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UBC Theses and Dissertations

Reactions in frozen solutions Kiovsky, Thomas Elstun 1966

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The U n i v e r s i t y o f B r i t i s h  Columbia  FACULTY OF GRADUATE STUDIES. PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY OF  THOMAS ELSTUN KIOVSKY  B . A . / U n i v e r s i t y o f C o l o r a d o , 1962 M.Sc,  U n i v e r s i t y o f B r i t i s h Columbia, 1965  THURSDAY, JANUARY 5, 1967 at.3:30 P.M. IN ROOM 261, CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman: B.A. D u n e l l R= S t e w a r t R.E. P i n c o c k  I . McT. Cowan '"  E. P i e r s G.B. P o r t e r G.M. Tener  E x t e r n a l Examiner: S. Y. Wang Department o f C h e m i s t r y Johns H o p k i n s . U n i v e r s i t y B a l t i m o r e , Maryland Research Supervisor:  R„ E. P i n c o c k  REACTIONS IN FROZEN SOLUTIONS Abstract In o r d e r  t o t r y t o e x p l a i n some of the r a t h e r  suprising features four d i f f e r e n t are  of r e a c t i o n s  i n frozen  systems are e x t e n s i v e l y  studied,,  the r e a c t i o n of methyl i o d i d e w i t h  to form the q u a t e r n a r y ammonium  salt  solutions, They  triethylamine  i n frozen  ben-  zene, the base c a t a l y z e d d e c o m p o s i t i o n o f t^-butylperoxy formate i n f r o z e n p_-xylene to g i v e J : - b u t y l a l c o h o l and carbon d i o x i d e ,  the r e a c t i o n of  c h l o r o h y d r i n w i t h h y d r o x i d e i o n to form  ethylene  ethylene  o x i d e i n f r o z e n aqueous s o l u t i o n and the mutarotat i o n of g l u c o s e i n ice„  In a d d i t i o n a demonstration  experiment i s p r e s e n t e d i n which i o d i d e i o n i s o x i d i z e d to i o d i n e by a r s e n i c a c i d i n f r o z e n aqueous s o l u t i o n . Several  new f e a t u r e s  s o l u t i o n s are r e p o r t e d ,  of reactions  i n frozen  i n c l u d i n g a maximum i n the  r a t e - t e m p e r a t u r e dependence c u r v e , r a t e enhancements as  l a r g e as 1 0 0 0 - f o l d o v e r r e a c t i o n i n u n f r o z e n s o l u -  t i o n s and s h i f t s  i n the e q u i l i b r i u m position,,  K i n e t i c e q u a t i o n s are developed which c o r r e l a t e all  of the r e s u l t s and which a l s o e x p l a i n some o f the  observations are  of other  investigators<,  based upon the assumptions t h a t  tion containing  reactive species  These e q u a t i o n s (1) when a s o l u -  i s f r o z e n a l l o f the  r e a c t a n t s as w e l l as any o t h e r s o l u t e s p r e s e n t are r e j e c t e d : by the c r y s t a l l i z i n g  s o l v e n t and  are c o n c e n t r a t e d  into  regions  j  which remain l i q u i d  and  m a l l y i n these r e g i o n s ,  t h a t (2) The  the r e a c t i o n proceeds  nor-  fundamental e q u a t i o n used f o r  c o r r e l a t i n g the r a t e data f o r the second-order  reactions  studied i s , x  V where  dm  A  =  kA B h  h  dt  h  i s the t o t a l volume of the l i q u i d r e g i o n s , m^  is  the t o t a l moles of r e a c t a n t A p r e s e n t i n the system a t time  and  Aft and  are the c o n c e n t r a t i o n s of the r e a c t a n t s  A and B i n the l i q u i d The  regions.  i d e a s developed  f o r the treatment  of r e a c t i o n s i n  f r o z e n s o l u t i o n s are extended to r e a c t i o n s i n o r g a n i c which have melted qualitatively solid  phase p r e s e n t .  The  of 5-norbornene-2,3-endo-dicarboxylic  and  accounts  a p p l i c a t i o n of the method to the  the ex6-i.somer a l l o w s the melt  T h i s treatment  solids  f o r the o b s e r v a t i o n s made on m u t a r o t a t i o n  glucose.  ization  any  i n the  s e p a r a t i o n of c o n c u r r e n t  solid.  in  isomer-  anhydride  to  reactions i n  GRADUATE STUDIES Organic  F i e l d o f Study:  Chemistry Jo Po Kutney  Seminar i n C h e m i s t r y Topics i n P h y s i c a l Chemical  Jo A, Ro Coope Ao V Bree  Chemistry  0  G„ Bo P o r t e r Do G„ L„ James  Kinetics  Wo Ro C u l l e n R„ C„ Thompson No B a r t l e t t  Topics i n Inorganic Chemistry  Ro E„ P i n c o c k R„ Stewart Do E „ G r e e r  P h y s i c a l O r g a n i c Seminar  P h y s i c a l Organic  Ro  Chemistry  O r g a n i c R e a c t i o n Mechanisms  Stewart  R. E . P i n c o c k  Organic Synthesis  Eo  Piers  PUBLICATIONS Bimolecular Reactions i n Frozen Organic S o l u t i o n s , R E. P i n c o c k and T, E K i o v s k y , Jo Am. Chem. Soc.'87_, 2072 (1965) 0  0  Base C a t a l y z e d D e c o m p o s i t i o n o f t > B u t y l p e r o x y Formate i n F r o z e n p_-Xylene, R„ E P i n c o c k and To E. K i o v s k y , i b i d . , 8 7 , 4100 (1965) 9  Reaction of Methyl Iodide w i t h Triethylamirie i n F r o z e n Benzene, R E P i n c o c k and T E K i o v s k y , i b i d . , 8 8 , 51 (1966) 0  0  0  0  The R e a c t i o n of E t h y l e n e C h l o r o h y d r i n w i t h H y d r o x y l I o n i n I c e , R E. P i n c o c k , and To E. 'Kiovsky, i b i d . , 8 8 , 4455 (1966) 0  Publications  5o  continued  The M u t a r o t a t i o n o f Glucose i n I c e , T E K i o v s k y and R E» P i n c o c k , ibid,,88^, 4704 0  0  3  (1966)  6o  K i n e t i c s of Reactions i n Frozen Solutions, R E , P i n c o c k and T E K i o v s k y J Chem. Educo 4 3 , 358 ( 1 9 6 6 ) 0  7.  0  c  0  D e m o n s t r a t i o n of a R e a c t i o n i n F r o z e n Aqueous S o l u t i o n , To E K i o v s k y and R„ E„ P i n c o c k , i b i d . , 4 3 , 361 ( 1 9 6 6 ) 0  8.  Thermal M u t a r o t a t i o n i n P o l y c r y s t a l l i n e . c<-D-Glucose, 'R E P i n c o c k , and T„ E . K i o v s k y , Chem. Comm., 1 9 6 6 , 864 0  0  REACTIONS INisFROZEN SOLUTIONS  by  THOMAS ELSTUN KIOVSKY  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department of CHEMISTRY  We accept t h i s t h e s i s as conforming t o t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA December, 1966  In presenting  this thesis  i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s  f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t t h e L i b r a r y s h a l l , make i t f r e e l y a v a i l a b l e study,  I f u r t h e r agree t h a t p e r m i s s i o n - f o r  f o r reference  and  extensive copying o f t h i s  t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r ' b y h i s r e p r e s e n t a t i v e s .  I t i s understood that  copying  or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  permission.  Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver Q, Canada  ABSTRACT Supervisor:  Dr. R. E. P i n c o c k  In o r d e r t o t r y t o e x p l a i n some o f t h e r a t h e r s u r p r i s i n g f e a t u r e s o f r e a c t i o n s i n f r o z e n s o l u t i o n s , f o u r d i f f e r e n t systems a r e e x t e n s i v e l y  studied.  They a r e the r e a c t i o n o f methyl i o d i d e w i t h t r i e t h y l a m i n e t o form t h e q u a t e r n a r y ammonium s a l t i n f r o z e n benzene, t h e base c a t a l y z e d d e c o m p o s i t i o n o f t ^ - b u t y l peroxy formate t o carbon d i o x i d e and t > b u t y l a l c o h o l i n f r o z e n p_-xylene, t h e r e a c t i o n o f ethylene  c h l o r o h y d r i n w i t h h y d r o x i d e i o n t o form e t h y l e n e  i n f r o z e n aqueous s o l u t i o n and t h e m u t a r o t a t i o n  o f glucose i n i c e .  oxide  In  a d d i t i o n , a d e m o n s t r a t i o n experiment i s p r e s e n t e d i n which i o d i d e i o n i s o x i d i z e d t o i o d i n e by a r s e n i c a c i d i n f r o z e n aqueous s o l u t i o n . S e v e r a l new f e a t u r e s o f r e a c t i o n s i n f r o z e n s o l u t i o n s a r e r e p o r t e d ; i n c l u d i n g a maximum i n . t h e r a t e - temperature dependence c u r v e , r a t e enhancements as l a r g e as 1000 - f o l d o v e r r e a c t i o n i n u n f r o z e n s o l u t i o n s and s h i f t s iii the e q u i l i b r i u m p o s i t i o n . , K i n e t i c e q u a t i o n s a r e d e v e l o p e d which c o r r e l a t e a l l o f t h e r e s u l t s and which a l s o e x p l a i n some o f the o b s e r v a t i o n s e q u a t i o n s a r e based upon t h e assumptions t h a t reactive species  o f other i n v e s t i g a t o r s .  These  (1) when a s o l u t i o n c o n t a i n i n g  i s frozen a l l o f the reactants  as w e l l as any o t h e r  p r e s e n t a r e r e j e c t e d by t h e c r y s t a l l i z i n g s o l v e n t and a r e c o n c e n t r a t e d  solutes into  r e g i o n s which remain l i q u i d and t h a t ( 2 ) t h e r e a c t i o n proceeds n o r m a l l y i n t h e s e regions=  The fundamental e q u a t i o n  used f o r c o r r e l a t i n g t h e r a t e d a t a  f o r the second-order r e a c t i o n s s t u d i e d i s , 1 Vih where V  n  X  diriA  dt  i s t h e t o t a l volume o f t h e l i q u i d r e g i o n s , m  A  i s t h e t o t a l moles o f  r e a c t a n t A p r e s e n t i n the system at any time and Ah and Bh  are the concen-  t r a t i o n s o f the r e a c t a n t s A and B i n the l i q u i d r e g i o n s . The i d e a s developed f o r the t r e a t m e n t o f r e a c t i o n s i n f r o z e n s o l u t i o n s are  extended t o r e a c t i o n s i n o r g a n i c s o l i d s which have a m e l t e d phase p r e s e n t .  T h i s t r e a t m e n t accounts q u a l i t a t i v e l y f o r the o b s e r v a t i o n s made on mutar o t a t i o n i n s o l i d glucose. of  The a p p l i c a t i o n o f the method t o the i s o m e r i z a t i o n  5 - n o r b o r n e n e - 2 , 3 - e n d o - d i c a r b o x y l i c / a n h y d r i d e t o the exo-isomer a l l o w s  s e p a r a t i o n o f c o n c u r r e n t r e a c t i o n s i n the melt and i n the s o l i d .  IV  TABLE OF CONTENTS  Page  I.  Introduction  1  II.  Reactions  7  A.,  Reaction o f Methyl i n Frozen Benzene  B„  Base C a t a l y z e d D e c o m p o s i t i o n o f t^-Butylperoxy Formate i n Frozen p_-Xylene  25  C.  R e a c t i o n o f E t h y l e n e C h l o r o h y d r i n w i t h H y d r o x i d e Ion i n f r o z e n Aqueous S o l u t i o n  47  D.  M u t a r o t a t i o n o f Glucose i n I c e  61  I I I . Reactions  IV.  V.  i n Frozen S o l u t i o n s Iodide with Triethylamine  i n Organic S o l i d s  7  81  A.  M u t a r o t a t i o n i n S o l i d Glucose  81  B.  I s o m e r i z a t i o n o f 5-Norbornene-2„3-endo-dicarboxylic Anhydride  89  G e n e r a l Remarks  98  A.  Demonstration Reaction  98  B.  Review o f P u b l i s h e d R e s u l t s  99  C  Conclusion  Experimental  103 105  V  LIST OF TABLES  Table  Title  Page  I  Rate C o n s t a n t s f o r R e a c t i o n o f E q u i m o l a r T r i e t h y l a m i n e w i t h M e t h y l I o d i d e i n F r o z e n Benzene S o l u t i o n s a t -5.0°.  10  II  Rate C o n s t a n t s f o r R e a c t i o n o f E q u i m o l a r T r i e t h y l a m i n e w i t h M e t h y l I o d i d e i n Frozen Benzene S o l u t i o n s a t V a r i o u s Temperatures  12  III  Rate C o n s t a n t s f o r R e a c t i o n o f Unequal C o n c e n t r a t i o n s o f T r i e t h y l a m i n e w i t h M e t h y l I o d i d e i n F r o z e n Benzene S o l u t i o n s at -5°.  13  IV  Rate C o n s t a n t s f o r Base C a t a l y z e d Decomposition F r o z e n £-Xylene a t 0°.  29  V  Rate C o n s t a n t s f o r 2 , 6 - L u t i d i n e C a t a l y z e d Decomposition TBF a t V a r i o u s Temperatures i n Frozen p__-Xylene.  VI  Rate C o n s t a n t s a t 0° f o r 2 , 6 - L u t i d i n e C a t a l y z e d Decomposition TBF i n Frozen p_-Xylene C o n t a i n i n g Added Compounds.  VII  Second-Order Rate C o n s t a n t s a t V a r i o u s I n i t i a l C o n c e n t r a t i o n s f o r R e a c t i o n o f E t h y l e n e C h l o r o h y d r i n w i t h Sodium H y d r o x i d e i n F r o z e n Aqueous S o l u t i o n s a t -5.0°.  o f TBF i n  of  31  of  38  50  V I I I E f f e c t o f Temperature on t h e R e a c t i o n o f 0.05 M E t h y l e n e C h l o r o h y d r i n w i t h 0.05M Sodium H y d r o x i d e i n Frozen Aqueous Solutions.  51  IX  E f f e c t o f Added S o l u t e s on t h e R e a c t i o n o f 0.05M E t h y l e n e C h l o r o h y d r i n w i t h 0„05M Sodium H y d r o x i d e i n Frozen Aqueous S o l u t i o n s a t -4.0°.  52  X  Rate C o n s t a n t s f o r U n c a t a l y z e d M u t a r o t a t i o n o f G l u c o s e i n Frozen Aqueous S o l u t i o n s a t -4.0°.  62  XI  E f f e c t o f HC1 C o n c e n t r a t i o n on F i r s t - O r d e r Rate C o n s t a n t s f o r M u t a r o t a t i o n o f Glucose a t -4.0° i n F r o z e n Aqueous S o l u t i o n s .  66  XII  V a r i a t i o n o f F i r s t - O r d e r M u t a r o t a t i o n Rate C o n s t a n t w i t h Glucose C o n c e n t r a t i o n f o r Frozen 0.10M HC1 S o l u t i o n s a t -4.0°.  68  X I I I Temperature V a r i a t i o n o f Rate C o n s t a n t s f o r M u t a r o t a t i o n o f Glucose i n Frozen Aqueous S o l u t i o n s .  70  XIV  Rate C o n s t a n t s f o r M u t a r o t a t i o n o f S o l i d Glucose a t V a r i o u s Temperatures  85  XV  Rate C o n s t a n t s f o r I s o m e r i z a t i o n o f M o l t e n 5-Norbornene-2,3e n d o - d i c a r b o x y l i c A n h y d r i d e a t V a r i o u s Temperatures.  90  vi  LIST OF TABLES (cont'd) Table XVI  Table S l o p e s o f P l o t s o f F r a c t i o n o f Product P r e s e n t v e r s u s Time f o r t h e I s o m e r i z a t i o n o f 5 - N o r b o r n e n e - 2 , 3 - e n d o - d i c a r b o x y l i c A n h y d r i d e a t V a r i o u s Temperatures.  Page 91  vii LIST OF FIGURES Figure  Title  Page  F i g u r e 1.  F i r s t - o r d e r p l o t s f o r r e a c t i o n o f equimolar c o n c e n t r a t i o n s o f methyl i o d i d e w i t h t r i e t h y l a m i n e i n f r o z e n benzene s o l u t i o n s a t -5°.  F i g u r e 2.  F i r s t - o r d e r p l o t s f o r r e a c t i o n a t -5° o f 0.2 M m e t h y l i o d i d e w i t h 0.2 M t r i e t h y l a m i n e i n f r o z e n benzene s o l u t i o n s c o n t a i n i n g v a r i o u s c o n c e n t r a t i o n s o f £-xylene.  18  F i g u r e 3.  C o r r e c t e d f i r s t o r d e r p l o t s ( a c c o r d i n g t o eq. 2) f o r r e a c t i o n a t -5° o f 0.2 M methyl i o d i d e w i t h 0.2 M t r i e t h y l a m i n e i n f r o z e n benzene s o l u t i o n s c o n t a i n i n g £-xylene.  19  F i g u r e 4.  Dependence o f o b s e r v e d f i r s t - o r d e r r a t e c o n s t a n t s ^obsd 2 h/ ^ P f° r e a c t i o n o f equi> m o l a r c o n c e n t r a t i o n s o f methyl i o d i d e w i t h t r i e t h y l a m i n e i n f r o z e n benzene s o l u t i o n s . - - - c a l c u l a t e d k ^ h ' observed C^.  21  F i g u r e 5.  N.m.r. s i g n a l (and i n t e g r a l curves a t v a r i o u s t i m e s ) a r i s i n g from l i q u i d benzene p r e s e n t a t -5° i n a f r o z e n benzene s o l u t i o n i n i t i a l l y c o n t a i n i n g 0.64 M methyl i o d i d e and 0.62 M t r i e t h y l a m i n e .  23  F i g u r e 6.  F i r s t - o r d e r p l o t s f o r 2 , 6 - l u t i d i n e c a t a l y z e d decomposition o f t ^ b u t y l p e r o x y formate i n £-xylene a t 0° ( f r o z e n ) and at 70° (not f r o z e n ) u s i n g i d e n t i c a l samples.  27  F i g u r e 7.  First-order plot f o r 2,6-lutidine catalyzed d e c o m p o s i t i o n o f t^-butylperoxy formate i n f r o z e n .o p_-xylene at 0° i n samples i n i t i a l l y f r o z e n at -195" and 8°.  F i g u r e 8.  R e l a t i o n o f o b s e r v e d f i r s t - o r d e r r a t e c o n s t a n t s t o the 33 base c o n c e n t r a t i o n f o r 2 , 6 - l u t i d i n e and p y r i d i n e c a t a l y z e d d e c o m p o s i t i o n o f t^-butylperoxy formate i n f r o z e n p - x y l e n e a t 0°. The v a l u e s o f k , ,. , , *o b s , h i g h base cone. used t o c a l c u l a t e t h e curves were 120 x 1 0 sec." f o r 2 , 6 - l u t i d i n e and 24.7 x 1 0 " s e c . for pyridine as c a t a l y s t .  =  k  C  2  o n  t  e  m  e  r  a  t  u  r  e  r t  n  9  e  2  28  }  - 5  5  F i g u r e 9.  First-order plots for 2,6-lutidine catalyzed d e c o m p o s i t i o n o f t^-butylperoxy formate i n f r o z e n £-xylene a t 11° and a t -20°  F i g u r e 10.  Temperature dependence o f o b s e r v e d r a t e c o n s t a n t s c o n s t a n t t > b u t y l p e r o x y formate and 2 , 6 - l u t i d i n e c o n c e n t r a t i o n s (curved l i n e i s c a l c u l a t e d from k  obsd.  =  k  2 h C  )  -  1  - 1  35  for  36  viii LIST OF FIGURES Figure F i g u r e 11.  (cont'd)  Title  Page  Changes i n observed r a t e c o n s t a n t , a t c o n s t a n t t j - b u t y l p e r o x y formate and 2 , 6 - l u t i d i n e c o n c e n t r a t i o n s , caused by a d d i t i o n o f v a r i o u s compounds.  37  F i g u r e 12.  R e l a t i o n o f f r e e z i n g p o i n t o f £-xylene s o l u t i o n s t o the c o n c e n t r a t i o n o f v a r i o u s s o l u t e s .  44  F i g u r e 13.  E f f e c t o f i m p u r i t i e s (ca.. 0.04 M) on t h e o b s e r v e d r a t e c o n s t a n t f o r r e a c t i o n o f t ^ b u t y l p e r o x y formate w i t h p y r i d i n e i n f r o z e n p_-xylene a t v a r i o u s concentrations of pyridine.  46  F i g u r e 14.  Second-order k i n e t i c p l o t s f o r r e a c t i o n o f equimolar e t h y l e n e c h l o r o h y d r i n w i t h sodium h y d r o x i d e i n f r o z e n aqueous s o l u t i o n s a t -5.0°. C o n c e n t r a t i o n s i n unfrozen s o l u t i o n s .  49  F i g u r e 15.  R e l a t i o n o f observed second-order r a t e constants f o r r e a c t i o n o f e t h y l e n e c h l o r o h y d r i n w i t h sodium h y d r o x i d e i n f r o z e n aqueous s o l u t i o n s a t -5.0° t o t o t a l i n i t i a l s o l u t e c o n c e n t r a t i o n (C ) . The curve i s c a l c u l a t e d from (1,07 % 10' )(2,3)/C k2ch/cs obs  56  F i g u r e 16..  Temperature v a r i a t i o n o f k ^ C f o r r e a c t i o n o f 0.05 M ethylene chlorohydrin with 0.05 M sodium h y d r o x i d e i n f r o z e n aqueous s o l u t i o n s . The s o l i d curve g i v e s c a l c u l a t e d values o f ^ C ^ , c i r c l e s are experimental values o f k , C . obs s  58  F i g u r e 17.  E f f e c t a t -4.0° o f added s o l u t e s on t h e r e a c t i o n o f 0.05 M e t h y l e n e c h l o r o h y d r i n w i t h 0.05 M sodium h y d r o x i d e i n f r o z e n aqueous s o l u t i o n s . The curve i s c a l c u l a t e d from k (1.26 x 1 0 ) (1.9)/(0.15 + Im ) obs 2 h s where I m i s the t o t a l c o n c e n t r a t i o n o f added impurities.  59  F i g u r e 18.  F i r s t - o r d e r k i n e t i c p l o t s f o r mutarotation o f glucose i n f r o z e n aqueous h y d r o c h l o r i c a c i d s o l u t i o n s a t -4.0°. O p t i c a l r o t a t i o n s (a) were measured i n thawed s o l u t i o n s and r a t e c o n s t a n t s c a l c u l a t e d by l o g [ (a - a )/(<*„. - a ) ] = k , t/2.303. obs  64  F i g u r e 19.  V a r i a t i o n o f observed f i r s t - o r d e r constants, with hydrochloric acid concentration f o r mutarotation of g l u c o s e i n f r o z e n s o l u t i o n s a t -4.0°. The s o l i d l i n e s f o l l o w t h e e x p e r i m e n t a l p o i n t s ; t h e b r o k e n l i n e s show the t h e o r e t i c a l r e l a t i o n a c c o r d i n g t o eq. 9.  65  1+  Q  s  s  utf  =  k  C  / C  Q  ix  LIST OF FIGURES Figure  (cont'd)  Title  Page  F i g u r e 20.  V a r i a t i o n o f observed f i r s t - o r d e r r a t e c o n s t a n t s w i t h g l u c o s e c o n c e n t r a t i o n f o r m u t a r o t a t i o n i n f r o z e n 0.10 M HC1 s o l u t i o n s a t -4.0°. The l i n e shows t h e t h e o r e t i c a l r e l a t i o n s h i p p r e d i c t e d by eq. 9.  67  F i g u r e 21.  E f f e c t o f t e m p e r a t u r e on m u t a r o t a t i o n o f g l u c o s e i n frozen s o l u t i o n s at constant reactant concentrations. The s o l i d l i n e s a r e e x p e r i m e n t a l l y d e t e r m i n e d ; the b r o k e n l i n e s are c a l c u l a t e d from eq. 9.  69  F i g u r e 22.  E f f e c t o f added NaCl on m u t a r o t a t i o n o f g l u c o s e i n f r o z e n s o l u t i o n s a t -6.3°. The r e a c t a n t c o n c e n t r a t i o n s were 0.0512 M g l u c o s e , 0.040 M HC1.  72  F i g u r e 23.  S p e c i f i c r o t a t i o n (0) o f s o l i d g l u c o s e samples v e r s u s time at various temperatures.  83  F i g u r e 24.  P l o t s o f l o g (a-0) v e r s u s time a t v a r i o u s temperatures f o r the mutarotation o f s o l i d glucose.  86.  F i g u r e 25.  Isomerization o f s o l i d 5-horbomene-2,3-endo-dicarboxylic a n h y d r i de.  92  F i g u r e 26.  A r r h e n i u s p l o t f o r s o l i d phase i s o m e r i z a t i o n o f 5-norbornene-2,3-endo-dicarboxylic anhydride.  96  X  ACKNOWLEDGEMENT I s h o u l d l i k e t o thank Dr. R i c h a r d E. P i n c o c k f o r h i s i n t e r e s t , e n t h u s i a s m and -'counsel d u r i n g t h e course o f t h i s r e s e a r c h . I s h o u l d a l s o l i k e t o thank my w i f e f o r h e r p a t i e n c e and encouragement and t h e o t h e r members o f t h e p h y s i c a l o r g a n i c group f o r t h e i r many helpful  suggestions. I g r a t e f u l l y acknowledge t h e f i n a n c i a l a s s i s t a n c e o f t h e Research  Committe o f t h e U n i v e r s i t y , t h e Dr. McKenzie American Alumni A s s o c i a t i o n , the Graduate Student F e l l o w s h i p Fund and t h e B r i t i s h Columbia Sugar R e f i n i n g Company.  I. Introduction  The f i r s t i n v e s t i g a t i o n s o f r e a c t i o n s i n f r o z e n s o l u t i o n s were r e p o r t e d o v e r twenty y e a r s ago and d e a l t w i t h enzyme c a t a l y z e d h y d r o l y s i s of s u g a r s , w i t h f a t t y a c i d s and food r e l a t e d p r o d u c t s . 3-13 s i n c e 1961, a number o f s t u d i e s  1 2 ' More r e c e n t l y ,  have been r e p o r t e d which show some  r a t h e r s u r p r i s i n g f e a t u r e s o f r e a c t i o n s c a r r i e d out i n f r o z e n s o l u t i o n s . Among these a r e enhanced r a t e s upon f r e e z i n g , i n s e n s i t i v i t y t o t h e method of f r e e z i n g , and changes i n k i n e t i c  order. 3  I n 1961 G r a n t , C l a r k and A l b u r n  observed t h a t t h e ^ - l a c t a m  ring  i n p e n i c i l l i n was c l e a v e d by i m i d a z o l e f a s t e r when an aqueous s o l u t i o n was h e l d f r o z e n a t -18° than i n l i q u i d water a t +38°i e.g.  Other s u b s t r a t e s *  t r y p s i n , a l s o l o s t more a c t i v i t y a f t e r b e i n g h e l d f r o z e n i n t h e  presence o f i m i d a z o l e . t h a n when t h e s o l u t i o n was h e l d u n f r o z e n a t h i g h e r temperatures. P r u s o f f ^ made s i m i l a r s e m i q u a n t i t a t i v e o b s e r v a t i o n s on 2'-deoxyuridine.  An aqueous s o l u t i o n o f t h i s compound q u i t e q u i c k l y l o s t i t s U. V.  a b s o r p t i o n on i r r a d i t i o n and then upon s t a n d i n g i n t h e p r e s e n c e o f a c i d regained  it.  The l o s s o f a b s o r p t i o n i s a t t r i b u t e d t o h y d r a t i o n and t h e  subsequent r e g e n e r a t i o n t o a c i d c a t a l y z e d d e h y d r a t i o n a b s o r p t i o n was r e g a i n e d  as shown.  The U.V.  f a s t e r i n i c e a t -20° than i n water a t room t e m p e r a t u r e .  2  Q u a n t i t a t i v e experiments on c a t a l y s i s i n i c e were c a r r i e d out by B r u i c e and B u t l e r ^ .  I n a s t u d y o f t h e spontaneous h y d r o l y s i s o f  a c e t i c a n h y d r i d e i n i c e a t -10° t h e y found t h e r a t e c o n s t a n t  t o be o n l y  about one n i n t h t h a t c a l c u l a t e d by e x t r a p o l a t i o n o f d a t a o b t a i n e d 0°, and t h a t added p o t a s s i u m c h l o r i d e i n c r e a s e d t h e r a t e .  above  They a l s o found  t h a t t h e a c i d c a t a l y z e d h y d r o l y s i s was 2.7 times f a s t e r i n i c e a t -10° than i n l i q u i d water a t +5° and t h a t added p o t a s s i u m c h l o r i d e d e c r e a s e d the r a t e i n i c e .  A c e t a t e i o n c a t a l y z e d h y d r o l y s i s was s i m i l a r t o t h e  acid catalyzed reaction. These a u t h o r s found no spontaneous h y d r o l y s i s o f i n i c e , b u t when p o t a s s i u m c h l o r i d e was added h y d r o l y s i s  8-propiolactone  occurred.  P o t a s s i u m c h l o r i d e i s known t o d e c r e a s e t h e r a t e o f h y d r o l y s i s i n u n f r o z e n solutions.  The i m i d a z o l e c a t a l y z e d h y d r o l y s i s o f 8 - p r o p i o l a c t o n e  good f i r s t - o r d e r p l o t s , but p l o t s o f o b s e r v e d r a t e c o n s t a n t c o n c e n t r a t i o n were c u r v e d , t e n d i n g  to l e v e l o f f at higher  gave  versus c a t a l y s t concentrations.  Upon r e i n v e s t i g a t i o n o f P r u s o f f " s work on t h e d e h y d r a t i o n  of  5 - h y d r o - 6 - h y d r o x y d e o x y u r i d i n e i n i c e , B r u i c e and B u t l e r were a b l e t o g e t good f i r s t - o r d e r p l o t s and found t h a t t h e observed r a t e c o n s t a n t s proportional to the hydrochloric acid concentration.  were not  Added p o t a s s i u m  c h l o r i d e g r e a t l y reduced t h e . r a t e . B r u i c e and B u t l e r ^ a l s o s t u d i e d t h e r e a c t i o n o f m o r p h o l i n e w i t h i - t h i o l v a l e r q l a c t p n e and  tf-thiolbutyrolactone  i n ice.  They were a b l e t o  o b t a i n f a i r l y good f i r s t - o r d e r k i n e t i c s and found t h e r a t e o f r e a c t i o n t o be a f u n c t i o n o f t h e c o n c e n t r a t i o n freezing.  o f morpholine i n the b u f f e r  before  The most s u r p r i s i n g r e s u l t o f t h i s i n v e s t i g a t i o n was t h a t t h e  r e a c t i o n r a t e was p r o p o r t i o n a l t o t h e m o r p h o l i n e c o n c e n t r a t i o n , not t o t h e  3  square o f t h e m o r p h o l i n e c o n c e n t r a t i o n as i n u n f r o z e n was a change i n t h e o r d e r o f t h e r e a c t i o n .  s o l u t i o n . Thus t h e r e  I n a d d i t i o n they- found a d i f f e r e n t  k i n e t i c s o l v e n t i s o t o p e e f f e c t i n f r o z e n than i n u n f r o z e n 4.2 i n u n f r o z e n  solution,  ^/^d  =  s o l u t i o n a t 30° and k^/k^ = 1.6 i n f r o z e n s o l u t i o n a t -10°.  CT° (^f r  morpholine  »  ( ^ O H  °  r  Q^"  7 Weatherburn and Logan c y a n i d e i o n which were n o r m a l l y  found t h a t s o l u t i o n s o f f e r r i c y a n i d e and s t a b l e produced f e r r o c y a n i d e when f r o z e n .  The l o w e r t h e temperature a t which t h e f r o z e n s o l u t i o n s were h e l d t h e f a s t e r the production o f ferrocyanide i o n . 8 Home  s t u d i e d t h e e l e c t r o n exchange r e a c t i o n o f F e ( I I ) and  F e ( I I I ) u s i n g r a d i o a c t i v e f e r r i c c h l o r i d e i n f r o z e n aqueous p e r c h l o r i c a c i d solution.  He was a b l e t o get smooth k i n e t i c s a t t e m p e r a t u r e s as low as  -78°. 9-11 Grant and A l b u r n  have s t u d i e d s e v e r a l r e a c t i o n s i n i c e and  water and i n each case found h i g h e r r a t e s i n i c e than i n water. d e c o m p o s i t i o n o f hydrogen p e r o x i d e  The  c a t a l y z e d by f e r r i c o r c u p r i c i o n was  f a s t e r i n i c e a t -18° than i n l i q u i d water a t +1° . The h y d r o x y l a m i n o l y s i s o f a m i d e s ^ and o f amino a c i d esters*''" gave g e n e r a l l y good k i n e t i c s and t h e .s \J  S  ICG  r a t e s were R-Cr h i g h e r i n+i cH.NOH e than i n l i q u i d w a"t e rX. R  NH  2 2  C X  N0H.  +  N^o  4  RC NH  OH  ice  + H NOH  C^  RC NH  2  OR'  2  C^T  R'OH  .^NOH  2  12 Wang  found t h a t when some p y r i m i d i n e s , e.g. 1 , 3 - d i m e t h y l -  thymine ( I i were i r r a d i a t e d i n i c e d i f f e r e n t p r o d u c t s were formed from when an u n f r o z e n aqueous s o l u t i o n was i r r a d i a t e d .  The p r o d u c t formed i n  i c e , t h e photodimer ( I I ) , was t h e same as t h a t formed when a d r y s o l i d f i l m was i r r a d i a t e d . solution  The p r o d u c t from i r r a d i a t i o n o f a l i q u i d aqueous  i s the hydrated product  ( I I I ) as shown.  was i r r a d i a t e d i n a f r o z e n aqueous s o l u t i o n product, 6-methoxy-l,3-dimethylhydrouracil solution  When d i m e t h y l u r a c i l (IV)  c o n t a i n i n g 2% methanol t h e same ( V ) , was formed as when a m e t h a n o l i c  was i r r a d i a t e d . CH,  hi) water  'OH  liquid  CH  CH,  III 0  i  CH,  11  CH„ L-o  .0  hi)  ice or dry f i l m  V  II  ht>  CH 0H 3  IV  OCH,  V  CH,  5  V a r i o u s explanations--have  been proposed: t o ;acco:unt. f o r the many.  d i f f e r e n c e s between r e a c t i o n s i n . f r o z e n and u n f r o z e n these are:  solvents.  Among  (a) c o n c e n t r a t i o n o f r e a c t a n t s i n l i q u i d r e g i o n s when pure  solvent i s frozen out^,  (b) c a t a l y t i c e f f e c t s o f the f r o z e n s o l v e n t ' 6  1 0  '  1 3  ,  9 (c) r e a c t i o n i n a s o l i d phase , (d) f o r m a t i o n o f complexes o f unknown structure , 6  (e) i m p o s i t i o n o f a f a v o r a b l e p o s i t i o n a l o r i e n t a t i o n ; between  r e a c t a n t s upon f r e e z i n g and  ( f ) the lower d i e l e c t r i c c o n s t a n t o f i c e as  compared t o w a t e r . 1 0  We began our i n v e s t i g a t i o n s ^ 1  ^  of reactions i n frozen solutions  a f t e r o b s e r v i n g t h a t samples o f t - b u t y l p e r o x y formate (TBF) base c a t a l y z e d d e c o m p o s i t i o n unfrozen  samples.  underwent  much f a s t e r i n f r o z e n p_-xylene than i n  A f t e r c o l l e c t i n g c o n s i d e r a b l e d a t a on the p y r i d i n e and  2 , 6 - l u t i d i n e c a t a l y z e d decomposition  o f TBF  i n f r o z e n p_-xylene and  r e a c t i o n o f methyl i o d i d e w i t h t r i e t h y l a m i n e t o form the  the  quaternary  ammonium s a l t i n f r o z e n benzene, we found t h a t the d a t a would not f i t the k i n e t i c treatment  used f o r o r d i n a r y s o l u t i o n s .  We d e c i d e d t h e n t o attempt  t o account q u a n t i t a t i v e l y f o r the c o n c e n t r a t i o n e f f e c t o r d e r t o do t h i s we used r a t e d a t a which was  ((a) above).  a v a i l a b l e f o r the r e a c t i o n s i n  ordinary s o l u t i o n s i n conjunction with f r e e z i n g point depression o f the s o l v e n t - s o l u t e systems.  The  In  approach was  diagrams  t o see what the p r e d i c t e d  e f f e c t o f c o n c e n t r a t i o n o f r e a c t a n t s due t o f r e e z i n g would be and how p r e d i c t i o n s would f i t the e x p e r i m e n t a l c o u l d be s e p a r a t e d  o u t , any e f f e c t s due  data.  I f the e f f e c t s o f  B are p r e s e n t e d  concentration  t o the o t h e r f a c t o r s mentioned above  would become apparent and perhaps open t o i n v e s t i g a t i o n . A and  In S e c t i o n I I ,  our d a t a on and d i s c u s s i o n o f the methyl i o d i d e -  t r i e t h y l a m i n e and TBF-base systems.  these  6  A l o g i c a l e x t e n s i o n o f the work i n f r o z e n o r g a n i c s o l v e n t s seemed t o be a s t u d y o f a w e l l known r e a c t i o n i n f r o z e n aqueous s o l u t i o n , e s p e c i a l l y c o n s i d e r i n g the many d i f f e r e n t s u g g e s t i o n s such r e a c t i o n s .  The  as t o the i n v o l v e m e n t o f i c e i n  conversion of ethylene chlorohydrin  to  ethylene  o x i d e w i t h h y d r o x y l i o n seemed t o f i t our r e q u i r e m e n t s (see S e c t i o n  II,C).  I n view o f the p r o p o s a l t h a t the g r e a t e r p r o t o n m o b i l i t y i n i c e as compared t o water might be a f a c t o r i n the r a t e enhancements o b s e r v e d i n f r o z e n aqueous s o l u t i o n s we d e c i d e d t o s t u d y a g e n e r a l a c i d c a t a l y z e d reaction i n ice. was  convenient  separate  The h y d r o c h l o r i c a c i d c a t a l y z e d m u t a r o t a t i o n  f o r such a s t u d y .  A g a i n our approach was  of  glucose  t o attempt t o  out the e f f e c t s o f c o n c e n t r a t i o n and then see what a d d i t i o n a l  hypotheses might be n e c e s s a r y  t o e x p l a i n the r e s u l t s .  T h i s p a r t o f the  work i s r e p o r t e d i n S e c t i o n I I , D. P a r t I I I o f the t h e s i s d e a l s w i t h our a p p l i c a t i o n o f the methods d e v e l o p e d f o r the treatment  of frozen solutions to reactions i n organic  s o l i d s i n which m e l t i n g o c c u r s d u r i n g the course o f the r e a c t i o n .  In  such a system the r e a c t i o n can presumably p r o c e e d i n the s o l i d p a r t o f the sample as w e l l as i n the melt and we hoped the a p p l i c a t i o n o f treatment,  our  d e v e l o p e d i n P a r t I I , would a l l o w the s e p a r a t i o n o f the  two  r e a c t i o n mechanisms. R e s u l t s and d i s c u s s i o n c o n c e r n i n g  the m u t a r o t a t i o n  of  below i t s m e l t i n g p o i n t i n p o l y c r y s t a l l i n e samples are p r e s e n t e d III,A.  glucose i n Section  S e c t i o n I I I , B d e a l s w i t h the i s o m e r i z a t i o n o f 5-norbornene-2,3-  e n d o - d i c a r b o x y l i c anhydride  t o i t s exo-isomer i n s o l i d samples.  7  REACTIONS IN FROZEN SOLUTIONS  A.  Methyl Iodide with Triethylamine The  i n Frozen Benzene  r e a c t i o n o f m e t h y l i o d i d e w i t h t r i e t h y l a m i n e t q form t h e 19  q u a t e r n a r y ammonium s a l t has been s t u d i e d f o r majny y e a r s understood i n unfrozen organic  solvents.'  20 '  and i s w e l l  The k i n e t i c s a r e s t r i c t l y  second-  o r d e r and t h e a c t i v a t i o n parameters have been Mel determined.  + E t j N — >  MeNEt*  I"  S i n c e t r i e t h y l a m i n e and methyl i o d i d e a r e cheap and r e a d i l y ,  a v a i l a b l e the rather large q u a n t i t i e s required f o r constructing  freezing,  p o i n t d e p r e s s i o n ;curves p r e s e n t no problem.  of effects  of reactants  Thus t h e s e p a r a t i o n  due  to concentration  brought about by f r e e z i n g i s p o s s i b l e .  The  r e a c t i o n i s e s p e c i a l l y i n t e r e s t i n g because o f t h e many a s p e c t s o f  r e a c t i o n s i n f r o z e n s o l u t i o n s which a r e demonstrated. Results The  r a t e o f r e a c t i o n i n f r o z e n benzene s o l u t i o n s was s t u d i e d  by measurement, a f t e r d e f r o s t i n g t h e samples o f a r u n , o f t h e l o s s o f methyl i o d i d e i n f r a r e d absorption triethylamine concentration was a l s o o b t a i n e d ,  utilizing  a t 1240 cm., } and by measurement o f t h e  by t i t r i m e t r i c . a n a l y s i s .  The r e a c t i o n r a t e  a s i n g l e ..frozen sample,, by n.m.r. s p e c t r o s c o p y .  For runs u s i n g t h e former two methods, i n d i v i d u a l k i n e t i c samples i n s m a l l ampoules were made up by combining measured volumes o f s o l u t i o n s o f t h e reactants  i n benzene.  As t h e r e a c t i o n a t room temperature i s r a t h e r  the ampoules were q u i c k l y s e a l e d and f r o z e n i n d r y ice-^acetone.  fast,  After  8  s i m i l a r p r e p a r a t i o n o f a l l the samples, they were brought t o the temperature o f the r u n , withdrawn p e r i o d i c a l l y , d e f r o s t e d and  analyzed.  F r e e z i n g o f samples i n d i f f e r e n t ways (e.g. i n l i q u i d n i t r o g e n ) had  no  e f f e c t on the o b s e r v e d r a t e . Methyl  iodide reacts with t r i e t h y l a m i n e i n unfrozen  benzene  19 s o l u t i o n s a c c o r d i n g t o s i m p l e second-order k i n e t i c s .  However, w i t h  equal c o n c e n t r a t i o n s o f r e a c t a n t s i n f r o z e n benzene s o l u t i o n s p l o t s o f r e c i p r o c a l c o n c e n t r a t i o n a g a i n s t t i m e were always d i s t i n c t l y curved  and  i t became apparent t h a t o n l y p l o t s o f l o g ( c o n c e n t r a t i o n ) a g a i n s t t i m e gave good s t r a i g h t l i n e s f o r more than two h a l f - l i v e s .  The  frozen solution  r e a c t i o n w i t h equal c o n c e n t r a t i o n s o f r e a c t a n t s i s then a f i r s t - o r d e r reaction.  F i g u r e 1 shows runs f o r e q u a l c o n c e n t r a t i o n s o f m e t h y l i o d i d e and  t r i e t h y l a m i n e from 0.05 order r a t e constants  M t o 0.63  M i n f r o z e n benzene at -5°.  The  first-  (see T a b l e I ) o v e r t h i s range o f i n i t i a l s o l u t i o n  c o n c e n t r a t i o n are a l l e s s e n t i a l l y the same, h a l f - l i v e s v a r y i n g o n l y from 62 t o 72 m i n u t e s . 20 From the a c t i v a t i o n parameters r e p o r t e d f o r second^order r e a c t i o n o f m e t h y l i o d i d e w i t h t r i e t h y l a m i n e i n l i q u i d benzene s o l u t i o n s the r a t e a t -5  i s c a l c u l a t e d t o be 2.4  x 10  -4  l i t e r mole  -1  sec.  -1  .  For a 0.05  i n i t i a l c o n c e n t r a t i o n o f b o t h r e a c t a n t s the h a l f - l i f e i s then 1400  M  minutes  and the observed h a l f ^ l i f e o f 65 minutes shows the moderate a c c e l e r a t i o n which o c c u r s on f r e e z i n g .  With more d i l u t e i n i t i a l s o l u t i o n s the  r a t e i n c r e a s e on f r e e z i n g would be  greater.  A d d i t i o n o f p_-xylene t o runs h a v i n g equal r e a c t a n t causes d e v i a t i o n s from the l i n e a r l o g ( c o n c e n t r a t i o n ) v e r s u s relationship.  relative  concentrations time  F i g u r e 2 shows f i r s t - o r d e r p l o t s . f o r runs at -5°  containing  9  0  30  60  90 Time,  Figure 1.  120  150  180  min  F i r s t - o r d e r p l o t s f o r r e a c t i o n o f equimolar  concentrations  of methyl iodide with t r i e t h y l a m i n e i n frozen benzene s o l u t i o n s at - 5 ° .  10 Table I Rate C o n s t a n t s f o r R e a c t i o n o f E q u i m o l a r T r i e t h y l a m i n e w i t h M e t h y l I o d i d e i n F r o z e n Benzene S o l u t i o n s at M e l , concn.,,  M  E t  3 ' concn., M N  -5.0°  Method  a  k  2  C  x 10 , 4  h  0.206  0.196  I.R.  3.24  0.118  0.117  I.R.  3.22  0.200  0.200  I.R.  3.35  0.199  0.206  titra.  3.40  0 .050  .;. 0.050  I.R.  3.56  0.474  0.500  titra.  3.55  0.636  0.616  n.m.r.  3.49  w i t h added p_-xylene*  3  0.217  0.212  0.0984 M  3.64  d  0.198  0.209  0.186  3.35  d  0.204  0.204  0.405  3.66  d  0.146  0.146  0.251  2.92  6  C  C a l c u l a t e d from f i r s t - o r d e r p l o t s , k , , = k~ C, /2 ' obsd 2 h r  ^  Rate c o n s t a n t s c a l c u l a t e d by use o f eq 3.  c  C o n c e n t r a t i o n o f p_-xylene.  d  T i t r a t i o n method o f a n a l y s i s used. I n f r a r e d method o f a n a l y s i s  used.  11  v a r i o u s c o n c e n t r a t i o n s of p_-xylene.  With g r e a t e r c o n c e n t r a t i o n s o f  t h i s s o l u b l e " i m p u r i t y " t h e r a t e o f l o s s o f methyl i o d i d e and t r i e t h y l a m i n e i s d e c r e a s e d , and t h e d e v i a t i o n from t h e f i r s t - o r d e r k i n e t i c s found i n t h e absence o f p_-xylene becomes, more e v i d e n t .  At the  h i g h e s t c o n c e n t r a t i o n o f p_-xylene used, 0.405 M, a p l o t o f t h e d a t a to second-order k i n e t i c s  according  ( i . e . r e c i p r o c a l , c o n c e n t r a t i o n a g a i n s t , t i m e ) gave  a s l i g h t l y S-shaped c u r v e , but w i t h a g r e a t d e a l more s i m i l a r i t y t o a s t r a i g h t l i n e than found i n a f i r s t - o r d e r p l o t . The  r e s u l t s f o r r a t e s t u d i e s with equimolar reactant  concentrations  at v a r i o u s t e m p e r a t u r e s (see T a b l e I I ) and f o r unequal c o n c e n t r a t i o n s a t -5° (Table I I I ) a r e d e s c r i b e d more f u l l y below.  The r e s u l t s ; may be  summarized by s t a t i n g t h a t t h e r e a c t i o n i n f r o z e n s o l u t i o n s shows a maximum r a t e a t c a . -5° and a l s o o c c u r s a t c o n v e n i e n t l y measurable r a t e s at +3 and a t -20°. r e a c t a n t s , treatment  F o r runs a t -5° w i t h unequal c o n c e n t r a t i o n s o f o f t h e d a t a a c c o r d i n g t o an e q u a t i o n developed, i n t h e  D i s c u s s i o n s e c t i o n gave r a t e c o n s t a n t s runs a t equal  concentrations.  c o n s i s t e n t w i t h those found f o r  12  Table I I  Rate C o n s t a n t s  f o r Reaction o f Equimolar Triethylamine with Methyl  I o d i d e i n F r o z e n Benzene S o l u t i o n s a t V a r i o u s Temperatures. concn., M  EtgN, concn., M  Temperature  V h  x  0.182  0.197  2.5°  1.97  0.206  0.200  0.0  2.92  0.206  0.200  -1.5  2.89  0.198  0.199  -3.0  3.26  0.200  0.200  -5.0  3.35  0.199  0.206  -5.0  3.40  0.200  0.200  -7.0  3.30  0.200  0.200  -9.3  3.10  0.200  0.200  -15.3  2.52  0.182  0.197  -20.0  1.85  b  b  b  C a l c u l a t e d from f i r s t - o r d e r p l o t s , k b i = k^C^ I^ 0  s c  T i t r a t i o n method o f a n a l y s i s used, a l l o t h e r s by i n f r a r e d  analysis.  13  Table I I I  Rate C o n s t a n t s f o r R e a c t i o n o f Unequal C o n c e n t r a t i o n s o f T r i e t h y l a m i n e w i t h M e t h y l I o d i d e i n . F r o z e n Benzene S o l u t i o n s a t -5.0°.  M e l , concn., M  ^ 3 ' concn.,M t  N  %MeI  a  b  ^2^h  X  Q.125  0.378  31  3.18  0.152  0.300  34  3.10  0.146  0.211  41  3.12  0.200  0.158  56  3.87  0.344  0.186  65  4.48  0.311  0.145  68  4.34  0.364  0.127  74  4.26  ^  4 '  s e c  Percentage of solute at the start of the reaction which i s methyl iodide. b  R a t e constants calculated by use of eq 4.  '  -1  14  DISCUSSION When a dilute solution containing two reactants is frozen the reactants may be rejected by the solid phase and become more concentrated  in the unfrozen liquid solution.  If the reactants are soluble  enough, when equilibrium is reached at a temperature above the eutectic temperature of the system, there will s t i l l exist highly concentrated regions present among the crystalline  solvent.  liquid  In these liquid regions,  the reaction between two solutes will be accelerated by the concentration  For a simple bimoleeular reaction, A + B  •* products, t h e  reaction i n a f r o z e n solution ©eeurs i n that portion of the system whieh remains l i q u i d with a normal r e a e t i e n r a t e equal t o k^B^. is i n terms § 1 m§ie§  §e§©nd g e r l i t e r Qf r e a e t i e n velume.  pet  _ 1 dpneles A)  " Vj:  It  o  .=  " rVh k  k  m  The notation used is as follows; eoneentrations  A^, B^ and A , §  B  g  2 l { l )  are t h e  of the reaetants i n the liquid regions o f a froaen solution  and i n the thawed solution, respectively. V liquid regions in the frozen solution and V solution;  This rate  g  h  is the t o t a l volume of the is the Volume of t h e thawed  c ^ is the total constant concentration of solutes i n the  liquid regions,  is the normal second-order rate Constant for  bimoleeular reaction.  Im  g  is the solution concentration of any inert solutes  To obtain t h e observed rate (in terms of moles per second per l i t e r o f thawed solution) i t is necessary to divide eq 1 by V  which  decreases the rate in the reaction volume o f frozen samples to that measured in thawed samples.  The observed rate o f reaction is then given  15  by eq 2.  The r e a c t i o n v o l u m e , V , may i n c r e a s e o r d e c r e a s e d u r i n g a  (2) V k i n e t i c - run as the number of moles which must be accommodated i n the l i q u i d r e g i o n s of the f r o z e n s o l u t i o n at constant  or  concentration increase  decrease. I t i s the high concentration  3.  o f the l i q u i d regions of a frozen  s o l u t i o n which g i v e r i s e t o the observed r a t e a c c e l e r a t i o n s and t h e r e q u i r e ment o f c o n s t a n t  t o t a l c o n c e n t r a t i o n which leads t o . t h e r a t h e r u n u s u a l changes  i n k i n e t i c o r d e r and s e n s i t i v i t y t o s o l u b l e i m p u r i t i e s . a constant  In o r d e r t o keep  c o n c e n t r a t i o n , t h e w a l l s o f t h e l i q u i d r e g i o n s may thaw o r  f r e e z e t o accommodate more o r l e s s s o l u t e .  In the case o f t h e r e a c t i o n o f  t r i e t h y l a m i n e w i t h m e t h y l i o d i d e , t h e f o r m a t i o n o f an i n s o l u b l e product* r e s u l t s i n a decrease o f t h e r e a c t i o n volume d u r i n g a r u n .  5  As m e t h y l t r i -  ethylammonium i o d i d e i s formed, i t i s p r e c i p i t a t e d out and t h e w a l l s o f t h e r e a c t i o n regions c l o s e i n to hold the concentration of the remaining at a c o n s t a n t v a l u e .  The observed f i r s t - o r d e r k i n e t i c s f o r t h i s  solute  bimolecular  r e a c t i o n i s a consequence o f t h i s volume change; t h e c o n c e n t r a t i o n s A^ and are c o n s t a n t  and a c c o r d i n g t o eq 1 the r a t e i s then p r o p o r t i o n a l t o the  t o t a l concentration i n a defrosted solution ( i . e . ,  = (A  the r e a c t i o n r a t e i s p r o p o r t i o n a l t o t h e sum o f r e a c t a n t  g  + B) s  ^/C^)>  concentrations  ( l e a d i n g t o f i r s t - o r d e r k i n e t i c s f o r equal r e a c t a n t c o n c e n t r a t i o n s ) than t h e product  of t h e i r concentrations  rather  ( i . e . , second-order k i n e t i c s ) .  a  From f r e e z i n g p o i n t - c o m p o s i t i o n d a t a f o r methyl i o d i d e o r t r i e t h y l a m i n e i n benzene t h e c o n c e n t r a t i o n o f t h e l i q u i d r e g i o n s a t -5° i s 1.6 M.  b  No f r e e z i n g p o i n t d e p r e s s i o n was observed f o r benzene s a t u r a t e d w i t h methyltriethylammonium i o d i d e .  16  To o b t a i n t h e i n t e g r a t e d r a t e e x p r e s s i o n f o r r e a c t i o n a t equal r e a c t a n t c o n c e n t r a t i o n s , w i t h t h e added c o m p l i c a t i o n o f t h e presence o f a s o l u b l e " i m p u r i t y " (Im), t h e assumption i s made t h a t a l l s o l u t e s i n an u n f r o z e n  s o l u t i o n are present  solution, i.e. A V  g  =  V^.  s  V  s  present  i n the l i q u i d regions o f the frozen  = A, V, , B V = B, V, and (A + B + Im ) h h' s s h h s s s' v  S u b s t i t u t i o n i n t o eq 1 and i n t e g r a t i o n t h e n g i v e s eq 3  Im 2 I n (A )  - —2-  = -k  A  C  2  h  t  +  constant  (3)  ':'•[•". s This equation i s a combination  o f t h e form o f t h e k i n e t i c e q u a t i o n s f o r ;  f i r s t - o r d e r r e a c t i o n ( I n A ) and f o r s e c o n d - o r d e r r e a c t i o n a t e q u a l g  concentrations  (1 /.A ) .  plot of log A  a g a i n s t t i m e s h o u l d be a s t r a i g h t l i n e w i t h  k^  s  / 2 x 2.3.  When no i n e r t s o l u t e s a r e p r e s e n t ,  Im  g  reactant  = 0, and a  slope  F i g u r e 1 shows t h a t t h i s . r e l a t i o n s h i p i s e x p e r i m e n t a l l y  o b t a i n e d , and that;, as r e q u i r e d by eq 3. the s l o p e s o f t h e p l o t s f o r runs w i t h d i f f e r e n t i n i t i a l s o l u t i o n c o n c e n t r a t i o n s a r e v e r y n e a r l y t h e same (see a l s o T a b l e I ) .  I n t h i s r e a c t i o n t h e observed f i r s t - o r d e r . r a t e  o b s d ~ 2 ^h ^ '  ^  k  k  2  n <  ^ P e  e n  ^  e n t  °^  t n e  constant  r e a c t i o n volume d u r i n g a r u n and  t h e r e f o r e independent o f t h e i n i t i a l s o l u t i o n c o n c e n t r a t i o n which determines t h i s i n i t i a l r e a c t i o n volume i n a f r o z e n s o l u t i o n . When an i n e r t s o l u t e , such as £-xylene i s p r e s e n t , t h e "secondo r d e r p o r t i o n " o f eq 3 comes i n t o p l a y . simple f i r s t - o r d e r k i n e t i c s  P l o t s o f the data according t o  (see F i g u r e 2) show t h e d e v i a t i o n caused by t h e  n e g l e c t o f t h i s " s e c o n d - o r d e r " term, which becomes more i m p o r t a n t " i m p u r i t y " c o n c e n t r a t i o n o r when the r e a c t i o n i s more complete.  at high The  r e a c t i o n slows down because t h e r e a c t i o n volumes no l o n g e r c o n t i n u e t o decrease i n p r o p o r t i o n t o the reactant c o n c e n t r a t i o n s .  A t low r e a c t a n t  17  c o n c e n t r a t i o n s the r e a c t i o n r e g i o n s are h e l d open by the " i n e r t " s o l u t e , the r e a c t a n t s t h e n become c o n t i n u o u s l y more d i l u t e and the r e a c t i o n k i n e t i c s t r a n s f o r m i n t o the o r d i n a r y s e c o n d - o r d e r k i n e t i c s which would be observed at c o n s t a n t volume. that a p l o t of r e c i p r o c a l A  The  f a c t , as i n d i c a t e d i n the R e s u l t s s e c t i o n ,  a g a i n s t time f o r a run w i t h h i g h p_-xylene  g  c o n c e n t r a t i o n i s a good a p p r o x i m a t i o n this  t o a s t r a i g h t l i n e i s an outcome o f  effect. Treatment o f the d a t a f o r runs c o n t a i n i n g p_-xylene a c c o r d i n g  the complete form o f eq 3 i s shown i n F i g u r e 3. d u r i n g a r u n , f o r the continuous t o t a l r e a c t i o n volume. equal t o k^ C^/2.3.  The  This equation c o r r e c t s ,  d e c r e a s e i n r a t e o f c o n t r a c t i o n o f the  slopes of these c o r r e c t e d p l o t s should  T a b l e I c o n t a i n s the d a t a f o r runs at  c o n c e n t r a t i o n , w i t h and w i t h o u t  added p_-xylene.  The  be  equal  values  of.k  2  o b t a i n e d i n b o t h cases are e s s e n t i a l l y the same and i n d i c a t e the o f eq  to  success  3. F r o z e n k i n e t i c runs i n s o l u t i o n s i n i t i a l l y c o n t a i n i n g w i d e l y  d i f f e r i n g c o n c e n t r a t i o n s o f r e a c t a n t s would be expected t o g i v e d a t a somewhat analogous t o t h a t from runs w i t h equal r e a c t a n t c o n c e n t r a t i o n w i t h an i n e r t s o l u t e p r e s e n t .  In o t h e r words, the excess o f one  but  reactant  ( a c t i n g l i k e an i n e r t i m p u r i t y ) would tend t o keep the r e a c t i o n volume from d e c r e a s i n g at a c o n s t a n t  r a t e as the r e a c t i o n p r o c e e d s .  Accordingly,  when d a t a from runs at d i f f e r e n t i n i t i a l r e a c t a n t c o n c e n t r a t i o n s were t r e a t e d by the normal e q u a t i o n  f o r s e c o n d - o r d e r r e a c t i o n s , the p l o t s o f l o g  ( A / B ) a g a i n s t time were good s t r a i g h t l i n e s . s  s  However, i n t e g r a t i o n o f  eq 2 f o r the case o f unequal r e a c t a n t c o n c e n t r a t i o n s and no i n e r t s o l u t e g i v e s r i s e t o eq 4, which i s more d i r e c t l y a p p l i c a b l e t o t h i s type bimolecular reaction i n frozen solutions.  P l o t s o f l o g (A  of  B ) against  18  0  60  120  180  240  300  360  Time, min.  Figure 2.  F i r s t - o r d e r p l o t s f o r r e a c t i o n at -5° of 0.2 M methyl  iodide with 0.2 M t r i e t h y l a m i n e i n frozen benzene s o l u t i o n s containing various concentrations  o f p_-xylene *  19  Figure 3.  Corrected f i r s t - o r d e r p l o t s (according t o eq 2) f o r  r e a c t i o n at -5° of 0.2 M methyl i o d i d e w i t h 0.2 M t r i e t h y l a m i n e i n frozen benzene s o l u t i o n s containing £-xylene.  20  time f o r runs a t unequal c o n c e n t r a t i o n were good s t r a i g h t l i n e s . In (A  B) g  o f ^2^\i o b t a i n e d  = -k C 2  t + constant  h  The v a l u e s  (4)  from t h e s l o p e s o f t h e s e l i n e s a r e g i v e n i n T a b l e I I . c  I t may be seen t h a t t h e s e v a l u e s obtained  a r e c o n s i s t e n t w i t h t h e same q u a n t i t y  from eq 3 f o r runs a t e q u a l c o n c e n t r a t i o n s ,  with or without  "impurity". The  temperature dependence o f t h e observed r a t e c o n s t a n t s a t  equal reactant c o n c e n t r a t i o n , [ 2 h ^ ' i f k and an i n c r e a s e i n C^. as t h e temperature i s lowered. k  =  k  C  2  a r  s e s  r  o b s c  2  k  m  a  decrease i n The change i n 20  may be c a l c u l a t e d from t h e a v a i l a b l e a c t i v a t i o n p a r a m e t e r s ,  2  i s obtained  from t h e e x p e r i m e n t a l  r e l a t i o n of concentration  t o f r e e z i n g p o i n t o f benzene s o l u t i o n s . observed v a l u e s  of  to c a l c u l a t e d values k C^ 2  o  d  while of solute  F i g u r e 4 shows t h e e x p e r i m e n t a l l y  ( s o l i d l i n e ) f o r runs from 2.5 t o -20° compared (broken l i n e ) . At.-.5° t h e t h e o r e t i c a l v a l u e o f  d i f f e r s from t h e e x p e r i m e n t a l  v a l u e by about 13%.  F i n a l l y , t h e v a r i a t i o n o f t h e volume o f r e a c t i o n r e g i o n s a k i n e t i c r u n suggested t h a t t h e r a t e o f r e a c t i o n o f t r i e t h y l a m i n e  during with  methyl i o d i d e might be d i r e c t l y measured i n a s i n g l e f r o z e n sample by a method based on n.m.r.  The 60 mc. p.m.r. spectrum a t -5° o f a s o l u t i o n  c  The s l i g h t i n c r e a s e i n observed r a t e c o n s t a n t f o r runs w i t h r e l a t i v e l y h i g h c o n c e n t r a t i o n o f methyl i o d i d e (see T a b l e I I I ) may be due t o a s o l v e n t e f f e c t . The r e a c t i o n r e g i o n s at -5° c o n t a i n 1.6 M (ca. 12 mole p e r c e n t ) s o l u t e ; i f t h i s i s p r e d o m i n a n t l y methyl i o d i d e ( d i e l e c t r i c c o n s t a n t 7.00) r a t h e r than t r i e t h y l a m i n e ( d i e l e c t r i c constant 2.42) an i n c r e a s e i n r a t e might o c c u r . The g r e a t s e n s i t i v i t y o f a l k y l h a l i d e amine r e a c t i o n s t o s o l v e n t v a r i a t i o n i s w e l l e s t a b l i s h e d . 2 2  d  The same m o l a r c o n c e n t r a t i o n o f methyl i o d i d e o r t r i e t h y l a m i n e i n benzene d e p r e s s e s t h e f r e e z i n g p o i n t t o t h e same e x t e n t down t o c a . -10° (2.4 M), but d i v e r g e n c e o f t h e f r e e z i n g p o i n t - c o n c e n t r a t i o n r e l a t i o n s h i p s f o r the two s o l u t e s o c c u r s below -10°.  21  Q.2  5  M  a y  0  -5  -10  -15  -20  Temperature, ° C  Figure 4. ^ obsd v  =  Dependency of observed first-order rate constants  ^2 S/^  o n  temperature ^  o r t n  e reaction of equimolar  concentrations of methyl iodide with triethylamine in frozen benzene solutions. - - - - - observed  k „ C, .  calculated  ^> n  ^—  22  o f 0.64  M methyl i o d i d e and 0.62  i n i t i a l l y f r o z e n at -70°)  M t r i e t h y l a m i n e i n benzene (the sample  showed a broad peak near the r e g i o n o f  a b s o r p t i o n o f l i q u i d benzene ( 2 . 6 3 ) . benzene p r e s e n t  T h i s peak, which i s due  t o the  i n the l i q u i d r e a c t i o n r e g i o n s o f the f r o z e n sample,  s l o w l y decreased i n i n t e n s i t y .  F i g u r e 5 shows the form o f the  spectrum and o f the i n t e g r a l curves taken at v a r i o u s t i m e s .  initial  These  i n t e g r a l v a l u e s are p r o p o r t i o n a l t o the number o f moles o f l i q u i d benzene i n t h a t s m a l l p o r t i o n o f the f r o z e n sample which g i v e s r i s e t o the As the. l i q u i d r e a c t i o n r e g i o n s are f i l l e d p r e d o m i n a n t l y i n t e g r a l v a l u e s are a l s o a p p r o x i m a t e l y  signal.  w i t h benzene the  p r o p o r t i o n a l t o the volume, V^,  the l i q u i d r e g i o n s o f the f r o z e n sample.  The  of  r e l a t i o n s h i p o f the changes  i n i n t e g r a l v a l u e , r e a c t i o n volume o f f r o z e n s o l u t i o n s i and  concentration  :  o f d e f r o s t e d s o l u t i o n s f o l l o w s from the assumptions t h a t a l l the s o l u t e s a r c present  i n the r e a c t i o n volumes ( i . e . ,  = 2A  g  V  g  f o r equal  reactant  c o n c e n t r a t i o n s ) , t h a t the c o n c e n t r a t i o n s i n the r e a c t i o n r e g i o n s are and t h a t the i n t e g r a l v a l u e i s p r o p o r t i o n a l t o the volume o f the regions of a frozen s o l u t i o n .  The  constant,  liquid  r e s u l t i s t h a t the change i n one i s  r e l a t e d t o the change i n a n o t h e r by d In ( i n t e g r a l v a l u e ) / d t = d In d In A  s  / dt = k ^ ^  = k^  / 2.  A p l o t of log ( i n t e g r a l value i n  a g a i n s t time i s a s t r a i g h t l i n e and the r a t e c o n s t a n t , k ^ ^  =  T h i s i s the same as the average v a l u e 3.4  as 3.5 - 4 - 1 x 10  sec.  x 10  2,  -1 sec.  o b t a i n e d by a n a l y s i s  o f d e f r o s t e d samples u s i n g i n f r a r e d and t i t r a t i o n t e c h n i q u e s The  mm.) /  -4 o b t a i n e d from the s l o p e o f t h i s l i n e gave  / dt =  (see T a b l e I ) .  r a t e o f r e a c t i o n ( o b t a i n e d from the r e a c t a n t c o n c e n t r a t i o n s i n  d e f r o s t e d samples o f a run) and the r a t e o f change o f the r e a c t i o n volume ( o b t a i n e d by measurement o f the l o s s o f n.m.r. s i g n a l a r i s i n g from the l i q u i d s o l v e n t ) i n f r o z e n benzene s o l u t i o n s are thus shown t o be  23  Figure 5.  N.m.r. signal (and integral curves at various times)  arising from liquid benzene present at -5° in a frozen benzene solution i n i t i a l l y containing 0.64 M methyl iodide and 0.62 M triethylamine.  24  experimentally related. A, g  Both the change o f c o n c e n t r a t i o n , d A / d t = k g  and the change o f r e a c t i o n volume, d V^/dt  processes.  The  = k b j V^, S (  are  o b s e r v e d r a t e c o n s t a n t s under the c o n d i t i o n o f  b  s  {  j  first-order equal  r e a c t a n t c o n c e n t r a t i o n s are e x p e r i m e n t a l l y i d e n t i c a l , as expected i f l o s s of reactants r e s u l t s i n a corresponding A disadvantage  c o n t r a c t i o n o f the r e a c t i o n volume.  o f t h i s n.m.r. k i n e t i c method i s the n e c e s s i t y t o  s o l u t i o n s with high i n i t i a l concentrations. 1.26  The  t o t a l concentration  M a l l o w s , at the s t a r t o f the r e a c t i o n , o n l y about 20% o f  s o l v e n t t o be c r y s t a l l i z e d , w h i l e 0.1 were 94% s o l i d at the s t a r t o f the  of  the  M runs a n a l y z e d by i n f r a r e d  run.  use  techniques  25  B.  Base C a t a l y z e d D e c o m p o s i t i o n o f t - B u t y l p e r o x y  Formate i n  F r o z e n p_-Xylene.  I n o r g a n i c s o l u t i o n s the base c a t a l y z e d d e c o m p o s i t i o n o f t_-butylperoxy  formate (TBF)  i s a simple bimolecular r e a c t i o n i n v o l v i n g 23  a t t a c k by base on the formate hydrogen.  A dipolar transition state i s  formed and the f i n a l p r o d u c t s are carbon d i o x i d e and t - b u t y l a l c o h o l . 0 II  H-C-0-0-C(CH ) '+ B: 3  —  3  >-  :  BH  +  II  0  C  _  0-C(CH ) 3  >-  3  0  B: I t was £-xylene t h a t we  + C0  2  + HO-C(CH ) 3  3  d u r i n g an i n v e s t i g a t i o n o f t h i s r e a c t i o n i n l i q u i d found t h a t samples which had been s t o r e d i n the  r e f r i g e r a t o r t o await a n a l y s i s decomposed i f t h e y happened t o f r e e z e . The  i n v e s t i g a t i o n r e p o r t e d here was  explanation for t h i s  i n i t i a t e d to t r y to f i n d  an  observation.  Results The  same p r o d u c t s as are formed i n the l i q u i d , are formed by  reaction i n frozen solutions. p y r i d i n e i n p_-xylene,  A s o l u t i o n o f 0.347 M TBF  and 0.0758 M  f r o z e n i n l i q u i d n i t r o g e n and h e l d at 0° f o r 24  h o u r s , r e s u l t e d i n 92% carbon d i o x i d e and 96% t - b u t y l a l c o h o l , w h i l e  4%  o f the TBF  15°  (the m.p.  was  undecomposed.  The  same s o l u t i o n h e l d u n f r o z e n  o f pure p_-xylene i s 13.26°) f o r 24 hours was  at ca.  50% decomposed,  c l o s e t o the e x p e c t e d v a l u e as e x t r a p o l a t e d from r a t e s i n s o l u t i o n a t higher temperatures.  At lower c o n c e n t r a t i o n s  of r e a c t a n t s ,  o f t - b u t y l a l c o h o l and carbon d i o x i d e i n f r o z e n s o l u t i o n s was  formation also  26  i n d i c a t e d by i n f r a r e d a n a l y s i s o f k i n e t i c run samples. For k i n e t i c studies the r e a c t i o n i n d i l u t e frozen s o l u t i o n s was s u f f i c i e n t l y accelerated i n the frozen s t a t e to allow quenching simply by d e f r o s t i n g the samples of a run. Measurement of peroxide  concentration  23a was then c a r r i e d out at room temperature.  Figure 6 shows f i r s t - o r d e r  p l o t s f o r 2 , 6 - l u t i d i n e catalyzed TBF decomposition i n l i q u i d p_-xylene at 70° and i n frozen p_-xylene at 0° using i d e n t i c a l samples.  The frozen '23  s t a t e k i n e t i c runs were always, as with l i q u i d s o l u t i o n s studied e a r l i e r , f i r s t - o r d e r i n peroxide at a l l concentrations o f base or TBF.  Runs were  followed f o r two to four h a l f ^ l i v e s with no d e v i a t i o n o f the p l o t s from the l o g ( r e l a t i v e peroxide concentration) vs. time r e l a t i o n s h i p . The r e a c t i o n i n i n d i v i d u a l samples of a run and the observed rate constants were not a f f e c t e d by the volume o f sample, by surface or volume of added insolubl-e m a t e r i a l , nor by the manner i n which the samples were frozen.  Figure 7 shows the r e s u l t s f o r two widely d i f f e r e n t f r e e z i n g  methods, r e l a t i v e l y large samples frozen slowly over several minutes by seeding at 8° and small samples frozen immediately by immersion i n l i q u i d nitrogen.  D i f f e r e n t macroscopic d i s t r i b u t i o n s o f the c r y s t a l l i n e samples  were r e a d i l y apparent from the d i f f e r e n t r e l a t i v e transparency  o f the .r  s o l i d p_-xylene as frozen these two ways, but the observed rates were the same when the samples were brought to 0° f o r the k i n e t i c run. For t h i s  /  frozen s t a t e r e a c t i o n , as i n ordinary s o l u t i o n k i n e t i c s , the relevant v a r i a b l e s are the concentrations o f reactants, the temperature o f the run' and the p u r i t y of the solvent.  These were considered i n turn as f o l l o w s .  E f f e c t o f Concentration.  The r e s u l t s of v a r i a t i o n s i n the  i n i t i a l concentration of base and o f TBF f o r k i n e t i c runs i n frozen p_-xylene s o l u t i o n s at 0° are given i n Table IV. The peroxide  concentration  27  Time, minutes  Figure 6.  First-order plots for 2,6-lutidine catalyzed  decomposition of i>butylperoxy formate in £-xylene at 0° (frozen) and at 70° (not frozen) using identical samples.  28  0 0 2 9 3 molor T B F 0.0112 molor 2 , 6 - l u t i d i n e  1.8  p-xylene ot 0.0°  No  1.6  a-  cn o  1.4  1.2  1.0  o » 2 ml samples, frozen ot +8° with seeding 0*0.5 ml somples, frozen ot -195°  20  40  60  Time, minutes  Figure 7. First-order plot for, 2 , 6 - l u ^ of £-butylperoxy formate in frozen jv-xylene' at 0° in/^s amp ies i n i t i a l l y frozen at -195° and at 8°.  29  o f t h e s o l u t i o n s was u s u a l l y from 0.025 t o 0.03 M, w h i l e t h e base -4 c o n c e n t r a t i o n was v a r i e d from 3,8 x 10  t o 0.3 M.  T a b l e IV Observed Rate C o n s t a n t s f o r Base C a t a l y z e d D e c o m p o s i t i o n o f TBF i n F r o z e n p_-Xylene a t 0° Cone. TBF,  Cone, b^ase,  M i n  M  2  X  k ^  x  1 q 5  '  s e c  10  M x 10 2,6-Lutidine Catalyzed 2.57  ; 0.0386  2.69  2.88  0.0773  4.82  2.95  ,' 0.154 .  9.09  a  2.95  0.154  9.39  b  2.85  0.249  14.6  2.84  0.535  26.9  3.12  0.869  39.6  2.82  1.13  44.4  2.93  1.12  46.2  b  2.93  1.12  50.2  a  2.93  1.63  60.8  3.05  2.06  62.4  2.84  2.58  74.6  2.93  3.52  79.7  3.05  4.98  77.0  2.82  7.50  85.7  3.03 27.4  14.1  74.6  0.579  3.61 (continued)  *  30  (Table I V , c o n t i n u e d ) 29.2  1.49 Pyridine  .  Catalyzed  2.97  0.314  2.31  2.75  1.04  7.36  2.95  2.08  3.26  3.13  2.62  4.62  18.4  2.62  8.46  19.9  2.83  15.2  21.4  2.92  15.0  19.3  2.82  20.8  19.9  3.14  26.4  21.8  2.82  31.3  19.9  28.5 a  0.09  11.0 ,  13.6  14.2  Samples o f r u n f r o z e n a t -195°.  b  6.56 F r o z e n a t 8°. _4  Even w i t h a v e r y low c o n c e n t r a t i o n o f 2 , 6 - l u t i d i n e (3.8 x 10  M)  the base i s not " l o s t " when t h e s o l u t i o n i s f r o z e n , b u t r e t a i n s i t s c a t a l y t i c e f f i c i e n c y t o completely greater solution concentration. at t h e lowest  decompose t h e TBF a t some s i x t y f o l d  Comparisons o f r a t e s i n u n f r o z e n  solutions  c o n c e n t r a t i o n o f base c a t a l y s t t o r a t e s when t h e s o l u t i o n i s  f r o z e n shows t h a t t h e base i s r e l a t i v e l y most e f f i c i e n t a t low c o n c e n t r a t i o n s . -4 Thus t h e k  Q b s  f o r 3.8 x 10  the c a l c u l a t e d r a t e c o n s t a n t  M l u t i d i n e i s f o u r hundred times g r e a t e r than f o r r e a c t i o n a t 0° i n a s o l u t i o n o f t h i s  c o n c e n t r a t i o n , a t 0.14 M l u t i d i n e t h e observed r a t e c o n s t a n t i s o n l y t h i r t y times g r e a t e r than t h e r a t e c o n s t a n t  i n f r o z e n samples  f o r reaction i n solution.  31  The  k i n e t i c d a t a o f T a b l e IV may  be summarized by s t a t i n g  c o n s t a n t p e r o x i d e c o n c e n t r a t i o n and at low l u t i d i n e c o n c e n t r a t i o n s o b s e r v e d r a t e c o n s t a n t s a r e n e a r l y p r o p o r t i o n a l t o the  the  lutidine  c o n c e n t r a t i o n ; at h i g h l u t i d i n e c o n c e n t r a t i o n s the o b s e r v e d r a t e become Independent o f l u t i d i n e c o n c e n t r a t i o n  t h a t at  (see F i g u r e 8 ) .  constants  That i s ,  the o b s e r v e d k i n e t i c o r d e r changes from f i r s t - o r d e r t o z e r o - o r d e r i n l u t i d i n e as the l u t i d i n e c o n c e n t r a t i o n i s i n c r e a s e d . i s found w i t h p y r i d i n e as  A similar  result  catalyst.  When the l u t i d i n e c o n c e n t r a t i o n i s h e l d c o n s t a n t , and the c o n c e n t r a t i o n i n c r e a s e d , , the observed r a t e c o n s t a n t s o c c u r s even though the i n d i v i d u a l throughout s e v e r a l h a l f - l i v e s .  decrease.  peroxide  This  runs were always f i r s t - o r d e r i n TBF  These odd k i n e t i c e f f e c t s  are  discussed  below. Effect TBF  o f Temperature. The  rate of r e a c t i o n of 2 , 6 - l u t i d i n e with  i n f r o z e n p_-xylene shows the e x p e c t e d t e m p e r a t u r e dependence.  V presents constant liquid  the d a t a f o r runs i n the f r o z e n s t a t e from 12 t o -30°  Table at  i n i t i a l c o n c e n t r a t i o n s , as w e l l as runs at 50, 70 and 90°  in  p_-xylene. Table V  Observed Rate C o n s t a n t s f o r 2 , 6 - L u t i d i n e C a t a l y z e d D e c o m p o s i t i o n o f  TBF  at V a r i o u s Temperatures i n F r o z e n p_-Xylene Cone. TBF M x 10  2  Concn. 2 , 6 - L u t i d i n e M x 10  Temp.,°C  2  k  obs x 10 , 5  3.11  1.19  12.0  2.9  3.08  1.16  11.0  8.56 (continued)  a  sec."  1  32  (Table V,  continued) Cone,. 2 , 6 - L u t i d i n e  Cone. TBF M x 10  M x 10  2  Temp  2  obs j x 10 , sec." 5  3.08  1.19  10.0  13.8  3.09  1.25  8.0  23. l  3.08  1.19  6.0  33.5  3.08  1.19  4.0  39.2  3.08  1.19  2.0  52.4  3.08  1.19  0.0  47.6  3.11  1.19  0.0  50.2  C  3.12  0.87  0.0  39.6  d  3.05  1.16  -30.0  3.12  0.87  -10.0  29.6  3.14  1.74  -10.0  47.2  3.14  3.37  -10.0  66.0  b  7.61  €  d  Unfrozen S o l u t i o n s 3.08  1.16  50.0  3.11  1.19  70.0  28.2  3.10  1.04  90.0  74.5  2.72  0.21  90.0  14.6  3.09  2.08  90.0  a  8.76 C  137.  R e a c t i o n not f o l l o w e d t o c o m p l e t i o n , i n i t i a l r a t e c o n s t a n t ,  b, c, d, e  Denotes p a i r e d runs u s i n g same s o l u t i o n s a t d i f f e r e n t  temperatures. The observed  r a t e c o n s t a n t i n f r o z e n s o l u t i o n s i n c r e a s e s by a  f a c t o r o f e i g h t e e n on d e c r e a s i n g t h e temperature  from 12 t o 2°.  However,  33  Concentration of Base Catalyst . m o l a r  Figure 8. R e l a t i o n o f observed f i r s t - o r d e r r a t e constants t o the base concentration  f o r 2 , 6 - l u t i d i n e and p y r i d i n e c a t a l y z e d decomposition  of tj-butylperoxy formate i n frozen p_-xylene at 0°. The values o f o b s , high base cone. ^ ™™s were 120 x 1 0 " -1 - 5 - 1 sec. f o r 2 , 6 - l u t i d i n e and 24.7 x 10 s e c . f o r p y r i d i n e as k  catalyst.  u s e d  t o  c a l c u l a t e  5  34  at ca. 2° a f u r t h e r decrease i n temperature b e g i n s t o lower the r a t e . -30°  the r e a c t i o n s t i l l o c c u r s at an e a s i l y measurable  no l o s s o f p e r o x i d e o c c u r s o v e r l o n g p e r i o d s .  r a t e , but at  At  -70°  F i g u r e 9 shows t h a t the  runs remain f i r s t - o r d e r i n TBF and a l s o i l l u s t r a t e s t h a t t h e r e a c t i o n i s f a s t e r at -20 than at 11°.  F i g u r e 10 shows the dependence on  temperature i n b o t h l i q u i d and f r o z e n p_-xylene.  From runs i n l i q u i d a t  50, 70 and 90° the a c t i v a t i o n parameters f o r second-order r e a c t i o n o f TBF +  w i t h 2 , 6 - l u t i d i n e a r e AH  +  =12.3  k c a l . , AS  = -30.5  e.u., c l o s e t o the  2 3b  reported values i n the s i m i l a r solvent Effects of Impurities.  benzene.  The k i n e t i c r e s u l t s o f a d d i t i o n o f  v a r i o u s compounds t o t h e t h r i c e - r e c r y s t a l l i z e d p_-xylene used as s o l v e n t a r e given i n Table VI. benzene,  The r a t e i s d e p r e s s e d by such n e u t r a l compounds as  o_-xylene, m-xylene,  heptane and c a r b o n t e t r a c h l o r i d e .  At low  c o n c e n t r a t i o n s o f p e r o x i d e and o f l u t i d i n e , the r a t e i s e x t r e m e l y s e n s i t i v e t o the p r e s e n c e o f t h e s e i m p u r i t i e s (see F i g u r e 11).  At t h e  -2  c o n c e n t r a t i o n o f r e a c t a n t s g i v e n i n T a b l e V I , 1.5 x 10  M benzene (one  m o l e c u l e p e r f i v e hundred o f s o l v e n t ) decreases the r a t e by one h a l f . dampening o f t h i s e f f e c t i s shown i n t h a t 5.7 x 10 t o b r i n g about a n o t h e r decrease by one h a l f .  A  M benzene i s r e q u i r e d  I t i s s i g n i f i c a n t that, with  the e x c e p t i o n s o f t - b u t y l a l c o h o l and a n t h r a c e n e , a l l the compounds t e s t e d were n e a r l y e q u a l l y e f f e c t i v e i n d e p r e s s i n g the r a t e .  Anthracene had no  e f f e c t on the r a t e , and t_-butyl a l c o h o l at r e l a t i v e l y h i g h caused a s m a l l decrease i n k , . obs  concentrations  The observed k i n e t i c e f f e c t s o f these  compounds c o n s t i t u t e d a t e s t which showed t h a t the r e a c t i o n i n the f r o z e n T B F - l u t i d i n e - p _ - x y l e n e system does p r o c e e d i n u n f r o z e n r e g i o n s o f h i g h reactant  concentration.  35  Time .minutes  Figure 9.  First-order plots f o r 2,6-lutidine catalyzed  decomposition of t-butylperoxy formate i n f r o z e n p_-xylene at 11° at  -20°.  and  36  O 031 molar T B F a 0 1 2 molor 2,6-lutidme p-xylene  2.8  3.2 1/T  Figure 10.  3.6  4.0  xl0 ,(in 3  °K)  Temperature dependence o f o b s e r v e d r a t e c o n s t a n t s  f o r constant t^-butylperoxy formate and 2 , 6 - l u t i d i n e c o n c e n t r a t i o n s (Curved l i n e i s c a l c u l a t e d from k ^  s  = IK.2 C^).  i 50 K  °  °0  n , h r 0 C  o  e n e  0 0301 molor TBF 0.0119 molor 2,6-lutidine  0.02  0.04  0.06  Molor concentration of added substance  Figure 11.  Changes in observed rate constant, at constant  _t-butylperoxy formate and 2,6-lutidine concentrations, caused by addition of various compounds.  38  T a b l e VI Observed Rate C o n s t a n t s a t 0° f o r 2 , 6 - L u t i d i n e C a t a l y z e d D e c o m p o s i t i o n of TBF  a  i n F r o z e n p_-Xylene C o n t a i n i n g Added Compounds  Substance  Cone,  M x io  k , x 10 , sec." obs 5  2  none .  -  48. l  benzene  0.898  32.5  .• 1,49 "  .  :  b  24.1  2.84  17.8  "  5.71  10.3  o-xylene  1.16  28.9  m-xylene  1.19  28.9  anthracene  1.51  48.7  p_-cresol  1.99  17.0  t-butyl alcohol  3.32  33.2  heptane  3.68.  10.2  carbontetrachloride  4.31  11.5*  4.73  11.l  2,6-di-t>butyl-  " none  -  a  C o n c e n t r a t i o n o f TBF 0.030 M, o f 2 , 6 - l u t i d i n e 0.012 M.  b  D i f f e r e n t batches o f s o l v e n t .  46.3  5  b  1  39  Discussion  As i n S e c t i o n A above, a g e n e r a l e x p l a n a t i o n f o r the observed r e a c t i o n s i n f r o z e n s o l u t i o n s i n v o l v e s the e x i s t e n c e o f  liquid  r e g i o n s , s c a t t e r e d throughout the pure c r y s t a l l i n e s o l v e n t , c o n t a i n i n g high concentrations of reactants.  Any  r e a c t i o n h i g h e r than f i r s t - o r d e r ,  whose components are s o l u b l e i n the l i q u i d s o l v e n t and i n s o l u b l e i n the c r y s t a l l i n e s o l v e n t below the temperature o f f r e e z i n g , s h o u l d an a c c e l e r a t i o n when the system i s f r o z e n .  experience  B a s i c t o any treatment  o f such  r e a c t i o n s i s the requirement t h a t the l i q u i d " h o l e s " i n a f r o z e n s o l u t i o n must a l l c o n t a i n the same c o n s t a n t Although  t o t a l concentration of solutes.  the average volume o f the h o l e s might r e a s o n a b l y  be  expected  t o depend on the method o f f r e e z i n g , w i t h a g r e a t e r number o f s m a l l e r h o l e s formed on f a s t f r e e z i n g , a c o n s t a n t the u n f r o z e n  solute concentration i s required i n  r e g i o n s by the phase e q u i l i b r i u m between s o l u t i o n and  pure  solid. The may  q u a l i t a t i v e aspects of r a t e s of r e a c t i o n s i n frozen s o l u t i o n s  be v i s u a l i z e d , as a p p l i e d below f o r the TBF-base r e a c t i o n i n f r o z e n  p_-xylene,  i n terms o f two f a c t o r s ; v a r i a b l e volumes o f l i q u i d  c o n t a i n i n g constant concentrations  regions  t o t a l c o n c e n t r a t i o n , and d i f f e r e n t r e l a t i v e  i n these regions.  reactant  E x p e r i m e n t a l l y o b t a i n e d r a t e s , however,  are measured i n terms o f moles p e r l i t e r o f s o l u t i o n ( i . e . ,  the  c o n c e n t r a t i o n i s measured a f t e r d e f r o s t i n g ) and not i n terms o f the volume o r the c o n c e n t r a t i o n o f the l i q u i d r e g i o n s i n f r o z e n s o l u t i o n s . The  o b s e r v e d r a t e c o n s t a n t s may  c o n c e n t r a t i o n s as f o l l o w s :  be r e l a t e d t o the known s o l u t i o n  40  Rate i n l i q u i d r e g i o n s  =  P^  B^  Rate i n s o l u t i o n ( a f t e r d e f r o s t i n g ) = 6  5 , „.  Vu - k _ P, B, r r 2 h h V s  =  11  d t where P r e f e r s t o the p e r o x i d e c o n c e n t r a t i o n ,  B t o the base  concentration  and the s u b s c r i p t s h and  s t o the l i q u i d r e g i o n s  r e s p e c t i v e l y , as above.  Assuming a l l the s o l u t e s are p r e s e n t i n the  regions  and thawed s o l u t i o n liquid  o f a f r o z e n s o l u t i o n then  P, V, = P V h h s s  B. V, h  = B  h  V  o  C, V, = (P + B + 1 + Prod ) V h h s o o s s  s  In terms o f the amount r e a c t e d , i f the e q u i v a l e n t  o f one  mole  o f p r o d u c t i s d e r i v e d from one mole o f p e r o x i d e (see d i s c u s s i o n below) then P  g  = (P  q  - x) and x = P r o d s  P The  2  o  h B  o  S u b s t i t u t i o n and  + P  observed r a t e c o n s t a n t  concentrations  +  o  Im  i n t e g r a t i o n gives  o  i n terms o f i n i t i a l s o l u t i o n  i s then k , obs  = k. C, 2 h  B  B  o  + P o o  In the d e c o m p o s i t i o n o f TBF  +  = Im  (5) o  i n f r o z e n p_-xylene, changes i n  r e a c t i o n c o n d i t i o n s by v a r i a t i o n o f b a s e , p e r o x i d e o r concentrations,  ''impurity"  o r by v a r i a t i o n i n t e m p e r a t u r e , a l l r e s u l t i n changes i n  the o b s e r v e d r a t e c o n s t a n t s Concentration pseudo-first-order  according  of Reactants.  rate constants  c a t a l y z e d d e c o m p o s i t i o n o f TBF  t o eq  5.  F i g u r e 8 shows the observed  at 0° f o r 2 , 6 - l u t i d i n e and  at near c o n s t a n t  TBF  pyridine  concentration  as  a  41  f u n c t i o n o f base c o n c e n t r a t i o n . equation n  curved  The r e l a t i o n s h i p p r e d i c t e d from B 1 i n t h e form k , = k , , v i s g i v e n by t h e obs obs, h i g h base g + P o o  lines.  The change i n observed k i n e t i c o r d e r from f i r s t - o r d e r i n  base a t low base c o n c e n t r a t i o n s t o z e r o - o r d e r  i n base a t h i g h base  c o n c e n t r a t i o n s a r i s e s from t h e changing r a t i o o f base t o t o t a l s o l u t e concentration.  A t low base c o n c e n t r a t i o n s t h e l i q u i d r e g i o n s i n which  the f r o z e n s o l u t i o n r e a c t i o n proceeds a r e f i l l e d p r e d o m i n a n t l y TBF,  and an i n c r e a s e i n base  the r e a c t i o n volume.  with  c o n c e n t r a t i o n does not a p p r e c i a b l y  increase  But as t h e a b s o l u t e c o n c e n t r a t i o n o f base i n t h e  l i q u i d regions i s increased the rate o f the r e a c t i o n i s also p r o p o r t i o n a t e l y i n c r e a s e d and t h e r e a c t i o n appears t o be f i r s t - o r d e r i n base as w e l l as i n TBF. On t h e o t h e r hand, a t h i g h base c o n c e n t r a t i o n s t h e l i q u i d are f i l l e d predominantly  regions  w i t h t h e base, a f u r t h e r i n c r e a s e i n base  concentration o f the i n i t i a l s o l u t i o n s serves only to enlarge the r e a c t i o n volumes i n t h e f r o z e n s o l u t i o n s .  The base c o n c e n t r a t i o n i n t h e r e a c t i o n  r e g i o n s remains c o n s t a n t , t h e f i r s t - o r d e r r a t e c o n s t a n t and t h e r e a c t i o n appears t o be z e r o - o r d e r  remains t h e same  i n base c o n c e n t r a t i o n .  I f runs a t c o n s t a n t base c o n c e n t r a t i o n b u t d i f f e r e n t c o n c e n t r a t i o n s a r e compared t h e r a t e c o n s t a n t s decrease with i n c r e a s i n g peroxide peroxide  observed (see T a b l e IV)  concentration.  c o n c e n t r a t i o n i n an u n f r o z e n  peroxide  The p r e s e n c e o f g r e a t e r  s o l u t i o n r e s u l t s i n a g r e a t e r volume  of l i q u i d regions i n a frozen s o l u t i o n .  T h i s l a r g e r volume d i l u t e s t h e  a v a i l a b l e base down t o a lower c o n c e n t r a t i o n and t h e observed r a t e constant i s correspondingly decreased. e. The g r e a t e r c a t a l y t i c e f f e c t o f l u t i d i n e i s expected from i t s g r e a t e r basicity. See r e f e r e n c e 23b.  42  Temperature Dependence.  The  second-order r a t e c o n s t a n t f o r  b i m o l e e u l a r r e a c t i o n i n s o l u t i o n decreases + + temperature (AH  = 12.3  k c a l , AS  = -30.5  w i t h a decrease i n e.u.)  but the  concentrations  o f the l i q u i d r e g i o n s i n f r o z e n s o l u t i o n s i n c r e a s e w i t h a decrease i n temperature.  As a consequence the r a t e shows a maximum at s e v e r a l degrees  below the f r e e z i n g p o i n t o f the s o l u t i o n . k^g  a g a i n s t 1/T  F i g u r e 10 i s a p l o t o f l o g  f o r r e a c t i o n i n l i q u i d and i n f r o z e n s o l u t i o n s at  constant i n i t i a l c o n c e n t r a t i o n s . the r e l a t i o n s h i p k ^  g  = k^C^  The  where k^  curved  l i n e i s c a l c u l a t e d from  i s o b t a i n e d by e x t r a p o l a t i o n o f  the r a t e s observed i n l i q u i d s o l u t i o n s at 90, 70 and 50°  and  is  o b t a i n e d from measurements o f the c o n c e n t r a t i o n o f 2 , 6 - l u t i d i n e r e q u i r e d to prevent  f r e e z i n g o f p_-xylene at v a r i o u s temperatures ( i . e . , from  the phase e q u i l i b r i a o f the p _ - x y l e n e - 2 , 6 - l u t i d i n e system.) . From the correspondence o f the observed r a t e c o n s t a n t s w i t h the t h e o r e t i c a l  curve  shown i n F i g u r e 10 i s apparent t h a t the form o f t h e observed temperature dependence i s w e l l r e p r o d u c e d by the r e l a t i o n s h i p k ^ Q  s  = k^ C^.  The  magnitude o f the c a l c u l a t e d f i r s t s - o r d e r r a t e c o n s t a n t s are n o t , however, g i v e n d i r e c t l y by t h i s r e l a t i o n s h i p but s h o u l d be m o d i f i e d by the r a t i o o f base c o n c e n t r a t i o n to t o t a l s o l u t e c o n c e n t r a t i o n (see eq 5 ) .  When t h i s i s  done the c a l c u l a t e d r a t e c o n s t a n t s are less by a f a c t o r o f about f i v e than the e x p e r i m e n t a l  rate constants.  T h i s d i s c r e p a n c y may  be due t o a  change i n r e l a t i v e r e a c t a n t c o n c e n t r a t i o n s i n the l i q u i d r e g i o n s from t h a t expected  from r e l a t i v e c o n c e n t r a t i o n s i n u n f r o z e n s o l u t i o n s o r i t may f caused by an i n c r e a s e i n r a t e due t o a s o l v e n t e f f e c t . S i n c e the  f  be  S i n c e both TBF and 2 , 6 - l u t i d i n e are more p o l a r t h a n p_-xylene, an i n c r e a s e i n r e a c t i o n r a t e at h i g h s o l u t e c o n c e n t r a t i o n (analogous t o the i n c r e a s e observed^^b f h i g h p y r i d i n e c o n c e n t r a t i o n s i n heptane as s o l v e n t ) might be expected. o  r  43  r e a c t i o n regions contain high concentrations  o f TBF and 2 , 6 - l u t i d i n e ,  the k^ as measured i n d i l u t e s o l u t i o n s and e x t r a p o l a t e d from h i g h e r t e m p e r a t u r e s cannot be s t r i c t l y a p p l i c a b l e . Effect of Impurities.  F i g u r e 11 p r e s e n t s  the e f f e c t s o f  a d d i t i o n o f v a r i o u s compounds t o f r o z e n k i n e t i c runs a t c o n s t a n t TBF  and base c o n c e n t r a t i o n s .  initial  F o r s o l u b l e compounds a d e c r e a s e i n r a t e  i s e x p e c t e d as t h e r e a c t i o n volumes i n c r e a s e t o i n c o r p o r a t e t h e o t h e r w i s e i n e r t compound.  F o r i d e a l s o l u t i o n s , t h e observed d e c r e a s e i n r a t e s h o u l d  depend o n l y on t h e c o n c e n t r a t i o n and not on t h e s t r u c t u r e o f t h e added compound.  This i d e a l behaviour  o f o-xylene,  m-xylene, benzene, and  c a r b o i ^ e t r a c h l o r i d e ; as s o l u t e s i n p_-xylene was shown s e p a r a t e l y by f r e e z i n g p o i n t - c o m p o s i t i o n measurements down t o -5° (see F i g u r e 1 2 ) .  A l l  o f t h e s e compounds a r e e q u a l l y a b l e t o depress t h e f r e e z i n g p o i n t o f p_-xylene.  The r a t e , depression:.given, by these compounds i s somewhat g r e a t e r ' ' B + P '. t h a n p r e d i c t e d from t h e r e l a t i o n k , = k , . — obs obs, no i m p u r i t y g p j o o 6 :  0  +  d e r i v e d from eq 5.  T h i s might be due t o r e l a t i v e l y lower  o f base o r p e r o x i d e  i n t h e l i q u i d r e g i o n s than' expected from  concentrations initial  setation*: concentrations;.;.-; The. impurity-: would, t h e n be a t r e l a t i v e l y c o n c e n t r a t i o n and t h e k , obs  +  higher  f u r t h e r decreased.  A s a t u r a t e d s o l u t i o n o f anthracene i n p_-xylene does n o t have a f r e e z i n g p o i n t l e s s than 13°.  No anthracene can be d i s s o l v e d i n l i q u i d  p_-xylene a t 0° and no e f f e c t on t h e r a t e o f TBF r e a c t i o n i n f r o z e n p_-xylene i s expected nor observed. t - B u t y l a l c o h o l i s much l e s s capable o f d e p r e s s i n g  the r a t e  o f r e a c t i o n o f TBF w i t h 2 , 6 - l u t i d i n e i n f r o z e n p_-xylene, o r o f d e p r e s s i n g t h e f r e e z i n g p o i n t o f p_-xylene than a r e t h e compounds mentioned above (see F i g u r e 1 2 ) . These o b s e r v a t i o n s  a r e r e l a t e d , o f c o u r s e , and c o n s i s t e n t w i t h  44  Molar concentration of substance in p-xylene  F i g u r e 12. R e l a t i o n o f f r e e z i n g p o i n t o f p_-xylene s o l u t i o n s t o the c o n c e n t r a t i o n o f v a r i o u s s o l u t e s .  45  the e x p e c t e d s e l f - a s s o c i a t i o n o f t_-butyl a l c o h o l by hydrogen b o n d i n g . T h i s f a c t o r f o r t u n a t e l y makes t h e TBF-base r e a c t i o n s i m p l e r than might be expected.  The  s t o i c h i o m e t r i c p r o d u c t i o n o f two moles o f  (carbon d i o x i d e and t - b u t y l a l c o h o l ) from one mole o f TBF  products  should  i n an enlargement o f the r e a c t i o n volume d u r i n g a k i n e t i c r u n .  result However,  carbon d i o x i d e i s not h i g h l y s o l u b l e i n p_-xylene at low t e m p e r a t u r e s t-butyl alcohol i s associated. d i o x i d e at one  atm.  pressure  and  For comparison, the s o l u b i l i t y o f carbon • 'o '  i n t o l u e n e at 0  i s c a . 0.14  M  24  .  This i s  c o n s i d e r a b l y l e s s than the 2.35  M c o n c e n t r a t i o n o f s o l u t e s i n the r e a c t i o n  r e g i o n s at 0°  The  products  (see F i g u r e 12).  forms from one mole o f TBF  T h i s -approximation  assumption t h a t one mole o f s o l u b l e i s r e q u i r e d i n o r d e r t o o b t a i n eq  seems r e a s o n a b l e ,  and i s c o n s i s t e n t w i t h the  5.  observation  of s t r a i g h t f i r s t - o r d e r k i n e t i c p l o t s . The  form o f the r a t e d e p r e s s i o n  i m p u r i t i e s at c o n s t a n t  caused by v a r i o u s amounts o f  r e a c t a n t c o n c e n t r a t i o n s as i l l u s t r a t e d i n F i g u r e  i s c o n s i s t e n t w i t h eq 5.  A n o t h e r way  o f i l l u s t r a t i n g the e f f e c t  11  of  i m p u r i t i e s i s shown i n F i g u r e 13 where r a t e s i i i pure and i n impure s o l v e n t s are compared o v e r a range o f base c o n c e n t r a t i o n s . As i s p r e d i c t e d by B + p the r e l a t i o n s h i p k , •= k , . ' —, the e f f e c t o f " obs obs, no i m p u r i t y g + p + I 0  o  o  o  i m p u r i t i e s i s g r e a t e s t at low r e a c t a n t c o n c e n t r a t i o n s .  At  high  r e a c t a n t c o n c e n t r a t i o n s the r a t e i n impure s o l v e n t i s the same as i n pure solvent.  46  Pyridine concentration, molar  Figure i 3 . E f f e c t o f i m p u r i t i e s (ca; 0.04 M) on the observed rate constant f o r r e a c t i o n o f t-butylperoxy formate w i t h p y r i d i i n frozen p_-xylene at various concentrations of p y r i d i n e .  47  C.  Ethylene Chlorohydrin  w i t h H y d r o x y l Ion i n I c e 25  The  r e a c t i o n o f ethylene  c h l o r o h y d r i n w i t h sodium h y d r o x i d e  i s c o n v e n i e n t f o r an i n v e s t i g a t i o n o f a r e a c t i o n i n i c e . Cl-CH -CH -OH 2  +  2  NaOH  +  A,  CH -CH 2  2  +  H 0 2  &  +  NaCl  T h i s r e a c t i o n s t r i c t l y f o l l o w s second-order k i n e t i c s and r a t e are w e l l e s t a b l i s h e d r i g h t down t o 0°  constants  . A s p e c i f i c reaction o f hydroxyl  i o n , r a t h e r $han g e n e r a l b a s e - c a t a l y s i s has been e s t a b l i s h e d , and l i t t l e 27 o r no s a l t e f f e c t i s observed and c o m p l i c a t i o n s  . Buffered s o l u t i o n s are not necessary  a r i s i n g from t h e i r u s e , as i n o t h e r s t u d i e s  i n i c e , may be a v o i d e d .  o f reactions  1 0  I n a d d i t i o n , t h e r e a c t a n t s and p r o d u c t s a r e a l l  h i g h l y s o l u b l e i n water and no n e t change i n t h e number o f s o l u t e s o c c u r s during the reaction. Results The  r e a c t i o n was s t u d i e d by a n a l y s i s f o r r e s i d u a l h y d r o x i d e i o n  i n thawed samples o f a r u n . reactant  concentrations  concentrations  Plots of r e c i p r o c a l concentration  f o r equal  o r l o g ([C1CH CH 0H]/[0H~]) f o r unequal 2  2  a g a i n s t time gave the b e s t s t r a i g h t l i n e s .  reactant  Although  i n d i v i d u a l runs then showed second-order k i n e t i c s , t h e o b s e r v e d r a t e constants  v a r i e d g r e a t l y from r u n t o r u n . As shown i n T a b l e V I I , t h e  l a r g e s t values °  o f k , were found a t t h e lowest i n i t i a l obs  reactant  concentrations.  g.  The use o f the word i . c e can be d e c e p t i v e i n t h a t i t seems t o denote the presence o f o n l y a s o l i d phase. However, depending on the s o l u t e , w  I!  f r o z e n s o l u t i o n s may c o n t a i n l i q u i d r e g i o n s i n e q u i l i b r i u m w i t h s o l i d at temperatures c o n s i d e r a b l y below t h e f r e e z i n g p o i n t . With t h i s i m p o r t a n t f a c t i n mind, the convenience o f the name would seem t o make p e r m i s s i b l e i t s use t o denote not o n l y pure s o l i d water, but a l s o the  apparent-,' s t a t e o f a f r o z e n aqueous s o l u t i o n .  48  F i g u r e 14 shows some r u n s , u s i n g e q u i m o l a r b u t d i f f e r e n t i n i t i a l c o n c e n t r a t i o n s o f r e a c t a n t s a t -5°, p l o t t e d as sepond-order reactions.  The d i f f e r e n t s l o p e s o f t h e l i n e s i l l u s t r a t e t h a t t h e observed  r a t e c o n s t a n t s depend on t h e i n i t i a l r e a c t a n t c o n c e n t r a t i o n s o f t h e unfrozen  solutions.  However, i t may be n o t e d from t h e f i g u r e , t h a t t h e  time taken t o d e c r e a s e t h e c o n c e n t r a t i o n by one h a l f i s e s s e n t i a l l y t h e same i n a l l t h e runs (about 250 m i n . ) . With an i n i t i a l r e a c t a n t c o n c e n t r a t i o n o f 0.01 M, t h e o b s e r v e d r a t e under f r o z e n c o n d i t i o n s a t -5° i s about one hundred times t h a n t h e r a t e i n an u n f r o z e n  greater  s o l u t i o n a t t h e same t e m p e r a t u r e .  lower i n i t i a l c o n c e n t r a t i o n t h e r e l a t i v e r a t e i n c r e a s e i s s t i l l  At a greater,  but i n d i v i d u a l p o i n t s o f a r u n become more s c a t t e r e d (see E x p e r i m e n t a l ) .  _3 C a r e f u l pH measurements o f thawed samples from a f r o z e n r u n i n i t i a l l y 10 m o l a r i n each r e a c t a n t showed t h a t t h e r e a c t i o n proceeded w i t h t h e e x p e c t e d h a l f - l i f e o f about 200-230 min. a t -5°. T h i s i s almost one thousand times f a s t e r than t h e r a t e o f r e a c t i o n i n a s u p e r c o o l e d  liquid  s o l u t i o n at t h i s temperature. A s e r i e s o f runs a t d i f f e r e n t temperatures b u t w i t h t h e same c o n c e n t r a t i o n o f e t h y l e n e c h l o r o h y d r i n and sodium h y d r o x i d e t h a t t h e f r o z e n r e a c t i o n had a maximum r a t e a t ca.. -5°  showed  (see T a b l e V I I I ) .  A d d i t i o n o f sodium c h l o r i d e , sodium n i t r a t e o r e t h a n o l had t h e same r a t e depressing solutions  e f f e c t p e r mole o f s o l u t e on t h e r e a c t i o n i n f r o z e n (Table I X ) .  49  0  100  '• 200  300  Time, min  Figure 14.  Second-order kinetic plots for reaction of equimolar ethylene chlorohydrin with sodium hydroxide in frozen aqueous solutions at - 5 ° " Concentrations are those in unfrozen solutions.  50  Table V I I  Observed Second-Order Rate C o n s t a n t s a t V a r i o u s I n i t i a l  Concentrations  f o r R e a c t i o n o f E t h y l e n e C h l o r o h y d r i n w i t h Sodium H y d r o x i d e i n F r o z e n Aqueous S o l u t i o n s a t -5.0°.  [0H~] o L  J  x 10  (moles/1.)  2 1  [ C l f C H J OH1 2'2 o v  (moles/1.)  x 10  2  k , obs  x 10  (l.mole  10.0  10.0  8.35  10.7  6.0  8.80  5.0  10.3  k . C obs s  4  sec. )  x 10  ( s e c . *)  2.50  a , b  2.41  10.4  2.11  5.0  9.82  10.5  2.08  4.7  4.83  17.5  2.52  3.26  3.26  22.6  2.21  2.50  2.50  27.3  2.05  1.67  1.65  41.2  2.05  1.3  1.3  56.4  2.20  1.0  1.07  87.6  2.69  0.1  0.1  843.  2.53°  0.1  0.1  953.  2.86°  a  C S  = total solute concentration = 2[OH ] 0  4  + [Cl(CH^) OHj Z  £  0  b  The value of k , C should be constant in a l l runs (see text). obs s  c  Reaction followed by changes in pH of thawed solutions (see Experimental)  51  Table V I I I  E f f e c t o f Temperature on t h e R e a c t i o n of. 0.05 M E t h y l e n e C h l o r o h y d r i n w i t h 0.05 M  Sodium H y d r o x i d e i n F r o z e n Aqueous S o l u t i o n s .  Temperature r  (°C)  A  k , x 10 obs, j (1.mole" sec." )  k . C x 10 obs s j (sec." )  A  -0.7.  0.96  6.34  -1.3  10.5  1.57  -3.0  15.2  2.27  -4.0  16.5  2.48  I -4.5  15.7 '  2.36  -5.0  17.5  2.52  -7.5  13,9  2.06  -10.0  11,5  1.76  -14.9  .  -2.9  a  T h i s run at 0.05  M NaOH and  6,18  0.925  9.40  1.96  0.108  M ethylene  a  chlorohydrin.  4  52  T a b l e IX  E f f e c t o f Added S o l u t e s on t h e R e a c t i o n o f 0.05 M E t h y l e n e  Chlorohydrin  w i t h 0.05 M Sodium Hydroxide i n F r o z e n Aqueous S o l u t i o n s a t -4.0° 1  Solute Concentration (moles/1.)  4  k , C x 10 obs s  (1. mole *sec. *)  ( s e c . *)  2.48  3.56 NaCl  10.9  2.50  "  9.91  3.27  "  .8.18  3.39  12.8  3.00  10.4  3.38  2.74 NaN0 6.09  "  12.65  "  3  8.33  ,  3.35  4.36 C H 0 H  14.2 •  2.72  8.83  11.4  2.70  2  =  k , x 10 obs  16.5  10.7  g  2  none  6.50  C  x 10  5  "  t o t a l solute concentration  ( i n c l u d i n g added s o l u t e s )  a  4  53  Discussion  I f e f f e c t s o t h e r than t h e c o n c e n t r a t i o n e f f e c t a r e a l s o o p e r a t i v e i n t h i s r e a c t i o n , then d e v i a t i o n s from t h e f o l l o w i n g q u a n t i t a t i v e treatment  o f t h e ClCf-^Ch^OH - NaOH r e a c t i o n i n i c e s h o u l d  appear. The a p p l i c a t i o n t o t h i s r e a c t i o n o f t h e g e n e r a l e q u a t i o n  f o r the  concentration effect gives the f o l l o w i n g r e l a t i o n s h i p .  d[OHJ  s  •k  2  [OH-] [ClCH CH 0H] h  2  2  (6)  u  dt  This equation r e l a t e s the r a t e o f l o s s o f hydroxide  i o n (as  measured i n thawed s o l u t i o n s ) t o c o n c e n t r a t i o n s and volumes o f t h e l i q u i d "reaction regions" i n the frozen s o l u t i o n s .  The c o n c e n t r a t i o n s  [0H~]^ and  [ C I C H ^ H ^ H ] ^ and t h e t o t a l volume o f t h e r e a c t i o n r e g i o n s , V^, were n o t d i r e c t l y measured.  In o r d e r t o s u b s t i t u t e f o r these v a r i a b l e s , t h e  assumptions made a r e t h a t t h e reagent c o n c e n t r a t i o n s i n t h e l i q u i d p a r t o f a f r o z e n s o l u t i o n a r e r e l a t e d t o t h e reagent c o n c e n t r a t i o n i n t h e thawed s o l u t i o n by [ 0 H " ]  h  V  = [ O H ] ^ and by [ C l C H C H O H ] -  h  2  2  h  V  h  = ,JG1CH CH 0H] 2  2  V .  In a d d i t i o n , s i n c e a l l t h e s o l u t e s i n v o l v e d a r e h i g h l y s o l u b l e ([ClCH CH OH] 2  ^ ^ s  s  =  2  s  /0, + [CH -CH ] 2  2  ^h^h where [Inv]  s  +  + [Na j  s  g  _ + [OH ]  g  _ + [Cl ]  g  + [Im] )V s  s  =  i s t h e c o n c e n t r a t i o n o f any i m p u r i t y o r o t h e r  added s o l u t e , C^ i s t h e t o t a l c o n c e n t r a t i o n o f t h e l i q u i d r e a c t i o n r e g i o n s o f a f r o z e n s o l u t i o n , and C  i s the t o t a l concentration o f solutes i n the s  thawed s o l u t i o n .  54  S u b s t i t u t i o n o f these r e l a t i o n s i n t o eq 6 g i v e s t h e f o l l o w i n g rate  expression.  d[0H"l  k C 1  =  .  dt  -LU  [OH ]  C •s  As C  g  [C1CH CH OH] *  s  1  (7)  s  has a c o n s t a n t v a l u e throughout t h e r e a c t i o n (one mole o f  s o l u b l e r e a c t a n t i s r e p l a c e d by one mole o f s o l u b l e p r o d u c t ) , and b o t h and C^ a r e f u n c t i o n s o n l y o f t e m p e r a t u r e , t h i s r e a c t i o n i n f r o z e n s o l u t i o n s i s p r e d i c t e d by eq 7 t o be s e c o n d - o r d e r under a l l c o n d i t i o n s . This i s consistent with the experimental  o b s e r v a t i o n s mentioned above.  From eq 7 i t i s a l s o seen t h a t t h e o b s e r v e d s e c o n d - o r d e r r a t e constants  f o r runs w i t h f r o z e n s o l u t i o n s a r e r e l a t e d t o normal second-  order r a t e constants  k , obs  i n unfrozen  =  s o l u t i o n s by eq 8.  ————-  (8)  s S i n c e C V = C,V, then k , i s a l s o equal t o k_V /V, . s s h h obs 2 s h n  constant  d i f f e r s from t h e r a t e c o n s t a n t  The observed r a t e  by t h e r a t i o o f volume o f  s o l u t i o n t o volume o f r e a c t i o n r e g i o n s i n a f r o z e n s o l u t i o n .  Since a  g i v e n number o f moles o f r e a c t a n t i s r e p l a c e d d u r i n g a r u n by t h e same number o f moles o f p r o d u c t s , However, i n s e p a r a t e  t h e volume  runs a g r e a t e r i n i t i a l  g i v e s a g r e a t e r volume  does not v a r y d u r i n g a r u n . concentration of solutes, C ,  and a d e c r e a s e i n k ^  s  occurs  F o r comparison o f o b s e r v e d r a t e c o n s t a n t s  (see T a b l e V I I ) .  to values p r e d i c t e d  by eq 8, C^ may be o b t a i n e d from t h e l i q u i d - s o l i d phase r e l a t i o n s h i p s o f the e t h y l e n e c h l o r o h y d r i n - water system, and k^ by e x t r a p o l a t i o n from h i g h e r t e m p e r a t u r e s o f t h e r a t e d a t a a v a i l a b l e from normal l i q u i d phase  55  kinetic studies.  C  i s known from t h e t o t a l i n i t i a l s o l u t e c o n c e n t r a t i o n  s f o r each r u n , i . e . , C  s  = [C1CH CH OH] 2  2  + [Na ] +  q  + [OH ]  + [Im] .  -  Q  At c o n s t a n t t e m p e r a t u r e t h e p r e d i c t e d r e l a t i o n s h i p o f k ^ to C  g  i s shown by t h e l i n e i n F i g u r e 15.  The c l o s e f i t o f e x p e r i m e n t a l  p o i n t s t o t h e t h e o r e t i c a l curve i n d i c a t e s t h a t t h i s r e a c t i o n i n f r o z e n s o l u t i o n s i s w e l l accounted f o r by t h e c o n c e n t r a t i o n e f f e c t .  This i s  a l s o shown i n T a b l e V I I by t h e n e a r l y c o n s t a n t v a l u e s o f t h e p r o d u c t o f observed r a t e c o n s t a n t  times t h e t o t a l s o l u t e c o n c e n t r a t i o n , i . e . k., C:. obs s  T h i s c o n s t a n c y a r i s e s from t h e r e l a t i o n s h i p k ^ g C that both k  2  and  = k C ^ and t h e f a c t 2  a r e dependent o n l y on t e m p e r a t u r e .  That t h e f i r s t h a l f - l i f e . i s independent o f i n i t i a l  concentration  i s consistent with a "concentration e f f e c t " s i n c e , i n the l i q u i d regions o f a f r o z e n s o l u t i o n , t h e same c o n c e n t r a t i o n o f r e a c t a n t s i s produced by t h e c o n t r a c t i o n o f volume brought about by c r y s t a l l i z a t i o n o f s o l v e n t . r e a c t i o n i n f r o z e n s o l u t i o n s always b e g i n s  As t h e  a t t h e same c o n c e n t r a t i o n ,  independent o f t h e c o n c e n t r a t i o n s o f t h e u n f r o z e n  s o l u t i o n s , the f i r s t  h a l f - l i f e s h o u l d be t h e same i n every r u n . A q u a n t i t a t i v e e v a l u a t i o n o f t h i s , observed i n i t i a l h a l f - l i f e f o r runs a t e q u i m o l a r c o n c e n t r a t i o n can be made u s i n g t h e u s u a l r e l a t i o n s h i p between h a l f - l i f e ( t j y ^ , r a t e c o n s t a n t concentration  ( k ) and  (C) f o r a second-order r e a c t i o n , i . e . t-|y  normal s e c o n d - o r d e r r a t e c o n s t a n t McCabe and Warner  is  2  = 2  l/k,,C.  The  a t -5°, e x t r a p o l a t e d from t h e d a t a o f  = 1.0 x 10 ^ l.mole ^ s e c . *.  The t o t a l  c o n c e n t r a t i o n i n t h e l i q u i d r e a c t i o n r e g i o n s o f a f r o z e n aqueous s o l u t i o n at -5° i s about 2.6 m o l a r , and t h i s c o n c e n t r a t i o n . d i v i d e d among t h e s o l u t e s , Na , +  0H~ and CICH.CH-OH, c o r r e s p o n d s t o 0.86 molar i n i t i a l  reactant  56  ClCH CH 0H +NoOH in H 0 2  2  2  Frozen, -5.0°C  0,1  0.2  03  Total Solute Concentration, M  Figure 15, Relation of observed second-order rate constants for r e a c t i o n of ethylene c h l o r o h y d r i n with sodium hydroxide i n frozen aqueous s o l u t i o n s at -5.0° to t o t a l i n i t i a l s o l u t e concentration (C ) . The curve s -4 i s c a l c u l a t e d firom k . = k-C,/C = (1.07 x. 10 ) obs 2 n s C2.3)/C . s  57  concentration.  The e x p e c t e d h a l f - l i f e i s then r o u g h l y t j y  = 2  -4 1/(1.0 x 10  ) ( 0 . 8 6 ) s e c . o r 195 min. T h i s i s r e a s o n a b l y  close t o the  observed t i m e o f c a . 250 min. The  temperature v a r i a t i o n o f t h i s r e a c t i o n i n f r o z e n s o l u t i o n s  i s shown i n F i g u r e 16, where e x p e r i m e n t a l  values o f "  at various  K  temperatures a r e compared t o c a l c u l a t e d v a l u e s o f kJZ^.  The maximum i n  t h e c u r v e , caused by t h e c o m p e t e t i v e e f f e c t s o f i n c r e a s e s i n decreases i n k of k ^ C Q  s  s  2  as t h e temperature i s lowered,  and  and t h e c l o s e r e l a t i o n s h i p  t o k Cp a r e apparent from t h e diagram. 2  i  F i n a l l y , t h e e f f e c t a t - 4 . 0 ° o f t h e s o l u t e s N a C l , NaNO^ and e t h a n o l on t h e observed r a t e c o n s t a n t  i s i l l u s t r a t e d i n F i g u r e 17.  g i v e s t h e r e l a t i o n s h i p p r e d i c t e d from eq 8 t h e form k _ QU  s  = k C^/C 2  (1.26 x 1 0 ~ ) ( 1 . 9 ) / ( 0 . 1 5 + I m ) . The o b s e r v e d r a t e c o n s t a n t s 4  Q  This =  s  are s l i g h t l y  g r e a t e r t h a n p r e d i c t e d ; however, w i t h a t o t a l o f 1.9 M s a l t and r e a c t a n t concentration i n the l i q u i d regions o f the frozen s o l u t i o n s , the a c t u a l r e a c t i o n c o n d i t i o n s d i f f e r from those used i n o b t a i n i n g t h e second-order rate constants, k  2>  at higher temperatures.  Such s m a l l v a r i a t i o n o f t h e  p r e d i c t e d from o b s e r v e d v a l u e s might be due t o i n e x a c t v a l u e s o f k  2  o r C^  as w e l l as s a l t o r s o l v e n t e f f e c t s a t t h e h i g h s o l u t e c o n c e n t r a t i o n s o f t h e reaction conditions. In summary, t h e c h a r a c t e r i s t i c s o f t h e e t h y l e n e c h l o r o h y d r i n sodium h y d r o x i d e  r e a c t i o n i n f r o z e n aqueous s o l u t i o n s a r e f u l l y accounted  f o r by t h e c o n c e n t r a t i o n e f f e c t a l o n e .  When t r e a t e d a c c o r d i n g t o eq 6,  which c o r r e l a t e s c o n c e n t r a t i o n changes d u r i n g a r u n and t h e volume changes h  To a l l o w f o r temperature e q u i l i b r a t i o n , t h e f i r s t sample o f a r u n was t a k e n 10-30 minutes a f t e r f r e e z i n g t h e samples; thus t h e observed i n i t i a l h a l f - l i f e s h o u l d be g r e a t e r than t h e v a l u e c a l c u l a t e d above, as i s t h e case.  58  I  Temperature, °C  F i g u r e 16 Temperature v a r i a t i o n o f " k k C 0  o  s  f o r r e a c t i o n o f 0.05 M  s  e t h y l e n e c h l o r o h y d r i n w i t h 0.05 M sodium h y d r o x i d e i n f r o z e n aqueous s o l u t i o n s .  The s o l i d c u r v e g i v e s  c a l c u l a t e d v a l u e s o f ^- h' C  c  i  r  c  l  e  s  a  r  e  2  v a l u e s o f k^gC^..  experimental  Dotted l i n e s a r e values o f second"  o r d e r r a t e c o n s t a n t s , k^, and t h e t o t a l s o l u t e c o n c e n t r a t i o n i n l i q u i d , r e g i o n s , C, .  59  F i g u r e 17  o  E f f e c t a t -4.0° o f added s o l u t e s on t h e r e a c t i o n o f 0.05 M e t h y l e n e  c h l o r o h y d r i n w i t h 0.05 M sodium  h y d r o x i d e i n f r o z e n aqueous s o l u t i o n s .  The c u r v e i s  -4 c a l c u l a t e d from k  Q b s  =  k  S / s = Cl-26 x 10 C  2  ( 1 . 9 ) / ( 0 . 1 5 + Im ) where I m Q  o f added i m p u r i t i e s .  Q  i s the t o t a l  )  concentration  60  between v a r i o u s r u n s , t h e o b s e r v e d r a t e c o n s t a n t s can be q u a n t i t a t i v e l y r e l a t e d t o known v a l u e s o f t h e l i q u i d phase r a t e c o n s t a n t and t o known p r o p e r t i e s o f t h e i c e - s o l u t i o n phase  equilibria.  61  D.  M u t a r o t a t i o n o f Glucose  i n Ice  As p o i n t e d out i n t h e I n t r o d u c t i o n the m u t a r o t a t i o n o f g l u c o s e i s 28 g e n e r a l - a c i d and g e n e r a l - b a s e  c a t a l y z e d . Known c a t a l y s t s i n c l u d e a v a r i e t y  o f s t r u c t u r e s and s o t h e r e would seem t o be a g r e a t e r l i k e l i h o o d o f the appearance o f any new e f f e c t s surface).  (such as a c a t a l y t i c e f f e c t o f t h e i c e  I n a d d i t i o n , as a convenience  i n the c a l c u l a t i o n o f the  c o n t r i b u t i o n due t o t h e c o n c e n t r a t i o n e f f e c t , the g l u c o s e - H 0 and 2  the  29  HC1  - H 0 phase r e l a t i o n s h i p s are known 2  needed t o c a l c u l a t e both k^ and k established.  2  and the a c t i v a t i o n parameters  a t low temperatures  have been c a r e f u l l y  3 0  oj - g l u c o s e  $-glucose  ,CH OH  CH OH  2  2  Spontaneous M u t a r o t a t i o n . ; The f i r s t - o r d e r , u n c a t a l y z e d m u t a r o t a t i o n i n f r o z e n aqueous s o l u t i o n s was s t u d i e d by measurements o f changes i n o p t i c a l r o t a t i o n o f thawed a-D-glucose s o l u t i o n s . m u t a r o t a t i o n was slow enough below 0° ( t j y  2  > 380 min.)  The  so t h a t any r e a c t i o n  d u r i n g t h e time n e c e s s a r y t o thaw and a n a l y z e an i n d i v i d u a l sample from a k i n e t i c run was n e g l i g i b l e .  Runs were f o l l o w e d t o about the f i r s t  half-life  and m u t a r o t a t i o n r a t e c o n s t a n t s were c a l c u l a t e d from the observed r o t a t i o n s by t h e u s u a l f i r s t - o r d e r k i n e t i c treatment..  The observed  r a t e constant f o r  spontaneous m u t a r o t a t i o n , k^, i s t h e sum o f the i n d i v i d u a l r a t e c o n s t a n t s k  and k a 8  62  The observed  r a t e c o n s t a n t s f o r r e a c t i o n a t -4.0° w i t h t h e  c o n c e n t r a t i o n o f g l u c o s e i n i n i t i a l u n f r o z e n s o l u t i o n s v a r i e d from 0,01 to 1.4 M a r e g i v e n i n T a b l e X. .Over t h i s wide range o f c o n c e n t r a t i o n , as w e l l as a t 0.05 M g l u c o s e w i t h 0.05 M sodium c h l o r i d e p r e s e n t , t h e r e a c t i o n proceeds w i t h t h e same r a t e i n a l l f r o z e n s o l u t i o n s (average 1.6 +_ 0.1 x 10  5  sec."  1  a t -4.0°).  =  The r a t e c o n s t a n t c a l c u l a t e d from t h e 30  A r r h e n i u s e q u a t i o n g i v e n by Smith and Smith,  as o b t a i n e d from  measurements i n l i q u i d s o l u t i o n s down t o 0°, i s 1.9 x 10"^ s e c .  1  a t -4.0  e  Table X  U n c a t a l y z e d M u t a r o t a t i o n o f Glucose  Glucose  concn., M '  0.011 0,051 0.500  a  i n Frozen Aqueous S o l u t i o n s a t -4.0'  k , x 10 , sec.' obs ' 5  1  Glucose  concn., M  k , x 10^, s e c . " obs '  1.63  0.555  1.73  1.57  1.39  1.42  1.38  1.92  a  With 0.051 M sodium c h l o r i d e .  b  C a l c u l a t e d from known a c t i v a t i o n parameters i n water.  1  b  30  As w i t h t h e c a l c u l a t e d r a t e c o n s t a n t i n i c e (see T a b l e X ) , t h e r a t e c o n s t a n t c a l c u l a t e d f o r r e a c t i o n i n o r d i n a r y , u n f r o z e n aqueous s o l u t i o n s i s s l i g h t l y h i g h e r than r e p o r t e d e x p e r i m e n t a l v a l u e s  ( c a l c u l a t e d a t 0°,  63  3.05  x 10  reference  sec." ; found  at 0 ° , 2.85,  2.80  and  2,82  x 10  sec.  , see  30). Hydrochloric Acid Catalyzed Mutarotation.  r e a c t i o n , the m u t a r o t a t i o n  of glucose  U n l i k e the  spontaneous  i n aqueous h y d r o c h l o r i c a c i d i s  a c c e l e r a t e d by  f r e e z i n g the s o l u t i o n .  concentrations  the r e a c t i o n i s s u f f i c i e n t l y slow so t h a t good k i n e t i c  p l o t s were o b t a i n e d run.  simply by thawing and  F i g u r e 18 shows two  both with  0.051  In thawed s o l u t i o n s a t low  M glucose  r a p i d l y a n a l y z i n g samples o f a  " f r o z e n r u n s " , w i t h 0.02  and  0.20  i n t e g r a l value.  where the two  observed  from 0.006 to 0.3 k  obs P ^  o t t e c  rate constants  (obtained from the s l o p e s o f f o r a v a r i a t i o n o f HC1  When runs are made over a range o f HC1  ' against H  glucose  (see T a b l e XI  low  i n the r e l a t i o n s h i p k  b  concentration  the v a l u e s  s i m i l a r v a r i a t i o n o f k i n e t i c o r d e r with c a t a l y s t  £-xylene s o l u t i o n s i n p a r t The glucose  two  separate  constants  the  from u n i t y at A  c o n c e n t r a t i o n was  ot t - b u t y l p e r o x y  observed  formate i n f r o z e n  B. curves  i n F i g u r e 19 f o r 0.05  a l s o show t h a t the observed  concentration of glucose.  of  x  a c i d c o n c e n t r a t i o n s to near zero at h i g h a c i d c o n c e n t r a t i o n s .  i n the base c a t a l y z e d decomposition  the  and F i g u r e 19), i t i s seen t h a t  = k^ + k^[H,.}:"''varies  s  18  concentration  c o n c e n t r a t i o n , and  +  o r d e r , x,  f o r the  T h i s i s shown, f o r example, i n F i g u r e  M at constant  The  However, the k i n e t i c o r d e r i n a c i d i s not  l i n e s ) d i f f e r by a f a c t o r o f o n l y 2.4 by a f a c t o r o f 10.  and  the  i n i c e i s f i r s t - o r d e r i n g l u c o s e , as i s the case  normal r e a c t i o n i n l i q u i d water. a constant,  M HC1  at -4.0°, p l o t t e d as f i r s t - o r d e r r e a c t i o n s .  l i n e a r i t y o f such p l o t s over s e v e r a l h a l f - l i v e s shows t h a t mutarotation  acid  r a t e constants  and  f o r 0.5  depend on the  M  initial  For the same c o n c e n t r a t i o n o f a c i d , the r a t e  are g r e a t e r f o r 0.05  M than  f o r 0.5  M glucose.  More complete  64  |  Figure  Time, min  18. F i r s t - o r d e r k i n e t i c p l o t s f o r m u t a r o t a t i o n o f g l u c o s e i n f r o z e n aqueous h y d r o c h l o r i c Optical, rotations and [(%  a c i d solutions at  (a) were measured i n thawed s o l u t i o n s  rate constants c a l c u l a t e d by l o g " * j / t \  -4.0°.  " OJ = k  Qbs  t/2.303.  65  \  •  6  Ql—  0  I  .05  I  .10  1  .15  1  1  1  .20  .25  .30  u ..! .35  Concentration of HCl , M  Figure 19, Variation of observed first-order rate constants with hydrochloric acid concentration for mutarotation of glucose in frozen solutions at -4.0°.  The solid lines  follow the experimental points; the broken lines show the theoretical relation according to eq 9.  66  T a b l e XI  E f f e c t o f HC1 C o n c e n t r a t i o n  on Observed F i r s t - O r d e r Rate C o n s t a n t s  f o r M u t a r o t a t i o n o f G l u c o s e a t -4.0° i n F r o z e n Aqueous S o l u t i o n s .  HC1 concn., M  k , obs  x 10 ,sec. 5  w i t h 0.555 M G l u c o s e  _ 1  HC1 concn., M  ik  x «5 10 , '  , obs  n  w i t h 0.0512 M G l u c o s e  none  1,,73  none  1.63  0.02  3,,82  0..006  8.54  0.05  7.,66  0.,020  17.4  0.10  12,,0  0.,052  28.2  0.15  18..0  0..10  30.8  0.20  18.,7  0.,14  36.0  0.25  22..0  0.,20  41.0  0.,30  40.4  on t h i s  e f f e c t i s g i v e n i n T a b l e X I I and i l l u s t r a t e d i n  i the observed f i r s t - o r d e r r a t e  -1 sec.  Figure  constants f o r r e a c t i o n i n frozen  HC1 s o l u t i o n s a r e r e l a t e d t o g l u c o s e c o n c e n t r a t i o n o v e r t h e range 0.05 t o 1.10 M.  I n t h e s e f r o z e n s o l u t i o n s an i n v e r s e dependency o f k ^  s  on  g l u c o s e c o n c e n t r a t i o n i s o b t a i n e d up t o a c o n c e n t r a t i o n s u f f i c i e n t t o prevent  f r e e z i n g a t -4°. " That a f i r s t - o r d e r r a t e c o n s t a n t  can depend  on i n i t i a l r e a c t a n t c o n c e n t r a t i o n b e f o r e f r e e z i n g b u t not on t h e a c t u a l r e a c t a n t c o n c e n t r a t i o n d u r i n g a r u n i s an i n t e r e s t i n g c h a r a c t e r i s t i c o f some r e a c t i o n s i n f r o z e n s o l u t i o n s .  67  0  0.2 0.4 0.6  0.8  1.0  1.2  1.4  1.6  1.8  Glucose Concentration , M  Figure 20.. Variation of observed first-order rate constants with glucose concentration for mutarotation in frozen 0.10 M HC1 solutions at -4.0°.  The line shows the  theoretical relationship predicted by eq 9.  68  Table X I I  V a r i a t i o n o f Observed F i r s t - O r d e r M u t a r o t a t i o n with Glucose Concentration  Glucose, M '  k , x 10^, s e c . obs  Rate Constant  f o r F r o z e n 0.10 M HC1 S o l u t i o n s a t -4.0°  Glucose, M  1  5  k , x 10^, s e c . obs  0.0512  30,8  0.833  7.21  0.278  18.7  1.10  7.18  0.390  13.8  1.18  4.9l  a  0.555  12.0  --  6.17  b  a  Supercooled l i q u i d s o l u t i o n .  b  C a l c u l a t e d f o r l i q u i d s o l u t i o n s a t -4° and 0.10 M HC1.  - 1  30  As demonstrated above f o r some b i m o l e c u l a r r e a c t i o n s i n f r o z e n o r g a n i c s o l v e n t s and i n i c e , a maximum i n t h e r a t e - t e m p e r a t u r e i s a general solutions.  relationship  feature of the concentration e f f e c t f o r reactions i n frozen The a c i d c a t a l y z e d m u t a r o t a t i o n  at about -7°.  The o b s e r v e d r a t e c o n s t a n t s  d i f f e r e n t sets of i n i t i a l concentrations  o f glucose  shows a r a t e maximum  a t v a r i o u s t e m p e r a t u r e s f o r two  a r e c o l l e c t e d i n T a b l e X I I I and  F i g u r e 21. At -6° w i t h 0.05 M g l u c o s e  and 0.04 M HC1 t h e o b s e r v e d r a t e 30  constant  i s seventeen times g r e a t e r than t h e c a l c u l a t e d r a t e  f o r a supercooled concentrations  l i q u i d s o l u t i o n at t h i s temperature.  constant  With these  reactant  t h e r a t e i n i c e i s d e p r e s s e d by 33% i f 0.051 M NaCl i s  69  Figure 2L Effect of temperature on mutarotation of glucose in frozen solutions at constant reactant concentrations. The solid lines are experimentally determined; the • broken lines are calculated from eq 9.  70 Table  Xltl  Temperature V a r i a t i o n o f Observed Rate C o n s t a n t s f o r M u t a r o t a t i o n o f G l u c o s e i n F r o z e n Aqueous S o l u t i o n s  F o r 0;555 M G l u c o s e , 0.10 M HC1.  Temperature  ,o  +2.  a  ^ bs  X  S e C  0  12.,3 7..16  -1.,6  ^  F o r 0.0512 M G l u c o s e , 0.040 M HC1.  Temperature  k  obs  X  s e c  -1.0  12. 4  -3.0  23.,0  -4,,0  12..0  -5.0  29.,2  -5.,4  14,.8  -6.3  30.,5  -7.,1  14,.8  -6.3  20.  -9,.1  13,.5  -6.3  14., 3  -8.0  30,.7  -9.5  31,.0  -11.0  28 .8  -13.5  24,.7  -14.9  21 .8  -17.0  17 .9  -11,.3  8,.67  a  S o l u t i o n not f r o z e n .  b  S o l u t i o n c o n t a i n e d 0.051 M sodium c h l o r i d e  c  S o l u t i o n c o n t a i n e d 0.097 M sodium c h l o r i d e  .o  b  C  ^  71  p r e s e n t and by 50% i f 0.097 M NaCl " i s p r e s e n t i n t h e i n i t i a l  solutions.  A l t h o u g h t h e r e a c t i o n i n o r d i n a r y aqueous s o l u t i o n s shows almost  negligible  32 salt effect.  Figure.22 i l l u s t r a t e s these r e s u l t s ; the mutarotation  remains f i r s t o r d e r i n g l u c o s e and t h e observed  r a t e constant i s less at  higher s a l t concentrations. S i m i l a r t o t h e r e a c t i o n s i n f r o z e n systems above, e x p e r i m e n t a l o b s e r v a t i o n s on t h e m u t a r o t a t i o n o f g l u c o s e i n f r o z e n aqueous s o l u t i o n s then i n c l u d e r a t e enhancements, changes i n k i n e t i c o r d e r , a r a t e maximum a t a temperature  s e v e r a l degrees below t h e f r e e z i n g p o i n t and s e n s i t i v i t y t o  added s o l u t e s .  Discussion Spontaneous R e a c t i o n .  I n t h e case o f g l u c o s e  a t -4°, t h e l i q u i d  29 phase o f a f r o z e n s o l u t i o n c o n t a i n s 27% g l u c o s e  and s u f f i c i e n t water i s  s t i l l p r e s e n t so t h a t e s s e n t i a l l y t h e same r a t e o f spontaneous m u t a r o t a t i o n i s o b t a i n e d i n " i c e " as i n an o r d i n a r y water s o l u t i o n .  The  r e s u l t s g i v e n i n T a b l e X show t h a t t h e r e a c t i o n r a t e i s not a p p r e c i a b l y a f f e c t e d by v a r i a t i o n o f t h e s u r f a c e a r e a o f t h e i c e i n c o n t a c t w i t h t h e l i q u i d regions  ( i . e . , t h e r e a c t i o n i s not s e n s i t i v e t o e i t h e r t h e i n i t i a l  c o n c e n t r a t i o n o f g l u c o s e from 0.01 t o 1.4 M, n o r t o t h e r a t e o f f r e e z i n g of samples).  The normal m u t a r o t a t i o n r a t e (at 0.051 M g l u c o s e ) i s a l s o  not changed by t h e a d d i t i o n o f 0.05 M sodium c h l o r i d e .  The a c t u a l s a l t  c o n c e n t r a t i o n i n t h e r e a c t i o n r e g i o n s a t -4° would be c a . 0.55 M; but s i n c e i t i s known t h a t even 1 M NaCl o r KC1 has no e f f e c t on t h e m u t a r o t a t i o n r a t e 33 in  l i q u i d water,  t h e absence o f a " s a l t e f f e c t " i n i c e i s r e a s o n a b l e .  Catalyzed Reaction. t h e second-order  U n l i k e the simple f i r s t - o r d e r mutarotation,  r e a c t i o n between g l u c o s e and a c i d i s promoted by t h e  72  F i g u r e 22a E f f e c t o f added N a C l o n - m u t a r o t a t i o n o f g l u c o s e i n frozen s o l u t i o n s at - 6 . 3 ° .  The r e a c t a n t  were 0 . 0 5 1 2 M g l u c o s e , 0 . 0 4 0 M H C 1 .  concentrations  73  concentration effect.  In. o r d e r t o determine i f o t h e r e f f e c t s are  the c o n t r i b u t i o n o f t h e ' c o n c e n t r a t i o n e f f e c t must be s e p a r a t e d glucose mutarotation  present  out.  For  i n f r o z e n h y d r o c h l o r i c a c i d s o l u t i o n s , the observed  r a t e c o n s t a n t s , a c c o r d i n g t o the c o n c e n t r a t i o n e f f e c t , a r e r e l a t e d t o hydronium i o n c o n c e n t r a t i o n o f the r e a c t i o n r e g i o n s by the k  obs  =  k  l  +  k  2  h"  H  T  ^ i s r e l a t i o n s h i p may  be d e r i v e d from the  e q u a t i o n f o r the c o n c e n t r a t i o n e f f e c t , d A / d t =-k g  to t h i s second-order r e a c t i o n .  equation  A necessary  /  v 2  n  general »  v s  as a p p l i e d  assumption i s t h a t no change  i n reaction'volume- o c c u r s d u r i n g a r u n , o r , i n o t h e r words, t h a t the concentration  i s constant  i n any r u n .  This  is  reasonable  s i n c e no  o v e r a l l change i n number o f moles o c c u r s d u r i n g m u t a r o t a t i o n . a c i d present  in initial  (or thawed) s o l u t i o n s i s p r e s e n t  r e a c t i o n r e g i o n s o f f r o z e n s o l u t i o n s , then H ° act s i m i l a r l y ,  +  V s  When a l l the  o n l y i n the  +  = H, V. . s h h  I f a l l solutes  the t o t a l number o f moles i n a thawed s o l u t i o n w i l l be  equal  t o the t o t a l number o f moles i n the l i q u i d p a r t o f the f r o z e n s o l u t i o n , i.e. C  s  unfrozen  V  s  3 c. V, h h  where C  s o l u t i o n and  s  i s the t o t a l i n i t i a l s o l u t e c o n c e n t r a t i o n  i s t h e t o t a l s o l u t e c o n c e n t r a t i o n i n the  r e g i o n s o f the f r o z e n , s o l u t i o n .  of  liquid  U s i n g these two r e l a t i o n s h i p s between  c o n c e n t r a t i o n s i n a f r o z e n and thawed s o l u t i o n , the observed r a t e constant  f o r mutarotation  i n i c e i s g i v e n i n terms o f measurable  i n thawed s o l u t i o n s as f o l l o w s : H+ k , = k. + k- V = k. +' k_ C, obs 1 2 _s v 1 2 h h The  H +  C  * s  (9)  t o t a l c o n c e n t r a t i o n i n the l i q u i d r e a c t i o n r e g i o n s  t h r o u g h o u t a run and, concentrations H  s  l i k e k^,  and C  fi  (C ) h  i s constant  depends o n l y on t e m p e r a t u r e .  The  are known f o r each r u n , the v a l u e o f C  e q u a l t o the t o t a l i n i t i a l  quantities  solute concentration, C  = Glucose s  s  + s  being H s +  74  + Cl  _ + added solute... s s  + In these terms the hydronium i o n c o n c e n t r a t i o n , H, , ' h' /  i s e q u a l t o the t o t a l p o s s i b l e c o n c e n t r a t i o n , C^, to  times the r a t i o o f a c i d  t o t a l s o l u t e c o n c e n t r a t i o n i n a thawed s o l u t i o n .  Therefore,  the  hydronium i o n c o n c e n t r a t i o n i n the l i q u i d p a r t o f a f r o z e n s o l u t i o n i s not always d i r e c t l y p r o p o r t i o n a l t o the hydronium i o n c o n c e n t r a t i o n o f the thawed s o l u t i o n , but depends a l s o on the c o n c e n t r a t i o n o f the o t h e r s o l u t e s . Qualitative Results. for  The  the e x p e r i m e n t a l : o b s e r v a t i o n s  k i n e t i c order i n H  +  and concentration.,  The  w h i l e the H  +  f o r mutarotation  in ice.  above account The  change i n  a r i s e s from compensating changes i n r e a c t i o n volume A t low c o n c e n t r a t i o n s o f a c i d the r e l a t i v e l y  amount o f g l u c o s e p r e s e n t solutions.  r e l a t i o n s h i p s presented  c o n t r o l s the r e a c t i o n volume i n the  r e a c t i o n r e g i o n s remain at n e a r l y c o n s t a n t  greater  frozen  t o t a l volume,  c o n c e n t r a t i o n and the r e a c t i o n r a t e i n the r e g i o n s i n c r e a s e i n  p r o p o r t i o n t o the a c i d c o n c e n t r a t i o n i n i n i t i a l s o l u t i o n s ; the o b s e r v e d order i n H  +  i s then u n i t y .  On the o t h e r hand, at h i g h a c i d c o n c e n t r a t i o n s  the s o l u t e i n the r e a c t i o n r e g i o n s i s e s s e n t i a l l y a l l HC1 at the possible concentration.  Any  highest  further increase i n acid concentration i n  i n i t i a l s o l u t i o n s o n l y i n c r e a s e s the volume o f l i q u i d r e g i o n s i n the frozen solution.  The  concentration  = ~r C, h  2  remains c o n s t a n t ,  the  n  r e a c t i o n r a t e t h e r e f o r e remains c o n s t a n t , and the r e a c t i o n appears t o be zero-order i n a c i d . A s i m i l a r change i n k i n e t i c o r d e r f o r g l u c o s e does not Although  occur.  the c o n c e n t r a t i o n o f g l u c o s e i n l i q u i d r e g i o n s i s a l s o not  d i r e c t l y p r o p o r t i o n a l t o i n i t i a l g l u c o s e c o n c e n t r a t i o n , and i s v a r i e d by changes i n c o n c e n t r a t i o n s o f o t h e r s o l u t e s , the k i n e t i c o r d e r i s independent o f g l u c o s e c o n c e n t r a t i o n .  For any  second-order c a t a l y t i c  75  r e a c t i o n , the general equation contains t h i s r e s u l t . then d A / d t = ^k^B^Ag and when B^ i s c o n s t a n t s  IfA V s  g  = A^V^  throughout a r u n (as i n a  c a t a l y t i c r e a c t i o n ) , t h e r e a c t i o n o r d e r i s seen t o be independent o f A . g  However, t h e observed r a t e c o n s t a n t k ^  = k2B^ w i l l depend on t h e  i n i t i a l concentration o f a l l solutes (including A ) . Therefore, solutes are involved i n determining the observed r a t e c o n s t a n t  as a l l  t h e t o t a l volume o f r e a c t i o n r e g i o n ,  depends on t h e i n i t i a l g l u c o s e  concentration.  A g r e a t e r number o f moles o f g l u c o s e r e s u l t s i n a g r e a t e r volume, V^, and,  f o r t h e same number o f moles o f a v a i l a b l e a c i d , t h e c o n c e n t r a t i o n H*  must be more d i l u t e , .  At a constant  i n i t i a l HC1 c o n c e n t r a t i o n o f 0.10 M,  the decrease i n o b s e r v e d r a t e c o n s t a n t w i t h i n c r e a s e i n g l u c o s e concentration  (see F i g u r e 20) r e s u l t s from such changes i n r e a c t i o n volume.  At t h e lowest g l u c o s e c o n c e n t r a t i o n a maximum r a t e c o n s t a n t , to  a maximum a c i d c o n c e n t r a t i o n o f H* =  corresponding  s h o u l d be o b t a i n e d .  c o n c e n t r a t i o n o f g l u c o s e t h e minimum r a t e c o n s t a n t  At h i g h  i s o b t a i n e d when  the s o l u t i o n c o n t a i n s t o o much g l u c o s e t o a l l o w f r e e z i n g a t -4°  (i.e.,  when V, = V ) . h s The  e f f e c t o f added sodium c h l o r i d e i s s i m i l a r .  A greater  c o n c e n t r a t i o n o f a s o l u b l e but i n e r t s o l u t e such as NaCl r e s u l t s i n a g r e a t e r volume o f t o t a l r e a c t i o n r e g i o n s , t h e r e a c t a n t s a r e made more d i l u t e and s l o w e r r a t e s o f r e a c t i o n a r e observed (see F i g u r e 2 2 ) . The  changes i n observed r a t e w i t h temperature may a l s o be  e x p l a i n e d i n terms o f c o n c e n t r a t i o n s and volumes o f l i q u i d r e a c t i o n regions.  With c o n s t a n t  i n i t i a l c o n c e n t r a t i o n s o f HC1 and o f g l u c o s e , a  d e c r e a s e i n temperature r e s u l t s i n a decrease i n r e a c t i o n volume as more pure s o l v e n t i s f r o z e n o u t . A c o r r e s p o n d i n g  increase i n concentration  C  n  78  occurs.  As l o n g as t h e i n c r e a s e i n c o n c e n t r a t i o n outweighs t h e decrease  i n second-order i s obtained  r a t e c o n s t a n t , k^, an o v e r a l l i n c r e a s e i n observed  (see eq.9).  f u r t h e r decreases f o r decreases  rate  A maximum r a t e i s reached, however, when  i n temperature  i n t h e second-order  f a i l to increase rate constant.  enough t o compensate This e f f e c t i s  i l l u s t r a t e d i n F i g u r e 21. Q u a n t i t a t i v e R e l a t i o n of K i n e t i c Equation.  For quantative  a p p l i c a t i o n o f eq 9, t h e r a t e c o n s t a n t f o r u n c a t a l y z e d m u t a r o t a t i o n , k^, and t h e second-order may be obtainec 30 down t o 0°.  r a t e constant f o r a c i d c a t a l y z e d mutarotation, k > 2  by e x t r a p o l a t i o n o f d a t a o b t a i n e d i n normal s o l u t i o n s  1  The v a l u e o f  i s o b t a i n e d from t h e  phase r e l a t i o n s h i p f o r t h e g l u c o s e - w a t e r temperature  system.  temperature-composition  The v a l u e o f  was t a k e n from t h e w e l l e s t a b l i s h e d g l u c o s e - w a t e r  a t any  phase  29 diagram  r a t h e r t h a n from t h e HCl-water system which d i f f e r  below -5°.  Freezing p o i n t s o f glucose-HCl-water  significantly  s o l u t i o n s , with the r a t i o  o f g l u c o s e t o HC1 near t h a t used i n t h e f r o z e n k i n e t i c r u n s , showed t h a t the g l u c o s e - w a t e r  phase r e l a t i o n s h i p i s s i m i l a r , down t o c a . -13°, t o t h a t  f o r glucose-HCl-water The observed  when r e l a t e d i n terms o f t o t a l s o l u t e c o n c e n t r a t i o n .  curved l i n e o f F i g u r e 20 shows t h e c a l c u l a t e d v a r i a t i o n o f  r a t e c o n s t a n t w i t h g l u c o s e c o n c e n t r a t i o n f o r runs a t c o n s t a n t  a c i d c o n c e n t r a t i o n o f 0.10 M. The v a l u e s p r e d i c t e d by eq 9 as obs - * ' " ~ )(l-64j 0.1 are very c l o s e to 0.2 + G s k  =  (  1  92  X  1 0 _ 5  )  +  (  4  25  X  1 0  4  the experimentally obtained values.  In a l l supercooled l i q u i d  solutions,  as i n a s o l u t i o n more c o n c e n t r a t e d than c a . 1.4 M g l u c o s e a t -4°, t h e same r a t e c o n s t a n t o f c a . 6.2 x 10 "* s e c .  1  i s expected  s i n c e above a  t o t a l c o n c e n t r a t i o n o f 1.6 M no i c e can form a t -4° (see Table X I I ) . A t  79  concentrations  lower than 1.4 M, t h e r a t e c o n s t a n t  i n frozen solutions  i n c r e a s e s as p r e d i c t e d by eq 9. The b r o k e n l i n e s i n F i g u r e 19 show t h e t h e o r e t i c a l r e l a t i o n s h i p of k  Q b s  t o H* (from eq 9 i n t h e form k H e  (1.64) G  +  s  = (1.92 x I O ) + (4.25 x I O ) - 5  Q b s  - 4  a t two d i f f e r e n t g l u c o s e c o n c e n t r a t i o n s , G 2  — H  = s  +  s  0.051 a n d 0.555 M) . At t h e h i g h e s t a c i d c o n c e n t r a t i o n s s t u d i e d , the c a l c u l a t e d r a t e constant  i s 20% l e s s than observed v a l u e s .  This d e v i a t i o n  o f p r e d i c t e d and observed l i n e s i s s m a l l , but a p p a r e n t l y r e a l , as such d e v i a t i o n occurs only at concentrations concentration i n the r e a c t i o n regions k , obs  corresponding  to high a c i d  ( i . e . , l a r g e H*) .  In t h e e q u a t i o n  = k, + k„ H v , a t h i g h a c i d c o n c e n t r a t i o n o n l y the k_H* term i s 1 2 n 2 h  important,  and as an e r r o r i n t h e v a l u e o f k^ would s h i f t a l l t h e c a l c u l a t e d  p o i n t s , the d e v i a t i o n s at high a c i d concentrations  (see F i g u r e XI) must be  due t o an i n c r e a s e i n e f f e c t i v e c a t a l y s t c o n c e n t r a t i o n as HC1 is  concentration  increased. The o b s e r v a t i o n t h a t t h e r a t e o f h y d r o c h l o r i c a c i d c a t a l y z e d  mutarotation  o f glucose  i n c r e a s e s f a s t e r than t h e a c t u a l a c i d c o n c e n t r a t i o n 28  ( f o r HC1 > 0.4 M) was r e p o r t e d by Lowry and Smith  and d i s c u s s e d i n terms  o f a " c a t a l y t i c c o e f f i c i e n t o f u n d i s s o c i a t e d m o l e c u l e s o f HC1 g r e a t e r than t h a t o f t h e hydrogen i o n s d e r i v e d from them". greater c a t a l y t i c e f f e c t too f a s t f o r c o n v e n i e n t although i  1  becomes i m p o r t a n t 34  measurement;  In o r d i n a r y s o l u t i o n s t h i s  o n l y when t h e m u t a r o t a t i o n i s  i n frozen s o l u t i o n s the e f f e c t ,  c o m p l i c a t e d by t h e two phase system, may be more a c c e s s i b l e  At -4.0° t h e r a t e c o n s t a n t s observed a t h i g h a c i d c o n c e n t r a t i o n s a r e not as g r e a t as would be t h e case i f t h e r e l a t i o n k = + k„ (h ) were f o l l o w e d where l o g h = -H , t h e Hammett a c i d i t y f u n c t i o n a t 25^35 and the v a l u e s o f H used c o r r e s p o n d t o t h e HC1 c o n c e n t r a t i o n s o f the r e a c t i o n r e g i o n s i n t h e f r o z e n system). Q b  Q  0  80  f o r study.  A t low i n i t i a l c o n c e n t r a t i o n s , a r e a c t i o n i n a f r o z e n  sample can be s u f f i c i e n t l y slowed by thawing so t h a t a n a l y s i s may be c a r r i e d out a t room t e m p e r a t u r e . The c a l c u l a t e d e f f e c t o f temperature on t h e a c i d c a t a l y z e d m u t a r o t a t i o n i n i c e a l s o shows t h a t t h e observed r a t e c o n s t a n t s a r e g r e a t e r than p r e d i c t e d .  The broken l i n e s o f F i g u r e 21 show t h e temperature  v a r i a t i o n a c c o r d i n g t o eq 9.  F o r t h e s e two s e r i e s o f runs a t c o n s t a n t  r e a c t a n t c o n c e n t r a t i o n s , t h e r a t e maximum a r i s e s from t h e d e c r e a s e i n k and an i n c r e a s e i n  as t h e temperature i s made l o w e r .  2  The e x p e r i m e n t a l  p o i n t s l i e above t h e r e s p e c t i v e c a l c u l a t e d l i n e s , and as d i s c u s s e d above, the d i f f e r e n c e c o u l d a r i s e from more e f f e c t i v e a c i d c a t a l y s t a t t h e h i g h e r c o n c e n t r a t i o n s encountered a t lower temperatures o r , p o s s i b l y , from inexact values o f  ( e s p e c i a l l y a t lower t e m p e r a t u r e s ) as o b t a i n e d from  t h e g l u c o s e - w a t e r phase diagram. Summary., I t i s apparent t h a t t h e m u t a r o t a t i o n o f g l u c o s e i n f r o z e n aqueous s o l u t i o n s  i s w e l l accounted f o r by t h e c o n c e n t r a t i o n e f f e c t .  The k i n e t i c t r e a t m e n t o f t h i s e f f e c t , as summarized by t h e e q u a t i o n k , = k, + k„C, H /C , c o r r e l a t e s t h e e x p e r i m e n t a l o b s e r v a t i o n s f o r obs 1 2 h s s +  v  changes i n r e a c t a n t c o n c e n t r a t i o n , i n t o t a l s o l u t e c o n c e n t r a t i o n and i n temperature.  A t t h e c o n c e n t r a t i o n s used i n t h i s s t u d y , any e f f e c t o f  the s o l i d i c e i s n e g l i g i b l e and t h e r e a c t i o n i n t h e r e m a i n i n g l i q u i d r e g i o n s i s normal.  81  III. Reactions i n Organic S o l i d s  A r e a c t i o n o f a s o l i d which i s accompanied  by m e l t i n g o f t h e  s o l i d might behave i n a manner s i m i l a r t o t h a t d e s c r i b e d above f o r r e a c t i o n s i n f r o z e n s o l v e n t s ; even b e f o r e t h e presence o f t h e melt n o r m a l l y becomes v i s i ^ l f c c o n s i d e r a b l e r e a c t i o n may t a k e p l a c e i n t h i s liquid  phase. 36 Morawetz,  i n a review of r e a c t i o n s i n organic s o l i d s ,  suggests t h a t some r e a c t i o n s which have been thought t o proceed i n t h e s o l i d phase might a c t u a l l y have had a m e l t e d phase p r e s e n t which a f f e c t t h e observed r e a c t i o n . been i n v e s t i g a t e d .  would  As f a r as we know h i s s u g g e s t i o n has not  The a u t h o r s o f r e c e n t papers on r e a c t i o n s i n o r g a n i c 37 38 39  s o l i d s i n which m e l t i n g o c c u r s  '  '  have not attempted t o s e p a r a t e t h e  c o n t r i b u t i o n o f r e a c t i o n i n t h e l i q u i d phase.  I t would seem t h a t such a  s e p a r a t i o n i s n e c e s s a r y b e f o r e v a l i d c o n c l u s i o n s about t h e k i n e t i c s and mechanism o f t h e r e a c t i o n can be drawn.  In t h e f o l l o w i n g s e c t i o n s a r e  p r e s e n t e d our attempts t o t a k e i n t o account r e a c t i o n i n t h e melt f o r the t h e r m a l m u t a r o t a t i o n o f p o l y c r y s t a l l i n e a-glucose and t h e i s o m e r i z a t i o n of s o l i d 5-norbornene-2,3-endo-dicarboxylic anhydride. A.  The M u t a r o t a t i o n o f G l u c o s e . A s t u d y o f t h e m u t a r o t a t i o n o f molten g l u c o s e has r e c e n t l y been  r e p o r t e d i n which a s o l i d s t a t e m u t a r o t a t i o n a t lower temperatures was 40 suggested  .  S i n c e t h e m u t a r o t a t i o n r e a c t i o n o c c u r s r a p i d l y i n t h e melt  and s i n c e samples o f g l u c o s e e v e n t u a l l y melt i f h e l d a few degrees  below  82  the  m e l t i n g p o i n t , i t i s r e a s o n a b l e t o t a k e i n t o account r e a c t i o n i n the  m e l t e d phase which s h o u l d be p r e s e n t i n s o l i d samples h e l d a t temperatures above t h e e u t e c t i c o f t h e r e a c t a n t - p r o d u c t system.  Results Weighed samples o f d r y , c r y s t a l l i n e a-D-glucose i n i n d i v i d u a l v o l u m e t r i c f l a s k s were h e a t e d i n a c o n s t a n t temperature b a t h .  The  flasks  were c o o l e d t o quench the r e a c t i o n and the c o n t e n t s d i s s o l v e d i n d i m e t h y l s u l f o x i d e i n which no m u t a r o t a t i o n o c c u r s at room t e m p e r a t u r e .  Optical  r o t a t i o n s were measured and s p e c i f i c r o t a t i o n s then c a l c u l a t e d from the weight o f g l u c o s e i n t h e sample.  The observed s p e c i f i c  rotations  at v a r i o u s times f o r runs a t s e v e r a l temperatures a r e p l o t t e d i n F i g u r e 23. The c u r v e s o b t a i n e d were independent o f sample s i z e f o r samples of  0.2  t o 1.2 g. and l a r g e l y independent o f c r y s t a l size-' and o r i g i n .  B r i t i s h Drug Houses A n a l y t i c a l Reagent Grade a-D-glucose and U. S. N a t i o n a l Bureau o f Standards d e x t r o s e ( s t a n d a r d sample No. 41) gave n e a r l y curves.  identical  The r e a c t i o n proceeds n o r m a l l y at 130° but does not seem t o go at  110°. The p r e s e n c e o f s m a l l amounts o f w a t e r have a f a i r l y  large  o  e f f e c t . At 143 u n d r i e d g l u c o s e reaches 50% r e a c t i o n n e a r l y one t h i r d than an i d e n t i c a l sample d r i e d at 100° under vacuum.  faster  The p r e s e n c e o f 5%  sodium c h l o r i d e n e a r l y doubles the r e a c t i o n r a t e w h i l e 3% anthracene speeds i t up by ca. 10%.  Added B-glucose does not seem t o a f f e c t the r a t e  d r a s t i c a l l y , but the i n t e r p r e t a t i o n i s d i f f i c u l t j.  s i n c e 6-glucose i s a l s o  E x t e n s i v e g r i n d i n g o f the samples caused t h e r a t e t o i n c r e a s e somewhat.  83  60  L  ,  0  100  . 200 TIME  F i g u r e 23. at v a r i o u s  Specific rotation temperatures.  300  (Min.)  (e) o f s o l i d g l u c o s e samples v e r s u s time  84  optically  active.  mutarotation  Paper chromatography o f a sample which had gone t o  e q u i l i b r i u m showed the presence o f o n l y a v e r y s m a l l amount  o f m a t e r i a l o t h e r than a- and  8-glucose ( c a . 1%); the many r e a c t i o n s which  g i v e r i s e t o v e r y complex m i x t u r e s  occur  later. * 4  Discussion As w i t h f r o z e n s o l v e n t r e a c t i o n s the r a t e o f r e a c t i o n i n the m e l t e d phase o f a s o l i d sample would be a f u n c t i o n o f b o t h the  concentration  o f r e a c t a n t s i n the l i q u i d phase and the t o t a l volume o f the l i q u i d phase. I f r e a c t i o n o c c u r s o n l y i n the melt the r e a c t i o n can be r e p r e s e n t e d A  .. ,  **-  T3  A,.  solid  >-  liquid  crystalline  B,.  .  ...  by  I m p u r i t i e s o r 8-glucose i n the  liquid  *  6  a-glucose c r e a t e l i q u i d r e g i o n s at temperatures near the  ideal melting point.  As  B-isomer i s formed i n t h e s e r e g i o n s they grow i n  volume by m e l t i n g more o f the a - g l u c o s e .  Before the sample has  m e l t e d phase e q u i l i b r i u m keeps the c o n c e n t r a t i o n s  (A^ and B^)  completely  o f a-  and  6-glucose i n the l i q u i d r e g i o n s c o n s t a n t , w h i l e the t o t a l volume o f the l i q u i d phase i n c r e a s e s i n p r o p o r t i o n t o the moles o f p r o d u c t , i . e . , = mg  / B^.  The  i n i t i a l p a r t o f the r e a c t i o n then t a k e s the form o f a  first-order auto-accelerating reaction, d m /d B  The  t  ... ( k A .  h  observed r a t e c o n s t a n t  -  W  V  h  is k , obs  =  (k A /B a  h  = (k A,/B, a h  o b t a i n e d from a p l o t o f l o g mg v e r s u s t i m e .  - k )m  h  g  - k. n  h  (10)  B  ,. ,  .,,  8) which c o u l d The  be  c o n c e n t r a t i o n s A^ and  as w e l l as k^ and kg are f u n c t i o n s o n l y o f t e m p e r a t u r e .  For the  B^  first  few p o i n t s o f each run p l o t s o f l o g (a-e) v e r s u s time were s t r a i g h t (see F i g u r e 24);  a i s the s p e c i f i c r o t a t i o n o f the p u r e s t a-glucose w h i l e  85  e i s t h e s p e c i f i c r o t a t i o n o f a sample.at time t . The q u a n t i t y (a-e) i s p r o p o r t i o n a l t o t h e moles o f p r o d u c t .  Values o f k ^ Q  s  a t v a r i o u s temper-  a t u r e s a r e l i s t e d i n T a b l e XIV.  T a b l e XIV  Observed  Rate C o n s t a n t s f o r M u t a r o t a t i o n o f S o l i d  Temp. °C  k  Q b s  x 10  140  1.7  141  2.2  142  4.4  143  8.2  144  Glucose  4  sec."  1  11.  The r e a c t i o n c o n t i n u e s t o a c c e l e r a t e u n t i l t h e s o l i d phase i s consumed.  When t h e g l u c o s e i s c o m p l e t e l y l i q u i f i e d t h e s i t u a t i o n s r e g a r d i n g  changes i n volume and i n c o n c e n t r a t i o n a r e r e v e r s e d ; t h e volume o f m e l t , V^, remains c o n s t a n t and t h e c o n c e n t r a t i o n s ,  and B^, now v a r y .  The  k i n e t i c form i s t h e n t h a t o f a normal f i r s t - o r d e r r e v e r s i b l e r e a c t i o n , d B, / d t = k A, - k.B, h' ot h 8 h As samples were observed t o be c o m p l e t e l y m e l t e d a f t e r t h e s p e c i f i c rotation of  c a . one hundred was p a s s e d , such a r e l a t i o n s h i p o c c u r s i n  the lower p a r t o f t h e r o r a t i o n - t i m e c u r v e a t 143° shown i n F i g u r e 23. The e f f e c t s o f a c c e l e r a t i v e m e l t i n g and t h e n t h e f u r t h e r approach t o e q u i l i b r i u m account f o r t h e S-shape o f t h e c u r v e .  86  0  I  1  0  100  '.  :  _J  glucose.  _ i _  300  (Min.)  P l o t s o f l o g (a-0) v e r s u s time a t v a r i o u s  f o r the m u t a r o t a t i o n o f s o l i d  ;  200 TIME  F i g u r e 24.  .  temperatures  8,7  The u n u s u a l l y l a r g e v a r i a t i o n o f k  Q b s  w i t h temperature (a s e v e n - f o l d  i n c r e a s e o v e r o n l y a f o u r degree range) seems u n r e a s o n a b l e f o r any t r u e r a t e constant  f o r mutarotation  o f g l u c o s e and a c o m p o s i t e , apparent r a t e  c o n s t a n t o f t h e t y p e found i n f r o z e n s o l v e n t r e a c t i o n s i s i n d i c a t e d .  The  r a t e i s much g r e a t e r , a t h i g h e r temperatures not o n l y because t h e t r u e r a t e c o n s t a n t , k . i n c r e a s e s w i t h t e m p e r a t u r e , but f o r a g i v e n number o f moles o f 8 - g l u c o s e t h e volume o f m e l t e d g l u c o s e i s a l s o g r e a t e r ( L e . d e c r e a s e s w i t h an i n c r e a s e i n t e m p e r a t u r e ) .  The r a t e c o n s t a n t k  n o r m a l l y w i t h temperature w h i l e t h e o b s e r v e d r a t e c o n s t a n t  Q  may v a r y  i s unusually  s e n s i t i v e t o temperature. The e f f e c t o f added i n e r t i m p u r i t i e s on t h e r e a c t i o n i s d i f f i c u l t t o p r e d i c t because thorough and u n i f o r m m i x i n g i s d i f f i c u l t o r impossible t o achieve with s o l i d glucose.  I f t h e o - g l u c o s e c o u l d be  m e l t e d and t h e i m p u r i t i e s d i s s o l v e d i n t h e melt and t h e n t h e m u t a r o t a t i o n e x p e r i m e n t s c a r r i e d out on t h i s r e s o l i d i f i e d m e l t , t h e i m p u r i t i e s would supposedly o n l y c o n t r i b u t e t o t h e t o t a l c o n c e n t r a t i o n o f s o l u t e s i n t h e l i q u i d phase.  The e f f e c t would be t o i n c r e a s e t h e observed r a t e s i n c e t h e  volume o f t h e l i q u i d phase, V^, would be i n c r e a s e d .  The l a r g e e f f e c t o f  sodium c h l o r i d e i s p r o b a b l y due t o c a t a l y s i s r a t h e r t h a n t o i n c r e a s i n g V  U n f o r t u n a t e l y , due t o t h e h i g h r a t e o f r e a c t i o n i n c o m p l e t e l y molten glucose neigher the t r u e r a t e constants k  and k , n o r t h e phase  r e l a t i o n s h i p o f a- and 8 - g l u c o s e ( i . e . t h e v a l u e s o f A v a r i o u s t e m p e r a t u r e s ) c o u l d be measured.  h  and B  h  at  The absence o f any r e a c t i o n a t  110°, however, may be because t h e e u t e c t i c i s above t h a t t e m p e r a t u r e . q u a n t i t a t i v e e v a l u a t i o n o f t h e observed r a t e c o n s t a n t f a v o r a b l e cases t h e k i n e t i c s o f d e c o m p o s i t i o n  can be made.  No  I n more  o f c r y s t a l l i n e s o l i d s by  83  t h i s mechanism might be p r e d i c t e d and more d i r e c t l y compared w i t h observations. 42 Some t h e r m a l  reactions  above f o r thermal m u t a r o t a t i o n  o f systems s i m i l a r t o t h a t  described  o f g l u c o s e have been t r e a t e d by  equations  suggested o r i g i n a l l y f o r t h e growth o f c r y s t a l l i n e d e f e c t s i n t r u e '43 solid state reactions.  The " s i g m o i d " shaped curves o f s o l i d s t a t e  r e a c t i o n s a r e s i m i l a r t o those observed i n m e l t i n g s o l i d s  (see r e f . 42 and  F i g u r e 2 3 ) , but a p p l i c a t i o n o f t h e same k i n e t i c treatment  can o n l y be  s u p e r f i c i a l l y u s e f u l (e.g., i n s t r a i g h t e n i n g out k i n e t i c p l o t s ) . mutarotation  o f c r y s t a l l i n e a-glucose,  t h e k i n e t i c treatment  For  f o r the  growth o f a l i q u i d phase and w i t h r e a c t i o n o n l y i n t h i s l i q u i d phase accounts a t l e a s t q u a l i t a t i v e l y f o r t h e a v a i l a b l e o b s e r v a t i o n s .  89  B.  Isomerization  The  of 5-Norbornene-2,3-endo-dicarboxylic Anhydride  thermal i s o m e r i z a t i o n of 5-norbornene-2,3-endo-dicarboxylic  a n h y d r i d e t o the exo-isomer i s b e t t e r t h a n the m u t a r o t a t i o n o f g l u c o s e f o r an i n v e s t i g a t i o n o f a t h e r m a l r e a c t i o n i n o r g a n i c  solids.  The  endo-isomer  is readily  endo  a v a i l a b l e and  exo  easy t o p u r i f y , the r a t e i n the melt can be measured and  a  44 phase diagram o f the endo-exo system i s a v a i l a b l e . s i m i l a r to that followed  The  i n frozen solution reactions.  approach  was  F i r s t , rate constants  were d e t e r m i n e d i n the melt above the normal m e l t i n g p o i n t  (165  and  143°  f o r the endo-and exo-isomers r e s p e c t i v e l y ) and v a l u e s f o r r e a c t i o n i n a l i q u i d phase below the m e l t i n g p o i n t o b t a i n e d  by e x t r a p o l a t i n g .  r a t e s p r e d i c t e d from t h i s e x t r a p o l a t i o n i n c o n j u n c t i o n  The  w i t h the phase  diagram were then compared w i t h e x p e r i m e n t a l r a t e s measured below the normal m e l t i n g  point. Results  R e a c t i o n i n the M e l t : ca. 0.1  g. samples i n one  temperature.  r e a c t i o n was  ml. v i a l s and  s t u d i e d by  thermbstating  at the  sealing desired  A f t e r a l l o w i n g time f o r temperature e q u i l i b r i u m t o  e s t a b l i s h e d the f i r s t sample was c o l d water.  The  be  withdrawn and quenched by d i p p i n g  A f t e r c o l l e c t i n g a l l the samples the v i a l s were opened  into  90  and t h e c o n t e n t s d i s s o l v e d i n c h l o r o f o r m e d . t h e sample was  determined by comparing  The p e r cent exo-isomer i n  t h e i n t e g r a l o f t h e p.m.r. peak a t  3.6 x (due t o t h e o l e f i n i c p r o t o n s o f b o t h isomers) t o the peak a t 7.0 T (due t o t h e p r o t o n s a d j a c e n t t o the c a r b o n y l groups i n t h e e x o - i s o m e r ) . T h e , r e a c t i o n was. f i r s t - o r d e r up t o one and one h a l f h a l f - l i v e s , a f t e r which i t speeded up somewhat. GO  of  l o g (% exo  -  The r a t e c o n s t a n t s o b t a i n e d from p l o t s  t % exo ) v e r s u s t i r e are summarized i n T a b l e XV.  The  r a t e c o n s t a n t s i n the melt were about t w i c e as g r e a t as t h o s e i n d e c a l i n s o l u t i o n determined by B a l d w i n and Roberts 175 and 187°  47  (14 and 38 x 10  _5  _ i sec. at  respectively).  T a b l e XV  '  Rate C o n s t a n t s f o r I s o m e r i z a t i o n o f M o l t e n 5-norbornene-2, 3-endod i c a r b o x y l i c Anhydride. Temp. °C  k  185 '•"  o b s x 10^ s e c . * ' 64  175.3  26  165  9.8  160.3  5.7  155.0  3.1  A p l o t o f l o g k v e r s u s */T was for and  t h e a c t i v a t i o n parameters A S * =6.6  e.u;.  f a i r l y s t r a i g h t , y i e l d i n g values  f o r the forward reaction:  o f AH  = 38  kcal/mole  The v a l u e s c a l c u l a t e d from the d a t a of B a l d w i n and  t assuming t h e same e q u i l i b r i u m c o n s t a n t , were A H = 3 3 The e q u i l i b r i u m p o s i t i o n was  Roberts  ± kcal/mole•and  s t u d i e d by h e a t i n g samples of  = -5.0 the-endo-  isomer f o r f i v e h a l f - l i v e s or more, auenching, by c o o l i n g and a n a l y z i n g i n the u s u a l way.  I t was  found t h a t h e a t i n g an equimolar. m i x t u r e  e.u,  91  o f t h e exo- and endo-isomers  f o r one h a l f - l i f e gave c o n s i s t e n t r e s u l t s .  Over  the temperature range s t u d i e d , . 130 t o 195°j t h e c o m p o s i t i o n o f t h e e q u i l i b r i u m m i x t u r e was 44% exo-isomer. Reaction i n the S o l i d ;  The method was t h e same as t h a t d e s c r i b e d  above f o r t h e melt except t h a t . t h e samples were m e l t e d i n a 175° o i l b a t h and t h e n c o o l e d t o room temperature b e f o r e t h e r m o s t a t i n g a t t h e temperature of the run.  I n F i g u r e 25 a r e p r e s e n t e d d a t a f o r runs a t f o u r d i f f e r e n t  t e m p e r a t u r e s below t h e m e l t i n g p o i n t .  Values f o r the slopes o f the s t r a i g h t  p o r t i o n s o f t h e p l o t s o f (moles o f exo-isomer/mole  o f sample) v e r s u s t i m e  are summarized i n T a b l e X V I .  ,"• T a b l e XVI S l o p e s o f P l o t s o f F r a c t i o n o f P r o d u c t P r e s e n t v e r s u s Time f o r I s o m e r i z a t i o n o f 5-Norbornene-2, 3 - e n d o - d i c a r b O x y l i c A n h y d r i d e a t V a r i o u s Temperatures. Temp. °C,  Slope x 1 0  ; 150  •  .145-  ''  •' 3.8 .  141  :'  2.7  6  sec."  1  ••. 6.9  135  0.89  A f t e r 5 days a t 118° a sample o f pure endo-isomer  c o n t a i n e d 12%  exo-isomer, w h i l e a sample o f pure exo-isomer h e l d a t t h e same temperature f o r t h e same l e n g t h o f time c o n t a i n e d o n l y 2-3% endo-isomer;  a f t e r 10 days  a t t h i s temperature t h e sample o f exo-isomer c o n t a i n e d 5T7% endo-isomer. Samples o f t h e endo-isomer  thermOstated a t 100°, which i s below t h e e u t e c t i c  temperature o f t h e endo-exo system, a l s o r e a c t e d s l o w l y . t h e r e were 6% exo-isomer i n t h e sample.  A f t e r 12 days  On t h e o t h e r hand a sample o f  F i g u r e 25.  Isomeriz.ation-.of -5T-Norbornene-2, 3 - endo - d i carboxy l i e A n h y d r i d e i n the S o l i d .  93  exo-isomer h e l d a t 100° f o r 12 days c o n t a i n e d no endo-isomer.  Discussion  I f r e a c t i o n o c c u r s o n l y , i n t h e m e l t e d p a r t o f t h e sample t h e observations f o r endo-exo-isomerization  s h o u l d be s i m i l a r t o t h o s e made  on g l u c o s e i n t h e p r e c e e d i n g s e c t i o n .  B e f o r e m e l t i n g i s complete t h e  r a t e e q u a t i o n would be t h e same as eq 10 and t h e observed  first'order  r a t e c o n s t a n t would be g i v e n by, k , - (k„ A,/B, - k ) . . . obs f h h r  As can be seen  1  from F i g u r e 25 t h e curves do not resemble those found f o r t h e m u t a r o t a t i o n of glucose  (see F i g u r e 2 3 ) ; r a t h e r they a r e s t e e p e r near t h e b e g i n n i n g  of the reaction.  The r a t e c o n s t a n t s c a l c u l a t e d from e x t r a p o l a t e d v a l u e s  o f r a t e c o n s t a n t s and A^/B^ o b t a i n e d from t h e phase diagram a r e t o o s m a l l t o account at 145° k  f o r t h e observed r a t e o f p r o d u c t i o n o f exo-isomer. F o r example = 0.49 x 1 0 " s e c . " , k = 0.63 x 1 0 " s e c . " and k./B^ = • . . h h 5  f r  1  5  1  r  78/22 = 3.55; then k  . = (1.74 - 0.63) x 1 0 " =-1.11 x 1 0 " s e c . " 5  & b  t h e h a l f - l i f e f o r f i r s t - o r d e r r e a c t i o n would be 1040 min.  5  1  and  I f t h e r e were 1%  k exo-isomer min.;  p r e s e n t a t t h e b e g i n n i n g o f t h e r u n t h e r e would be 2% a f t e r 1040  however, as can be seen from F i g u r e 25 t h e r e would be more than 20%  exo-isomer p r e s e n t a f t e r t h i s time a t 145°. However, i f a c o n c u r r e n t s o l i d phase r e a c t i o n i s c o n s i d e r e d t h e r e s u l t s can be e x p l a i n e d . A  k  solid  The s o l i d phase r e a c t i o n s h o u l d be i r r e v e r s i b l e k liq. —-£—>liq k r A i•j ^s B,. solid *»- l i q A  B  I t i s u n l i k e l y t h a t more than 1% i m p u r i t i e s i n c l u d i n g exo-isomer were p r e s e n t s i n c e t h e m e l t i n g p o i n t o f t h e endo-isomer used was 164-165° ( l i t . 165°).  94  s i n c e a l l t h e p r o d u c t , j u s t as any o t h e r i m p u r i t y , s h o u l d go i n t o t h e l i q u i d phase.  I f t h e r e a c t i o n o c c u r s o n l y i n t h e melt t h e shape o f t h e curve s h o u l d  be s i m i l a r t o those observed f o r g l u c o s e , i . e . slow a t f i r s t a n d speeding up as t h e r e a c t i o n p r o c e e d s .  I f t h e r e a c t i o n o c c u r s o n l y i n t h e s o l i d t h e shape  o f t h e c u r v e would be s t e e p a t f i r s t and t h e n l e v e l o f f as t h e s o l i d phase d i s a p p e a r s by m e l t i n g .  I f b o t h p r o c e s s e s a r e g o i n g on a t once t h e shape o f  the curve would be between t h e s e two extremes, t h e e x a c t shape  depending  on t h e r e l a t i v e s i z e s o f k_, k and k . f r s One o f t h e i n t e r e s t i n g f e a t u r e s o f t h e r e a c t i o n as f o r m u l a t e d i s t h a t t h e two p r o c e s s e s a r e n o t independent. s o l i d phase r e a c t i o n , endo-isomer of the l i q u i d r e g i o n s . o c c u r s i n them.  As exo-isomer i s produced by t h e  must m e l t t o m a i n t a i n t h e c o n c e n t r a t i o n  As t h e l i q u i d r e g i o n s i n c r e a s e i n s i z e more r e a c t i o n  T h i s i n t e r a c t i o n e x p l a i n s why t h e r e a c t i o n i s f a s t e r than  would be expected from r e a c t i o n  only i n the melt.  the p l o t s c u r v e more a t lower temperatures  I t may a l s o e x p l a i n why  (see F i g u r e 2 5 ) . As t h e  temperature i s lowered t h e l i q u i d phase r e a c t i o n may become l e s s i m p o r t a n t s i n c e t h e l i q u i d phase would be s m a l l e r and have a h i g h e r c o n c e n t r a t i o n of exo-isomer i n i t ; t h e c u r v e s would t h e n be more l i k e t h o s e e x p e c t e d f o r r e a c t i o n o n l y i n t h e s o l i d phase. For c o n c u r r e n t r e a c t i o n i n b o t h a s o l i d and a l i q u i d phase, t h e r a t e i n t h e m e l t e d p a r t , t h e s o l i d p a r t and t h e t o t a l r a t e would be w r i t t e n as f o l l o w s : dm  B  (k, f Bh v  dt  melt  dm dt  - k ) r  solid solid  B  95 dm C—) dt  , N , solid k ) m + k m . r B s A J  (11)  D  total  Eq 11 can be made i n t o an e q u a t i o n w i t h o n l y one v a r i a b l e by s u b s t i t u t i n g for m ^ ^ ' i n  terms o f m . fi  The moles o f A i n t h e s o l i d phase a t any time  are e q u a l t o t h e t o t a l moles o f A i n t h e sample ( m the moles o f A i n t h e melt ( m ™  =  e l t  Au^).  t 0 t  = m°  r 1  ^ - mg) minus  Substituting for m ^ °  l i d  i n eq 11 and c o l l e c t i n g terms y i e l d s ,  - [Ck A L - V " ( f c t ^ B s r  A  m  f  total  d t  s  k  m  8  (12)  +  h  h  A l l t h e terms i n s i d e t h e square b r a c k e t s depend o n l y on t e m p e r a t u r e ,  and so  are c o n s t a n t d u r i n g any one r u n . For t h e s t r a i g h t p o r t i o n s o f t h e curves o f F i g u r e 25, ( d g / d t )  ^  m  i s c o n s t a n t and so cannot depend on mg, t h e moles o f p r o d u c t  present.  A c c o r d i n g t o eq 12 t h e o n l y way t h i s c o n d i t i o n can h o l d i s i f (k^A^/B^ _ ^ ) k  -(k +k h) i s c l o s e t o z e r o . s s —  I n t h i s case ( d m / d t ) . . = k , t h e r a t e *• B 'tot s' n  h  c o n s t a n t f o r t h e s o l i d phase r e a c t i o n ( s i n c e t h e a n a l y s i s i s always on t h e b a s i s o f one mole ^ m  r i  ^  'is u n i t y ) .  An i n d i c a t i o n t h a t t h e s l o p e s a r e  a c t u a l l y p r o p o r t i o n a l t o a r a t e c o n s t a n t o f t h e form k = Aexp(-a/T) i s the l i n e a r i t y o f a p l o t o f l o g k v e r s u s 1/T (see F i g u r e 2 6 ) . parameters o b t a i n e d from t h e p l o t a r e AH* = 43 k c a l / m o l e Many o r g a n i c m o l e c u l e s g l o b u l a r molecules,  The a c t i v a t i o n  and AS+ = 18 e.u.  w i t h n e a r l y s p h e r i c a l shape, so c a l l e d  e x h i b i t a h i g h e r temperature s o l i d " r o t a t o r " phase  i n which t h e a c t i v a t i o n energy f o r r o t a t i o n i s s m a l l , i n some cases  being  2.40  2.45  2 , 5 0  10 /T 3  F i g u r e 26.  A r r h e n i u s P l o t f o r S o l i d Phase R e a c t i o n o f 5-Norbornene-2,  3-endo-dicarboxylic Anhydride.  97  even smaller than i n the melt  . Such s o l i d phases tend to be "waxy" or  amorphous and are more e a s i l y deformed than the lower temperature c r y s t a l l i n e phases.  47  46 Both endo -  48 and exo-  5-norbornene-2, 3-dicarboxylic anhydride  are such globular molecules and the endo-isomer has such a phas . The e  t r a n s i t i o n temperature f o r the endo-isomer i s f a r below the melting point 48 while that f o r the exo-isomer i s very near i t s melting p o i n t .  I f rotation  i n such phases i s e a s i e r then perhaps isomerization i s also e a s i e r .  The  f a c t that the s o l i d - s o l i d t r a n s i t i o n temperature f o r the endo-isomer i s lower may e x p l a i n the d i f f e r e n t rates of r e a c t i o n reported above. In summary, i t may be s a i d that although r e a c t i o n only i n the melted part of the system studied here cannot account f o r the observations, the system cannot be treated without considering r e a c t i o n i n the melt. In any case, i n s o l i d materials above the e u t e c t i c temperature of the r e a c t i n g system a l i q u i d phase i s present.  Even at temperatures considerably  below the formal melting point of a pure s o l i d , the existence of a true s o l i d state r e a c t i o n can only be d e f i n i t e l y established by separating out any r e a c t i o n which may occur i n such a l i q u i d phase.  98  IV. G e n e r a l Remarks A.  A Demonstration  Reaction.  As shown by the d i s c u s s i o n above many a s p e c t s o f r e a c t i o n s f r o z e n s o l u t i o n s may the c o n c e n t r a t i o n  be c o r r e l a t e d , by the g e n e r a l  effect.  One  of•'...the...aspects  e f f e c t o f f r e e z i n g on e q u i l i b r i u m . . . A n y o r d e r o f r e a c t i o n i n one  in  k i n e t i c treatment of  not y e t d e a l t w i t h i s the  r e a c t i n g system which has  a  greater  d i r e c t i o n than i n the o t h e r s h o u l d e x p e r i e n c e a  s h i f t i n e q u i l i b r i u m p o s i t i o n upon f r e e z i n g out p a r t o f the s o l v e n t .  The  d i r e c t i o n and magnitude o f such a, s h i f t can be p r e d i c t e d on the b a s i s  of  the c o n c e n t r a t i o n  effect.  For a r e a c t i o n which i s . f i r s t - o r d e r i n the f o r w a r d d i r e c t i o n and  s e c o n d - o r d e r i n the r e v e r s e  d i r e c t i o n the f o l l o w i n g r e l a t i o n s h i p s , where  m denotes moles o f r e a g e n t , s h o u l d h o l d .  B + C  K  =  eq  B C — f — A  s •=  m  B  s m  C  s  *  1  s  m. n  r> B  h h  =  C  A  h  (V  >  those of A increase.  'h h B C m  m  According to t h i s equation, out s o l v e n t  m  h  x  1 V  h  i f the r e a c t i o n volume i s d e c r e a s e d by  V ^ ) , the number o f moles o f B and C must decrease The  and  e q u i l i b r i u m would s h i f t t o the l e f t by a f a c t o r  r e l a t e d t o the r e l a t i v e s i z e s o f the r e a c t i o n volume b e f o r e and freezing.  freezing  after  99  That such e q u i l i b r i u m s h i f t s do o c c u r was  shown by measuring the  absorbance o f samples o f a s o l u t i o n , o f h y d r o i o d i c . a n d  arsenic acids i n  water a f t e r a l l o w i n g e q u i l i b r i u m . t o . b e a t t a i n e d at room temperature and i n a sample f r o z e n at -5°. H As0 3  3I"  +  4  In t h i s case the s h i f t was  +  2H  +  —  d i r e c t i o n o f fewer s p e c i e s . unfrozen  sample was  thawing) was  HjAsOj  0.724.  The  1^  +  Re-  absorbance at 475 my o f the 1^ i n t h e  The  o n l y 0.015  '+  t o the r i g h t , i . e . , i n the  w h i l e t h a t i n the f r o z e n sample  (after  samples were o r i g i n a l l y 0.0012 M i n a r s e n i c a c i d  and 0.068 M i n h y d r o i o d i c a c i d .  The  c o l o r change thus brought about  v i s i b l e and s t r i k i n g .  An even more s t r i k i n g c o l o r change was  when more c o n c e n t r a t e d  samples were f r o z e n .  was  brought about  C o l o r l e s s samples 0.01  M in  each r e a c t a n t , which were s e a l e d i n 5 ml. v i a l s , changed w i t h i n two  minutes  t o y e l l o w , then organe, and f i n a l l y t o a y e l l o w - b r o w n c o l o r when p l a c e d i n a dry i c e - a c e t o n e b a t h at -80°. water the c o l o r was c o u l d be r e p e a t e d demonstration  B.  completely  Upon thawing by h o l d i n g under hot d i s c h a r g e d w i t h i n a few m i n u t e s .  as o f t e n as. d e s i r e d , thus b e i n g u s e f u l as a  tap  The  cycle  simple  of various aspects of r e a c t i o n s i n frozen s o l u t i o n s .  Review o f P u b l i s h e d R e s u l t s . I t i s o f i n t e r e s t t o r e c o n s i d e r some o f the e v i d e n c e which  led to suggestions  o f s p e c i a l e f f e c t s i n f r o z e n systems.  The  has  rate increases  3-13 upon f r e e z i n g which have been o b s e r v e d by v a r i o u s workers are probably  consequences o f the. c o n c e n t r a t i o n e f f e c t .  a u t h o r s have not s e p a r a t e d  1 0 , 1 1  However, these  out the e f f e c t o f c o n c e n t r a t i o n and  enhancements due t o o t h e r f a c t o r s systems**'  (see P a r t I )  may  are r a t h e r c o m p l i c a t e d  be p r e s e n t .  Many o f  rate these  due t o the l a r g e number o f s o l u t e s  100  o r the r e a c t i o n i t s e l f and such a . s e p a r a t i o n o f e f f e c t s would be  difficult.  I n the case o f the r e a c t i o n s o f amino a c i d e s t e r s w i t h h y d r o x y l a m i n e i n i c e as r e p o r t e d by Grant and A l b u r n * * , the observed i n h i b i t i o n brought about by the p r e s e n c e o f amino a c i d s and o t h e r s o l u t e s seems g e n e r a l l y c o n s i s t e n t * w i t h , t h e r a t e d e c r e a s e s u s u a l l y o b s e r v e d when " i m p u r i t i e s " are added t o f r o z e n s o l u t i o n s (see e.g.,  Figure  22.).  49 These same a u t h o r s  i n a v e r y r e c e n t paper have r e p o r t e d  p o l y m e r i z a t i o n o f s e v e r a l N-carboxyamino a c i d a n h y d r i d e s acids i n f r o z e n dioxane.  Their observations  (NGA)  the  t o polyamino  i n c l u d e r a t e enhancements on  f r e e z i n g , changes i n the r a t e c o n s t a n t s o f r e a c t i o n w h i l e i n d i v i d u a l runs remain f i r s t - o r d e r , and h i g h e r r a t e : c o n s t a n t s when u s i n g lower c o n c e n t r a t i o n s o f NCA's. o f the o b s e r v a t i o n s " . . . a l i g n m e n t may simultaneous  They c o n c l u d e t h a t the most l i k e l y  initial  explanation  i s a s p e c i a l e f f e c t o f the f r o z e n s o l v e n t i n t h a t  o c c u r i n a channel  o f m o l e c u l a r dimensions d u r i n g  c r y s t a l l i z a t i o n o f s o l v e n t and s o l u t e .  The phenomenon c o u l d  resemble c l a t h r a t e f o r m a t i o n , w i t h the s o l v e n t a c t i n g as host and p a r t i a l l y or f u l l y enclosing s o l u t e  the  template  molecules."  T h e i r o b s e r v a t i o n s , however, appear t o be c o n s i s t e n t w i t h e x p e c t a t i o n s f o r the c o n c e n t r a t i o n e f f e c t i f i t i s assumed t h a t the s o l v e n t they used c o n t a i n e d a d v e n t i t i o u s i n i t i a t o r s . u n l i k e l y s i n c e the a u t h o r s (Matheson Coleman and  T h i s assumption i s not  s t a t e t h a t they used commercial d i o x a n e  B e l l , S p e c t r b q u a l i t y ) without  further purification.  In t h e i r f i r s t paper on r e a c t i o n s i n f r o z e n s o l u t i o n s , B u t l e r and  B r u i c e ^ r e p o r t e d s t u d i e s on t h e h y d r o l y s i s o f a c e t i c a n h y d r i d e ,  p r o p i o l a c t o n e and p_-nitrophenyl a c e t a t e and on the d e h y d r a t i o n 6-hydroxydeoxyuridine.  Although  p r e d i c t i o n s , they concluded  6-  o f 5-hydro-  they were not a b l e t o make q u a n t i t a t i v e  t h a t the o b s e r v a t i o n s were q u a l i t a t i v e l y  explained  101  by " c o n c e n t r a t i o n o f r e a c t a n t s i n r e g i o n s between t h e i c e c r y s t a l s which remain l i q u i d " .  However, i n t h e i r second p a p e r , on t h e r e a c t i o n o f  t h i o l a c t o n e s with morpholine i n i c e , concentration effect  6  they were o f t h e o p i n i o n t h a t " t h e  ... appears to. b e . e n t i r e l y inadequate t o e x p l a i n t h e  e f f e c t s a s s o c i a t e d w i t h t h e two systems examined". B r u i c e and B u t l e r ' s o b s e r v a t i o n t h a t t h e r a t e o f r e a c t i o n o f 6  t h i o l a c t o n e s w i t h m o r p h o l i n e i n i c e was a f u n c t i o n o f t h e m o r p h o l i n e c o n c e n t r a t i o n and n o t t h e square o f i t as i n u n f r o z e n s o l u t i o n s can a l s o be e x p l a i n e d on t h e b a s i s o f t h e c o n c e n t r a t i o n e f f e c t . experimental  In obtaining the  r e s u l t s , the morpholine concentration i n i n i t i a l  unfrozen  s o l u t i o n s was v a r i e d i n a s e r i e s o f runs s i m p l y by d i l u t i o n o f a s t a n d a r d buffer solution.  The volume o f t h e l i q u i d r e g i o n s o f f r o z e n s o l u t i o n s would  t h e n be p r o p o r t i o n a l t o m o r p h o l i n e c o n c e n t r a t i o n s i n thawed s o l u t i o n s , i.e.  = K"N , w h i l e t h e a c t u a l c o n c e n t r a t i o n , N^, i n t h e l i q u i d r e a c t i o n s  r e g i o n s would be t h e same c o n s t a n t v a l u e i n a l l t h e f r o z e n r u n s .  I f the  r e a c t i o n i n the l i q u i d regions i s normal, then the r a t e i s p r o p o r t i o n a l t o 2 N, . h  When measured i n thawed s o l u t i o n s t h e a c t u a l r a t e i s m o d i f i e d so t h a t  2 2 the o b s e r v e d r a t e c o n s t a n t i s k . = KN, V./V which i s e q u a l t o KN, K"N /V . obs h h s h s s M  As  i s c o n s t a n t and t h e volume V  rate constants observed.  g  i s always i n terms o f one l i t e r , t h e  a r e p r o p o r t i o n a l t o N^, i . e .  k  = 0  D  S  ^'^  a s s  experimentally  The odd change i n k i n e t i c o r d e r f o r r e a c t i o n i n i c e a r i s e s o n l y  from t h e v a r i a t i o n i n r e a c t i o n volumes f o r runs a t d i f f e r e n t  initial  concentrations. The  d i f f e r e n c e i n s o l v e n t k i n e t i c i s o t o p e e f f e c t which they observed  can l i k e w i s e be e x p l a i n e d .  They found k^/k^ = 4.2 i n u n f r o z e n  30° and k^/k^ = 1 . 6 i n f r o z e n s o l u t i o n a t -10°.  s o l u t i o n at  Since the f r e e z i n g point  o f D_0 i s +3.8° t h e c o n c e n t r a t i o n o f r e a c t a n t s i n t h e l i q u i d r e g i o n s o f  102  heavy water at -10° would be greater, than that i n the l i q u i d regions o f normal water at the same temperature and the observed r a t e constant, k^, correspondingly  greater. 8 study o f the F e ( I I ) - F e ( I I I ) e l e c t r o n exchange r e a c t i o n  Home's  i n frozen aqueous p e r c h l o r i c a c i d i s e s p e c i a l l y i n t e r e s t i n g i n that he c a r r i e d out rate Studies both above and below the e u t e c t i c temperature (-58°) of the HC10 -H 0 system and found no d i s c o n t i n u i t y . This f a c t seems 4  2  to i n d i c a t e that the mechanism i s the same i n both cases. to observe the segregation o f a concentrated of HCIO^ and ^ 0 , corresponding Fe(III).  He was not able  s o l u t i o n upon f r e e z i n g a mixture  t o the e u t e c t i c composition,  containing  Nevertheless, such a l i q u i d , phase may have been present below  -58° i n the frozen r e a c t i o n mixture; since the phase r e l a t i o n s h i p s i n the system HCIO^-^O would not be expected t o be the same as those i n the HC10^-H 0-FeCl system. 2  3  This author, appears t o be the f i r s t t o have  attempted t o make a c o r r e c t i o n i n the rate equation f o r concentration of reactants upon f r e e z i n g .  Unfortunately, the r e a c t i o n i t s e l f and the  phase r e l a t i o n s h i p s are very complicated and so h i s conclusion that the r e a c t i o n proceeds i n a s o l i d phase below -58° i s probably not j u s t i f i e d . Fuchtbauer and M a z u r ^ were able t o show the water-thymine e u t e c t i c t o be at -0.2° and that photochemical dimerization occuring i n frozen s o l u t i o n s below t h i s temperature proceeds i n a s o l i d phase i n 12 12 agreement with the conclusion o f Wang.  Wang's  conclusion that the  photochemical r e a c t i o n o f 1,3-dimethyluracil with methanol i n frozen aqueous s o l u t i o n s containing 2% methanol proceeds i n "puddles" containing mainly methanol i s undoubtedly correct and i n agreement with our conclusion that many reactions i n frozen s o l u t i o n s take place i n h i g h l y l i q u i d regions present among the c r y s t a l s o f frozen solvent.  concentrated  103  While many f e a t u r e s o f f r o z e n s o l u t i o n r e a c t i o n s predicted  are a c t u a l l y  by a g e n e r a l t r e a t m e n t o f t h e c o n c e n t r a t i o n e f f e c t , t h e e x i s t e n c e  o f o t h e r e f f e c t s cannot be d i s c o u n t e d .  However, no c l e a r e v i d e n c e o f such  o t h e r e f f e c t s has been p r e s e n t e d i n any c a s e .  I t i s clear that, for  reactions  known t o p r o c e e d i n normal l i q u i d s o l u t i o n s near t h e f r e e z i n g p o i n t , any discussion  o f rates i n a frozen  contribution  s o l u t i o n which does n o t s e p a r a t e t h e  o f t h e c o n c e n t r a t i o n , e f f e c t must be i n e r r o r .  Quantitative  s e p a r a t i o n o f r e s u l t s due t o t h i s e f f e c t from t h o s e a r i s i n g from any o t h e r p o s s i b i l i t y i s n o t e a s i l y c a r r i e d o u t when t h e system c o n t a i n s many when t h e r e a c t i o n i s n o t w e l l known under normal ( i . e . , u n f r o z e n ) •  solutes,  conditions,  t  o r when t h e s o l i d - l i q u i d phase r e l a t i o n s h i p i s n o t a v a i l a b l e .  • V C.  Conclusion. In t h e c o u r s e o f t h i s r e s e a r c h some new f e a t u r e s o f r e a c t i o n s i n  frozen  s o l u t i o n s have been f o u n d , i n c l u d i n g a maximum i n t h e r a t e -  temperature dependence c u r v e , up t o 1000-fold r a t e enhancements, s u r p r i s i n g changes i n k i n e t i c o r d e r and e q u i l i b r i u m  s h i f t s upon f r e e z i n g .  method o f t r e a t i n g t h e e f f e c t o f c o n c e n t r a t i o n , out pure s o l v e n t ,  A general  brought about by f r e e z i n g  on r e a c t i n g systems has been developed.  This treatment  not o n l y e x p l a i n e d o u r own o b s e r v a t i o n s b u t a l s o some o f those o b t a i n e d by other investigators. detection  The a p p l i c a t i o n o f t h i s t r e a t m e n t s h o u l d a l l o w  o f any o t h e r p o s s i b l e  concentration effect. The reactions  ideas o f frozen  the  e f f e c t s o f f r e e z i n g b e s i d e s the  . s o l u t i o n k i n e t i c s have been extended to  o f o r g a n i c s o l i d s i n which m e l t i n g o c c u r s d u r i n g t h e r e a c t i o n .  S e p a r a t i o n o f r e a c t i o n i n t h e melt from p o s s i b l e r e a c t i o n i n t h e s o l i d has been demonstrated.  104  T h i s work has r e s u l t e d i n a b e t t e r u n d e r s t a n d i n g o f t h e e f f e c t s o f f r e e z i n g on r e a c t i n g systems.  The i d e a s d e v e l o p e d here may  find practical  a p p l i c a t i o n t o problems encountered i n the f r e e z i n g o f f o o d s , the low temperature p r e s e r v a t i o n water.  o f organs f o r s u r g e r y and t h e d e s a l i n i z a t i o n o f sea  F o r a d i s c u s s i o n o f f r e e z i n g on some a s p e c t s o f t h e s e problems  r e f e r e n c e 51.  see  105  V. Experimental  Materials  Reagents. M e t h y l i o d i d e (Eastman O r g a n i c C h e m i c a l s , reagent grade) was washed w i t h d i l u e aqueous sodium t h i o s u l f a t e s o l u t i o n and w i t h water. d r y i n g over anhydrous  c a l c i u m c h l o r i d e and d i s t i l l a t i o n  After  (b.p. 44°, l i t . * 4 3 ° )  through a column packed w i t h g l a s s beads, t h e p r o d u c t was s t o r e d i n a brown b o t t l e o v e r a drop o f mercury. distilled  T r i e t h y l a m i n e was r e f l u x e d o v e r and  (b.p. 89°, l i t . 89-90) from barium o x i d e . 23 t - B u t y l p e r o x y formate was p r e p a r e d as d e s c r i b e d by P i n c o c k  t - b u t y l h y d r o p e r o x i d e and f o r m i c a c e t i c a n h y d r i d e .  The p r o d u c t was s t o r e d  i n p o l y e t h y l e n e b o t t l e s a t c a . 0° t o a v o i d t h e slow d e c o m p o s i t i o n by g l a s s .  from  caused  2 , 6 - L u t i d i n e (Eastman O r g a n i c C h e m i c a l s , p r a c t i c a l grade) was  r e f l u x e d w i t h methyl p _ - t o l u e n e s u l f o n a t e then d i s t i l l e d and from barium o x i d e .  redistilled 52a  The sample used had f . p . -6.5° ( l i t . -6.9°  -6.07°^k, - 5 . 9 ° ^ ) . c  ,  Reagent grade p y r i d i n e was r e f l u x e d and d i s t i l l e d  (b.p. 115°, l i t . 115.5°) from b a r i u m o x i d e . E t h y l e n e c h l o r o h y d r i n (Eastman O r g a n i c C h e m i c a l s , p r a c t i c a l  grade)  was d i s t i l l e d through a 7 5 c m . V i g r e u x column. A f t e r d i s c a r d i n g a l a r g e 1  f o r e r u n , a c e n t e r f r a c t i o n w i t h b.p. 128.5 - 130 ( l i t . 128°) was c o l l e c t e d . Sodium h y d r o x i d e s o l u t i o n s were made up from B r i t i s h Drug Houses c o n c e n t r a t e d v o l u m e t r i c s o l u t i o n s o r by d i s s o l v i n g U.S.P: grade p e l l e t s . The s o l u t i o n s 1. L i t e r a t u r e v a l u e s o f p h y s i c a l c o n s t a n t s were t a k e n from t h e "Handbook o f C h e m i s t r y and P h y s i c s " , F o r t y - S i x t h Ed., The Chemical Rubber Co., C l e v l a n d (1965) u n l e s s o t h e r w i s e n o t e d .  106  were s t a n d a r d i z e d a g a i n s t p o t a s s i u m a c i d p h t h a l a t e . G l u c o s e used f o r f r o z e n s o l u t i o n s t u d i e s was B r i t i s h Drug Houses a n a l y t i c a l r e a g e n t grade a-D-glucose.  F o r t h e neat r e a c t i o n , i n a d d i t i o n t o  t h i s g l u c o s e F i s c h e r C e r t i f i e d Reagent: grade and U.S. N a t i o n a l Bureau o f Standards d e x t r o s e , s t a n d a r d sample No. 41 was used.  Hydrochloric acid  s o l u t i o n s were made up from B r i t i s h Drug Houses c o n c e n t r a t e d v o l u m e t r i c solutions.. 5-Norbornene-2, m.p.  154-155°)  3 - e n d o - d i c a r b o x y l i e a n h y d r i d e ( A l d r i c h Chemical Co.,  was p u r i f i e d by t w i c e r e c r y s t a l l i z i n g from benzene and t h e n  once more from p e t r o l e u m e t h e r (b.p. 65-110°). a m a t e r i a l used was 164-165  : e  (lit.  165  The m e l t i n g p o i n t o f t h e  44  ).  The exo-isomer was p r e p a r e d  44  by t h e method o f C r a i g .  Crude endo-isomer was h e a t e d a t 190° f o r 2 h r . ,  c o o l e d and t h e crude m i x t u r e r e c r y s t a l l i z e d from benzene.  The crude m a t e r i a l  was then r e c r y s t a l l i z e d from m i x t u r e s o f benzene and p e t r o l e u m e t h e r (b.p.  65-110°)  t o a c o n s t a n t m e l t i n g p o i n t , m.p. 141-143° ( l i t .  143° ). 44  A r s e n i c a c i d used was May and Baker 80% s o l u t i o n o r Merck reagent grade A s ^ .  analytical  H y d r o i o d i c a c i d was made up from B r i t i s h Drug Houses  a n a l y t i c a l r e a g e n t grade v i a l s o f t h e c o n s t a n t b o i l i n g m i x t u r e . Solvents Reagent grade benzene was r e c r y s t a l l i z e d t h r e e times by slow f r e e z i n g o f c a . 75-85% o f t h e t o t a l volume.  Benzene which had been d r i e d  o v e r anhydrous magnesium s u l f a t e , d i s t i l l e d , t h e n c r y s t a l l i z e d once, gave the  same r a t e f o r r e a c t i o n o f m e t h y l i o d i d e w i t h t r i e t h y l a m i n e .  had f . p . 5 . 6 ° ( l i t .  Benzene used  5.53° ). 53  p_-Xylene (Eastman O r g a n i c C h e m i c a l s , White L a b e l grade) was p u r i f i e d by slow c r y s t a l l i z a t i o n o f about one h a l f o f t h e t o t a l .volume o f  107  l i q u i d three times. sodium,  The £= xylene was then r e f l u x e d and d i s t i l l e d from  T h i s j)=xylene then f r o z e to over 90% i n a 0,2  a  range, i n d i c a t i n g  t h a t the t o t a l i m p u r i t y c o n c e n t r a t i o n was l e s s than 0.1 mole pes- cent. D e i o n i z e d water was used without f u r t h e r p u r i f i c a t i o n except i n the runs with ethylene e h i e r e h y d r i n , For use i n these runs the water was b e l l e d t e remove carbon d i o x i d e and §tared i n a f l a s k equipped with an A s e a r i t e d r y i n g tube.  For use i n the runs at the lowest c h l o r o h y d r i n  c o n c e n t r a t i o n (.001 M) the water was d i s t i l l e d f i r s t from a c i d i c permanganate and then  from  barium hydroxide.  F r e e z i n g P o i n t Depression Diagrams F r e e z i n g p o i n t d e p r e s s i o n diagrams were c o n s t r u c t e d by t a k i n g the f r e e z i n g p o i n t s o f s o l u t i o n s o f k n o w n c o n c e n t r a t i o n . About 21 ml. o f the s o l u t i o n was p l a c e d i n a f i a t bottomed g l a s s tube ea. 100 x 20 mm.  The  s o l u t i o n was s t i r r e d with a motor d r i v e n s t i r r e r and the bulb o f a thermometer p l a c e d i n i t ,  The s o l u t i o n was then s l o w l y eooled (l=2 /min). e  i i n e e the s o l u t i o n s always supercooled b e f o r e f r e e z i n g the f r e e z i n g p o i n t was taken as the maxifflum temperature reached a f t e r f r e e z i n g began.  The  procedure was repeated two or t h r e e times on the same sample and the average value taken.  The values u s u a l l y agreed w i t h i n a few tenths o f a degree.  108  Kinetics Methyl Iodide with Triethylamine A.  I n f r a r e d Method.  S o l u t i o n s o f e q u a l (or n e a r l y e q u a l )  c o n c e n t r a t i o n s o f methyl i o d i d e and o f t r i e t h y l a m i n e were p r e p a r e d , e q u a l volumes o f t h e s e combined, and.the r e s u l t i n g s o l u t i o n shaken to t h o r o u g h l y mix the r e a c t a n t s .  vigorously  T h i s m i x t u r e (some p r o d u c t i m m e d i a t e l y  b e g i n s t o p r e c i p i t a t e ) was q u i c k l y drawn i n t o a l a r g e s y r i n g e and i n t o a number o f samples h e l d i n 1 ml. v i a l s ,  divided  t h e v i a l s were s e a l e d and  plunged i n t o a Dry I c e - a c e t o n e o r l i q u i d n i t r o g e n b a t h .  When the s o l u t i o n s  i n t h e v i a l s were f r o z e n , the v i a l s were a l l t r a n s f e r r e d t o a c o n s t a n t temperature b a t h at t h e d e s i r e d t e m p e r a t u r e . ; A f t e r a l l o w i n g the samples t o warm up t o t h e b a t h t e m p e r a t u r e , t h e f i r s t v i a l and p l a c e d i n a Dry I c e - a c e t o n e b a t h .  (time z e r o ) was  A f t e r a l l the samples o f a run had  been c o l l e c t e d i n t h i s manner,; they were thawed and a n a l y z e d by the change i n absorbance  a t 1240 cm.  removed  * due t o methyl i o d i d e .  measuring  Both benzene  and t r i e t h y l a m i n e absorb r e l a t i v e l y weakly i n t h i s r e g i o n , however benzene was compensated f o r by pure s o l v e n t i n the r e f e r e n c e c e l l . c h l o r i d e c e l l s used had p a t h l e n g t h s o f 0.5 mm.  The  sodium  The observed r a t e c o n s t a n t ,  f o r r e a c t i o n s w i t h e q u a l r e a c t a n t c o n c e n t r a t i o n s , were o b t a i n e d by (A  Q  this  - A ^  / A^ - A ^ )  plotting  a g a i n s t . t i m e i n minutes and m u l t i p l y i n g the s l o p e o f :  l i n e by 2.303/60.  A , A^ and A ^ q  are the v a l u e s o f sample  absorbance,  measured a g a i n s t pure benzene i n the r e f e r e n c e c e l l , a t time z e r o , time t , and time i n f i n i t y  ( u s u a l l y 10 h a l f - l i v e s ) , r e s p e c t i v e l y .  which the absorbance be z e r o .  o f an i n f i n i t y sample was  I n a l l cases i n  measured i t was  ;  found to.  109  B. T i t r a t i o n Method.  Solutions o f the reactants having twice the  d e s i r e d c o n c e n t r a t i o n o f t h e r u n were made up, t h e n two o r t h r e e m l . p o r t i o n s of  one s o l u t i o n were p i p e t t e d i n t o a number o f c a . 6 m l . v i a l s .  An equal  amount o f t h e second s o l u t i o n was p i p e t t e d i n t o t h e f i r s t v i a l which was then i m m e d i a t e l y shaken, s e a l e d and f r o z e n i n a Dry I c e - a c e t o n e o r l i q u i d n i t r o g e n bath..  A f t e r a l l t h e v i a l s had been p r e p a r e d i n t h i s manner they  were p l a c e d i n t h e c o n s t a n t temperature b a t h .  The f i r s t sample was  withdrawn about 10 min. l a t e r when temperature e q u i l i b r a t i o n was complete. The samples were thawed i m m e d i a t e l y a f t e r w i t h d r a w i n g from t h e b a t h by s h a k i n g under warm t a p water. hydrochloric acid red  The s o l u t i o n was washed i n t o excess s t a n d a r d  (0.1 N) and t h e excess a c i d back t i t r a t e d t o t h e methyl  end p o i n t w i t h s t a n d a r d 0.1 N sodium h y d r o x i d e s o l u t i o n .  Some l i t t l e  s c a t t e r i n t h e p o i n t s o f a r u n seemed due t o t h e use o f i n d i v i d u a l l y p r e p a r e d samples, r a t h e r than a l i q u o t s o f a s i n g l e s o l u t i o n .  F o r runs w i t h unequal  r e a c t a n t c o n c e n t r a t i o n s (A and B Y t h e observed r a t e c o n s t a n t s were o b t a i n e d s s J  by p l o t t i n g l o g ( A B ) a g a i n s t time i n minutes and m u l t i p l y i n g t h e s l o p e s  of  s  the l i n e by 2.303/60.  When p_-xylene was added as an " i m p u r i t y " i t was  added t o t h e o r i g i n a l t r i e t h y l a m i n e s o l u t i o n so t h a t i t s c o n c e n t r a t i o n was t w i c e as g r e a t as i n t h e f i n a l r e a c t i o n m i x t u r e .  F o r runs w i t h p_-xylene  p r e s e n t t h e r a t e c o n s t a n t s were o b t a i n e d from a p l o t o f 2 l o g Im 12. 303 A a g a i n s t t i m e , s s C.  N u c l e a r M a g n e t i c Resonance Method.  (A /A ) S  Q  -  A s o l u t i o n 0.6 M i n both  methyl i o d i d e and t r i e t h y l a m i n e i n benzene was p r e p a r e d and about 1 m l . was q u i c k l y t r a n s f e r r e d w i t h a s y r i n g e t o a normal n.m.r. sample tube.  The  sample was f r o z e n i n Dry I c e - a c e t o n e and then p l a c e d i n a V a r i a n A-60 n.m.r. s p e c t r o m e t e r equipped w i t h v a r i a b l e temperature c o n t r o l .  The temperature  110  o f -5° was measured by t h e s e p a r a t i o n o f the peaks o f a methanol  sample.  A f t e r the sample came up t o -5° the i n t e g r a l curve f o r t h e broad benzene peak was  run about every 15 min.  The peak w i d t h at h a l f h e i g h t was  ca.  50 c p s , much narrower than s i g n a l s ' a r i s i n g from c r y s t a l l i n e s o l i d s .  An  i n f i n i t y sample, p r e p a r e d as above f o r t h e s i n g l e sample used i n the r u n , had been h e l d a t -5° o v e r n i g h t and gave an i n t e g r a l curve o n l y 2% as h i g h as t h a t g i v e n by the i n i t i a l ( i n t e g r a l v a l u e i n mm.)  zero time i n t e g r a l curve.  A plot of log  a g a i n s t time was a good s t r a i g h t l i n e o v e r 80%  r e a c t i o n , the s l o p e o f the l i n e m u l t i p l i e d by 2 x 2.303 gave the v a l u e o f k„C, as 3.5 x 10 2 h  - 4 - 1 sec.  .  t - B u t y l p e r o x y Formate i n F r o z e n p_-Xylene S o l u t i o n s were u s u a l l y made up by adding a known f r e s h l y p r e p a r e d s o l u t i o n o f 2 , 6 - l u t i d i n e ( o r p y r i d i n e ) i n p_-xylene t o a weighed q u a n t i t y o f TBF and then d i l u t i n g t d 25 ml. w i t h p_-xylene.  The s o l u t i o n was  i n volumes o f 1-2 ml. i n t o about t e n t o f i f t e e n g l a s s ampoules.  divided  The  ampoules were s e a l e d under a i r a t a t m o s p h e r i c p r e s s u r e and f r o z e n , u s u a l l y by dumping them i n t o a Dry Ice-acetone mixture.  Two  were r e t a i n e d f o r c o n t r o l s as d e s c r i b e d below.  No s p e c i a l t e c h n i q u e s f o r  sample p r e p a r a t i o n were, n e c e s s a r y .  o r t h r e e u n f r o z e n samples  There was no d i f f e r e n c e i n r a t e o f  TBF d e c o m p o s i t i o n i n f r o z e n - s a m p l e s which d i f f e r e d i n any o f t h e f o l l o w i n g ways; p r e s e n c e o f i n s o l u b l e m a t e r i a l s , d i f f e r e n t volumes o f s o l u t i o n , degassed o r not degassed, and samples f r o z e n by placement 0°  i n baths at 8 o r  ( w i t h s e e d i n g ) , a t -70 o r a t -195°. The f r o z e n samples were p l a c e d i n a c o n s t a n t temperature b a t h  and, a f t e r a l l o w i n g a few minutes f o r temperature e q u i l i b r a t i o n , the " z e r o t i m e " sample was withdrawn.  T h i s was q u i c k l y d e f r o s t e d , u s u a l l y by s h a k i n g  Ill  under t a p w a t e r a t room temperature.; Other samples were c o l l e c t e d s i m i l a r l y a t v a r i o u s t i m e s and a l l were s t o r e d a t room temperature a n a l y s i s as d e s c r i b e d below.  until  I n runs a t h i g h base c o n c e n t r a t i o n s the  d e c o m p o s i t i o n at room temperature was s u f f i c i e n t l y f a s t t o r e q u i r e e i t h e r immediate a n a l y s i s when each sample was d e f r o s t e d , o r s t o r a g e at c a .  -70°  u n t i l c o l l e c t i o n was complete and t h e a n a l y s i s o f a l l the samples c o u l d be c a r r i e d out o v e r a few minutes. f r o z e n at -70°  I n e v e r y run s e p a r a t e samples were s t o r e d  (or -195°), u n f r o z e n at room temperature and, i f p o s s i b l e ,  at the temperature o f the r u n .  The p_-xylene s o l u t i o n s c o u l d be o f t e n  r e t a i n e d as s u p e r c o o l e d l i q u i d samples a t 0° f o r l o n g e r t i m e s than r e q u i r e d f o r the run and t h e a n a l y s i s . o f k i n e t i c r u n samples was  These samples were a n a l y z e d a f t e r t h e a n a l y s i s  completed and, except a t the h i g h e s t base  c o n c e n t r a t i o n s , were l e s s decomposed than t h e " z e r o t i m e " sample o f the run. The d e f r o s t e d samples were a n a l y z e d by measurement o f the i n f r a r e d 23 c a r b o n y l a b s o r p t i o n o f TBF as d e s c r i b e d by P i n c o c k o f l o g P/P  .  In e v e r y case p l o t s  -vs.' time f o l l o w e d u s u a l l y t o 80-90% d e c o m p o s i t i o n were s t r a i g h t .  S i n c e i n f i n i t y samples t a k e n a f t e r 8-10  h a l f - l i v e s f o r v a r i o u s runs  showed no a b s o r p t i o n f o r TBF, t h e i n f i n i t e time o p t i c a l d e n s i t y f o r runs i n which i t was not measured was assumed t o be z e r o .  Observed  first-order  r a t e c o n s t a n t s f o r c o m p l e t e l y independent runs at s i m i l a r c o n c e n t r a t i o n s sometimes v a r i e d by 10%, but t h e r e was no s c a t t e r o f p o i n t s i n each i n d i v i d u a l run.  112  Ethylene Chlorohydrin with Hydroxide Ion i n Ice E t h y l e n e c h l o r o h y d r i n s o l u t i o n s were made up f r e s h each day by w e i g h i n g out t h e m a t e r i a l , and d i l u t i n g w i t h water.  The r e q u i r e d amount  o f t h i s s o l u t i o n was mixed w i t h t h e a p p r o p r i a t e volume o f sodium  hydroxide  s o l u t i o n and t h e n d i l u t e d w i t h Water t o g i v e t h e c o n c e n t r a t i o n d e s i r e d f o r a run. vials.  A f t e r thorough m i x i n g , t h e s o l u t i o n was d i v i d e d i n t o s e v e r a l  F r e e z i n g o f t h e s e i n d i v i d u a l samples o f a r u n was u s u a l l y  accomplished s i m p l y by p l a c i n g t h e samples i n t o a Dry Ice-acetone Sometimes t h e samples were s u p e r c o o l e d  bath.  t o t h e temperature o f a r u n and  t h e n dipped q u i c k l y i n t o a Dry Ice-acetone  bath t o i n i t i a t e  crystallization.  At v a r i o u s times i n d i v i d u a l - samples were removed from t h e c o n s t a n t temperature b a t h and q u i c k l y thawed by s h a k i n g under h o t t a p water.  A n a l y s i s o f t h e samples was c a r r i e d o u t by t i t r a t i o n w i t h  s t a n d a r d h y d r o c h l o r i c a c i d s o l u t i o n ( u s u a l l y 0.05 M) w i t h as i n d i c a t o r .  phenolphthalein  M i c r o b u r e t s o f 5 and 2 m l . c a p a c i t y were used, t h e 2 m l .  b u r e t b e i n g equipped w i t h a micrometer p l u n g e r .  F o r runs a t low  c o n c e n t r a t i o n s o f base pH measurements on i n d i v i d u a l thawed samples were made u s i n g a Radiometer Model 4 pH meter which was s t a n d a r d i z e d pH 10 b u f f e r .  against  No c o r r e c t i o n was made f o r t h e d e v i a t i o n o f t h e a c t i v i t y  c o e f f i c i e n t from u n i t y .  F o r example, a r u n w i t h 0.001 M r e a c t a n t s  gave t h e f o l l o w i n g pH r e a d i n g s a t t h e g i v e n t i m e s ; 10.967 a t 0 min., 10.848 a t 46 min., 188 min.,  10.718 a t 99 min.,  10.632 a t 239 min.,  10.681 a t 150 min.,  10.493 a t 409 min.  10.698 a t  and 10.385 a t 607 min.  K i n e t i c d a t a were t r e a t e d a c c o r d i n g t o normal second-order k i n e t i c equations.  Rate c o n s t a n t s were c a l c u l a t e d from t h e s l o p e s o f t h e  lines i nplots of reciprocal concentrationagainst  time o r p l o t s o f  113  log[ClCH CH OH]/[OH"] against time. 2  2  showed some s c a t t e r . measuring  Runs at the lowest concentration  This seemed due to experimental d i f f i c u l t i e s i n  low concentrations of base rather than to r e a l v a r i a t i o n s i n  the amount reacted.  As i n d i c a t e d by changes i n pH, t h i s r e a c t i o n i n  frozen s o l u t i o n s proceeds even with i n i t i a l concentrations less than _3  10  M, but i n d i v i d u a l thawed samples gave very e r r a t i c pH readings at  these low concentrations of base. The values of k at one degree i n t e r v a l s were c a l c u l a t e d 26 -1 -1 (IBM 7040 computer) from the equation k ( l i t e r mole" sec." ) = 16 8 -23300/RT 10 ' /60 x e" . . R u n s using supercooled l i q u i d samples showed 2  2  that our method of a n a l y s i s gave r a t e constants i n agreement with McCabe and Warner  (at -1.4° found, 2.06 x 10" l i t e r mole" s e c . " ; at ' ••• -4 . _ i _ i ' c a l c u l a t e d 2.04 x 10 l i t e r mole sec. ). 26  4  1  1  -1.0°  Mutarotation of Glucose i n Ice Solutions were made up by d i s s o l v i n g a weighed amount of a-D-glUcose i n a volumetric f l a s k , then adding the appropriate amount of HC1 s o l u t i o n , and making up to the mark.  A f t e r thorough mixing the  s o l u t i o n was divided i n t o ca. 15 ml. a l i q u o t s held i n t e s t tubes which were then supercooled to the temperature of the run.  Freezing was  initiated  by dipping the tubes f o r a few seconds i n t o a Dry Ice-acetone bath.  The  f i r s t sample was withdrawn from the constant temperature bath approximately ten  minutes a f t e r f r e e z i n g .  A n a l y s i s of samples having 0.25 M glucose  or higher was c a r r i e d out by f i r s t d i l u t i n g the sample immediately a f t e r thawing with an NaOH s o l u t i o n containing b u f f e r (Coleman pH4 b u f f e r t a b l e t s ) . The r e s u l t i n g s o l u t i o n was about pH4, and the mutarotation near the slowest p o s s i b l e rate.  The angle of r o t a t i o n (+_ 0.05°) was then measured with a  114  B e l l i n g h a m and S t a n l e y Model D p o l a r i m e t e r .  Samples h a v i n g l e s s than 0.25 M  g l u c o s e were a n a l y z e d by use o f a Bendix t y p e 143A A u t o m a t i c equipped  w i t h a mercury f i l t e r .  Polarimeter  The 40 mm c e l l was f i t t e d w i t h a syphon  arrangement so t h a t samples c o u l d be q u i c k l y exchanged i n t h e c e l l removing i t from t h e o p t i c a l u n i t .  without  Samples c o u l d be thawed and a n a l y z e d  v e r y q u i c k l y , t h e r o t a t i o n (+ 0.001°) was t a k e n when t h e meter n e e d l e was at maximum d e f l e c t i o n .  M u t a r o t a t i o n i n t h e thawed samples c o n t i n u e d  as t h e sample was warmed, o f c o u r s e , b u t thawing s u f f i c i e n t l y the r e a c t i o n t o a l l o w t h e r a p i d a n a l y s i s d e s c r i b e d above.  slowed  The r o t a t i o n s  o f t h e i n f i n i t y samples were t a k e n a f t e r a l l o w i n g t h e s o l u t i o n t o s t a n d at  room temperature  c a . 24 h r .  Observed r a t e c o n s t a n t s ware o b t a i n e d from t h e s l o p e s o f p l o t s o f log  (a  - ot^/a .'- a j a g a i n s t time  (where a i s observed  s t r a i g h t l i n e was drawn v i s u a l l y through t h e p o i n t s .  rotation).  The b e s t  The r a t e c o n s t a n t s  30 for  spontaneous" m u t a r o t a t i o n , k j w e r e  calculated  from -30 t o +20° by  the e q u a t i o n l o g k j = - l o g 60 + 10,785 - 16900/2.303 RT ( a t -4.0° ^ 1.92 x 10  sec. ^ .  1  The r a t e c o n s t a n t s f o r second-order  acid catalyzed  from l o g k^ = - l o g 60 - l o g 0.04 + 12.111 -  r e a c t i o n were c a l c u l a t e d 18600/2.303 RT ( a t -4.0° k  =  2  = 4.25 x l O  Mutarotation of P o l y c r y s t a l l i n e  - 4  l i t e r mole"  1  sec; ) . 1  Glucose  Weighed samples o f g l u c o s e which had been d r i e d a t 100° under vacuum were heated i n i n d i v i d u a l 25 m l . v o l u m e t r i c f l a s k s i n a c o n s t a n t temperature  o i l bath.  The f l a s k s were withdrawn a t v a r i o u s t i m e s , c o o l e d  and t h e c o n t e n t s d i s s o l v e d i n d i m e t h y l s u l f o x i d e i n which no m u t a r o t a t i o n t a k e s p l a c e at room temperature.  O p t i c a l r o t a t i o n s were measured on a  115  Bendix type 143A Automatic Polarimeter to *_ .001° and specific rotations calculated from the weight of glucose in the sample.  Rate constants were  obtained from the slopes of plots of log (a - e) against time in minutes by multiplying by 2.303/60.a is the specific rotation of the purest a-D-glucose and e is that of a sample after time t.  The function (o-e)  is proportional to the mole fraction ofS-glucose in the sample, which is given by (o - e / a - 8) i f a - and 6-glucose are the only optically active materials in the mixture. Isomerization of 5-Norbornene-2,3-carboxy1ic Anhydride Samples (ca. 0.1 g.) were sealed in 1 ml. vials and for the solid studies, melted in an o i l bath at 175°. Melting usually took about two minutes; in this time at this temperature practically no reaction can take place.  The samples were then cooled and finally thermostated at the  temperature of the run.  The f i r s t sample was withdrawn after sufficient  time had elapsed for a detectable amount of product (2-3%) to be formed. The samples were cooled to room temperature and stored until an opportunity to analyze them arose; this was often only after several days. The method of analysis was poor compared to those used in the other studies reported here, the error being as much as '+_'.2%. reasonably consistent results were obtained.  Nevertheless  For analysis the contents of  the vials were dissolved in chloroform-d and the p.m.r. spectra and integral taken on either a 60 or 100 m.c. spectrometer.  The fraction of product  was determined by comparing the integral of the peak at 3.6 x (arising from the olefinic protons of both isomers) to the integral of the peak at 7.Or (arising from the protons adjacent to the carbonyl groups of the exo-isomer) P.m.r. spectra were taken by Mrs. A. Brewster, Miss C. Burfitt and Mr. R. Burton.'  116  BIBLIOGRAPHY 1.  I . W.. S i z e r and E. S. 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