69 Photo-Oxygenation of Mono-Olefins Reaction Steps Involving the Olefin FRED
A.
LITT
and
ALEX
NICKON
Enjay Additives Laboratory, L i n d e n , N. J., and T h e Johns Hopkins University, Baltimore, M d .
Early studies on photosensitized oxygenation of mono-olefins have shown the non-involvement of mesomeric allylic intermediates, based on the shifting of the position of the double bond during reaction. In this work, six other intermediates, all involving preliminary formation of the C—O bond are considered. Data from the literature are used to disprove formation of some of these, and data are presented ruling out the others. The reaction steps involving the olefin are thus shown to be concerted.
All p r i m a r y p r o d u c t s i s o l a t e d f r o m olefin photo-oxygenations
contain
the u n s a t u r a t i o n i n a p o s i t i o n adjacent to the o r i g i n a l p o s i t i o n , as i l l u s -
^ C — C p = C
3
^
"
^
l
C
H
=
2 ~ ~ ^
C
HOO
Figure 1. Primary products from olefin photo-oxygenations, showing unsaturation in position adjacent to original position t r a t e d i n F i g u r e 1. M e s o m e r i c a l l y l i c intermediates, s u c h as 1, are there-
C
1
C
2
C —^ 3
1 fore p r e c l u d e d . A p a r t i c u l a r l y elegant e x a m p l e of this r u l e is t h e p h o t o o x y g e n a t i o n of o p t i c a l l y active l i m o n e n e ( 2 ) . O n e p r o d u c t of this 118
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r e a c t i o n , after r e d u c t i o n , is trans-carweol
2
(3), w h i c h has the absolute
3
stereochemistry i n d i c a t e d , r u l i n g out i n t e r m e d i a c y of species s u c h as the a l l y l i c free r a d i c a l , 4 (8, 9 ) .
4 T h e p h o t o s e n s i t i z e d o x y g e n a t i o n of t h e c h o l e s t e r o l - 7 - d i
molecules
c o n t a i n i n g e p i m e r i c isotopic labels ( 5 a a n d 5 b ) has d e m o n s t r a t e d t h e c y c l i c n a t u r e of t h e r e a c t i o n ; the C — H or C — D b o n d b r o k e n w a s a l w a y s
5a: R = H , R = D 5b: R = D, R = H t
2
x
2
6a: = H 6b: R = D x
the b o n d o n t h e a side of the steroid skeleton, cis to t h e C — O b o n d f o r m e d (11).
A t the time, h o w e v e r , n o conclusions r e g a r d i n g the t i m i n g
of t h e f o r m a t i o n of the C — O a n d O — H b o n d s c o u l d b e d r a w n . T h e species that reacts w i t h the olefin has b e e n v a r i o u s l y c i t e d as singlet o x y g e n a n d as a c o m p l e x b e t w e e n o x y g e n a n d sensitizer. W e find o n l y six reasonable w a y s to c o m b i n e a n olefin w i t h singlet o x y g e n . T h e s e
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possible intermediates are s h o w n i n F i g u r e 2. T h e sensitizer, i f still present, c o u l d b e c o n s i d e r e d b o u n d to the o x y g e n i n some m a n n e r . W h i l e t h e first five intermediates, 7 t h r o u g h 11, c o u l d b e c o n s i d e r e d extreme forms of a resonance h y b r i d , w e are o b l i g e d to consider these structures separately, l a c k i n g a priori i n f o r m a t i o n o n t h e relative c o n t r i b u t i o n s of these forms.
7
10
Figure 2.
8
11
Possible intermediates olefin
9
12
in photo-oxygenation
of
Intermediate 7 w a s first p r o p o s e d b y D . B . S h a r p (14) a n d n a m e d b y h i m a " p e r e p o x i d e . " T h e f o l l o w i n g discussion, r e g a r d i n g the p h o t o o x y g e n a t i o n of a s i m p l e t r i s u b s t i t u t e d olefin, shows that the l i k e l i h o o d of i n v o l v e m e n t of this i n t e r m e d i a t e is s m a l l . I n the p h o t o - o x y g e n a t i o n of a t r i s u b s t i t u t e d olefin, s u c h as t r i m e t h y l ethylene ( 1 3 ) , t w o perepoxides are p o s s i b l e — a si/n-perepoxide ( 1 4 ) , a n d a n a n f i - p e r e p o x i d e ( 1 5 ) — a s s h o w n i n F i g u r e 3. W h i l e 14 c o u l d give either the tertiary h y d r o p e r o x i d e 16 or the secondary h y d r o p e r o x i d e 17, p e r e p o x i d e 15 c o u l d o n l y y i e l d 17. Statistically, therefore, o n l y onef o u r t h of the olefin u n d e r g o i n g r e a c t i o n w o u l d g i v e 16. I n r e a c t i o n of 13, t h e p r e d o m i n a t i n g p e r e p o x i d e s h o u l d b e 15, f o r steric reasons. F u r thermore, i n the r e a c t i o n of 14, i f there is a n y p a r t i a l p o s i t i v e charge o n the oxirane c a r b o n , 17 w o u l d p r e d o m i n a t e since t h e p a r t i a l positive c h a r g e w o u l d b e at a tertiary center rather t h a n a secondary one, as f o r the f o r m a t i o n of 16. T h e r e f o r e the statistical result above is the u p p e r l i m i t r e q u i r e d b y this m e c h a n i s m . T h e o b s e r v e d result w a s that t h e t w o h y d r o p e r o x i d e s w e r e f o r m e d i n e q u a l y i e l d s (8, 9 ) . T h e p h o t o - o x y g e n a t i o n of t r i s u b s t i t u t e d olefins other t h a n 13 t y p i c a l l y also gives n e a r l y
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Mono-Olefins 0" 00H
Figure 3.
Mechanism for photo-oxygenation
of a trisubstituted
e q u a l y i e l d s of secondary a n d tertiary h y d r o p e r o x i d e s ( 1 ) .
olefin
Involvement
of p e r e p o x i d e intermediates is not, therefore, l i k e l y . A n u m b e r of studies h a v e s h o w n that i n c r e a s i n g a l k y l s u b s t i t u t i o n of the d o u b l e b o n d facilitates the r e a c t i o n (9, 10, 14).
I n t e r m e d i a c y of
10 is, therefore, p r e c l u d e d since it requires the opposite substituent effect. N o r b o r n e n e ( 1 8 ) p r o v e d to b e a u s e f u l substrate i n testing for inter mediates 8 a n d 9. T h e b r i d g e h e a d h y d r o g e n s are k e p t f r o m p a r t i c i p a t i n g b y the consequent r u l e ) (7).
i n t r o d u c t i o n of a b r i d g e h e a d d o u b l e b o n d
(Bredt's
T h e olefinic l i n k a g e i n n o r b o r n e n e has b e e n s h o w n to b e at
least as reactive to a v a r i e t y of reagents as that of a n a c y c y l i c or m o n o c y c l i c olefins (6).
T h e dioxetane i n t e r m e d i a t e , 19, if f o r m e d w o u l d b e
c a p a b l e of g i v i n g d s - l , 3 - d i f o r m y l c y c l o p e n t a n e , 20.
T h e z w i t t e r i o n inter
m e d i a t e , 2 1 , if f o r m e d , w o u l d be c a p a b l e of g i v i n g a n y of a host
of
u l t i m a t e p r o d u c t s , t h r o u g h skeletal rearrangements c u s t o m a r i l y associated w i t h the 2 - n o r b o r n o n i u m i o n system
(12).
T h e s e r e a c t i o n paths
are
s h o w n i n F i g u r e 4. W i t h these possibilities i n m i n d w e a t t e m p t e d the p h o t o - o x y g e n a t i o n of n o r b o r n e n e .
W i t h either m e t h y l e n e b l u e or h e m a t o p o r p h y r i n as sen
sitizer a n d m e t h a n o l or p y r i d i n e as solvent, w e o b t a i n e d no e v i d e n c e of a n y r e a c t i o n b y i n f r a r e d or N M R s p e c t r u m , b y gas c h r o m a t o g r a p h y , or b y spot test for h y d r o p e r o x i d e ( p o t a s s i u m i o d i d e / s t a r c h i n 2 - p r o p a n o l / acetic a c i d ) or p e r o x i d e ( h y d r i o d i c a c i d / s t a r c h i n 2 - p r o p a n o l ) .
While
the h a l f - l i f e of r e a c t i o n of cyclohexene was o n l y a b o u t one d a y u n d e r our r e a c t i o n c o n d i t i o n s , no e v i d e n c e of r e a c t i o n of n o r b o r n e n e w a s o b t a i n e d i n a p e r i o d of one m o n t h . A s s a y of n o r b o r n e n e b y gas c h r o m a t o g r a p h y w i t h b e n z e n e as i n t e r n a l s t a n d a r d f a i l e d to s h o w a n y d e p l e t i o n of n o r b o r n e n e over the a t t e m p t e d r e a c t i o n i n t e r v a l . W h i l e w e f o u n d no e v i d e n c e of a n y r e a c t i v i t y of n o r b o r n e n e ,
the
relevant p o i n t is that the r e a c t i v i t y , if existent, is at least f o u r orders of m a g n i t u d e l o w e r t h a n that of cyclohexene, a s i m i l a r l y s u b s t i t u t e d olefin c o n t a i n i n g reactive
allylic hydrogens.
W e therefore
find
that the d i -
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Figure 4.
Reaction paths in the photo-oxygenation
oxetane a n d z w i t t e r i o n intermediates
III
OOH
of
norbornene
8 a n d 9, d o not c o n t r i b u t e signifi
c a n t l y to the p h o t o - o x y g e n a t i o n p a t h of " r e a c t i v e "
olefins.
T h e possible i n v o l v e m e n t of singlet d i r a d i c a l 11 o r triplet d i r a d i c a l 12 w a s tested b y s t u d y i n g t h e p h o t o - o x y g e n a t i o n
of various
cis-trans
olefin pairs as f o l l o w s . F i g u r e 5 indicates a p o t e n t i a l scheme f o r p h o t o -
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Mono-Olefins
o x y g e n a t i o n of a 1,2-disubstituted
olefin.
( T h e scheme w o u l d a p p l y to
r e a c t i o n of a n u n s y m m e t r i c a l t r i - or tetrasubstituted olefin as w e l l . )
The
i m p o r t a n t feature of this sequence is t h e presence of a single b o n d i n the p o s i t i o n of the o r i g i n a l d o u b l e b o n d .
R o t a t i o n a r o u n d this
single
b o n d converts d i r a d i c a l 2 2 , p r o d u c e d b y a d d i t i o n of o x y g e n to t h e cis olefin, to 2 3 , that p r o d u c e d f r o m the trans olefin. If these intermediates w e r e f o r m e d r e v e r s i b l y , the geometric isomers of the olefin w o u l d interconvert d u r i n g r e a c t i o n . W e felt it best to select a n u n r e a c t i v e olefin p a i r f o r this s t u d y since the r e d u c e d r e a c t i v i t y c o u l d reflect the slowness of the final step a n d m a x i m i z e the i s o m e r i z a t i o n p o s s i b i l i t y . T h e c y c l o d o d e c e n e isomers w e r e
Figure 5.
Potential scheme for photo-oxygenation olefin
of a
1,2-disubstituted
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H I
U n d e r the c o n d i t i o n s i n w h i c h cyclohexene r e a c t e d w i t h
a o n e - d a y h a l f - l i f e , t h e h a l f - l i f e o f Jrans-cyclododecene
photo-oxygenation
was about 3 weeks. T h e trans isomer, 24, w a s a b o u t three times as reactive as t h e cis isomer 2 5 . Samples of the c y c l o d o d e c e n e s , separated f r o m a
24
25
c o m m e r c i a l m i x t u r e b y p r e p a r a t i v e gas c h r o m a t o g r a p h y , w e r e separately p h o t o - o x y g e n a t e d w i t h m e t h y l e n e b l u e as sensitizer. A l t h o u g h t h e detec t i o n l i m i t of t h e isomer of the starting o l e f i n w a s less t h a n 1 % , r e l a t i v e to the starting isomer, i n n o case w a s i s o m e r i z a t i o n detected. Since i t w a s d e s i r a b l e to i n c l u d e a n o l e f i n w i t h a p a r t i c u l a r l y large d r i v i n g force t o w a r d i s o m e r i z a t i o n w e chose c a r y o p h y l l e n e ( 2 6 ) .
The
frans-cyclononene l i n k a g e of c a r y o p h y l l e n e is r e a d i l y i s o m e r i z e d b y r a d i cals s u c h as t h e n i t r o g e n oxides ( 4 ) . isomerization was apparent. w o u l d have been detected
E v e n i n this case, h o w e v e r , n o
W e c o n f i r m e d that i s o c a r y o p h y l l e n e
26 formed.
(27)
under the reaction conditions h a d it been
27
W e f u r t h e r f o u n d that c a r y o p h y l l e n e w a s a b o u t five times as
reactive as i s o c a r y o p h y l l e n e , a n d therefore, i f i s o c a r y o p h y l l e n e h a d b e e n f o r m e d , i t w o u l d h a v e persisted f o r d e t e c t i o n . T o extend the g e n e r a l i t y of these results, w e e x a m i n e d the p h o t o oxygenation
of trans,
trans,
£rans-l,5,9-cyclododecatriene
28
29
(28).
The
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m o n o i s o m e r i z e d m a t e r i a l ( 2 9 ) f a i l e d to a p p e a r d u r i n g reactions.
Exami
n a t i o n of the p h o t o - o x y g e n a t i o n of b o t h g e o m e t r i c a l isomers of 4 - m e t h y l 2-pentene a n d 2-octene ( 3 0 t h r o u g h 3 3 ) f a i l e d to s h o w i s o m e r i z a t i o n i n these cases.
30
31
32
33
Q u a n t i t a t i v e l y , unless the p h o t o - o x y g e n a t i o n rate of the isomer n o t i n i t i a l l y present is n e g l i g i b l e c o m p a r e d w i t h t h e p h o t o - o x y g e n a t i o n rate of t h e starting isomer, the d e t e c t i o n l i m i t of t h e i s o m e r i z a t i o n rate constant (as a f r a c t i o n of t h e rate constant f o r p r o d u c t f o r m a t i o n ) is greater t h a n that f o r the isomer i n i t i a l l y absent since, i f f o r m e d , some of the latter w o u l d react b e f o r e detection.
T o evaluate
the d e t e c t i o n l i m i t of the
i s o m e r i z a t i o n rate constant, the d e t a i l e d scheme of F i g u r e 5 is s i m p l i f i e d to give t h e scheme o f F i g u r e 6.
Figure 6.
Simplified scheme for photo-oxygenation a 1,2-disubstituted olefin
of
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R a t e constants i n F i g u r e 6 are r e l a t e d to those i n F i g u r e 5 b y t h e following equations:
* i = j ^ - J [*.*»(*. +
**=
(i)
[*.*-.*.,]
* [i]
k
+ **) + hk.M
=
+
(2)
»)
k
W » ]
+
(4)
where T h e details of this d e r i v a t i o n , b a s e d o n the steady-state a p p r o x i m a t i o n f o r the d i r a d i c a l intermediates, are f o u n d i n the A p p e n d i x . T h e d e r i v a t i o n of the i s o m e r i z a t i o n rate constant u p p e r l i m i t expres s i o n is as f o l l o w s . F o r definiteness, assume the starting isomer to h a v e the trans c o n f i g u r a t i o n . U n d e r the h i g h d i l u t i o n c o n d i t i o n s w i t h these r e l a t i v e l y u n r e a c t i v e d i s u b s t i t u t e d olefins w e f o u n d the p h o t o - o x y g e n a t i o n to p r o c e e d b y pseudo-first-order kinetics.
T h e rates of change
concentrations of t h e t w o isomers are g i v e n b y E q u a t i o n s 5 a n d 6. dT/dt=-(k + fc )T + k C 4
s
dC/dt=-(k
2
+ k )C
1
(5) (6)
+ hj
2
of t h e
w h e r e C a n d T represent the concentrations of the cis a n d trans isomers, r e s p e c t i v e l y , a n d t is t i m e . Since t h e experiment shows that fc
4
c o m p a r a b l e w i t h fc , it f o l l o w s that k C 4
2
>>
x
2
T since C <
> k , the latter 2
d i f f e r e n t i a l e q u a t i o n is s o l v e d w i t h the i n i t i a l c o n d i t i o n C
0
=
0 to give
E q u a t i o n 9. C =
[exp
(-M)
- exp
(-M)]
(9)
O n e u n f o r t u n a t e aspect of these l o n g - d u r a t i o n photo-oxygenations is that the sensitizer b l e a c h e d at a significant rate d u r i n g the r e a c t i o n a n d h a d to b e r e p l e n i s h e d at intervals. It w a s desirable, therefore, to e l i m i -
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nate t i m e as a v a r i a b l e i n E q u a t i o n 9. I n v e r s i o n of E q u a t i o n 8 expresses the t i m e as a f u n c t i o n of t h e c o n c e n t r a t i o n of the trans olefin, a n d E q u a t i o n 10 results f r o m thus s u b s t i t u t i n g E q u a t i o n 8 i n t o E q u a t i o n 9. C = ^ [ ( T / T
0
)
-
(T/T ) 10
F o r frans-cyclododecene t u m y i e l d m a y b e estimated c o n d i t i o n s , photo-oxygenates
1 1
2 1
^
2
mole/
for 0 ( % ) . +
2
( 2 4 ) , t h e o r d e r of m a g n i t u d e o f t h e q u a n as f o l l o w s .
Cholesterol, under identical
100-200 times as fast as 2 4 . E i s f e l d has
s h o w n that cholesterol photo-oxygenates
at about 1/40 t h e rate of 2,5-
d i m e t h y l f u r a n ( 5 ) , w h i c h i n t u r n has b e e n s h o w n t o photo-oxygenate w i t h a q u a n t u m y i e l d of t h e order of 0.5 ( 9 ) . T h e q u a n t u m y i e l d of frarw-cyclododecene p h o t o - o x y g e n a t i o n is thus about 10" at t h e c o n c e n 4
t r a t i o n s t u d i e d , a b o u t 10~ moles/liter. 2
Schenck a n d K o c h have shown
that t h e species that reacts w i t h t h e olefins decays w i t h a rate constant of a b o u t 1 0 s e c . (13). 8
liters/mole-sec.
1
T h e v a l u e of h
f o r 2 4 therefore is a b o u t 1 0
T h e r e f o r e , f o r t h e *A a n d g
states of o x y g e n , k
s
6
^
130 10
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OXIDATION
and 10
sec." , respectively.
1 8
1
O F ORGANIC
COMPOUNDS
T h e s e are, of course,
E y r i n g ' s transition-state v i b r a t i o n a l f r e q u e n c y kT/h. t i o n o f d i r a d i c a l s is, therefore, i m p o s s i b l e .
III
greater t h a n
Irreversible f o r m a
W e therefore c o n c l u d e that
the r e a c t i o n of the olefin is c o n c e r t e d . S u p p o r t i n g e v i d e n c e against i r r e v e r s i b l e i n t e r m e d i a t e f o r m a t i o n is f o u n d i n some u n p u b l i s h e d studies b y H . G . V i l h u b e r ( 1 5 ) , E . W e r s t i u k (16), a n d V . C h u a n g ( 3 ) o n the p r i m a r y d e u t e r i u m isotope effect. P r i m a r y isotope effects of 1.2 t o 2.1 w e r e d e t e r m i n e d f o r d e u t e r a t e d olefins 3 4 - 3 6 . D
D
H ) 2
D*
D
2
2
34
i
k
C H
H
CH
3
3
CD
CH
H
3
CD
3
3
CD ^
3
CH
CH
H
3
3
CD CD -v-
35
3
3
CD
3
C H CH
3
36
P a r t i c i p a t i o n o f t h e h y d r o g e n ( o r d e u t e r i u m ) d u r i n g the r a t e - d e t e r m i n i n g r e a c t i o n is thus i n d i c a t e d since, as s h o w n earlier, the O — H b o n d c o u l d not b e f o r m e d p r i o r to f o r m a t i o n of t h e C — O b o n d .
Experimental Photo-oxygenations w e r e p e r f o r m e d i n a t u b u l a r apparatus p r e v i o u s l y r e p o r t e d ( 4 ) . I n t h e p h o t o - o x y g e n a t i o n of the m o r e v o l a t i l e olefins ( 3 0 t h r o u g h 3 3 ) , the solvent w a s saturated w i t h o x y g e n b e f o r e d i s s o l u t i o n of the olefin, a n d n o o x y g e n w a s a d m i t t e d d u r i n g i r r a d i a t i o n . I n the p h o t o o x y g e n a t i o n of t h e slower olefins ( 2 4 , 2 5 , 2 8 ) a 500-watt slide projector was u s e d i n c o n j u n c t i o n w i t h a flat-sided c e l l a n d a c a p i l l a r y b u b b l e r . P r e p a r a t i v e gas c h r o m a t o g r a p h y w a s u s e d to separate the c y c l o d o d e c e n e isomers. A n A e r o g r a p h A - 7 0 0 i n s t r u m e n t w i t h a 20-foot X 3/8 i n c h d i e t h y l e n e g l y c o l succinate polyester c o l u m n at 160 ° C . w a s u s e d . T h e c r u d e fractions w e r e r e c h r o m a t o g r a p h e d to o b t a i n samples of ca. 99.8% purity. cis-2-Octene ( 3 3 ) w a s p u r i f i e d b y p r e p a r a t i v e gas c h r o m a t o g r a p h y i n the same i n s t r u m e n t w i t h a 12 foot X 1/4 i n c h silver n i t r a t e / d i e t h y l e n e g l y c o l c o l u m n at r o o m temperature. T h e p u r i t y of the p r o d u c t w a s ca. 99.9%. trans, trans, tfrans-l,5,9-Cyclododecatriene ( 2 8 ) was isolated b y par t i a l f r e e z i n g of the c o m m e r c i a l m i x t u r e of isomers a n d r e c r y s t a l l i z i n g the solid product from methanol. T h e c a r y o p h y l l e n e ( 2 6 ) u s e d c o n t a i n e d about 3 % i s o c a r y o p h y l l e n e ( 2 7 ) ( w e are i n d e b t e d to D r . J . R o b e r t s f o r s u p p l y i n g this s a m p l e ) . A t t e m p t s to r e m o v e this i m p u r i t y b y p r e p a r a t i v e gas c h r o m a t o g r a p h y l e d to n o i m p r o v e m e n t . O t h e r olefins w e r e c o m m e r c i a l samples of > 9 9 % purity. Reactions w e r e m o n i t o r e d b y gas c h r o m a t o g r a p h y . C y c l o d o d e c a n e w a s u s e d as i n t e r n a l s t a n d a r d f o r olefins 2 4 t h r o u g h 29 o n a P e r k i n - E l m e r m o d e l 226 i n s t r u m e n t w i t h a 9 foot X 1 / 8 i n c h d i e t h y l e n e g l y c o l succinate
69.
LITT
Mono-Olefins
A N D NICKON
131
polyester c o l u m n at 150 ° C . B e n z e n e w a s u s e d as i n t e r n a l s t a n d a r d i n t h e p h o t o - o x y g e n a t i o n of 18 a n d 30 t h r o u g h 33 o n a n A e r o g r a p h i n s t r u m e n t w i t h a 10 foot X 1/8 i n c h silver n i t r a t e / d i e t h y l e n e g l y c o l c o l u m n at r o o m temperature.
Acknowledgments W e gratefully acknowledge
financial
tutes of H e a l t h ( G r a n t G M 0 9 6 9 3 ) .
support b y the N a t i o n a l Insti
T h e w o r k w a s c o n d u c t e d at T h e
Johns H o p k i n s U n i v e r s i t y .
Literature Cited
(1) Benson, S. W., J. Am. Chem. Soc. 87, 972 (1965). (2) Calvett, J. G., Pitts, Jr., J. N., "Photochemistry," p. 91, Wiley, New York, 1966. (3) Chuang, V., Nickon, A., unpublished results. (4) Deussen, E., Lewinsohn, A., Ann. 356, 20 (1907). (5) Eisfeld, W., Ph.D. Dissertation, Göttingen, 1965. (6) Eliel, E. L., "Stereochemistry of Carbon Compounds," p. 303, McGrawHill, New York, 1962. (7) Fawcett, F. S., Chem. Rev. 47, 219 (1950). (8) Foote, C. S., Wexler, R., Ando, W., Tetrahedron Letters 46, 4111 (1965). (9) Gollnick, K., Schenck, G. O., Pure Appl. Chem. 9, 507 (1964). (10) Kopecky, K. R., Reich, H. J., Can. J. Chem. 43, 2265 (1965). (11) Nickon, A., Bagli, J. F., J. Am. Chem. Soc. 83, 1498 (1961). (12) Sargent, G. D., Quart. Rev. 20, 301 (1966). (13) Schenck, G. O., Koch, E., Z. Electrochem. 64, 170 (1960). (14) Sharp, D. B., "Abstracts of Papers," 138th Meeting, ACS, Sept. 1960, 79P. (15) Vilhuber, H. G., Nickon, A., unpublished results. (16) Werstiuk, E., Nickon, A., unpublished results. RECEIVED
February 5, 1968.
Appendix Simplification of isomerization kinetics: T h e c o m p l e t e k i n e t i c scheme f o r i s o m e r i z a t i o n a n d r e a c t i o n is s h o w n i n F i g u r e 5. A s s u m i n g l a n d I* are at steady-state c o n c e n t r a t i o n s : 0
d(l )/dt
= 0=k C
d(l )/dt
= 0 = kT + k\
c
t
a
c
+ kl e
e
- k l
t
a
c
- k l c
- k l
c
e
t
- kl e
t
c
- kl
c
(A-l)
- k l,
(A-2)
b
d
t
w h e r e t is t i m e , C a n d T represent cis a n d trans olefins, I a n d I* represent the intermediates, a n d a l l k's are pseudo-first-order rate constants. c
132
OXIDATION
O F ORGANIC
COMPOUNDS
III
Rearranging Equations A - l and A - 2 U*-a +
+ h) + (-k )I e
t
0
9
d
e
(A-3)
= k T.
(A-4)
a
I (k_ + k + k ) + (-k_ )I t
= k C. c
c
S o l v i n g E q u a t i o n s A - 3 a n d A - 4 s i m u l t a n e o u s l y f o r I a n d I* c
kaP(k_ + k c
+
e
+ &&T c
,
e
^
(*_ +fc_ + * )(fc + *-c + *d) - M . a
e
j
&
c
e
+ fc. + fc ) + k k_ C
k T(k.
e
a
b
a
(A6)
e
+ * ) - M-e
^' '
k k (k +fc_ + k ) + (k k_ k ) (k_ + &_ + (fc_ + fc + — k k.
^ ^^
' ~ (*.. +
+ * ) (* + k. 6
e
d
c
Defining ^
a
b
c
e
d
e
a
a
c
e
d
e
e
e
k k_ k_ n
e
a
*» =
6
c
e
k k.
d
e
kj^ek., , ? r ^ (k_ + k_ + & ) (fc_ + k + a
^
k k (k_ ^-e c
(^-a
&
e
d
e
(A-8)
P
(k_ + &_ + fc ) (fc. + & + k )
c
e
— & fc_ e
e
(A-9) e
H~fc_ + + (k k k ) k ) (k_ -\- k -\- k ) — k k_ a
b
c
c
e
e
d
(A-10)
b
e
e
T h e d e t a i l e d system is k i n e t i c a l l y e q u i v a l e n t t o t h e s i m p l i f i e d system o f F i g u r e 6, dQ/dt=-(k + k )C + fc T (A-ll) x
3
2
+ fc )T +
dT/dt=-(k
4
s
fc C 2
(A-12)
as m a y b e v e r i f i e d b y s u b s t i t u t i n g E q u a t i o n s A - 5 t h r o u g h A - 1 0 into t h e k i n e t i c l a w f o r F i g u r e 5, w h i c h is dC/dt=-k C
+ kI
a
a
dT/dt = -k T c
+ kl
c
c
t
