9 14.0 13.1, 13.3 13.5 13.1 13.5 13.5 13.6

jjj ee q ee

jj gg hh k 1

46.5 43.7 53.7 50.0 53.5 36.9 50.0 54.3

ii

4-Bromopent-l-eneu 2,3-Dimethyl-2-bromobutaneh

12.94 44.7 zz 13.54 39.0 M M

13.1, 13.4 12.9, 13.6

Othere

&Butyl alcohol &Amyl alcohol &Butyl mer captan a-Phenylethyl chloride" a-Phenylethyl bromide' 1,l-Dibromoethane CICHzCHzSiCla C1CH2CH2SiCl2C2H5 ClCH2CH2SiCl(C2H5)2 CHF2CH2SiFs

14.68 11.51 13.4 13.52 13.3 10.8 12.18 12.9 11.26 12.26 11.88 12.27

65.5 54.5 61.6 60 55.0 39.3 38.8 49.5 45.5 46.5 41.1 32.7

hhh

...

13.6

62.2

aaa U

hhh U

kkk kkk 111 mmm nnn 000

PPP

12.6,13.5 13.6 12.9 12.9 13.6 12.3 12.3 12.4 12.3

56.5 45.4 40.6 51.6 48.5 46.6 42.7 32.8

Volume 71, A'umber 9 August 1967

H. E. O'NEALAND S. W. BENSON

2912

Table V

(Continued)

+

'

a These parameters are obtained from the rate constant for the back reaction H I C2Hd and the reaction thermodynamics. secButyl compounds can eliminate in two ways. Primary hydrogen reactions from the methyl group give l-butene while secondary hydrogen eliminations from the methylene group produce cis- and trans-but-2-enes. Calculated values are: 10'3. sec-1 (l-butene), sec-l (cis- and trans-Zbutene), E e a t d 'v Et-pr - 2.0, which predicts a product ratio of: 2-butene/l-butene 'v Eesa'v E.I-P~..x; 2.5/1 or 707, 2-butene to 30% l-butene. The observed values in the chloride system were 57% 2-butene to 43% l-butene.' Two elimination paths for t-amyl-X are possible. The A factors for the Zmethylbut-l-ene formation and the 3-methylbut-sene are lola.' sec-l and sec-l, respectively. The estimated activation energies are E~-B"-xand E ~ - B ~-- x 2, respectively. Thus, the isomer product ratios should be 2-methylbut-l-ene/3-methylbut-2-ene E 1.3. Cyclopentyl halide eliminations of H-X may well be special systems, since, although no ground-state internal rotations are lost in going to the activated complex, partial formation of the double bond in the ring could well freeze out much, or all, of the pseudo-rotation of the cyclopentane ring. The entropy loss in going from cyclopentane to cyclopentene is 5.4 gibbs/mole. The calculated A factor of 1012.8 sec-l has been obtained, assuming an equivalent entropy loss. e There are three possible elimination products. However, elimination to give (CH2=CClCIII) should be much slower than eliminations involving the Zchlorine atom. Estimated parameters are: for 3-chloroprop-l-ene: A = 1013.3sec-l, E 'v Et-Pr-ci = 51.2 kcal/nole; for 1-chloroprop-l-ene: A = 10'3.1 sec-1, E 'v Ei.pr.c, - 1 'v 50.2 kcal/mole. The observed A4factor for this reaction is much too low to be reasonable. A value of A S * II -13.7 gibbs/mole is inferred. This is in excess of t'he maximum entropy loss The estimated parameters for the two possible elimination product's are: for 1,3-pentaof 8.5 gibbs/mole due to internal rotation. diene: A = 10'3.' see-', E 'v Ef-pr-x - 2.0; for 1,4-pentadiene: A 'v 101a.4sec-1, E =~-pI-x. The predicted isomer ratios are 1,s pentadiene/l,4pentadiene 'v 2.5/1. The estimated parameters for the two possible isomer products are: for 2,3-dimethylbut-l-ene: A ? 1013,6 sec-I, E = E ~ - B ~ for - x ;2,3-dimethylbut-%ene: A 'v 1012.9sec-1, E 'v E ~ - B " - ~Estimated isomer ratios are 2,3-dimethylbut. l-ene/2,3-dimethylbut-2-ene 'v 1/2.5. Glpc analysis indicated the major product to be the 2,3-dimethylbut-2-ene. a The parameters of the or-phenylethyl chloride reaction are certainly low. Those of the a-phenylethyl bromide are more reasonable. The differencein activation energies bet'ween et,hyl-X and a-phenylethyl-X is about 12 kcal/mole which is close to the benzyl resonance energy. Development of the benzyl resonance in the transition state would increase the barrier to phenyl rotation to about (13 4) = 17 kca1/ mole, thereby decreasing the transition-state entropy by an additional 2 gibbs/mole. j W. Tsang, J . Chem. Phys., 41, 2487 (1964). H. Hartman, H. G. Bosche, D. H. R. Barton and K. E. Howlett, J . Chem. SOC., 165 (1949). K. E. Howlett, ibid., 3695 (1952). and H. Heydtmann, 2. Physik. Chem. (Frankfurt), 42, 329 (1964). D. H. R. Barton, A. S. Head, and R. S. Willimas, J . Chem. Sot., E. C. S.Grant and E. s. 2039 (1951). ' H. Hartman, H. Heydtmann, and G. Rinck, 2. Physik. Chem. (Frankfurt), 28, 85 (1961). Swinbourne, J. Chem. Soc., 4423 (1965). * D. H. R. Barton and A. J. Head, Trans. Faraday SOC.,46, 114 (1950). A. Maccoll and R . H. Stone, J . Chem. Soc., 2756 (1961). H. Heydtmann and G. Rinck, 2. Physik. Chem. (Frankfurt), 30, 250 (1961). * H. Heydtr mann and G. Rinck, ibid., 36, 75 (1963). W. Tsang, J . Chem. Phys., 40, 1498 (1964). ' W. Tsang, ibid., 40, 1171 (1964). "s. 45, 725 (1949). ' B. D. €I. R. Barton and P. F. Onyon, Trans. Faraday SOC., Wong, Ph.D. Thesis, University of London, 1958. Brearley, G. 1%.Kistiakowsky, and C. H. Stauffer, J . Am. Chem. Soc., 58, 43 (1936). R. L. Failes and 1'. R. Stimson, Australian J . Chem., 15,437 (1962). E. S. Swinbourne, Australian J . Chem., 11, 314 (1958). cc K. E. Howlett, J . Chem. Soc., 4487 (1952). C. Herndon, 11. B. Henly, and J. M. Sullivan, J . Phys. Chem., 67, 2842 (1963). dd E . S. Swinbourne, J . Chem. SOC.,4668 (1960). K. E. Rowlatt, ibid., 945 (1953). " P. J. Thomas, ibid., 136 (1961). Io R. C. Bicknell and A. Maccoll, Chem. Znd. (London), 1912 (1961). hh A. Maccoll, see footnote r. H. Hartman, H. Heydtmann, and G. Rinck, 2. Physik. Chem., (Frankfurt), 28, 71 (1961). A. T. Blades, " A . T. Blades and G. W. Murphy, J . A m . Chem. Soc., 74, 6219 (1952). kk P. J. Thomas, J . Chem. SOC.,1192 (1959). Can. J . Chem., 36, 1043 (1958). mm A. E. Goldberg and F. Daniels, J . Am. Chem. SOC.,79, 1314 (1957). nn A. Maccoll and p. J . Thomas, J . Chem. Soc., 5033 (1957). J. H. S. Green, A. Maccoll, and P. J. Thomas, ibid., 5028 (1957). p p A. Maccoll and p. J. Thomas, ibid., 960 (1955). qq A. Maccoll and P. J. Thomas, ibid., 2445 (1955). '' M.N. Kale, A. Maccoll, and P. J. Thomas, ibid., 3016 (1958). *'G. B. Kistiskowsky and C. H. Stauffer, J. Am. Chem. Soc., 59, 165 (1937). t t G. D. Hardon and A. Maccoll, J . Chem. SOC.,2455 (1955). 71u G. I). Harden, ibid., 5024 (1957). '"G. D. Harden and A. Maccoll, ibid., 1197 (1959). ww J . H. S.Green and A. Maccoll, ibid., 2449 (1955). " S. S. W. Price, R. Shaw, and A. F. Trotman-Dickenson, ibid., 3855 (1956). '' M. N. Kale and A. J. H. Yang hlaccoll, ibid., 5020 (1957). G. 1).Harden and A. Maccoll, ibid., 5028 (1957). P. J. Thomas, ibid., 1192 (1959). and D. C. Conway, J . Chem. Phys., 43, 1296 (1965). ccc A. N. Base and S. W. Benson, ibid., 37, 2935 (1962). d d d J. L. Holmes and H. Teranishi and s. W. A. Maccoll, Proc. Chem. SOC.,175 (1957). J. L. Holmes and A. Maccoll, J . Chem. SOC.,5919 (1963). Benson, J . Chem. Phys., 40, 2946 (1964). J. L. Jones and R. A. Ogg, J . A m . Chem. Soc., 5 9 , 1939 (1937). hhh R. F. Schultz and G. B. Kistiakowsky, ibid., 56, 395 (1934). iii J. A. Barnard, Trans. Faraday SOC., 5 5 , 947 (1959). ijj P. F. Onyon and D. H. R. P. T. Good, Ph.D. Thesis, Barton, J . Am. Chem. Soc., 72,988 (1950). kkk B. Stevenson, Ph.D. Thesis, University of London, 1957. University of London, 1956. mmm I. M . T. Davidson, C. Eaborn, and M.N. Lilly, J . Chem. Soc., 2624 (1964). nnn I. bI. T. Davidson and C. J. L. hletcalfe, ibid., 2630 (1964). I. M. T. Davidson and M. R. Jones, ibid., 5481 (1965). p p p R. N. Hazeldine, P. J. Robinson, and R. F. Simmons, ibid., 367 (1964).

'

+

''

w.

''

O0

**'

"'

"'

Oo0

internal rotation and torsion about the carbonyl oxygen single bond has been equated to an isopropyl (massreduced) rot'or and a 2-methbut-2-ene bond order torsion, respectively. Note should also be taken of the abnorinally high barrier to internal rotation about The Journal of Physical Chemistry

this same bond (Le., -12 kcal), which seeins to be characteristic of rotation about the carbonyl-oxygen bond in esters and acids. From the intrinsic entropies of activation, one obR In (c/c*) = -6.5 2.2 = tains A S * =

+

+

2913


Table VI: The Ethyl Acetate Reaction Ground state Freq, Vibrations

w,

cm-1

w , cm-1

C

\H)

3(H/

1450

H’

0.87

C‘H

1450

0.29

800

1.0

1000

0.65

1150 1325 1400

2.1 0.31 0.31

1300 3000 2200

0.38 0.0 0.05

700

1.2

0

420

2.0

. \c C

290

2.8

280

2.8 2.1 4.4 6.7

kc

H

C

H

. \

‘H C

C \C),.t

c-0 (C-O),

c-c

5(C-H)

c-0 4(H/

1150 1700 1100 1200 1000 3000

2.1 0.17 0.58 0.46 0.65 0.0

700

1.2

420

2.0

0

420

2.0

c

CH, (ir, 3 . 5 kcal) i-Pr (ir, 12 kcal) C2Hs (ir, 1 kcal)

0

c‘-

2.1 5.8 7.0 8.8

410

S O T

=

\C>,.t

c-0 Reaction C c-c

L

-

o

(CH2-CHCHa)t cHacH~1-C (CHs)*t C2Hs (ir, 13-kcal barrier)

33.63

SOT*

=

27.09

- 6 . 5 gibbs/mole Entropies have been estimated from tables prepared by Pitaer and Brewer.6 AS*i,t

a

Entropies,a S0(6000K), gibbs/mole

Freq, Vibrations

C

4(H/ c=o

-

Activated complexEntropies,a S o(BOO’K), gibbs/mole

=

-4.3 eu. Thus, at 600°K, A = 1 O I 2 a 6 sec-l in excellent agreement with observation (10l2J Ou3, Tables VI1 and VIII) . The problem of calculating activation entropies for the four- and six-center reactions can be simplified by dividing the entropy of activation into four parts: (1) a ring entropy (AS*,i,,) evaluated by considering entropy changes due to bond stretching and bending vibrations, (2) a rotational-torsional entropy (AS evaluated by considering the entropy changes due to the replacement of ground-state internal rotations (Table IIA) by out-of-plane torsions (Table IIB) of the transition state, (3) a symmetry correction evaluated from AS*,,, = R In (m*/ncr*), and (4) a correction term (AS*oor) required to adjust the freerotor entropies (Table IIA) to the appropriate rotational barriers (Table IIC). Barriers used are given in Table IIC. To a reasonably good approximation, the entropies of the four- and six-center reactions may be calculated froin the sum A S = A S *ring A S *ir-t

*‘,J

*

+

+

+

A S *cor, where the A S *ring will be a constant AS specific value for each basic “ring” ~ k e l e t o n . ~The pertinent A S * ring contributions required in the A factor calculations of this communication are shown in Table IV. The over-all method for calculating the activation entropies is illustrated for a few compounds in the Appendix. I n spite of the many approximations made in calculating AS*, for most reactions the resultant A factors should be reliable to about a factor of 2 on the average. The observed Arrhenius parameters and the calculated A factors for a number of four-center reactions are given in Table V. All calculated A factors refer to a mean reaction temperature of 600°K. These (9) By the method of assigning frequencies, group substitution at the transition state “ring” centers will increase the entropies of the ground state and the transition state by identical amounts except for effects on internal rotations and torsions. Thus, the entropies of activation due to changes in bond stretches and bends have been evaluated separately for the basic ring structures.

Volume 7 1 , Xumber 3

August 1367


2914

Table VI1 : Six-Center Elimination Reactions

Reactions

1. Ethyl acetate

+

Log A

+

C Z H ~ CHaCOOH

+ CzHsCOOH + CHaCOOH (CHa)&=CH2 + CHaCOOH cis-trans-2-butene +

2. Ethyl propionate + CzH4 3. Isopropyl acetate + CsH6 4. f-Butyl acetate +

5. sec-Butyl acetate' + CHaCOOH 1-butene CH&OOH 6. t-Amylacetate" + CHaCOOH 2-methylbut-1-ene 2-methylbut-2-ene CHaCOOH CHaCOOH 7. &Butyl propionate + isobutene isobutene 8. &Butyl chloroacetate CHzClCOOH 9. &Butyl dichloroacetate 4 isobutene CHCliCOOH 10. 1-11 ethyl-3-oxobutyl acetateb --c CHaCOOCH=CHCHa CHaCOOH 11. 1-3lethylbut-3-enyl acetate + pent-lJ4-diene CH3COOH cis-truns-pent-lJ3-diene CHaCOOH CHaCOOH 12. Acetic anhydride" ketene 13. 1-Phenylethyl acetated vinylbenzene CHaCOOH vinylbenzene 14. 2-Phenylethyl acetate' CH3COOH 15. lJ2-Diphenylethyl acetate' + CsHbCH=CHCeHb CHsCOOH HCOOH 16. Ethyl formate' + CzHd

E

12.48 12.59 12.71 13.0 13.4 13.3 13.15 13.3

47.75 48.0 48.5 45.0 46.3 40.5 40.0 46.6

13.43

40.26

+

+ +

-

+

+ +

+

+

- -+ + +

--

*

26. 27. 28.

787-883 773-876 778-875 715-801 586-635 516-576 514-564 576-632

m

12.6

48.2

12.6 12.9

48.1 44.7

13.1

40.0

12.4

45.2

12.6

45.2 501-562

0

39.4 39.4 40.0 38.1

513-569 489-540

q r

n n m 0

P 0

0

12.8 13.09

39.16 38.11

12.95 12.5 13.1 13.1

12.77

36.09

13.1

36.8

487-520

r

11.88

37.4

11.6

36.6

564-628

S

13.0

44.4

564-628

S

43.9 43.9 36.1 43.7

553-646 585-641

U

34.5 43.7

+

12.33

45.4

12.2

45.1

616-682

U

13.0

43.3

12.4

41.7

575-625

V

11.33 9.41 12.58 12.58 9.4 11.1 11.0

44.14 40.01 44.0 44.2 39.66 34.6 38.1

12.5

47.8

m

12.8

44.8

12.2 13.0

47.8 39.3

648-698 648-698 721-811 596-608 613-673 503-573 569-615

C3H6

t

W

m 2 2

2/ 2

4- ca5cOog

13.0

44.1

t c,H,cooH

12.7

44.1

12.3

47.4

725-810

aa

12.2

46.0

725-810

aa

12.2 12.2

46.4 46.4

725-810 725-810

aa

11.9 11.9

47.3 46.7

725-810 725-810

aa

11.9

45.8

725-810

aa

12.2

48.6

715-810

aa

-

+ CHaCOOH

+ CHaCOOH n-Pentyl acetate 1-pentene + CHaCOOH 3-1lethylbutyl acetate CHaCOOH +

22. n-Biityl acetate

25.

Ref

12.0 12.8

+

21. n-Propyl acetate --c C3Ha

23. 24.

ATOK

+

18. n-Propyl formate* 19. t-Butyl formate' 20. (-)Menthyl benzoatei +

-m

E

12.4 12.6 12.6 12.6

+ HCOOH propylene + HCOOH isobutene + HCOOH

17. Isopropyl formate

-Calcd-Log A

1-butene

4

CH2=CH(CH3)2 2-Methylpropyl acetate isobutene CHaCOOH 2-RIethylbutyl acetate CHaCOOH CHz=C(CHI)CZHS 2-Ethylbutyl acetate -.t CHaCOOH CHz=C(Cd&)z 2-*Methoxyethyl acetate -+ CHaCOOH CHz=CHOCHa

+


+ + +

12.4 11.27 12.27 12.19 13.28 12.2 12.63

47.7 43.7 48.3 46.0 49.3 46.4 47.9

11.06 12.38 12.61 11.60 13.04

44.1 48.8 49.0 45.7 49.7

11.96

47.8

aa

aa


-0bsdLog A

-

Reactions

+

CHsCOOH 29. 2-Ethoxyethyl acetate CHz=CHOCzHj 30. %Pentyl acetate" CH3COOH 2-pentenes (cis,trans) CH3COOH 1-pentene CH3COOH 2-pentenes 31. 3-Pentyl acetate (cis, trans) 32. 2-Heptyl acetate" -+ CHaCOOH 2-heptenes (cis, trans) CHICOOH 1-heptene 33. 3-Heptyl acetate" + CHICOOH 2-heptenes (cis, trans) CH3COOH 3-heptenes (cis,trans) 34. 4-Heptyl acetate CHaCOOH 3-heptenes (cis,trans) 35. 3-Methyl-2-pentyl acetate" 3-methylpent-1-ene CH3COOH 3-methylpent-2-enes (cis, trans) CHaCOOH 36. 2,4-Dimethyl-?-pentyl acetate + CHICOOH (CHa)zC=CH(i-C3H7) 37. 1-Chloro-2-propyl acetate" + CHaCOOH 1-chloropropene (cis,trans) CHaCOOH 3-chloropropene 38. 1-Methoxy-2-propyl acetate' + CHaCOOH CII,=CHCHzOCHa CHaCOOH CH3CH=CHOCH3 (cis, trans) 39. 1-Dimetbylamino-2-propyl acetate + CHaCOOH CHz==CHCHzN(CHa)z CHaCOOH CHsCH=CHN(CHa)z (cis, t r ~ n s ) 40. 2,3-Dimethyl-2-butyl acetate" + CHaCOOH tetramethylethylene CHaCOOH CH,=C(CH,)CH(CHa), 41. 3-Methyl-3-pentyl acetatea + CHaCOOH 3-methylpent-2-ene (cis,trans) CH3COOH 2-ethylbut-1-ene 42. 2-Methyl-2-pentyl acetatea -+ CHaCOOH 2-methylpent-1-ene CHaCOOH 1-methylpent-2-ene 43. 1-Methylcyclohexyl acetate"' CHaCOOH 1-methylcyclohexene CHaCOOH methylenecyclohexane 44 * Cyclohexyl acetatez cyclohc3xene CH&OOH

+ +

-

+ + + +

+

-

+

+

-+

+

+

+ + + +

+ + + + +

+ + + + + +

-

-

2915

-CalcdE

12.09

47.9

12.73

43.7

13.09

44.7

13.32

45.3

13.93

44.9

12.6

43.2

12.84

44.7

11.9

43.8

12.14 14.22 14.6 13.85 15.36 11 56 I

E

ATOK

Ref

12.2

48.3

725-810

aa

650-710

aa

12.35 12.6 12.9

43.8 43.8 44.1

650-710

aa

650-710

aa

12.3 12.6

43.6 43.6

12.35 12.30 12.6

42.8 42.8 42.7

650-710 650-710 650-710

aa aa

650-710

aa

12.6 12.0 12.3

43.5 43.5 43.0

650-710

aa

650-710

aa

12.35 12.6

46.6 46.6

12.6 12.35

45.8 45.8 650-710

aa

12.6 12.35

44.2 44.2 560-610

aa

12.0 12.9

37.9 37.9 560-610

aa

12.7 12.6

38.0 38.0 560-610

aa

12.9 12.35

38.3 38.3 560-610

aa

13.0 12.6

38.8 38.8 623-7 7 3

bb

13.0

44.5

46.9

13.32

13.05

Log A

46.6 42.2 41.3 42.4 40.6 45.2 40.3

'

' See Table VIII for the observed olefin productd istribution. The rate and activation energy for this reaction indicate strong participation of the carbonyl group and enhanced acidity of the &carbon hydrogen. This is supported by the fact that, unlike l-methylbut3-enyl acetate, only one product was formed. Since an enolic resonance is implied, the barrier to internal rotation of the acetyl group has been increased from 1 to about 15 kcal/mole, thereby lowering the transition-state entropy by an additional 2.4 gibbs/mole. If all Szwarc's data a.re used in the Arrhenius plot, an A factor of lO1a.a sec-I is obtained. See also Table I V for assumptions made regarding carbonyl "ring" conjugation in the transition state. Eighteen other substituted 1-arylethyl acetates were studied. The Arrhenius parameters were all very similar with A factors ranging from 101a.6ato 1018.17sec-1 and activation energies varying from 41.7 to 44.7 kcal/mole. The meta and para compounds were found to fit a p-u+ plot quite well, with p = -0.66 a t 600°K. The U + constants used were those given by H. C. Brown and Y. Okamoto, J . Am. Chem. Soc., 80, 4979 (1958). Since the activation energy is nearly the same as that for isopropyl acetate, no conjugative interaction between the phenyl group and the "ring" in the transition state occurs and none has been used in the A-factor calculation. The polar nature of the transition states in the ester eliminations is strongly supported by these results. Three other substituted Zarylethyl acetates were studied. A factors varied from 10'*.a7to 101a.46sec-l and activation energies from 44.8 to 45.9 kcal/mole. Ten other substituted diarylethyl acetates were studied. A factors ranged from 101a.64 to 1011.06 sec-l and activation energies from 40.6 to 43.8 kcal/rnole. A large discrepancy in absolute rates exists between

'

Volume 71, Number 9 Auguet 1967


2916

Table VI1

(Continued)

these two studies. If a 47.5 kcal/mole activation energy is assumed (see discussion of activation energies), a rate constant of log k = -2.99 is calculated a t 675'K. This is in excellent agreement with the observed rate constants of the more recent study" of log k = -2.97. The same kinds of experimental complications which produced the very low Arrhenius parameters of the ethyl formate decompositionw were present in this study. By comparison with the activation energies observed for ethyl acetate and isopropyl formate, it is quite clear that the reported activation energy for the n-propyl formate decomposition is at least 5 kcal and probably as much as 7 lrcal too low. ' The ilrrhenius parameters reported are clearly too low. By analogy with the t-butyl acetate decomposition activation energy, one would estimate the t-butyl formate activation energy to be about 39.2 kcal/mole. This is in excellent agreement wilh the 39.3-kcal/mole value obtained from the estimated A factor and the observed rate constant. ' The temperature range of this study was rather narrow, and therefore appreciable errors in the activation energy and A factor are quite possible. Both reported parameters are certainly low from the standpoint of energy and entropy considerations. The isomer product ratios in this reaction are not statistical because one less internal rotation is restricted when H atoms of the cyclohexane ring react. The calculated A factors reflect this reaction path preference. The "corrected" activation energy is close to that of t-butyl acetate, as one might expect. These parameters are certainly too low. The "corrected" values give the same activation energy as that for isopropyl A. T. Blades and P. W. Gilderson, ibid., 38, 1407 acetate which is reasonable. A. T. Blades, Can. J. Chem., 32, 366 (1954). C. E. Rudi, Jr., and P. Fugassi, J. Phys. Chem., 52, 357 335 (1962). (1960). E. V. Emovan and A. Maccoll, J . Chem. SOC., (1948). * E. Warrick and P. Fugassi, ibid., 52, 1314 (1948). ' E. V. Emovan, J. Chem. Soc., 1246 (1963). * A. Maccoll, ibid., 227 47,269 (1951). " R. Taylor, G. G. Smith, and W. H. Wetxel, J . -4m. Chem. (1964). J. Murawski and M.Szwarc, Trans. Faraday SOC., R. F. Makens and W. G. Eversole, ibid., 61, Soc., 84,4817 1'1962). ' G. G. Smith, F. D. Bagley, and R. Raylor, ibid., 83,3647 (1961). 3203 (1939). R. B. Anderson and €I. H. Rowley, J. Phys. Chem., 47,454 (1943). ' E. Gordon, S. J. W. Price, and A. F. TrotmanDickenson, J . Chem. Soc., 2813 (1047). E D. H. R. Barton, A. J. Head, and R. J. Williams, ibid., 1715 (1953). "'J. C. Scheer, E. C. Kooyman, and F. S. J. Sixma, Rec. Trav. Chim., 82, 1123 11963). The experimental technique of these studies was unusual and not conducive to giving high accuracy in the Arrhenius parameters. Errors in excess of 1 log unit in A would be quite possible. Rate constants, however, are probably fairly reliable. M. Kraus, M. Vavruska, and V. Bazant,, Collection Czech. Chem. Commun., 22,484 (1957).

'

'*

Table VI11 Reactant

1. 2. 3. 4. 5. 6. 7.

sec-Butyl acetate 2-Pentyl acetate 2-Heptyl acetate 3-Heptyl acetate 3-Methyl-2-pentyl acetate 1-Chloro-2-propyl acetate I-Methoxy-2-propyl acetate

8.

1-Methylcyclohexyl acetate

9. t-Amyl acetate 10. 2-Methyl-2-pentyl acetate 11. 3-Methyl-3-pentyl acetate 12. 2.3-Dimethyl-2-butyl acetate

' Glpc experimental peak

Observed ratio

l-olefin/2-olefin = 1 .4 1-olefin/%olefin = 1 . 4 l-olefin/2-olefin = 1.41 2-olefin/3-olefin = 0.85 l-olefin/2-olefin = 3.2 1-chloro/&chloro = 1.1" l-methoxy/3-methoxy =0.68" 1-methylcyclohexene/ methylene cyclohexane = 3 . 0 l-olefin/2-olefin = 3.0 l-olefin/Zolefin = 2 . 6 I-olefin/2-olefin = 1.8" l-olefin/2-olefin = 9.0"

Statistical ratio

A-factor ratio

1.5 1.5 1.5 1.0 3.0 0.67 0.67

1.5 1.8 2.0 1.1 4.0 0.57 0.57

0.67

2.5

3.0 3.0 1.33 6.0

2.8 3.5 1.3 8.0

ratios uncorrected for compound detector sensitivities.

values, however, should be fairly representative of the A factors at other temperatures, too, since A S * is not very sensitive to the temperature.'O I n almost all cases, the agreement between calculat,ed and observed A factors is quite good. Increase of A , due primarily t o an increase in reaction path degeneracy, for^ the series ethyl-X, i-Pr-X, and i-butyl-X is predicted, In addition, the estimated olefin product ratios are very close to those observed (see Table V Tho Journal of Physical Chemistry

footnotes). I n those few cases where the observed values of A fall appreciably outside the limits of error of the calculated values, we are inclined to place more confidence in the calculated values. Arrhenius parameters and calculated A factors for six-center eliminations are shown in Tables VI1 and (10) Calculations of the A factors for ethyl chloride a t 300 and 1000°K indicates a small increase (a factor of "2) over this 700'K temperature range.

ARR,HENIUS A FACTORS FOR UNIMOLECULAR REACTIONS

2917

Table IX -0bsdReactions

-+

2CHaCOCH3 1. 4-Hydroxy-4-methyl-2-pentanone 2. 3-Butenoic acid CHsCH=CH, COZ -c 3. l-Phenyl-4-ethyl-4-hydroxyhex-l-ene c 6 I l 5 c I ~ 2 c ~ ~ = c I I 2(C2Hs)zCO 4. Ethyl vinyl ether" C Z H ~ CH3CHO 5. 6. 7. 8. 9. 10. 11. 12. 13.

14. 15. 16. 17. 18. 19. 20. 21.

-+

+

+

+

Vinyl isopropyl ether" CaHe CHaCHO But-3-ene-1-01 CIH6 HzCO Pent-4-ene-2-01- C&f6 CHICK0 2-Methylpent-4-ene-2-01C3H6 CHaCOOH 3-Phenylbut-3-ene-1-01 -+ C H I C ( C ~ H ~ ) = C H ~CHzO 4-Phenylbut-3-ene-l-ol-+ COH~CHZCH=CHZ CHlO Methyl ethyl carbonateb COZ CzHa CHaOH Diethyl carbonateb -+ COZ C Z H ~ CZHaOH 1-Phenylethyl methyl carbonate' CeH&H=CI-IZ COz CHaOH Ethylidene diacetated acetic anhydride CHaCHO Butylidene diacetated 4 CH~(CHZ)ZCHO (CH~CO)ZO Ethylidene dipropionated -+ CHSCHO (CzH5CO)zO Heptylidene diacetated acetic anhydride aldehyde Ethylidene dibutyrated .-t (CHI(CH&CO)ZO CHBCHO Trichloroethylidene dibutyrated + (CHa(CHZ)nC0)20 CClaCHO Trichloroethylidene diacetated (cII&0)20 CCl3CIIO Crotonylidene diacetated (CH3CO)ZO CH&H=CHCHO -+

+

-+

+

-+

+

+

-

+

+

+

+

-+

+ +

+

+ + + + +

-

-

+

+

22. Furfurylidene diacetated + -k (CH$O)P

QCHO

--

+ + + + + 1-butene + HC1 + COZ

CHZO (CHaC0)ZO 23. Methylene diacetated" CHZO (CHsCH2CO)zO 24. Methylene dipropionated,' CHzO 25. RIethylene dibutyratedi' (CH3CHzCHzCO)zO HC1 COZ C3H6 26. Isopropyl chloroformate' -+

+

27. sec-Butyl chloroformate' cis-2-butene HCl CO, trans-2-butene IICl COS HC1 28. Isobutyl rhloroformatee .-t isobutene 29. Trichloromethyl chloroformate' 2C12CO

+

+

+

+

-+

+ CO,

YCalcdLog A

E

ATOK

Ref

32.3 39.9 40.6

595-628 587-651 579-607

h i

Log A

E

11.63 11.34 12.04 12.14 11.43 11.60 12.58 11.65 11.93 12.14 11.80 11.58 13.7 13.9 12.33

32.3 40.6 41.75 41.80 43.8 44.4 43.56 41.0 40.9 40.7 38.9 42.8 46 =I=2 46 39.9

11.65 11.1 11.6

10.27 10.47 10.40 10.48 10.25

32.9 32.9 32.9 33.0 33.0

11.0 11.0 11.0 11.0 11.0

10.11

33.0

11.0

U

10.11

33.0

11.0

U

11.1

33.0

11.0

2,

11.1

33.0

11.o

21

9.23 9.23 9.23

33.0 33.0 33.0

10.7 10.7 10.7

W

9.11 12.71 10.21 13.7 13.8 13.0 13.15

25.8 39.2 31.5 40.0 40.4 40.0 41.5

12.9

39.7

12.6 12.1 12.1 11.9 13.0

37.2 36.2 36.4 37.2

j lt

12.2

46.3

12.5 11.7 11.9 11.9 11.9 11.6 12.6 12.9 12.6

43.3 41.1 40.9 41.4 39.2 42.8 43.0 43.3 40.6

770-859 650-721 720-794 643-685 625-663 607-643 GO.i-G31 661-700 573-648 573-645 .580-614

1 m

493-541 484-8538 484-538

r

n 0

0 0 0

0

P P P

9

S

t t

W W

453-493 513-528 513428 540-575 ,533-583

X

Y Y

2,

aa

a The reported Arrhenius parameters of ethyl vinyl ether are undoubtedly low. One would expect, by analogy with the acetate decompositions, that the activation energy for the ethyl vinyl ether should be about 3 kcal higher than that of the isopropyl vinyl ether. This is the difference predicted from the estimated A factors and observed rate constants. The increase in A factors in proceeding from the ethyl to the isopropyl ether has been rationalized (see footnotes v of Table VI1 and n of this table) in terms of groundstate restricted inrernal rotation for the isopropyl ether. If the rotation barrier were 3.5 and 0 kcal for isopropyl and ethyl ethers, respectively, this effect would at most amount to only 1 eu in A(AS*). This is hardly enough to account for the observed difference. * The reported Arrhenius parameters of this reaction are prohibitively high since they suggest a near-zero entropy of activation in the six-membered transition state. The corresponding 1-phenylethyl methyl carbonate, which would be expected to have a similar entropy Three other substituted 1-phenyl of activation, has been found to have an appreciably negative AS*, in agreement with expectation. ethyl methyl carbonates were studied with A factors ranging from 1012.22 to 1 O I 2 sec-1 and activation energies in the range of 38.8The diester eliminations studies by Coffin, et al., are very interesting reactions in that they exhibit the lowest A 41.9 kcallmole. factors of all of the ester eliminations and have activation energies that are strikingly insensitive to the nature of the diesters. Although four-center and eight-center transition states can be proposed, a six-center reaction seems the most consistent with the facts. If

Volume 71, Number 9

August 1967

2918

H. E. O’NEALAND S. W. BENSON

~~~

~

Table IX (Continued) A-factor estimates are also in reasonable agreement with the six-center transition state. A peculiar feature of these reactions has been noted (see S. W. Benson, “Foundations of Chemical Kinetics,” McGraw-Hill Book Co., Inc., New York, N. Y., 1960, p 2,57), namely that the rate constant for the decomposition of the acetic anhydride product is an order of magnitude greater than the rate constant

4-CENTER

8-CENTER

6-CENTER

for the diester decompositions. This dilemma can be resolved, however, by examining the thermodynamics of the acetic anhydride decomposition. At the temperatures of study (-500°K), the acetic anhydride 9 ketene CH,COOH equilibrium constant may be estimated as Re, = 10-‘.06 atm (see R. Shaw and S. W. Benson, “Group Additivities of Oxygen Compounds,” to be published). At a total pressure of 20 torr, this would mean only about 7% dissociation of the anhydride product. Thus, the above equilibrium is rapidly established although well on the side of the anhydride. At the higher temperatures, ketene was observed as a minor product. A final point of interest with regard to the ethylidene diacetate reaction is that a t 600°K (where ethyl acetate begins to decompose a t an observable rate) small yields of vinyl acetate were obtained. Thus, the “normalJ’ ester (six-center) decomposition involving the ethylidene hydrogens (with parameters similar to the ethyl acetate decomposition) apparently begins to dominate a t the higher temsec-’. e The results peratures. This would be expected since the A factor for this six-center elimination would then be about on the chloroformate decompositions are subject to considerable uncertainty. Surface effects were observed in both the low-temperature static experiments and in the higher temperature flow studies. Parallel competing reactions forming CO2 and the corresponding alkyl halides occurred in all systems. Although these latter reactions were reported as homogeneous unimolecular reactions, they very probably have large heterogeneous and freeradical chain components, Kinetically reasonable and simple free-radical chain mechanisms can be written which also produce C o n C1 olefin. Thus for the chloroformate reactions, one must accept the reported values with extreme caution since these reactions are probably not unimolecular. If the barriers to rotation around two C-0 bonds of the diester are as low as 1 kcal, instead of the average 4 kcal employed in the calculations, the calculated A factors are lower (i.e., - J ~ O ~sec-l). .~ A four-center transition state was assumed for this reaction

+

+ +

G. G. Smith and B. L. Yates, J . Org. Chem., 30, 2067 (1965). ’ G. G. Smith and s. E. with some carbonyl conjugative stiffening. Blau, J . Phys. Chem., 68, 1231 (1964). G. G. Smith and R. Taylor, Chem. Znd. (London), 949 (1961). G. G. Smith and R.Taylor, S. Wang and C. A. Winkler, J . Chem. SOC.,7242 (1965). A. T. Blades and G. W. Murphy, J . Am, Chem. SOC.,74, 1039 (1952). Can. J. Res., 21B, 97 (1943). A. T. Blades, Can. J . Chem., 31, 418 (1953). G. G. Smith and B. L. Yates, J . Chem. Soc., 7242 (1965). A. 9. Gordon and W. P. Norris, J . Phys. Chem., 69, 3013 (1965). G. G. Smith and B. L. Yates, J . Org. Chem., 30, 434 (1965). ‘ C. C. Coffin, Cun. J . Res., 5, 636 (1931). ’ C. C. Coffin, ibid., 6, 417 (1932). ‘ C. C. Coffin, J. R. Dacey, and N. A. D. Parlee, ibid., B15,247 (1937). N. A. D. Parlee, J. R. Dacey, and C. C. Coffin, ibid., B15,254 (1937). ’J. R. Dacey and c. c. Coffin, ibid., B15, 260 (1937). C. C. Coffin and W. B. Beazley, ibid., B15, 229 (1937). A. R. Choppin and E. L. Compere, J . Am. Chem. S ~ C .70, , 3797 (1948). ’ E. S. Lewis and W. C. Herndon, ibid., 83, 1955 (1961). ’ E. T. Lessig, J . Phys. Chem., 36, 2325 (1932). ” H. C. Ramsperger and G. Waddington, J . Am. Chem. Soc., 55, 214 (1933).

’

IX. The general agreement between calculated and observed A factors is again excellent. As indicated in the table footnotes, there are often good reasons for suspecting the data for many of those reactions having large A-factor discrepancies. I n some of the reactions of Table VII, elimination occurs in more than one way. The olefin product distributions for these reactions seem to be roughly statistical (ie., directly proportional to the degeneracy of each reaction path). Within the error limits noted, the calculated A factors The JOtITnal of Physical Chemistry

are in good agreement with these observations (see Table VIII). Calculations of the A factors in a few systems, L e . , acetic anhydride, 3-butenoic acid, and all of the acetal reactions, require special comment. These reactions all possess two carbonyl carbons in the six-center transition state. In order to obtain relatively reasonable agreement between calculated and observed A factors shown in the tables, conjugation of the T electrons of the carbonyl group with the forming ring of the transi-


Table X : S i x - C d e r Elimination Reactions -0bsdReaciion

$hfethyl-1,5-hexadiene + 1J-heptadiene 1,s-Heptadiene -+ $methyl1J-hexadiene 1,1,6,6-Tetradeu terio-1,5hexadiene -+ 3,3,4,4-tetrade u terio-l,5- hexadiene Hexa-l-cis-3,5-triene cyclohexa-1, %diene Vinyl allyl ether -+ allylacetaldehyde 2-llethallyl vinyl ether -P 4-methylpent-4-enal Isopropenyl allyl ether -+ ally lacetone 1-Ethylpropenylall ylmalonitrile + 1-ethyl-2-methyl4-pentenylidenemalonitrile 1-Cyclohexenylall ylmalonitrile -,2-allylcyclohexylidenemalonif rile Ethyl (1,3-dimethyl-1buteny1)allylc:yanoacetate + ethyl (1-methyl-2-isopropyl-4-pen tcny1idene)cyanoacetate cis-2-Met hylpent a-lf3-diene 4-rnethylpenta-l,$diene 4-hfethylpenta-1 ,&diene + cis-%rnethylpenta-l,3-diene 3,7-Dimethyl-l,€i-octadiene 1,2-dimeth yl-3-isopropen ylcyclopen tane -+

-CalcdLog A

Ref

LogA

E

9.84

32.5

11.3" d

9.09

32.5

ll.la d

11.1

35.5

11.1

e

11.85

29.9

11.5

f

10.9

30.6

11.1

g

11.15

29.1

11.3

h

11.7

29.3

11.3

i

10.94

25.78

11.3

j

10.8

26.16

11.3

j

10.36

28.62

10.8

j

11.24

32.76

12.3* k

11.72

36.19

12.5b k

9.06

35.2

--+

I

9.6"

a There is no reason to believe that these reactions should have A factors appreciably different from the very analogous vinyl allyl ether isomerizations or the tetradeuterio-1,5-hexadienereactions. Therefore, one would suspect that the reported parameters are in error by at least an order of magnitude. The reasons for the discrepancies between observed and calculated A factors here are riot known. It seems altogether unlikely that these 1,3-pentadienes should have A factors less than that observed for the hexa-l-cis-3,5-triene. We believe that the reported A factors are low. The calculation for the isomeriaation of 3,7-dimethyl-1,6-octadienetends to confirm this belief. See the calculation in Appendix. A. Amano and M. Uchiyama, J . Phys. Chem., 69, 1278 (1965). e V. Toscano and W. von E. Doering, unpublished work. K. E. Lewis and H. Steiner, J . Chem. SOC., 3080 (1964). F. W. Schuler and G. W. Murphy, J . A m . Chem. SOC.,72, 3155 (1950). * M. H. Frey and B. M. Pope, J. Chem. Soc., Sect. B, 209 (1966). ' L. Stein and G. W. Murphy, J . Am. Chem. Soc., 74, 1041 (1952). G. Foster, A. Cope, and F. Daniels, ibid., 69, 1893 (1947). H. M. Frey and R. J. Ellis, J . Chem. SOC., 4470 (1965). W. D. Huntsman and T . H. Curry, J . Am. Chem. SOC., 80, 2252 (1958).

'

'

'

'

29 19

tion state was assumed. Thus an additional entropy loss between 3 and 5 gibbs/mole in the transition state was rationalized. Such an interaction seems to us quite reasonable (see the Appendix and Tables VI1 and IX) . The estimated A factors for various six-center isomerizations reactions are shown in Table X. Again, agreement between calculated and observed values is very satisfactory.

Activation Energy Correlations In the last three columns of Table V and the next to the last columns of Tables VI1 and I X are listed activation energies for the elimination reactions which have been calculated from the observed rate constants and the calculated A factors. Although order-ofmagnitude variations in reported Arrhenius parameters for any given reaction are fairly common, the rate constants reported around the middle of the temperature ranges seldom differ by more than 10%. Assuming for the moment that the calculated A factors are correct to within a factor of 2 (ie., A log A = &0.3), "corrected" activation energies so obtained should then be reliable to within zkO.8 kcal/mole. Some very interesting and systematic substitution effects on the activation energies now become apparent." I n the four-center elimination for the series ethyl-X, isopropyl-X, and t-butyl-X, which represents successive alkyl substitution a t the a (to the halogen) carbon position, the respective activation energy decreases are (in kcal): X = C1, 5.3, 6.0; X = Br, 5.7, 6.0; X = I, 5.6, 6.6. Thus, to a good approximation, each alkyl substitution at the acarbon position produces an activation energy lowering of about 5.7 kcal/substitution. A similar, but smaller, activation energy reduction seems to occur with alkyl substitution at the ti-carbon position. Thus, in the series ethyl-X, n-propyl-X, and isobutyl-X, the activation energy differences are: X = C1, 2.3, 1.0; X = Br, 2.0, 1.4; or an average of 1.7 kcal/substitution. Chlorine substitution a t the a position also effects an activation energy reduction of the order of 1.5 kcal/Cl. Similar substituent effects are apparent for the activation energies of the six-center eliminations. Thus, methyl substitution at the 1-carbon position of the esters (i.e., the saturated carbon singly bonded to oxygen), as in the series ethyl, isopropyl, and t-butyl (11) These have been discussed in some detail by S. W. Benson and A. N. Bose, J. Chem. Phys., 39, 3463 (1963). See also A. Rlaccoll, Advan. Phys. Org. Chem., 3, 91 (1965), who first called attention to these large CHI effects and who also takes a more extreme point of

view in considering the transition states as ionic, rather than merely polar.

Volume 71I Number 9 August 1967

2920

acetates, appears to lower the activation energies by 3.5 and 4.7 kcal/CH3, respectively. The “corrected” formate ester activation energies for the same series differ by 3.0 and 5.5 kcal/CH3, and the ethyl and isopropyl vinyl ether activation energies differ by 3.0 kcal/ CH3 substitution. Thus, all three series-the formate and acetate esters and the vinyl ethers-show very similar substituent effects on the activation energies. Methyl substitution at a 2-carbon position (from the singly bonded oxygen) seems to lower the activation energy slightly (-0.5 kcal/CHJ. Thus, in the series isopropyl acetate, 3-pentyl acetate, and 2,4-dimethyl3-pentyl acetate, the “corrected” activation energies are 44.7, 44.1, and 43.0 kcal, respectively. Larger alkyl group substitution a t the 2-carbon position appears to be slightly more effective (Le., -1.0 kcal/ R > CH3). Thus, 2-heptyl acetate (with a C4 group substitution) and 4-heptyl acetate (with two C, substitutions) have corrected activation energies of 43.6 and 42.7 kcal/inole, respectively. It can be shown that the activation energy substituent effects noted for t,he 1- and 2-carbon positions are consistent with the “corrected” activation energies. They are also consistent with the statistical olefin product distributions observed in the inultipath ester decompositions (see Table VIII). Phenyl substitution at the l-carbon position results in an activation energy reduction larger than that produced by methyl substitution. The difference in activation energies between ethyl acetate and l-phenylethyl acetate is 4.5 kcal. Chlorine substitution at the a-carbon position also lowers the activation energy. I n the series t-butyl acetate, t-butyl chloroacetate, and t-butyl dichloroacetate, the activation energy differences are 1.9 and 1.3 kcal/Cl, respectively. Finally, substitution of an electronegative group a t the 2-carbon position seems to increase the activation energy. Thus, l-chloro-2-propyl acetate and l-methoxy-2-propyl acetate both have activation energies greater than that of isopropyl acetate. The explanation of these substituent effects has been attributed to a polar transition state1*

H. E. O’NEALAND S. W. BENSON

charge centers of the activated complex effect reductions in the activation energies relative t o the unsubstituted reactants. Substituents which destabilize the growing charge centers have the opposite effect. The sizable effects a t the l-carbon relative to the 2carbon position are consistent with the fact that stabilizations are more readily effecteda t the positive centers than a t the negative centers. We feel that the systematic effects on the activation energies by various substituents are real and inherently reasonable. The fact that they are apparent in a few systems only when the activation energies have been “corrected” seeins to provide additional evidence for the reliability of the calculated A factors and of the method for their calculation. Some discussion of the uncertainties of the A-factor calculations are worth considering. A perusal of thermodynamic tables for oscillator functions will show that high frequencies (6 > kT/hc) contribute very little to the entropy, and errors in assigning 5 of up to =t30yo contribute very little error in the total entropy. As an example, a t 600°K a 1600-cm-’ vibration contributes 0.23 gibbs/mole, while a 1200cm-1 vibration contributes 0.35 gibbs/mole. The discrepancy would lead to an error of 0.03 in log A . At low frequencies (6< kT/hc) an error of 30% in the frequency assignment will lead to an error of =t R In 1.30 = =t0.52 gibbs/mole or =kO.11 in log A . Because of this relative insensitivity of log A to frequency assignments, it is not worthwhile trying to make very precise analysis of the molecular frequencies.

Appendix Calculations of the Activation Entropies for a Few Characteristic Four- and Six-CenterReactions13 (1) Isopropyl acetate

A S *ring AS*i-rot-tt

AS Semiion-pair charge separation in the activated complex is supported by activation energy calculations of Benson and Haugen“ and by the experimental results of Smith, et at. (see footnote d, Table VIII). It is also consistent with the loose cyclic transition states proposed here. Substituents which are able to stabilize the growing The Journal of Physical Chemistrg

A S *a A&’*total

IV) = [i-Pr(l2) i-Pr(1) 4- JJe(3.5)] 4(2MB-2 i-B)$ [i-Pr(l2)] = -(9.3 9.3 6.5) (4.4 2.4) (9.3) = -9.0 = (2.3 0.1 0.7) - 2.3 = 0.8 = R In 6 = 3.6 = -2.7 gibbs/mole; A(c) N 1012.9 sec-I

= 1.9 gibbs/mole (see Table

+ +

+ + + +

+

+

+

+

(12) (a) A. Maccoll, J. Chem. SOC.,3398 (1958); (b) A. H.DePuy and R. W. King, Chem. Rev.,60, 431 (1960). (13) The numbers in parentheses after the designation of the internal rotations are the estimated barriers to rotation in kcal/mole. If not otherwise indicated, all torsions refer to 3/rorder bonds.


2921

*

(2) But-3-e ne- 1-01

(CH&OH

AS*ring

1.25 gibbs/mole AS*i-rot+t = -(Et(l) Et(4) OH(2)) (cis-2-B Et(12) P) = -(8.9 8.9 5.3) 3.5 8.9 2.1 = -8.6 = +(0.1 0.9 0.3) - 2.3 = -1.0 A s *cor AS = 0 AS*total = -8.35 gibbs/mole; A(c) = sec-l =

+

+ +

*,,

+

+

+ +

+ +

+

+

+

- (&[;)

AS*ring

= 0.5 gibbs/mole

AS*i-rot-t

= =

AS 'cor AS AS *total

*,,

+

+ +

+

-(Me(4.5 OH(3)) i-B OH(6) -(6.5 5.3) 2.4 5.3 = -4.1 = +(0.9 0.6) - 1.4 = $0.1 = R In 9 = 4.4 = +0.4 gibbs/mole; A (e) = l O I 3 e 6 sec-'

+ +

+

(6) 3,7-Dimethyl-1,g-octadiene

(3) Vinyl allyl ether

0.S gibbs/mole i-Pr(1) Et(1)) (cis-2-B cis-2-B) i-Pr(l2) = --(8.9 9.3 8.9) 3.5 3.5 9.3 -10.8 = +0.9 0.1 0.1 - 2.3 = -1.2 = 0 = -11.2 gibbs/mole; A ( c ) = lo".' sec-l

AS*ring

=

AS*i-rot+t

= -(Et(4)

A s *,,

+ +

+ + + + + + +

+

+

+

(4) 3-Butenoic acid14

The activation entropy is reasonably estimated by observing that it may be divided into two parts. First, there is the entropy loss in forming the five-membered ring which should be approximately given by the intrinsic entropy differences between n-pentane and cyclopentane

c

--t

0

~ s ~ ~ , ~ = 7 4 . 6 - 8=9 .-13.5gibbS/mole 1

Second, there is the entropy of activation for the formation of the loose six-centered ring. This should be given by the entropy loss in activation for the isomeriwhich is calculated zation of 4-1nethylpenta-l,3-diene, to be

c - *ti

A S f = -4.5 gibbshole

AS*ring

=

AS*i-rot+t

=

0.7 gibbs/mole -(Et(l) i-Pr(0) OH(12)) (cis-2-B i-Ble 2JIB-2) = --(8.9 9.3 5.3) (3.5 2.4 1.4) = -14.2 = -(0.1 2.3) = 2.4

+

AS *cor AS

*,,

=o

AS*total (5)

=

+ +

+ + + +

+

+

+

+

--11.1 gibbs/mole; A(c) = lo".' sec-'

&Butyl &0h01

Thus we estimate AS *total = - 18.0 gibbs/mole, which gives an A factor of A = 109.6sec-l (Ao = 109.06 sec-1). It is quite likely that some of the 5.4 gibbs/niole of pseudo-rotation in the five-membered ring is also lost. The A factor would then be lower and be in better agreement with that observed. (14) Notice carbonyl conjugation is taken as a maximum interaction. The calculated A factor then, should be nearly a minimum value.

Volume 71, Number 9 Aupat 1967

and SixXenter Unimolecular Reactionsla

Recommend Documents