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Reactions in frozen solutions Kiovsky, Thomas Elstun 1966

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The U n i v e r s i t y of 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 of Colorado, 1962 M.Sc, U n i v e r s i t y of 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: I . McT. Cowan B.A. Dunell E. P i e r s R= Stewart '" G.B. Porter R.E. Pincock G.M. Tener E x t e r n a l Examiner: S. Y. Wang Department of Chemistry Johns H o p k i n s . U n i v e r s i t y Baltimore, Maryland Research Supervisor: R„ E. Pincock REACTIONS IN FROZEN SOLUTIONS Abstract In order to t r y to explain some of the rather suprising features of reactions i n frozen solutions, four d i f f e r e n t systems are extensively studied,, They are the reaction of methyl iodide with triethylamine to form the quaternary ammonium s a l t i n frozen ben-zene, the base catalyzed decomposition of t^-butyl-peroxy formate i n frozen p_-xylene to give J:-butyl alcohol and carbon dioxide, the reaction of ethylene chlorohydrin with hydroxide ion to form ethylene oxide i n frozen aqueous s o l u t i o n and the mutarota-t i o n of glucose i n ice„ In addi t i o n a demonstration experiment i s presented i n which iodide ion i s oxidized to iodine by arsenic acid i n frozen aqueous s o l u t i o n . Several new features of reactions i n frozen solutions are reported, including a maximum i n the rate-temperature dependence curve, rate enhancements as large as 1000-fold over reaction i n unfrozen solu-tions and s h i f t s i n the equ i l i b r i u m position,, K i n e t i c equations are developed which cor r e l a t e a l l of the r e s u l t s and which also explain some of the observations of other investigators<, These equations are based upon the assumptions that (1) when a solu-t i o n containing reactive species i s frozen a l l of the reactants as well as any other solutes present are rejected : by the c r y s t a l l i z i n g solvent and are concentrated into regions j which remain l i q u i d and that (2) the reaction proceeds nor-mally i n these regions, The fundamental equation used f o r c o r r e l a t i n g the rate data for the second-order reactions studied i s , x dmA = k A h B h V h dt where i s the t o t a l volume of the l i q u i d regions, m^ i s the t o t a l moles of reactant A present i n the system at any time and Aft and are the concentrations of the reactants A and B i n the l i q u i d regions. The ideas developed f o r the treatment of reactions i n frozen solutions are extended to reactions i n organic s o l i d s which have melted phase present. This treatment accounts q u a l i t a t i v e l y f o r the observations made on mutarotation i n s o l i d glucose. The a p p l i c a t i o n of the method to the isomer-i z a t i o n of 5-norbornene-2,3-endo-dicarboxylic anhydride to the ex6-i.somer allows separation of concurrent reactions i n the melt and i n the s o l i d . GRADUATE STUDIES F i e l d of Study: Organic Chemistry Seminar i n Chemistry Topics i n P h y s i c a l Chemistry Chemical K i n e t i c s Topics i n Inorganic Chemistry P h y s i c a l Organic Seminar P h y s i c a l Organic Chemistry Organic Reaction Mechanisms Organic Synthesis Jo Po Kutney Jo A, Ro Coope Ao V 0 Bree G„ Bo P o r t e r Do G„ L„ James Wo Ro C u l l e n R„ C„ Thompson No B a r t l e t t Ro E„ Pincock R„ Stewart Do E„ Greer Ro Stewart R. E . Pincock Eo P i e r s PUBLICATIONS Bimolecular Reactions i n Frozen Organic S o l u t i o n s , R 0 E. Pincock and T, E 0 Kiovsky, Jo Am. Chem. Soc.'87_, 2072 (1965) Base Catalyzed Decomposition of t>Butylperoxy Formate i n Frozen p_-Xylene, R„ E 9 Pincock and To E. Kiovsky, i b i d . , 8 7 , 4100 (1965) Reaction of Methyl Iodide w i t h Triethylamirie i n Frozen Benzene, R 0 E 0 Pincock and T 0 E 0 Kiovsky, i b i d . , 8 8 , 51 (1966) The Reaction of Ethylene Chlorohydrin w i t h Hydroxyl Ion i n I c e , R 0 E. Pincock, and To E. 'Kiovsky, i b i d . , 8 8 , 4455 (1966) Publications continued 5o The Mutarotation of Glucose i n Ice, T 0 E 0 Kiovsky and R 3 E» Pincock, ibid,,88^, 4704 (1966) 6o K i n e t i c s of Reactions i n Frozen Solutions, R 0 E, Pincock and T 0 E c Kiovsky J 0 Chem. Educo 43, 358 (1966) 7. Demonstration of a Reaction i n Frozen Aqueous Solution, To E 0 Kiovsky and R„ E„ Pincock, i b i d . , 4 3 , 361 (1966) 8. Thermal Mutarotation i n P o l y c r y s t a l l i n e . c<-D-Glucose, 'R0 E 0 Pincock, and T„ E. Kiovsky, Chem. Comm., 1966, 864 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 the Department of CHEMISTRY We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1966 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y shall, make i t f r e e l y avail able f o r reference and study, I f u r t h e r agree that permission-for extensive copying of 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 granted by the Head of my Department or'by h i s representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. The U n i v e r s i t y of B r i t i s h Columbia Vancouver Q, Canada Department of ABSTRACT Supervisor: Dr. R. E. Pincock In order t o t r y to e x p l a i n some of the r a t h e r s u r p r i s i n g features of rea c t i o n s i n frozen s o l u t i o n s , four d i f f e r e n t systems are e x t e n s i v e l y s t u d i e d . They are the r e a c t i o n of 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 quaternary ammonium s a l t i n frozen benzene, the base c a t a l y z e d decomposition of t^-butyl-peroxy formate to carbon d i o x i d e and t>butyl a l c o h o l i n frozen p_-xylene, the r e a c t i o n o f ethylene c h l o r o h y d r i n with hydroxide i o n to form ethylene oxide i n frozen aqueous s o l u t i o n and the mutarotation of glucose i n i c e . In a d d i t i o n , a demonstration experiment i s presented 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 ar s e n i c a c i d i n frozen aqueous s o l u t i o n . Several new features of r e a c t i o n s i n frozen s o l u t i o n s are reported; i n c l u d i n g a maximum in . t h e r a t e - temperature dependence curve, r a t e enhance-ments as large as 1000 - f o l d over r e a c t i o n i n unfrozen s o l u t i o n s and s h i f t s i i i the e q u i l i b r i u m position., K i n e t i c equations are developed which c o r r e l a t e a l l of the r e s u l t s and which a l s o e x p l a i n some of the observations o f other i n v e s t i g a t o r s . These equations are based upon the assumptions that (1) when a s o l u t i o n c o n t a i n i n g r e a c t i v e species i s frozen a l l of the reactants as w e l l as any other s o l u t e s present 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 olvent and are concentrated i n t o regions which remain l i q u i d and that ( 2 ) the r e a c t i o n proceeds normally i n these regions= The fundamental equation used f o r c o r r e l a t i n g the rate data f o r the second-order re a c t i o n s s t u d i e d i s , 1 X diriA Vi h dt where V n i s the t o t a l volume of the l i q u i d r e g i o n s , mA i s the t o t a l moles o f reactant A present 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 reactants A and B i n the l i q u i d regions. The ideas developed f o r the treatment of r e a c t i o n s i n frozen s o l u t i o n s are extended to r e a c t i o n s i n organic s o l i d s which have a melted phase present. This treatment accounts q u a l i t a t i v e l y f o r the observations made on muta-r o t a t i o n i n s o l i d glucose. The a p p l i c a t i o n o f the method to the i s o m e r i z a t i o n o f 5-norbornene-2,3-endo-dicarboxylic/anhydride to the exo-isomer allows separation of concurrent r e a c t i o n s i n the melt and i n the s o l i d . I V TABLE OF CONTENTS Page I. I n t r o d u c t i o n 1 I I . Reactions i n Frozen S o l u t i o n s 7 A., Reaction of Methyl Iodide with Triethylamine 7 i n Frozen Benzene B„ Base Catalyzed Decomposition of t^-Butylperoxy Formate 25 i n Frozen p_-Xylene C. Reaction of Ethylene Chlorohydrin w i t h Hydroxide Ion i n 47 frozen Aqueous S o l u t i o n D. Mutarotation of Glucose i n Ice 61 I I I . Reactions i n Organic S o l i d s 81 A. Mutarotation i n S o l i d Glucose 81 B. Isom e r i z a t i o n of 5-Norbornene-2„3-endo-dicarboxylic 89 Anhydride IV. General Remarks 98 A. Demonstration Reaction 98 B. Review of Published Results 99 C Conclusion 103 V. Experimental 105 V LIST OF TABLES Table T i t l e Page I Rate Constants f o r Reaction of Equimolar Triethylamine w i t h 10 Methyl Iodide i n Frozen Benzene S o l u t i o n s at -5.0°. II Rate Constants f o r Reaction of Equimolar Triethylamine with 12 Methyl Iodide i n Frozen Benzene S o l u t i o n s at Various Temperatures I I I Rate Constants f o r Reaction of Unequal Concentrations o f 13 Triethylamine with Methyl Iodide i n Frozen Benzene S o l u t i o n s at -5°. IV Rate Constants f o r Base Catalyzed Decomposition of TBF i n 29 Frozen £-Xylene at 0°. V Rate Constants f o r 2,6-Lutidine Catalyzed Decomposition of 31 TBF at Various Temperatures i n Frozen p__-Xylene. VI Rate Constants at 0° f o r 2,6-Lutidine Catalyzed Decomposition o f 38 TBF i n Frozen p_-Xylene Containing Added Compounds. VII Second-Order Rate Constants at Various I n i t i a l Concentrations 50 f o r Reaction of Ethylene Chlorohydrin w i t h Sodium Hydroxide i n Frozen Aqueous S o l u t i o n s at -5.0°. V I I I E f f e c t of Temperature on the Reaction of 0.05 M Ethylene 51 Chlorohydrin with 0.05M Sodium Hydroxide i n Frozen Aqueous S o l u t i o n s . IX E f f e c t of Added Solutes on the Reaction of 0.05M Ethylene 52 Chlorohydrin w i t h 0„05M Sodium Hydroxide i n Frozen Aqueous So l u t i o n s at -4.0°. X Rate Constants f o r Uncatalyzed Mutarotation of Glucose i n 62 Frozen Aqueous S o l u t i o n s at -4.0°. XI E f f e c t o f HC1 Concentration on F i r s t - O r d e r Rate Constants f o r 66 Mutarotation of Glucose at -4.0° i n Frozen Aqueous S o l u t i o n s . XII V a r i a t i o n o f F i r s t - O r d e r Mutarotation Rate Constant with 68 Glucose Concentration f o r Frozen 0.10M HC1 S o l u t i o n s at -4.0°. X I I I Temperature V a r i a t i o n of Rate Constants f o r Mutarotation o f 70 Glucose i n Frozen Aqueous S o l u t i o n s . XIV Rate Constants f o r Mutarotation of S o l i d Glucose at Various 85 Temperatures XV Rate Constants f o r Isomerization of Molten 5-Norbornene-2,3- 90 e n d o - d i c a r b o x y l i c Anhydride at Various Temperatures. v i LIST OF TABLES (cont'd) Table Table Page XVI Slopes o f P l o t s o f F r a c t i o n o f Product Present versus 91 Time f o r the Isomerization o f 5-Norbornene-2,3-endo-dicarboxylic Anhydride at Various Temperatures. v i i LIST OF FIGURES Figure T i t l e Page Figure 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 of equimolar 9 concentrations 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 frozen benzene s o l u t i o n s at -5°. 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 18 io 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 c o n t a i n i n g various concentrations o f £-xylene. Figure 3. Corrected f i r s t order p l o t s (according to eq. 2) f o r 19 r e a c t i o n at -5° of 0.2 M methyl i o d i d e 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 c o n t a i n i n g £-xylene. Figure 4. Dependence o f observed f i r s t - o r d e r r a t e constants 21 ^ o b s d = k 2 C h / 2 ^ o n t e m P e r a t u r e f ° r t n e r e a c t i o n of equi> molar concentrations of methyl i o d i d e with 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 2^h' observed C^. Figure 5. N.m.r. s i g n a l (and i n t e g r a l curves at various times) 23 a r i s i n g from l i q u i d benzene present at -5° i n a frozen 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 . Figure 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 27 of t^butylperoxy formate i n £-xylene at 0° (frozen) and at 70° (not frozen) u s i n g i d e n t i c a l samples. Figure 7. F i r s t - o r d e r p l o t f o r 2 , 6 - l u t i d i n e c a t a l y z e d 28 decomposition of t^-butylperoxy formate i n frozen p_-xylene at 0° i n samples i n i t i a l l y f rozen at -195" and 8°. Figure 8. R e l a t i o n of observed f i r s t - o r d e r r a t e constants to the 33 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 t^-butylperoxy formate i n frozen p-xylene at 0°. The values o f k , , . , , *- } obs, high base cone. used to c a l c u l a t e the curves were 120 x 1 0 - 5 s e c . " 1 f o r 2 , 6 - l u t i d i n e and 24.7 x 10" 5 s e c . - 1 f o r p y r i d i n e as c a t a l y s t . Figure 9. 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 35 decomposition of t^-butylperoxy formate i n frozen £-xylene at 11° and at -20° . o Figure 10. Temperature dependence of observed r a t e constants f o r 36 constant t>butylperoxy formate and 2 , 6 - l u t i d i n e concentrations (curved l i n e i s c a l c u l a t e d from kobsd. = k 2 C h ) -v i i i LIST OF FIGURES (cont'd) Figure T i t l e Page Figure 11. Changes i n observed r a t e constant, at constant 37 tj-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 , caused by a d d i t i o n o f various compounds. Figure 12. R e l a t i o n of 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 to 44 the concentration o f various s o l u t e s . Figure 13. E f f e c t of i m p u r i t i e s (ca.. 0.04 M) on the observed 46 r a t e constant f o r r e a c t i o n of t^butylperoxy formate with p y r i d i n e i n frozen p_-xylene at various concen-t r a t i o n s o f p y r i d i n e . Figure 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 of equimolar 49 ethylene c h l o r o h y d r i n w i t h sodium hydroxide i n frozen aqueous s o l u t i o n s at -5.0°. Concentrations i n unfrozen s o l u t i o n s . Figure 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 ethylene c h l o r o h y d r i n w i t h sodium hydroxide i n f r o z en aqueous s o l u t i o n s at -5.0° t o t o t a l i n i t i a l s o l u t e concentration (C ). The curve i s c a l c u l a t e d from obs k 2 c h /c s (1,07 % 10'1 +)(2,3)/C 56 Figure 16.. Temperature v a r i a t i o n of k Q ^ s C s f o r r e a c t i o n o f 0.05 M ethylene c h l o r o h y d r i n with 0.05 M sodium hydroxide i n frozen aqueous s o l u t i o n s . The s o l i d curve gives c a l c u l a t e d values of ^ C ^ , c i r c l e s are experimental values o f k , C . obs s 58 Figure 17. E f f e c t at -4.0° of added solu t e s on the r e a c t i o n of 0.05 M ethylene c h l o r o h y d r i n with 0.05 M sodium hydroxide i n frozen aqueous s o l u t i o n s . The curve i s c a l c u l a t e d 59 from k = k 2 C h / C s (1.26 x 10u t f) (1.9)/(0.15 + Im ) obs where Im Q i s the t o t a l concentration of added i m p u r i t i e s . Figure 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 of glucose i n frozen 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 at -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 constants c a l c u l a t e d by l o g [ (a - a )/(<*„. - a ) ] = k , t/2.303. obs 64 Figure 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 h y d r o c h l o r i c a c i d concentration f o r mutarotation of glucose i n frozen s o l u t i o n s at -4.0°. The s o l i d l i n e s f o l l o w the experimental p o i n t s ; the broken 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 according to eq. 9. 65 i x LIST OF FIGURES (cont'd) Figure T i t l e Page Figure 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 constants with 67 glucose concentration f o r mutarotation i n frozen 0.10 M HC1 s o l u t i o n s at -4.0°. The l i n e shows the 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. Figure 21. E f f e c t o f temperature on mutarotation of glucose i n 69 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 are experimentally determined; the broken l i n e s are c a l c u l a t e d from eq. 9. Figure 22. E f f e c t of added NaCl on mutarotation of glucose i n 72 frozen s o l u t i o n s at -6.3°. The reactant concentrations were 0.0512 M glucose, 0.040 M HC1. Figure 23. S p e c i f i c r o t a t i o n (0) of s o l i d glucose samples versus 83 time at various temperatures. Figure 24. P l o t s o f l o g (a-0) versus time at various temperatures 86. f o r the mutarotation of s o l i d glucose. Figure 25. Isomerization of s o l i d 5-horbomene-2,3-endo-dicarboxylic 92 anhydri de. Figure 26. Arrhenius 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 of 96 5-norbornene-2,3-endo-dicarboxylic anhydride. X ACKNOWLEDGEMENT I should l i k e to thank Dr. Richard E. Pincock f o r h i s i n t e r e s t , enthusiasm and -'counsel during the course o f t h i s research. I should a l s o l i k e t o thank my wif e f o r her patience and encourage-ment and the other members o f the p h y s i c a l organic group f o r t h e i r many h e l p f u l suggestions. I g r a t e f u l l y acknowledge the f i n a n c i a l a s s i s t a n c e o f the Research Committe of the U n i v e r s i t y , the Dr. McKenzie American Alumni A s s o c i a t i o n , the Graduate Student Fellowship Fund and the B r i t i s h Columbia Sugar R e f i n i n g Company. I . I n t r o d u c t i o n The f i r s t i n v e s t i g a t i o n s of r e a c t i o n s i n frozen s o l u t i o n s were reported over twenty years 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 1 2 of sugars, w i t h f a t t y a c i d s and food r e l a t e d products. ' More r e c e n t l y , 3-13 s i n c e 1961, a number of s t u d i e s have been reported which show some ra t h e r s u r p r i s i n g features of r e a c t i o n s c a r r i e d out i n frozen s o l u t i o n s . Among these are 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 to the method of f r e e z i n g , and changes i n k i n e t i c order. 3 In 1961 Grant, C l a r k and Alburn observed that t h e ^ - l a c t a m r i n g i n p e n i c i l l i n was cleaved by imidazole f a s t e r when an aqueous s o l u t i o n was held frozen at -18° than i n l i q u i d water at +38°i Other substrates * e.g. 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 being held f r o z e n i n the presence of imidazole.than when the s o l u t i o n was held unfrozen at higher 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 observations on 2'-deoxy-u r i d i n e . An aqueous s o l u t i o n of 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. absor p t i o n on i r r a d i t i o n and then upon standing i n the presence of a c i d regained i t . The l o s s of absorption i s a t t r i b u t e d to h y d r a t i o n and the subsequent regeneration to a c i d c a t a l y z e d dehydration as shown. The U.V. absor p t i o n was regained f a s t e r i n i c e at -20° than i n water at room temperature. 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 Bruice and B u t l e r ^ . In a study o f the spontaneous h y d r o l y s i s of a c e t i c anhydride i n i c e at -10° they found the r a t e constant to be only about one n i n t h that c a l c u l a t e d by e x t r a p o l a t i o n of data obtained above 0°, and that added potassium c h l o r i d e increased the r a t e . They a l s o found th a t the 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 at -10° than i n l i q u i d water at +5° and that added potassium c h l o r i d e decreased the r a t e i n i c e . Acetate 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 to the a c i d c a t a l y z e d r e a c t i o n . These authors found no spontaneous h y d r o l y s i s of 8-propiolactone i n i c e , but when potassium c h l o r i d e was added h y d r o l y s i s occurred. Potassium c h l o r i d e i s known to decrease the r a t e o f h y d r o l y s i s i n unfrozen s o l u t i o n s . The imidazole c a t a l y z e d h y d r o l y s i s of 8-propiolactone gave good f i r s t - o r d e r p l o t s , but p l o t s of observed r a t e constant versus c a t a l y s t c o n c e n t r a t i o n were curved, tending to l e v e l o f f at higher 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 the dehydration of 5-hydro-6-hydroxydeoxyuridine i n i c e , Bruice and B u t l e r were able to get good f i r s t - o r d e r p l o t s and found that the observed r a t e constants were not p r o p o r t i o n a l to the h y d r o c h l o r i c a c i d c o n c e n t r a t i o n . Added potassium c h l o r i d e g r e a t l y reduced t h e . r a t e . Bruice and B u t l e r ^ a l s o s t u d i e d the r e a c t i o n of morpholine with i - t h i o l v a l e r q l a c t p n e and tf-thiolbutyrolactone i n i c e . They were able to ob 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 the r a t e o f r e a c t i o n to be a f u n c t i o n of the concentration o f morpholine i n the b u f f e r before f r e e z i n g . The most s u r p r i s i n g r e s u l t of t h i s i n v e s t i g a t i o n was that the 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 the morpholine c o n c e n t r a t i o n , not to the 3 square of the morpholine concentration as i n unfrozen s o l u t i o n . Thus there was a change i n the order of the r e a c t i o n . In 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 isotope e f f e c t i n frozen than i n unfrozen s o l u t i o n , ^ / ^ d = 4.2 i n unfrozen s o l u t i o n at 30° and k^/k^ = 1.6 i n frozen s o l u t i o n at -10°. CT°r (^f morpholine » ( ^ O H ° r Q "^ 7 Weatherburn and Logan found that s o l u t i o n s o f f e r r i c y a n i d e and cyanide i on which were normally s t a b l e produced ferro c y a n i d e when froz e n . The lower the temperature at which the frozen s o l u t i o n s were he l d the f a s t e r the production o f ferrocy a n i d e i o n . 8 Home st u d i e d the e l e c t r o n exchange r e a c t i o n of F e ( I I ) and F e ( I I I ) using 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 frozen aqueous p e r c h l o r i c a c i d s o l u t i o n . He was able to get smooth k i n e t i c s at temperatures as low as -78°. 9-11 Grant and Alburn 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 higher r a t e s i n i c e than i n water. The decomposition of hydrogen peroxide c a t a l y z e d by f e r r i c or c u p r i c i o n was f a s t e r i n i c e at -18° than i n l i q u i d water at +1° . The hydroxylaminolysis of a m i d e s ^ and of 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 the r a t e s were higher i n i c e than i n l i q u i d water. .s \J I C G S R-Cr + H.NOH R " C X + N^o NH 2 2 X N 0 H . 4 RC - C ^ NH 2 OR' i c e + H2NOH OH RC - C^T NH 2 .^NOH R'OH 12 Wang found that when some p y r i m i d i n e s , e.g. 1,3-dimethyl-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 products were formed from when an unfrozen aqueous s o l u t i o n was i r r a d i a t e d . The product formed i n i c e , the photodimer (II), was the same as that formed when a dry s o l i d f i l m was i r r a d i a t e d . The product from i r r a d i a t i o n o f a l i q u i d aqueous s o l u t i o n i s the hydrated product ( I I I ) as shown. When d i m e t h y l u r a c i l (IV) was i r r a d i a t e d i n a frozen aqueous s o l u t i o n c o n t a i n i n g 2% methanol the same product, 6-methoxy-l,3-dimethylhydrouracil (V), was formed as when a methanolic s o l u t i o n was i r r a d i a t e d . i CH, CH, hi) l i q u i d water h i ) i c e or dry f i l m CH CH, 'OH I I I 0 CH„ 11 L-o .0 VCH, I I ht> CH30H OCH, IV V 5 Various explanations--have been proposed: to ;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 unfrozen s o l v e n t s . Among these are: (a) c o n c e n t r a t i o n of reactants i n l i q u i d regions when pure so l v e n t i s frozen out^, (b) c a t a l y t i c e f f e c t s of the frozen 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) formation of complexes of unknown s t r u c t u r e 6 , (e) i m p o s i t i o n of a favorable p o s i t i o n a l o r i e n t a t i o n ; between reactants upon f r e e z i n g and (f) the lower d i e l e c t r i c constant of i c e as compared to 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 r e a c t i o n s i n frozen s o l u t i o n s a f t e r observing that samples of t-butylperoxy formate (TBF) underwent base c a t a l y z e d decomposition much f a s t e r i n frozen p_-xylene than i n unfrozen samples. A f t e r c o l l e c t i n g considerable data 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 of TBF i n frozen p_-xylene and the r e a c t i o n of methyl i o d i d e w i t h t r i e t h y l a m i n e to form the quaternary ammonium s a l t i n f rozen benzene, we found that the data 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 decided then to attempt to 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 ((a) above). In order to do t h i s we used r a t e data which was a v a i l a b l e f o r the r e a c t i o n s i n o r d i n a r y s o l u t i o n s i n conjunction w i t h f r e e z i n g p o i n t depression diagrams of the s o l v e n t - s o l u t e systems. The approach was to 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 of reactants due to f r e e z i n g would be and how these p r e d i c t i o n s would f i t the experimental data. I f the e f f e c t s of concentration could be separated out, any e f f e c t s due to the other f a c t o r s mentioned above would become apparent and perhaps open to i n v e s t i g a t i o n . In S e c t i o n I I , A and B are presented our data on and d i s c u s s i o n of 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. 6 A l o g i c a l extension of the work i n frozen organic s o l v e n t s seemed to be a study of a w e l l known r e a c t i o n i n frozen 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 suggestions as to the involvement of i c e i n such r e a c t i o n s . The conversion of ethylene c h l o r o h y d r i n to ethylene oxide w i t h hydroxyl i o n seemed to f i t our requirements (see S e c t i o n I I , C ) . In view of the proposal that the greater proton m o b i l i t y i n i c e as compared to water might be a f a c t o r i n the r a t e enhancements observed i n f r o z en aqueous s o l u t i o n s we decided to study a general a c i d c a t a l y z e d r e a c t i o n i n i c e . 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 mutarotation of glucose was convenient f o r such a study. Again our approach was to attempt to separate out the e f f e c t s of concentration and then see what a d d i t i o n a l hypotheses might be necessary to e x p l a i n the r e s u l t s . This p a r t of the work i s reported i n S e c t i o n I I , D. Part I I I of the t h e s i s deals w i t h our a p p l i c a t i o n of the methods developed f o r the treatment of f r o z e n s o l u t i o n s to r e a c t i o n s i n organic s o l i d s i n which m e l t i n g occurs during the course of the r e a c t i o n . In such a system the r e a c t i o n can presumably proceed i n the s o l i d part of 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 of our treatment, developed i n Part I I , would allow the s e p a r a t i o n of the two r e a c t i o n mechanisms. Results and d i s c u s s i o n concerning the mutarotation of glucose 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 presented i n S e c t i o n I I I , A . S e c t i o n I I I , B deals w i t h the i s o m e r i z a t i o n of 5-norbornene-2,3-en d o - d i c a r b o x y l i c anhydride to i t s exo-isomer i n s o l i d samples. 7 REACTIONS IN FROZEN SOLUTIONS A. Methyl Iodide w i t h Triethylamine i n Frozen Benzene The r e a c t i o n of methyl i o d i d e with t r i e t h y l a m i n e t q form the 19 20 quaternary ammonium s a l t has been s t u d i e d f o r majny years ' and i s w e l l understood i n unfrozen organic solvents.' The k i n e t i c s are s t r i c t l y second-order and the a c t i v a t i o n parameters have been Mel + E t j N — > MeNEt* I" determined. Since t r i e t h y l a m i n e and methyl i o d i d e are cheap and rea d i l y , a v a i l a b l e the r a t h e r large q u a n t i t i e s r e q u i r e d f o r c o n s t r u c t i n g freezing, p o i n t depression ;curves present no problem. Thus the separation of e f f e c t s due to concentration of reactants 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 of the many aspects of re a c t i o n s i n fr o z e n s o l u t i o n s which are demonstrated. Results The r a t e of r e a c t i o n i n frozen benzene s o l u t i o n s was st u d i e d by measurement, a f t e r d e f r o s t i n g the samples of a run, o f the l o s s of methyl i o d i d e i n f r a r e d absorption at 1240 cm., } and by measurement of the t r i e t h y l a m i n e concentration 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 was a l s o obtained, u t i l i z i n g a s i n g l e ..frozen sample,, by n.m.r. spectroscopy. For runs using the former two methods, i n d i v i d u a l k i n e t i c samples i n small ampoules were made up by combining measured volumes of s o l u t i o n s of the reac t a n t s i n benzene. As the r e a c t i o n at room temperature i s r a t h e r f a s t , the ampoules were q u i c k l y sealed and frozen i n dry ice-^acetone. A f t e r 8 s i m i l a r p r e p a r a t i o n of a l l the samples, they were brought to the temperature of the run, withdrawn p e r i o d i c a l l y , d e f r o s t e d and analyzed. Freezing of samples i n d i f f e r e n t ways (e.g. i n l i q u i d nitrogen) had no e f f e c t on the observed r a t e . Methyl i o d i d e r e a c t s w i t h 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 according to simple second-order k i n e t i c s . However, with equal concentrations of reactants i n frozen benzene s o l u t i o n s p l o t s of r e c i p r o c a l c o n c e n t r a t i o n against time were always d i s t i n c t l y curved and i t became apparent that only p l o t s of log (concentration) against time 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 s o l u t i o n r e a c t i o n with equal concentrations of reactants i s then a f i r s t - o r d e r r e a c t i o n . Figure 1 shows runs f o r equal concentrations of methyl i o d i d e and t r i e t h y l a m i n e from 0.05 M to 0.63 M i n frozen benzene at -5°. The f i r s t -order r a t e constants (see Table I) over t h i s range of 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 only from 62 to 72 minutes. 20 From the a c t i v a t i o n parameters reported f o r second^order r e a c t i o n of methyl i o d i d e with 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 -4 -1 -1 at -5 i s c a l c u l a t e d to be 2.4 x 10 l i t e r mole sec. . For a 0.05 M i n i t i a l c o n centration of both reactants the h a l f - l i f e i s then 1400 minutes and the observed h a l f ^ l i f e of 65 minutes shows the moderate a c c e l e r a t i o n which occurs 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 e l a t i v e r a t e increase on f r e e z i n g would be greater. A d d i t i o n of p_-xylene to runs having equal reactant concentrations causes d e v i a t i o n s from the l i n e a r log (concentration) versus time r e l a t i o n s h i p . Figure 2 shows f i r s t - o r d e r p l o t s . f o r runs at -5° c o n t a i n i n g 9 0 30 60 90 120 150 180 Time, min Figure 1. First-order plots for reaction of equimolar concentrations of methyl iodide with triethylamine i n frozen benzene solutions at - 5 ° . 10 Table I Rate Constants f o r Reaction o f Equimolar Triethylamine with Methyl Iodide i n Frozen Benzene S o l u t i o n s at -5.0° Mel, concn.,, M E t 3 N ' concn., M Method a k 2 C h x 10 4, 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 t i t r a . 3.40 0 .050 .;. 0.050 I.R. 3.56 0.474 0.500 t i t r a . 3.55 0.636 0.616 n.m.r. 3.49 with added p_-xylene*3 0.217 0.212 0.0984 M C 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 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 r ' obsd 2 h ^ Rate constants c a l c u l a t e d by use of eq 3. c Concentration of 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 of a n a l y s i s used. 11 various concentrations of p_-xylene. With gr e a t e r concentrations of t h i s s o l u b l e " i m p u r i t y " the r a t e of loss 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 decreased, and the d e v i a t i o n from the f i r s t - o r d e r k i n e t i c s found i n the absence of p_-xylene becomes, more evident. At the highest concentration of p_-xylene used, 0.405 M, a p l o t of the data according to second-order k i n e t i c s ( 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 against, time) gave a s l i g h t l y S-shaped curve, but w i t h a great deal more s i m i l a r i t y to 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 w i t h equimolar reactant concentrations at v a r i o u s temperatures (see Table I I ) and f o r unequal concentrations at -5° (Table I I I ) are described 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 that the r e a c t i o n i n frozen s o l u t i o n s shows a maximum r a t e at ca. -5° and a l s o occurs at conveniently measurable ra t e s at +3 and at -20°. For runs at -5° with unequal concentrations of r e a c t a n t s , treatment of the data according to an equation developed, i n the Di s c u s s i o n s e c t i o n gave r a t e constants c o n s i s t e n t w i t h those found f o r runs at equal concentrations. 12 Table I I Rate Constants f o r Reaction of Equimolar Triethylamine w i t h Methyl Iodide i n Frozen Benzene S o l u t i o n s at Various Temperatures. concn., M EtgN, concn., M Temperature V h x 0.182 0.197 2.5° 1.97 b 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 b 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 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 0 b s c i = k^C^ I^ T i t r a t i o n method of a n a l y s i s used, a l l others by i n f r a r e d a n a l y s i s . 13 Table I I I Rate Constants f o r Reaction of Unequal Concentrations o f Triethylamine wit h Methyl Iodide in.Frozen Benzene S o l u t i o n s at -5.0°. a b 4 -1 Mel, concn., M ^ t 3 N ' concn.,M %MeI ^2^h X ^ ' s e c ' 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 Percentage of solute at the start of the reaction which is methyl iodide. b R a t e constants calculated by use of eq 4. 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 liquid regions present among the crystalline solvent. In these liquid regions, the reaction between two solutes will be accelerated by the concentration For a simple bimoleeular reaction, A + B •* products, the reaction i n a fr 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 rate equal to k^B^. This rate is i n terms § 1 m§ie§ pet §e§©nd ger liter Qf r e a e t i e n velume. _ 1 dpneles A) o k . = m 2 l " Vj: I t " k r V h { l ) The notation used is as follows; A^ , B^  and A§, Bg are the eoneentrations of the reaetants i n the liquid regions of a froaen solution and i n the thawed solution, respectively. Vh is the t o t a l volume of the liquid regions in the frozen solution and Vg is the Volume of the thawed solution; c^ is the total constant concentration of solutes i n the liquid regions, is the normal second-order rate Constant for bimoleeular reaction. Img is the solution concentration of any inert solutes To obtain the observed rate (in terms of moles per second per  liter o f thawed solution) i t is necessary to divide eq 1 by V which decreases the rate in the reaction volume of frozen samples to that measured in thawed samples. The observed rate of reaction is then given 15 by eq 2. The r e a c t i o n volume,V, may increase or decrease during a (2) V kinetic- run as the number of moles which must be accommodated i n the l i q u i d regions of the frozen s o l u t i o n at constant concentration increase or decrease. 3. I t i s the high concentration of the l i q u i d regions of a frozen s o l u t i o n which give r i s e to the observed r a t e a c c e l e r a t i o n s and the r e q u i r e -ment of constant t o t a l c o ncentration which leads to.the r a t h e r unusual changes i n k i n e t i c order and s e n s i t i v i t y to s o l u b l e i m p u r i t i e s . In order to keep a constant c o n c e n t r a t i o n , the w a l l s of the l i q u i d regions may thaw or freeze to accommodate more or l e s s s o l u t e . In the case of the r e a c t i o n of t r i e t h y l a m i n e w i t h methyl i o d i d e , the formation of an i n s o l u b l e product* 5 r e s u l t s i n a decrease of the r e a c t i o n volume during a run. 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 the w a l l s of the r e a c t i o n regions c l o s e i n to hold the concentration of the remaining s o l u t e at a constant value. 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 b i m o l e c u l a r r e a c t i o n i s a consequence of t h i s volume change; the concentrations A^ and are constant and according to eq 1 the rat e i s then p r o p o r t i o n a l to the t o t a l c o n c e n t r a t i o n i n a defr o s t e d s o l u t i o n ( i . e . , = (A g + B s) ^/C^)> 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 to the sum of reactant concentrations ( l e a d i n g to f i r s t - o r d e r k i n e t i c s f o r equal reactant concentrations) r a t h e r than the product of t h e i r concentrations ( 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 - composition data f o r methyl i o d i d e or t r i e t h y l a m i n e i n benzene the concentration of the l i q u i d regions at -5° i s 1.6 M. b No f r e e z i n g p o i n t depression was observed f o r benzene saturat e d w i t h methyltriethylammonium i o d i d e . 16 To o b t a i n the i n t e g r a t e d r a t e expression f o r r e a c t i o n at equal reactant c o n c e n t r a t i o n s , with the added complication of the presence of a s o l u b l e " i m p u r i t y " (Im), the assumption i s made that a l l s o l u t e s present i n an unfrozen s o l u t i o n are present i n the l i q u i d regions of the frozen s o l u t i o n , i . e . A V = A, V, , B V = B, V, and (A + B + Im ) s s h h' s s h h v s s s' V g = 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 then gives eq 3 Im 2 In (A ) - A—2- = -k 2 C h t + constant (3) ' : ' • [ • " . s This equation i s a combination o f ; t h e form of the k i n e t i c equations f o r f i r s t - o r d e r r e a c t i o n (In A g) and f o r second-order r e a c t i o n at equal reactant concentrations (1 /.A ). When no i n e r t s o l u t e s are present, Im g = 0, and a p l o t of log A s against time should be a s t r a i g h t l i n e w i t h slope k^ / 2 x 2.3. Figure 1 shows that t h i s . r e l a t i o n s h i p i s experimentally obtained, and that;, as r e q u i r e d by eq 3. the slopes of the p l o t s f o r runs with d i f f e r e n t i n i t i a l s o l u t i o n concentrations are very n e a r l y the same (see a l s o Table I ) . In t h i s r e a c t i o n the observed f i r s t - o r d e r . r a t e constant k o b s d ~ k 2 ^h ^ 2 ' ^ n < ^ e P e n ^ e n t °^ t n e r e a c t i o n volume during a run and th e r e f o r e independent of the i n i t i a l s o l u t i o n concentration 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 frozen 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 present, the "second-order p o r t i o n " of eq 3 comes i n t o p l a y . P l o t s of the data according to simple f i r s t - o r d e r k i n e t i c s (see Figure 2) show the d e v i a t i o n caused by the neglect o f t h i s "second-order" term, which becomes more important at high " i m p u r i t y " concentration or when the r e a c t i o n i s more complete. The r e a c t i o n slows down because the r e a c t i o n volumes no longer continue to decrease i n p r o p o r t i o n to the reactant concentrations. At low reactant 17 concentrations the r e a c t i o n regions are h e l d open by the " i n e r t " s o l u t e , the reactants then become continuously 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 transform i n t o the o r d i n a r y second-order k i n e t i c s which would be observed at constant volume. The f a c t , as i n d i c a t e d i n the Results s e c t i o n , that a p l o t of r e c i p r o c a l A g against time f o r a run with high p_-xylene con c e n t r a t i o n i s a good approximation to a s t r a i g h t l i n e i s an outcome of t h i s e f f e c t . Treatment of the data f o r runs c o n t a i n i n g p_-xylene according to the complete form of eq 3 i s shown i n Figure 3. This equation c o r r e c t s , during a run, f o r the continuous decrease i n r a t e of c o n t r a c t i o n of the t o t a l r e a c t i o n volume. The slopes of these c o r r e c t e d p l o t s should be equal to k^ C^/2.3. Table I contains the data f o r runs at equal c o n c e n t r a t i o n , with and without added p_-xylene. The values o f . k 2 obtained i n both 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 success of eq 3. Frozen 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 widely d i f f e r i n g concentrations of reactants would be expected to give data some-what analogous to that from runs with equal reactant c o n c e n t r a t i o n but w i t h an i n e r t s o l u t e present. In other words, the excess of one reactant ( a c t i n g l i k e an i n e r t impurity) would tend to keep the r e a c t i o n volume from decreasing at a constant r a t e as the r e a c t i o n proceeds. A c c o r d i n g l y , when data from runs at d i f f e r e n t i n i t i a l reactant concentrations were t r e a t e d by the normal equation f o r second-order r e a c t i o n s , the p l o t s of log (A s/B s) against time were good s t r a i g h t l i n e s . However, i n t e g r a t i o n of eq 2 f o r the case of unequal reactant concentrations and no i n e r t s o l u t e gives r i s e to eq 4, which i s more d i r e c t l y a p p l i c a b l e to t h i s type of b i m o l e c u l a r r e a c t i o n i n frozen s o l u t i o n s . P l o t s of log (A B ) against 18 0 60 120 180 240 300 360 Time, min. Figure 2. First-order plots f o r reaction at -5° of 0.2 M methyl iodide with 0.2 M triethylamine i n frozen benzene solutions containing various concentrations of p_-xylene * 19 Figure 3. Corrected f i r s t - o r d e r p l o t s (according to eq 2) f o r reaction at -5° of 0.2 M methyl iodide with 0.2 M triethylamine i n frozen benzene solutions containing £-xylene. 20 time f o r runs at unequal con 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 . The values In (A B g) = - k 2 C h t + constant (4) of ^2^\i obtained from the slopes of these l i n e s are given i n Table I I . c I t may be seen that these values are co n s i s t e n t with the same q u a n t i t y obtained from eq 3 f o r runs at equal co n c e n t r a t i o n s , w i t h or without " i m p u r i t y " . The temperature dependence of the observed r a t e constants at equal reactant c o n c e n t r a t i o n , k o b s c [ = k 2 C h ^ 2 ' a r i s e s f r o m a decrease i n k 2 and an increase i n C^ . as the temperature i s lowered. The change i n 20 k 2 may be c a l c u l a t e d from the a v a i l a b l e a c t i v a t i o n parameters, while i s obtained from the experimental r e l a t i o n of conc e n t r a t i o n of s o l u t e to f r e e z i n g point of benzene s o l u t i o n s . d Figure 4 shows the experimentally observed values o f ( s o l i d l i n e ) f o r runs from 2.5 to -20° compared to c a l c u l a t e d values (broken l i n e ) . At.-.5° the t h e o r e t i c a l value of k 2C^ d i f f e r s from the experimental value by about 13%. F i n a l l y , the v a r i a t i o n of the volume of r e a c t i o n regions during a k i n e t i c run suggested that the r a t e of r e a c t i o n of t r i e t h y l a m i n e w i t h 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 frozen sample by a method based on n.m.r. The 60 mc. p.m.r. spectrum at -5° of a s o l u t i o n c The s l i g h t increase i n observed r a t e constant f o r runs with r e l a t i v e l y high concentration of methyl i o d i d e (see Table I I I ) may be due to a solvent e f f e c t . The r e a c t i o n regions at -5° contain 1.6 M (ca. 12 mole percent) s o l u t e ; i f t h i s i s predominantly methyl i o d i d e ( d i e l e c t r i c constant 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 increase i n r a t e might occur . The great s e n s i t i v i t y of a l k y l h a l i d e -amine r e a c t i o n s to solvent v a r i a t i o n i s w e l l established.22 d The same molar concentration of methyl i o d i d e or t r i e t h y l a m i n e i n benzene depresses the f r e e z i n g point to the same extent down to ca. -10° (2.4 M), but divergence of the f r e e z i n g p o i n t - concentration 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 occurs below -10°. 21 Q.2 M a y 5 0 -5 -10 -15 -20 Temperature, °C Figure 4. Dependency of observed first-order rate constants ^vobsd = 2^ S/^ o n temperature ^ o r t n e reaction of equimolar concentrations of methyl iodide with triethylamine in frozen benzene solutions. - - - - - - calculated ^n> ^ — o b s e r v e d k „ C, . 22 of 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 i n benzene (the sample i n i t i a l l y f r o z e n at -70°) showed a broad peak near the region of absorption of l i q u i d benzene ( 2 . 6 3 ) . This peak, which i s due to the benzene present i n the l i q u i d r e a c t i o n regions of 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 . Figure 5 shows the form of the i n i t i a l spectrum and of the i n t e g r a l curves taken at various times. These i n t e g r a l values are p r o p o r t i o n a l to the number of moles of l i q u i d benzene i n that small p o r t i o n of the frozen sample which gives r i s e to the s i g n a l . As the. l i q u i d r e a c t i o n regions are f i l l e d predominantly w i t h benzene the i n t e g r a l values are a l s o approximately p r o p o r t i o n a l to the volume, V^, of the l i q u i d regions of the frozen sample. The r e l a t i o n s h i p of the changes i n : i n t e g r a l v a lue, r e a c t i o n volume of frozen s o l u t i o n s i and c o n c e n t r a t i o n of 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 that 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 ) , that the concentrations i n the r e a c t i o n regions are constant, and that the i n t e g r a l value i s p r o p o r t i o n a l to the volume of the l i q u i d regions of a frozen s o l u t i o n . The r e s u l t i s that the change i n one i s r e l a t e d to the change i n another by d In ( i n t e g r a l v a l u e ) / d t = d In / dt = 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 mm.) against time i s a s t r a i g h t l i n e and the r a t e constant, k ^ ^ = / 2, -4 -1 obtained from the slope of t h i s l i n e gave as 3.5 x 10 sec. - 4 - 1 This i s the same as the average value 3.4 x 10 sec. obtained by a n a l y s i s of d e f r o s t e d samples using i n f r a r e d and t i t r a t i o n techniques (see Table I ) . The r a t e of r e a c t i o n (obtained from the reactant concentrations i n d e f r o s t e d samples of a run) and the r a t e of change of the r e a c t i o n volume (obtained by measurement of the l o s s of 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 frozen benzene s o l u t i o n s are thus shown to 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 in i t ia l ly containing 0.64 M methyl iodide and 0.62 M triethylamine. 24 experimentally r e l a t e d . Both the change of c o n c e n t r a t i o n , d A g/dt = k b s { j A g, and the change of r e a c t i o n volume, d V^/dt = k b S ( j V^, are f i r s t - o r d e r processes. The observed r a t e constants under the c o n d i t i o n of equal reactant concentrations are experimentally 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 c o n t r a c t i o n of the r e a c t i o n volume. A disadvantage of 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 to use s o l u t i o n s with high i n i t i a l c o n c entrations. The t o t a l c o ncentration of 1.26 M a l l o w s , at the s t a r t of the r e a c t i o n , only about 20% of the solvent to be c r y s t a l l i z e d , w h i l e 0.1 M runs analyzed by i n f r a r e d techniques were 94% s o l i d at the s t a r t of the run. 25 B. Base Catalyzed Decomposition of t-Butylperoxy Formate i n Frozen p_-Xylene. In 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 decomposition of t_-butylperoxy formate (TBF) i s a simple b i m o l e c u l a r 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 d i p o l a r t r a n s i t i o n s t a t e i s formed and the f i n a l products are carbon d i o x i d e and t - b u t y l a l c o h o l . 0 0 II + II _ H-C-0-0-C(CH 3) 3'+ B: — : >- BH C 0-C(CH 3) 3 >-0 B: + C0 2 + HO-C(CH 3) 3 I t was during an i n v e s t i g a t i o n of t h i s r e a c t i o n i n l i q u i d £-xylene that we found that samples which had been stored i n the r e f r i g e r a t o r to await a n a l y s i s decomposed i f they happened to f r e e z e . The i n v e s t i g a t i o n reported here was i n i t i a t e d to t r y to f i n d an e x planation f o r t h i s o b servation. Results The same products as are formed i n the l i q u i d , are formed by r e a c t i o n i n frozen s o l u t i o n s . A s o l u t i o n of 0.347 M TBF and 0.0758 M p y r i d i n e i n p_-xylene, frozen 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 hours, 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 , while 4% of the TBF was undecomposed. The same s o l u t i o n h e l d unfrozen at ca. 15° (the m.p. of pure p_-xylene i s 13.26°) f o r 24 hours was 50% decomposed, c l o s e to the expected value 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 at higher temperatures. At lower concentrations of r e a c t a n t s , formation of t - b u t y l a l c o h o l and carbon d i o x i d e i n frozen s o l u t i o n s was a l s o 26 indicated by infrared analysis of k i n e t i c run samples. For k i n e t i c studies the reaction i n d i l u t e frozen solutions was s u f f i c i e n t l y accelerated i n the frozen state to allow quenching simply by defrosting the samples of a run. Measurement of peroxide concentration 23a was then carried out at room temperature. Figure 6 shows f i r s t - o r d e r plots for 2,6-lutidine 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 ' 2 3 state k i n e t i c runs were always, as with l i q u i d solutions 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 of base or TBF. Runs were followed for two to four h a l f ^ l i v e s with no deviation of the plots from the log (relative peroxide concentration) vs. time relationship. The reaction i n individual samples of a run and the observed rate constants were not affected by the volume of sample, by surface or volume of added insolubl-e material, nor by the manner i n which the samples were frozen. Figure 7 shows the results for two widely different freezing 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. Different macroscopic d i s t r i b u t i o n s of the c r y s t a l l i n e samples were readily apparent from the different r e l a t i v e transparency of 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° for the k i n e t i c run. For th i s / frozen state reaction, as i n ordinary solution k i n e t i c s , the relevant variables are the concentrations of reactants, the temperature of the run' and the purity of the solvent. These were considered i n turn as follows. Effect of Concentration. The results of variations i n the i n i t i a l concentration of base and of TBF for k i n e t i c runs i n frozen p_-xylene solutions 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 1.8 1.6 a- 1.4 cn o 1.2 1.0 No 0 0 2 9 3 molor T B F 0.0112 molor 2 ,6 - lu t id ine p-xylene ot 0.0° 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- lu^ of £-butylperoxy formate in frozen jv-xylene' at 0° in/^ s amp i e s in i t ia l ly frozen at -195° and at 8°. 29 of the s o l u t i o n s was u s u a l l y from 0.025 to 0.03 M, while the base -4 concentration was v a r i e d from 3,8 x 10 to 0.3 M. Table IV Observed Rate Constants f o r Base Catalyzed Decomposition of TBF i n Frozen p_-Xylene at 0° Cone. TBF, Cone, b^ase, k ^ x 1 q 5 ' s e c * M i n 2 M X 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 14.1 74.6 27.4 0.579 3.61 (continued) 30 (Table IV, continued) 29.2 1.49 0.09 P y r i d i n e Catalyzed 2.97 0.314 2.31 2.75 1.04 7.36 2.95 2.08 11.0 3.26 3.13 , 13.6 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 14.2 6.56 a Samples of run frozen at -195°. b Frozen at 8°. _ 4 Even with a very low concentration of 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 the s o l u t i o n i s f r o z e n , but 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 to completely decompose the TBF at some s i x t y f o l d g r e a t e r s o l u t i o n c o n c e n t r a t i o n . Comparisons of rat e s i n unfrozen s o l u t i o n s at the lowest concentration of base c a t a l y s t to rat e s when the s o l u t i o n i s frozen shows that the base i s r e l a t i v e l y most e f f i c i e n t at low concentrations. -4 Thus the k Q b s f o r 3.8 x 10 M l u t i d i n e i s four hundred times greater than the c a l c u l a t e d r a t e constant f o r r e a c t i o n at 0° i n a s o l u t i o n of t h i s c o n c e n t r a t i o n , at 0.14 M l u t i d i n e the observed r a t e constant i n frozen samples i s only t h i r t y times gr e a t e r than the r a t e constant f o r r e a c t i o n i n s o l u t i o n . 31 The k i n e t i c data of Table IV may be summarized by s t a t i n g that at constant peroxide c o n c e n t r a t i o n and at low l u t i d i n e concentrations the observed r a t e constants are n e a r l y p r o p o r t i o n a l to the l u t i d i n e c o n c e n t r a t i o n ; at high l u t i d i n e concentrations the observed r a t e constants become Independent of l u t i d i n e c oncentration (see Figure 8). That i s , the observed k i n e t i c order changes from f i r s t - o r d e r to zero-order i n l u t i d i n e as the l u t i d i n e c oncentration i s increased. A s i m i l a r r e s u l t i s found with p y r i d i n e as c a t a l y s t . 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 constant, and the peroxide concentration increased,, the observed r a t e constants decrease. This occurs even though the i n d i v i d u a l runs were always f i r s t - o r d e r i n TBF throughout s e v e r a l h a l f - l i v e s . These odd k i n e t i c e f f e c t s are discussed below. E f f e c t of Temperature. The r a t e of r e a c t i o n of 2 , 6 - l u t i d i n e w i t h TBF i n frozen p_-xylene shows the expected temperature dependence. Table V presents the data f o r runs i n the frozen s t a t e from 12 to -30° at constant 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° i n l i q u i d p_-xylene. Table V Observed Rate Constants f o r 2,6-Lutidine Catalyzed Decomposition of TBF at Various Temperatures i n Frozen p_-Xylene obs Cone. TBF Concn. 2,6-Lutidine Temp.,°C k M x 10 2 M x 10 2 x 10 5, s e c . " 1 3.11 1.19 12.0 2.9 a 3.08 1.16 11.0 8.56 (continued) 32 (Table V, continued) Cone. TBF Cone,. 2,6-Lutidine Temp M x 10 2 M x 10 2 3.08 1.19 10.0 3.09 1.25 8.0 3.08 1.19 6.0 3.08 1.19 4.0 3.08 1.19 2.0 3.08 1.19 0.0 3.11 1.19 0.0 3.12 0.87 0.0 3.05 1.16 -30.0 3.12 0.87 -10.0 3.14 1.74 -10.0 3.14 3.37 -10.0 Unfrozen S o l u t i o n s 3.08 1.16 50.0 3.11 1.19 70.0 3.10 1.04 90.0 2.72 0.21 90.0 3.09 2.08 90.0 obs j x 10 5, sec." 13.8 23. l b 33.5 39.2 52.4 47.6 50.2 C 39.6 d 7.61€ 29.6 d 47.2 66.0 8.76 28.2 C 74.5 14.6 137. a Reaction not followed to completion, i n i t i a l r a t e constant, b, c, d, e Denotes p a i r e d runs using same s o l u t i o n s at d i f f e r e n t temperatures. The observed r a t e constant i n frozen s o l u t i o n s increases by a f a c t o r of eighteen on decreasing the temperature from 12 to 2°. However, 33 Concentration of Base Catalyst .mo la r Figure 8. Relation of observed f i r s t - o r d e r rate constants to the base concentration for 2,6-lutidine and pyridine catalyzed decomposition of tj-butylperoxy formate i n frozen p_-xylene at 0°. The values of kobs, high base cone. u s e d t o c a l c u l a t e ^ ™™s were 120 x 10" 5 -1 - 5 - 1 sec. for 2 , 6 - l u t i d i n e and 24.7 x 10 sec. fo r pyridine as catalyst. 34 at ca. 2° a f u r t h e r decrease i n temperature begins to lower the r a t e . At -30° the r e a c t i o n s t i l l occurs at an e a s i l y measurable r a t e , but at -70° no loss of peroxide occurs over long p e r i o d s . Figure 9 shows that 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 that the r e a c t i o n i s f a s t e r at -20 than at 11°. Figure 10 shows the dependence on temperature i n both l i q u i d and frozen p_-xylene. From runs i n l i q u i d at 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 of TBF + + with 2 , 6 - l u t i d i n e are AH =12.3 k c a l . , AS = -30.5 e.u., c l o s e to the 2 3b reported values i n the s i m i l a r solvent benzene. E f f e c t s of I m p u r i t i e s . The k i n e t i c r e s u l t s of a d d i t i o n of various compounds to the t h r i c e - r e c r y s t a l l i z e d p_-xylene used as solvent are given i n Table VI. The ra t e i s depressed by such n e u t r a l compounds as benzene, 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 concentrations of peroxide and of l u t i d i n e , the r a t e i s extremely s e n s i t i v e to the presence of these i m p u r i t i e s (see Figure 11). At the -2 c o n c e n t r a t i o n of reactants given i n Table VI, 1.5 x 10 M benzene (one molecule per f i v e hundred of solvent) decreases the r a t e by one h a l f . A dampening of t h i s e f f e c t i s shown i n that 5.7 x 10 M benzene i s r e q u i r e d to b r i n g about another decrease by one h a l f . I t i s s i g n i f i c a n t t h a t , with the exceptions of t - b u t y l a l c o h o l and anthracene, 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 depressing 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 high concentrations caused a small decrease i n k , . The observed k i n e t i c e f f e c t s of these obs compounds c o n s t i t u t e d a t e s t which showed that the r e a c t i o n i n the frozen TBF-lutidine-p_-xylene system does proceed i n unfrozen regions of high reactant c o n c e n t r a t i o n . 35 Time .minutes Figure 9. First-order plots f o r 2,6-lutidine catalyzed decomposition of t-butylperoxy formate i n frozen p_-xylene at 11° and at -20°. 36 O 031 molar T B F a012 molor 2,6-lutidme p-xylene 2.8 3.2 3.6 4.0 1/T x l 0 3 , ( i n °K) Figure 10 . Temperature dependence of observed r a t e constants f o r constant t^-butylperoxy formate and 2,6-lutidine concentrations (Curved l i n e i s calculated from k ^ s = IK.2 C^). i 0 0301 molor TBF 50 K ° n , h r 0 C o e n e 0.0119 molor 2,6-lutidine °0 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 Table VI Observed Rate Constants at 0° f o r 2,6-Lutidine Catalyzed Decomposition of TBF a i n Frozen p_-Xylene Containing Added Compounds Substance Cone, k , x 10 5, s e c . " 1 obs M x i o 2 none . - 48. l b benzene 0.898 32.5 .• 1,49 : 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 2,6-di-t>butyl-p_-cresol 1.99 17.0 t - b u t y l a l c o h o l 3.32 33.2 heptane 3.68. 10.2 c a r b o n t e t r a c h l o r i d e 4.31 11.5*5 " 4.73 1 1 . l b none - 46.3 a Concentration of TBF 0.030 M, of 2 , 6 - l u t i d i n e 0.012 M. b D i f f e r e n t batches of solvent . 39 D i s c u s s i o n As i n S e c t i o n A above, a general explanation f o r the observed r e a c t i o n s i n frozen s o l u t i o n s i n v o l v e s the existence of l i q u i d 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 r e a c t a n t s . Any r e a c t i o n higher 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 solvent and i n s o l u b l e i n the c r y s t a l l i n e solvent below the temperature of f r e e z i n g , should experience an a c c e l e r a t i o n when the system i s f r o z e n . Basic to any treatment of such r e a c t i o n s i s the requirement that the l i q u i d " h o l e s " i n a frozen s o l u t i o n must a l l c o n t a i n the same constant t o t a l c o ncentration of s o l u t e s . Although the average volume of the holes might reasonably be expected to depend on the method of f r e e z i n g , w i t h a g r e a t e r number of smaller holes formed on f a s t f r e e z i n g , a constant s o l u t e concentration i s r e q u i r e d i n the unfrozen regions 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 s o l i d . The 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 may 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 frozen p_-xylene, i n terms of two f a c t o r s ; v a r i a b l e volumes of l i q u i d regions c o n t a i n i n g constant 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 reactant concentrations i n these regions. Experimentally obtained r a t e s , however, are measured i n terms of moles per l i t e r of 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 of the volume or the concentration of the l i q u i d regions i n frozen s o l u t i o n s . The observed ra t e constants may be r e l a t e d to the known s o l u t i o n concentrations as f o l l o w s : 40 Rate i n l i q u i d regions = P^ B^ 5 Vu 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 ) = = - k _ P, B, r r 1 1 6 , „. 2 h h V d t s where P r e f e r s to the peroxide c o n c e n t r a t i o n , B to the base concentration and the s u b s c r i p t s h and s to the l i q u i d regions and thawed s o l u t i o n 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 present i n the l i q u i d regions of a frozen s o l u t i o n then P, V, = P V B. V, = B V C, V, = (P + B + 1 + Prod ) V h h s s h h o s h h s o o s s In terms of the amount reacted, i f the equivalent of one mole of product i s derived from one mole of peroxide (see d i s c u s s i o n below) then P g = (P q - x) and x = Prod s- S u b s t i t u t i o n and i n t e g r a t i o n gives P 2 h B + P + Im o o o o The observed r a t e constant i n terms of i n i t i a l s o l u t i o n concentrations i s then k , = k. C, Bo (5) obs 2 h = B + P + Im o o o In the decomposition of TBF i n frozen 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 of base, peroxide or ''impurity" c o n c e n t r a t i o n s , or by v a r i a t i o n i n temperature, a l l r e s u l t i n changes i n the observed r a t e constants according to eq 5. Concentration of Reactants. Figure 8 shows the observed p s e u d o - f i r s t - o r d e r r a t e constants at 0° 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 TBF at near constant TBF concentration as a 41 f u n c t i o n of base co n c e n t r a t i o n . The r e l a t i o n s h i p p r e d i c t e d from B equation 1 i n the form k , = k , , v i s given by the n obs obs, high base g + P o o curved l i n e s . The change i n observed k i n e t i c order from f i r s t - o r d e r i n base at low base concentrations to zero-order i n base at high base concentrations a r i s e s from the changing r a t i o of base 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 . At low base concentrations the l i q u i d regions i n which the frozen s o l u t i o n r e a c t i o n proceeds are f i l l e d predominantly w i t h TBF, and an increase i n base concentration does not appr e c i a b l y increase the r e a c t i o n volume. But as the absolute c o n c e n t r a t i o n of base i n the l i q u i d regions i s increased the r a t e of the r e a c t i o n i s a l s o p r o p o r t i o n a t e l y increased and the r e a c t i o n appears to be f i r s t - o r d e r i n base as w e l l as i n TBF. On the other hand, at high base concentrations the l i q u i d regions are f i l l e d predominantly w i t h the base, a f u r t h e r increase i n base conc e n t r a t i o n of 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 the frozen s o l u t i o n s . The base con c e n t r a t i o n i n the r e a c t i o n regions remains constant, the f i r s t - o r d e r r a t e constant remains the same and the r e a c t i o n appears to be zero-order i n base co n c e n t r a t i o n . I f runs at constant base c o n c e n t r a t i o n but d i f f e r e n t peroxide concentrations are compared the rate constants observed (see Table IV) decrease with i n c r e a s i n g peroxide c o n c e n t r a t i o n . The presence of grea t e r peroxide c o n c e n t r a t i o n i n an unfrozen s o l u t i o n r e s u l t s i n a greater volume of l i q u i d regions i n a frozen s o l u t i o n . This l a r g e r volume d i l u t e s the a v a i l a b l e base down to a lower c o n c e n t r a t i o n and the observed r a t e constant i s correspondingly decreased. e. The grea t e r c a t a l y t i c e f f e c t of l u t i d i n e i s expected from i t s greater b a s i c i t y . See reference 23b. 42 Temperature Dependence. The second-order r a t e constant f o r bimoleeular r e a c t i o n i n s o l u t i o n decreases w i t h a decrease i n + + temperature (AH = 12.3 k c a l , AS = -30.5 e.u.) but the concentrations of the l i q u i d regions i n frozen s o l u t i o n s increase 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 of the s o l u t i o n . Figure 10 i s a p l o t of log k ^ g against 1/T f o r r e a c t i o n i n l i q u i d and i n frozen s o l u t i o n s at constant i n i t i a l c o n c entrations. The curved l i n e i s c a l c u l a t e d from the r e l a t i o n s h i p k ^ g = k^C^ where k^ i s obtained by e x t r a p o l a t i o n of the rates observed i n l i q u i d s o l u t i o n s at 90, 70 and 50° and i s obtained from measurements of the c o n c e n t r a t i o n of 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 of p_-xylene at various temperatures ( i . e . , from the phase e q u i l i b r i a of the p_-xylene-2,6-lutidine system.) . From the correspondence of the observed r a t e constants with the t h e o r e t i c a l curve shown i n Figure 10 i s apparent that the form of the observed temperature dependence i s w e l l reproduced by the r e l a t i o n s h i p k Q ^ s = k^ C^. The magnitude of the c a l c u l a t e d firsts-order r a t e constants are not, however, given 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 should be modified by the r a t i o of base concentration to t o t a l s o l u t e concentration (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 constants are less by a f a c t o r of about f i v e than the experimental r a t e constants. This discrepancy may be due to a change i n r e l a t i v e reactant concentrations i n the l i q u i d regions from that expected from r e l a t i v e concentrations i n unfrozen s o l u t i o n s or i t may be f caused by an increase i n r a t e due to a solvent e f f e c t . Since the f Since 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 increase i n r e a c t i o n r a t e at high s o l u t e concentration (analogous to the increase observed^^b f o r high p y r i d i n e concentrations i n heptane as s o l v e n t ) might be expected. 43 r e a c t i o n regions contain high concentrations of 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 ex t r a p o l a t e d from higher temperatures cannot be s t r i c t l y a p p l i c a b l e . E f f e c t of I m p u r i t i e s . Figure 11 presents the e f f e c t s of a d d i t i o n o f various compounds to frozen k i n e t i c runs at constant i n i t i a l T B F and base concentrations. For s o l u b l e compounds a decrease i n r a t e i s expected as the r e a c t i o n volumes increase to inco r p o r a t e the otherwise i n e r t compound. For i d e a l s o l u t i o n s , the observed decrease i n r a t e should depend only on the conc e n t r a t i o n and not on the s t r u c t u r e of the 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 so 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 point-composition measurements down to -5° (see Figure 12). A l l of these compounds are e q u a l l y able to depress the f r e e z i n g p o i n t of p_-xylene. The rate, depression:.given, by these compounds i s somewhat grea t e r : ' ' B + P '. than p r e d i c t e d from the r e l a t i o n k , = k , . — 0 obs obs, no im p u r i t y g + p + j o o 6 deri v e d from eq 5. This might be due to r e l a t i v e l y lower concentrations of base or peroxide i n the l i q u i d r e g i o n s than' expected from i n i t i a l setation*: concentrations;.;.-; The. impurity-: would, then be at r e l a t i v e l y higher concentration and the k , f u r t h e r decreased. obs A saturat e d s o l u t i o n of anthracene i n p_-xylene does not 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 at 0° and no e f f e c t on the r a t e of TBF r e a c t i o n i n frozen 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 depressing the r a t e of r e a c t i o n of TBF with 2 , 6 - l u t i d i n e i n frozen p_-xylene, or of depressing the f r e e z i n g p o i n t of p_-xylene than are the compounds mentioned above (see Figure 12). These observations are r e l a t e d , of course, and c o n s i s t e n t w i t h 44 Molar concentration of substance in p-xylene Figure 12. R e l a t i o n of 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 to 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 expected s e l f - a s s o c i a t i o n of t_-butyl a l c o h o l by hydrogen bonding. This f a c t o r f o r t u n a t e l y makes the TBF-base r e a c t i o n simpler than might be expected. The s t o i c h i o m e t r i c production of two moles of products (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 of TBF should r e s u l t i n an enlargement of the r e a c t i o n volume during a k i n e t i c run. 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 temperatures and t - b u t y l a l c o h o l i s a s s o c i a t e d . For comparison, the s o l u b i l i t y of carbon • ' o ' 24 d i o x i d e at one atm. pressure i n toluene at 0 i s ca. 0.14 M . This i s considerably l e s s than the 2.35 M concentration of s o l u t e s i n the r e a c t i o n regions at 0° (see Figure 12). The assumption that one mole of s o l u b l e products forms from one mole of TBF i s r e q u i r e d i n order to o b t a i n eq 5. This -approximation seems reasonable, and i s c o n s i s t e n t with the 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 of the r a t e depression caused by various amounts of i m p u r i t i e s at constant reactant concentrations as i l l u s t r a t e d i n Figure 11 i s c o n s i s t e n t w i t h eq 5. Another way of i l l u s t r a t i n g the e f f e c t of i m p u r i t i e s i s shown i n Figure 13 where ra t e s i i i pure and i n impure solvents are compared over a range of base concentrations. As i s p r e d i c t e d by B 0 + p the r e l a t i o n s h i p k , •= k , . ' — - , the e f f e c t of " obs obs, no i m p u r i t y g + p + I o o o i m p u r i t i e s i s greatest at low reactant concentrations. At high reactant concentrations the r a t e i n impure solvent i s the same as i n pure s o l v e n t . 46 Pyridine concentration, molar Figure i 3 . Effect of impurities (ca; 0.04 M) on the observed rate constant for reaction of t-butylperoxy formate with p y r i d i i n frozen p_-xylene at various concentrations of pyridine. 47 C. Ethylene Chlorohydrin w i t h Hydroxyl Ion i n Ice 25 The 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 s convenient f o r an i n v e s t i g a t i o n of a r e a c t i o n i n i c e . & A, Cl-CH 2-CH 2-OH + NaOH + CH 2-CH 2 + H 20 + NaCl This 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 constants are w e l l e s t a b l i s h e d r i g h t down to 0° . A s p e c i f i c r e a c t i o n of hydroxyl i o n , r a t h e r $han general 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 or no s a l t e f f e c t i s observed . Buffered s o l u t i o n s are not necessary and complications a r i s i n g from t h e i r use, as i n other s t u d i e s 1 0 of re a c t i o n s i n i c e , may be avoided. In a d d i t i o n , the reactants and products are a l l h i g h l y s o l u b l e i n water and no net change i n the number of sol u t e s occurs during the r e a c t i o n . Results The r e a c t i o n was st 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 hydroxide i o n i n thawed samples of a run. P l o t s of r e c i p r o c a l concentration f o r equal reactant concentrations or log ([C1CH 2CH 20H]/[0H~]) f o r unequal reactant concentrations against time gave the best s t r a i g h t l i n e s . Although i n d i v i d u a l runs then showed second-order k i n e t i c s , the observed r a t e constants v a r i e d g r e a t l y from run to run. As shown i n Table V I I , the la r g e s t values of k , were found at the lowest i n i t i a l reactant ° obs conce n t r a t i o n s . g. The use of the word wi.ce I ! can be deceptive i n that i t seems to denote the presence of only a s o l i d phase. However, depending on the solute, frozen s o l u t i o n s may contain l i q u i d regions i n e q u i l i b r i u m with s o l i d at temperatures considerably below the f r e e z i n g p o i n t . With t h i s important fact i n mind, the convenience of the name would seem to make p e r m i s s i b l e i t s use to denote not only pure s o l i d water, but also the apparent-,' s t a t e of a frozen aqueous s o l u t i o n . 48 Figure 14 shows some runs, using equimolar but d i f f e r e n t i n i t i a l concentrations o f reactants at -5°, p l o t t e d as sepond-order r e a c t i o n s . The d i f f e r e n t slopes of the l i n e s i l l u s t r a t e that the observed r a t e constants depend on the i n i t i a l reactant concentrations of the unfrozen s o l u t i o n s . However, i t may be noted from the f i g u r e , that the time taken to decrease the conc 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 the same i n a l l the runs (about 250 min.). With an i n i t i a l reactant c o n c e n t r a t i o n of 0.01 M, the observed r a t e under f r o z e n c o n d i t i o n s at -5° i s about one hundred times g r e a t e r than the r a t e i n an unfrozen s o l u t i o n at the same temperature. At a lower i n i t i a l c o n c e n t r a t i o n the r e l a t i v e r a t e increase i s s t i l l g r e a t e r , but i n d i v i d u a l p o i n t s of a run become more s c a t t e r e d (see Experimental). _3 C a r e f u l pH measurements of thawed samples from a frozen run i n i t i a l l y 10 molar i n each reactant showed that the r e a c t i o n proceeded w i t h the expected h a l f - l i f e of about 200-230 min. at -5°. This i s almost one thousand times f a s t e r than the r a t e of r e a c t i o n i n a supercooled l i q u i d s o l u t i o n at t h i s temperature. A s e r i e s of runs at d i f f e r e n t temperatures but with the same concentration of ethylene c h l o r o h y d r i n and sodium hydroxide showed that the frozen r e a c t i o n had a maximum r a t e at ca.. -5° (see Table V I I I ) . A d d i t i o n of sodium c h l o r i d e , sodium n i t r a t e or ethanol had the same r a t e depressing e f f e c t per mole of s o l u t e on the r e a c t i o n i n frozen s o l u t i o n s (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 VII Observed Second-Order Rate Constants at Various I n i t i a l Concentrations f o r Reaction o f Ethylene Chlorohydrin with Sodium Hydroxide i n Frozen Aqueous S o l u t i o n s at -5.0°. [0H~] x 10 2 [ C l f C H J OH1 x 10 2 k , x 10 4 k . C x 10 4 L Jo 1 v 2'2 o obs obs s (moles/1.) (moles/1.) (l.mole sec. ) (sec. *) 10.0 10.0 8.35 2 . 5 0 a , b 10.7 6.0 8.80 2.41 5.0 10.3 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 = total solute concentration = 2[OH ] + [Cl(CH^) OHj S 0 Z £ 0 b The value of k , C should be constant in all 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 of Temperature on the Reaction of. 0.05 M Ethylene Chlorohydrin w i t h 0.05 M Sodium Hydroxide i n Frozen Aqueous S o l u t i o n s . A 4 Temperature k , x 10 k . C x 10 r obs, j obs s j (°C) (1.mole" Asec." ) (sec." ) -0.7. 6.34 0.96 -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 . 6,18 0.925 -2.9 9.40 1.96 a a This run at 0.05 M NaOH and 0.108 M ethylene chlorohydrin. 52 Table IX E f f e c t of Added Solutes on the Reaction of 0.05 M Ethylene Chlorohydrin w i t h 0.05 M Sodium Hydroxide 1 i n Frozen Aqueous S o l u t i o n s at -4.0° 2 4 4 Solute Concentration x 10 k , x 10 k , C x 10 obs obs s (moles/1.) (1. mole *sec. *) (sec. *) none 16.5 2.48 a 3.56 NaCl 10.9 2.50 6.50 " 9.91 3.27 10.7 " . 8 . 1 8 3.39 2.74 NaN0 3 12.8 3.00 6.09 " 10.4 3.38 12.65 " 8.33 , 3.35 4.36 C 2H 50H 14.2 • 2.72 8.83 " 11.4 2.70 C g = t o t a l s o l u t e concentration ( i n c l u d i n g added s o l u t e s ) 53 Dis c u s s i o n I f e f f e c t s other than the concentration e f f e c t are 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 the f o l l o w i n g q u a n t i t a t i v e treatment of the ClCf-^Ch^OH - NaOH r e a c t i o n i n i c e should appear. The a p p l i c a t i o n to t h i s r e a c t i o n of the general equation f o r the concentration e f f e c t 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 dt This equation r e l a t e s the r a t e of l o s s of hydroxide i o n (as measured i n thawed s o l u t i o n s ) to concentrations and volumes o f the l i q u i d " r e a c t i o n r e g i o n s " i n the frozen s o l u t i o n s . The concentrations [0H~]^ and [CICH^H^H]^ and the t o t a l volume of the r e a c t i o n r e g i o n s , V^, were not d i r e c t l y measured. In order to s u b s t i t u t e f o r these v a r i a b l e s , the assumptions made are that the reagent concentrations i n the l i q u i d part of a frozen s o l u t i o n are r e l a t e d to the reagent concentration i n the thawed s o l u t i o n by [0H"] h V h = [ O H - ] ^ and by [ClCH 2CH 2OH] h V h = ,JG1CH2CH20H] V . In a d d i t i o n , since a l l the s o l u t e s i n v o l v e d are h i g h l y s o l u b l e / 0 , + _ _ ([ClCH 2CH 2OH] s + [CH 2-CH 2] s + [Na j g + [OH ] g + [Cl ] g + [I m ] s ) V s = ^ s ^ s = ^h^h where [Inv] s i s the concentration of any imp u r i t y or other added s o l u t e , C^ i s the t o t a l c o n c e n t r a t i o n o f the l i q u i d r e a c t i o n regions of a fr o z e n s o l u t i o n , and C i s the t o t a l c o ncentration of so l u t e s i n the s thawed s o l u t i o n . •k 2 [OH-] h[ClCH 2CH 20H] u (6) 54 S u b s t i t u t i o n of these r e l a t i o n s i n t o eq 6 gives the f o l l o w i n g r a t e expression. d[0H"l k C 1 = . -LU [OH ] [C1CH CH OH] (7) dt C s 1 * s •s As C g has a constant value throughout the r e a c t i o n (one mole of s o l u b l e reactant i s replaced by one mole of s o l u b l e p r o d u c t ) , and both and C^ are fu n c t i o n s only of temperature, t h i s r e a c t i o n i n frozen s o l u t i o n s i s p r e d i c t e d by eq 7 to be second-order under a l l c o n d i t i o n s . This i s c o n s i s t e n t w i t h the experimental observations mentioned above. From eq 7 i t i s a l s o seen that the observed second-order ra t e constants f o r runs w i t h frozen s o l u t i o n s are r e l a t e d to normal second-order r a t e constants i n unfrozen s o l u t i o n s by eq 8. k , = ————- (8) obs s Since C V = C,V, then k , i s a l s o equal to k_V /V, . The observed r a t e s s h h obs n 2 s h constant d i f f e r s from the r a t e constant by the r a t i o of volume of s o l u t i o n to volume of r e a c t i o n regions i n a frozen s o l u t i o n . Since a given number of moles of reactant i s replaced during a run by the same number of moles of products, the volume does not vary during a run. However, i n separate runs a gre a t e r i n i t i a l c oncentration of s o l u t e s , C s, gives a gre a t e r volume and a decrease i n k ^ occurs (see Table V I I ) . For comparison of observed r a t e constants to values p r e d i c t e d by eq 8, C^ may be obtained from the 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 ethylene 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 higher temperatures of the r a t e data a v a i l a b l e from normal l i q u i d phase 55 k i n e t i c s t u d i e s . C i s known from the t o t a l i n i t i a l s o l u t e concentration s f o r each run, i . e . , C s = [C1CH 2CH 2OH] q + [ N a + ] Q + [OH -] + [Im] . At constant temperature the p r e d i c t e d r e l a t i o n s h i p of k ^ to C g i s shown by the l i n e i n Figure 15. The c l o s e f i t of experimental p o i n t s to the t h e o r e t i c a l curve i n d i c a t e s that t h i s r e a c t i o n i n frozen s o l u t i o n s i s w e l l accounted f o r by the concentration e f f e c t . This i s a l s o shown i n Table VII by the n e a r l y constant values o f the product o f observed r a t e constant times the 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 This constancy a r i s e s from the r e l a t i o n s h i p k^gC = k 2C^ and the f a c t that both k 2 and are dependent only on temperature. That the f i r s t h a l f - l i f e . i s independent of i n i t i a l c oncentration i s c o n s i s t e n t with a "concentration e f f e c t " s i n c e , i n the l i q u i d regions of a frozen s o l u t i o n , the same concentration of reactants i s produced by the c o n t r a c t i o n of volume brought about by c r y s t a l l i z a t i o n of s o l v e n t . As the r e a c t i o n i n fr o z e n s o l u t i o n s always begins at the same co n c e n t r a t i o n , independent of the concentrations of the unfrozen s o l u t i o n s , the f i r s t h a l f - l i f e should be the same i n every run. 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 at equimolar co n c e n t r a t i o n can be made using the usual 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 constant ( k 2 ) and conce n t r a t i o n (C) f o r a second-order r e a c t i o n , i . e . t-|y 2 = l/k,,C. The normal second-order r a t e constant at -5°, ex t r a p o l a t e d from the data of McCabe and Warner i s = 1.0 x 10 ^ l.mole ^ sec. *. The 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 regions of a frozen aqueous s o l u t i o n at -5° i s about 2.6 molar, and t h i s c oncentration .divided among the s o l u t e s , Na +, 0H~ and CICH.CH-OH, corresponds to 0.86 molar i n i t i a l reactant 56 ClCH2CH20H +NoOH in H 20 Frozen, -5.0°C 0,1 0.2 Total Solute Concentration, M 03 Figure 15, Relation of observed second-order rate constants for reaction of ethylene chlorohydrin with sodium hydroxide in frozen aqueous solutions at -5.0° to t o t a l i n i t i a l solute concentration (C ). The curve s -4 i s calculated firom k . = k-C,/C = (1.07 x. 10 ) obs 2 n s C2.3)/Cs. 57 concentration. The expected h a l f - l i f e i s then roughly t j y 2 = -4 1/(1.0 x 10 )(0.86) sec. or 195 min. This i s reasonably c l o s e to the observed time of ca. 250 min. The temperature v a r i a t i o n of t h i s r e a c t i o n i n frozen s o l u t i o n s i s shown i n Figure 16, where experimental values of "K at various temperatures are compared to c a l c u l a t e d values of kJZ^. The maximum i n the curve, caused by the competetive e f f e c t s of increases i n and decreases i n k 2 as the temperature i s lowered, and the c l o s e r e l a t i o n s h i p of k Q ^ s C s to k2Cpi are apparent from the diagram. F i n a l l y , the e f f e c t at - 4 .0° of the solut e s NaCl, NaNO^ and ethanol on the observed r a t e constant i s i l l u s t r a t e d i n Figure 17. This gives the r e l a t i o n s h i p p r e d i c t e d from eq 8 the form k Q U_ s = k 2C^/C s = (1.26 x 10~ 4)(1.9)/(0.15 + Im Q). The observed r a t e constants are s l i g h t l y g reater than p r e d i c t e d ; however, with a t o t a l of 1.9 M s a l t and reactant concentration i n the l i q u i d regions of 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 the second-order r a t e constants, k 2 > at higher temperatures. Such small v a r i a t i o n o f the p r e d i c t e d from observed values might be due to inexact values o f k 2 or C^ as w e l l as s a l t or solvent e f f e c t s at the high s o l u t e concentrations o f the r e a c t i o n c o n d i t i o n s . In summary, the c h a r a c t e r i s t i c s of the ethylene c h l o r o h y d r i n -sodium hydroxide r e a c t i o n i n frozen aqueous s o l u t i o n s are f u l l y accounted f o r by the concentration e f f e c t alone. When t r e a t e d according to eq 6, which c o r r e l a t e s concentration changes during a run and the volume changes h To allow f o r temperature e q u i l i b r a t i o n , the f i r s t sample of a run was taken 10-30 minutes a f t e r f r e e z i n g the samples; thus the observed i n i t i a l h a l f - l i f e should be greater than the value c a l c u l a t e d above, as i s the case. I 58 Temperature, °C Figure 160 Temperature v a r i a t i o n o f " k o k s C s f o r r e a c t i o n o f 0.05 M ethylene c h l o r o h y d r i n w i t h 0.05 M sodium hydroxide i n fro 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 ^ -2Ch' c i r c l e s a r e experimental values o f k^gC^.. Dotted l i n e s are va l u e s of second" order r a t e c o n s t a n t s , k^, and the 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 Figure 17o E f f e c t at -4.0° of added s o l u t e s on the r e a c t i o n o f 0.05 M ethylene c h l o r o h y d r i n 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 . The curve i s -4 c a l c u l a t e d from k Q b s = k 2 S/ Cs = Cl-26 x 10 ) (1.9)/(0.15 + Im Q) where Im Q i s the t o t a l c o n c e n t r a t i o n o f added i m p u r i t i e s . 60 between various runs, the observed r a t e constants can be q u a n t i t a t i v e l y r e l a t e d to known values of the l i q u i d phase r a t e constant and to known p r o p e r t i e s of the i c e - s o l u t i o n phase e q u i l i b r i a . 61 D. Mutarotation of Glucose i n Ice As pointed out i n the I n t r o d u c t i o n the mutarotation of glucose i s 28 g e n e r a l - a c i d and general-base 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 of s t r u c t u r e s and so there would seem to be a great e r l i k e l i h o o d of the appearance of any new e f f e c t s (such as a c a t a l y t i c e f f e c t of the i c e s u r f a c e ) . In 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 of the c o n t r i b u t i o n due to the concentration e f f e c t , the glucose - H 20 and the 29 HC1 - H 20 phase r e l a t i o n s h i p s are known and the a c t i v a t i o n parameters needed to c a l c u l a t e both k^ and k 2 at low temperatures have been c a r e f u l l y e s t a b l i s h e d . 3 0 oj -glucose $-glucose ,CH2OH CH2OH Spontaneous Mutarotation.; The f i r s t - o r d e r , uncatalyzed mutarotation i n frozen aqueous s o l u t i o n s was stu 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 of thawed a-D-glucose s o l u t i o n s . The mutarotation was slow enough below 0° ( t j y 2 > 380 min.) so that any r e a c t i o n during the time necessary to thaw and analyze 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 followed to about the f i r s t h a l f - l i f e and mutarotation r a t e constants were c a l c u l a t e d from the observed r o t a t i o n s by the usual 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 mutarotation, k^, i s the sum of the i n d i v i d u a l r a t e constants k and k a 8 62 The observed r a t e constants f o r r e a c t i o n at -4.0° with the concentration of glucose i n i n i t i a l unfrozen s o l u t i o n s v a r i e d from 0,01 to 1.4 M are given i n Table X. .Over t h i s wide range of co n c e n t r a t i o n , as w e l l as at 0.05 M glucose with 0.05 M sodium c h l o r i d e present, the r e a c t i o n proceeds with the same r a t e i n a l l frozen s o l u t i o n s (average = 1.6 +_ 0.1 x 10 5 s e c . " 1 at -4.0°). The r a t e constant c a l c u l a t e d from the 30 Arrhenius equation given by Smith and Smith, as obtained from measurements i n l i q u i d s o l u t i o n s down to 0°, i s 1.9 x 10"^ sec. 1 at -4.0 e Table X Uncatalyzed Mutarotation of Glucose i n Frozen Aqueous S o l u t i o n s at -4.0' Glucose concn., M k , x 10 5, s e c . ' 1 Glucose concn., M k , x 10^, s e c . " 1 ' obs ' obs ' 0.011 1.63 0.555 1.73 0,051 a 1.57 1.39 1.42 0.500 1.38 1.92 b a With 0.051 M sodium c h l o r i d e . 30 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. As w i t h the c a l c u l a t e d r a t e constant i n i c e (see Table X ) , the r a t e constant 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 , unfrozen aqueous s o l u t i o n s i s s l i g h t l y higher than reported experimental values ( c a l c u l a t e d at 0°, 63 3.05 x 10 sec." ; found at 0°, 2.85, 2.80 and 2,82 x 10 s e c . , see reference 30). Hydrochloric Acid Catalyzed Mutarotation. Unlike the spontaneous reaction, the mutarotation of glucose i n aqueous hydrochloric acid i s accelerated by freezing the s o l u t i o n . In thawed solutions at low acid concentrations the reaction i s s u f f i c i e n t l y slow so that good k i n e t i c p l o t s were obtained simply by thawing and r a p i d l y analyzing samples of a run. Figure 18 shows two "frozen runs", with 0.02 and 0.20 M HC1 and both with 0.051 M glucose at -4.0°, p l o t t e d as f i r s t - o r d e r reactions. The l i n e a r i t y of such p l o t s over several h a l f - l i v e s shows that the mutarotation i n i c e i s f i r s t - o r d e r i n glucose, as i s the case f o r the normal reaction i n l i q u i d water. However, the k i n e t i c order i n acid i s not a constant, i n t e g r a l value. This i s shown, for example, i n Figure 18 where the two observed rate constants (obtained from the slopes of the li n e s ) d i f f e r by a f a c t o r of only 2.4 f o r a v a r i a t i o n of HC1 concentration by a factor of 10. When runs are made over a range of HC1 concentration from 0.006 to 0.3 M at constant glucose concentration, and the values of kobs P^ o t t e c' against H (see Table XI and Figure 19), i t i s seen that the + x order, x, i n the r e l a t i o n s h i p k b s = k^ + k^[H,.}:"''varies from unity at low acid concentrations to near zero at high acid concentrations. A s i m i l a r v a r i a t i o n of k i n e t i c order with c a t a l y s t concentration was observed i n the base catalyzed decomposition ot t-butylperoxy formate i n frozen £-xylene solutions i n part B. The two separate curves i n Figure 19 f o r 0.05 and for 0.5 M glucose also show that the observed rate constants depend on the i n i t i a l concentration of glucose. For the same concentration of acid, the rate constants are greater f o r 0.05 M than for 0.5 M glucose. More complete 64 | Time, min Figure 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 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 at - 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 constants c a l c u l a t e d by l o g [(% " * j / t \ " O J = kQ b s t / 2 . 3 0 3 . 6 5 \ • 6 Q l — I I 1 1 1 1 u ..! 0 .05 .10 .15 .20 .25 .30 .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 Table XI E f f e c t of HC1 Concentration on Observed F i r s t - O r d e r Rate Constants f o r Mutarotation o f Glucose at -4.0° i n Frozen Aqueous S o l u t i o n s . HC1 concn., M with 0.555 M Glucose k , x 1 0 5 , s e c . _ 1 obs i n«5 -1 k , x 10 , sec. obs ' HC1 concn., M with 0.0512 M Glucose 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 given i n Table XII and i l l u s t r a t e d i n Figure i the observed f i r s t - o r d e r r a t e constants f o r r e a c t i o n i n f r o z en HC1 s o l u t i o n s are r e l a t e d to glucose concentration over the range 0.05 to 1.10 M. In these frozen s o l u t i o n s an inverse dependency of k ^ s on glucose concentration i s obtained up to a concentration s u f f i c i e n t to prevent f r e e z i n g at -4°. " That a f i r s t - o r d e r r a t e constant can depend on i n i t i a l reactant concentration before f r e e z i n g but not on the a c t u a l reactant c o n c e n t r a t i o n during a run 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 of some r e a c t i o n s i n frozen s o l u t i o n s . 6 7 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 XII V a r i a t i o n o f Observed F i r s t - O r d e r Mutarotation Rate Constant with Glucose Concentration f o r Frozen 0.10 M HC1 S o l u t i o n s at -4.0° Glucose, M k , x 10^, sec. 1 Glucose, M k , x 10^, s e c . - 1 ' obs 5 obs 0.0512 30,8 0.833 7.21 0.278 18.7 1.10 7.18 0.390 13.8 1.18 4 . 9 l a 0.555 12.0 -- 6.17 b a Supercooled l i q u i d s o l u t i o n . 30 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 at -4° and 0.10 M HC1. As demonstrated above f o r some bimolecu l a r r e a c t i o n s i n frozen organic solvents and i n i c e , a maximum i n the rate-temperature r e l a t i o n s h i p i s a general f e a t u r e of the co n c e n t r a t i o n e f f e c t f o r r e a c t i o n s i n frozen s o l u t i o n s . The a c i d c a t a l y z e d mutarotation of glucose shows a r a t e maximum at about -7°. The observed r a t e constants at various temperatures f o r two d i f f e r e n t sets of i n i t i a l concentrations are c o l l e c t e d i n Table X I I I and Figure 21. At -6° with 0.05 M glucose and 0.04 M HC1 the observed r a t e 30 constant i s seventeen times gr e a t e r than the c a l c u l a t e d r a t e constant f o r a supercooled l i q u i d s o l u t i o n at t h i s temperature. With these reactant concentrations the r a t e i n i c e i s depressed 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 X l t l Temperature V a r i a t i o n of Observed Rate Constants f o r Mutarotation of Glucose i n Frozen Aqueous S o l u t i o n s For 0;555 M Glucose, 0.10 M HC1. Temperature ^ 0 b s X S e C ^ For 0.0512 M Glucose, 0.040 M HC1. Temperature kobs X s e c ^ +2. , o a 12. ,3 -1.0 12. 4 -1. ,6 7. .16 -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. . o b -9, .1 13, .5 -6.3 14. ,3 C -11, .3 8, .67 -8.0 30, .7 -9.5 31, .0 -11.0 28 .8 -13.5 24, .7 -14.9 21 .8 -17.0 17 .9 a S o l u t i o n not froz e n . b S o l u t i o n contained 0.051 M sodium c h l o r i d e c S o l u t i o n contained 0.097 M sodium c h l o r i d e 71 present and by 50% i f 0.097 M NaCl " i s present i n the i n i t i a l s o l u t i o n s . Although the 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 n e g l i g i b l e 32 s a l t e f f e c t . 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 order i n glucose and the observed r a t e constant i s l e s s at higher s a l t c oncentrations. S i m i l a r to the r e a c t i o n s i n frozen systems above, experimental observations on the mutarotation of glucose i n frozen 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 order, a r a t e maximum at a temperature s e v e r a l degrees below the 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 to added s o l u t e s . D i s c u s s i o n Spontaneous Reaction. In the case of glucose at -4°, the l i q u i d 29 phase of a frozen s o l u t i o n contains 27% glucose and s u f f i c i e n t water i s s t i l l present so that e s s e n t i a l l y the same r a t e of spontaneous mutarotation i s obtained i n " i c e " as i n an ord i n a r y water s o l u t i o n . The r e s u l t s given i n Table X show that the r e a c t i o n r a t e i s not appreciably a f f e c t e d by v a r i a t i o n of the surface area of the i c e i n contact with the l i q u i d regions ( i . e . , the r e a c t i o n i s not s e n s i t i v e to e i t h e r the i n i t i a l c o n c e n t r a t i o n of glucose from 0.01 to 1.4 M, nor to the r a t e of f r e e z i n g of samples). The normal mutarotation r a t e (at 0.051 M glucose) i s a l s o not changed by the a d d i t i o n of 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 the r e a c t i o n regions at -4° would be ca. 0.55 M; but since i t i s known that even 1 M NaCl or KC1 has no e f f e c t on the mutarotation r a t e 33 i n l i q u i d water, the absence of a " s a l t e f f e c t " i n i c e i s reasonable. Catalyzed Reaction. U n l i k e the simple f i r s t - o r d e r mutarotation, the second-order r e a c t i o n between glucose and a c i d i s promoted by the 72 Figure 22a E f f e c t o f added NaCl on-mutarotation o f glucose i n f r o z e n s o l u t i o n s at - 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 . 0 5 1 2 M glucose, 0 . 0 4 0 M H C 1 . 73 c o n c e n t r a t i o n e f f e c t . In. order t o determine i f other e f f e c t s are present the c o n t r i b u t i o n of the'concentration e f f e c t must be separated out. For glucose mutarotation i n frozen 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 constants, according to the concentration e f f e c t , are r e l a t e d to hydronium i o n concentration of the r e a c t i o n regions by the equation kobs = k l + k 2 H h" T ^ i s r e l a t i o n s h i p may be derived from the general equation f o r the c o n c e n t r a t i o n e f f e c t , dA g/dt =-k2 v n / v s » as a p p l i e d to t h i s second-order r e a c t i o n . A necessary assumption i s that no change i n reaction'volume- occurs during a run, or, i n other words, that the concentration i s constant i n any run. This i s reasonable s i n c e no o v e r a l l change i n number of moles occurs during mutarotation. When a l l the a c i d present i n i n i t i a l (or thawed) s o l u t i o n s i s present only i n the + + r e a c t i o n regions of frozen s o l u t i o n s , then H V = H, V. . I f a l l s o l u t e s ° s s h h act s i m i l a r l y , the t o t a l number of moles i n a thawed s o l u t i o n w i l l be equal to the t o t a l number of moles i n the l i q u i d part of the frozen s o l u t i o n , i . e . C V 3 c. V, where C i s the t o t a l i n i t i a l s o l u t e concentration of s s h h s unfrozen s o l u t i o n and i s the t o t a l s o l u t e concentration i n the l i q u i d regions of the frozen, s o l u t i o n . Using these two r e l a t i o n s h i p s between concentrations i n a frozen 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 given i n terms of measurable q u a n t i t i e s i n thawed s o l u t i o n s as f o l l o w s : H+ H + k , = k. + k- V = k. +' k_ C, * (9) obs 1 2 _s v 1 2 h C h s The 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 regions (C h) i s constant throughout a run and, l i k e k^, depends only on temperature. The concentrations H s and Cfi are known f o r each run, the value of C s being equal t o 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 , C = Glucose + H + s s s 74 _ + + C l + added solute... In these terms the hydronium i o n c o n c e n t r a t i o n , H, , s s / ' h' i s equal to 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^, times the r a t i o of a c i d to t o t a l s o l u t e concentration 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 part of a frozen 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 to the hydronium i o n c o n c e n t r a t i o n of the thawed s o l u t i o n , but depends a l s o on the concentration of the other s o l u t e s . Q u a l i t a t i v e R e s u l t s . The r e l a t i o n s h i p s presented above account f o r the experimental: observations f o r mutarotation i n i c e . The change i n k i n e t i c order i n H + a r i s e s from compensating changes i n r e a c t i o n volume and concentration., At low concentrations of a c i d the r e l a t i v e l y greater amount of glucose present c o n t r o l s the r e a c t i o n volume i n the frozen s o l u t i o n s . The r e a c t i o n regions remain at n e a r l y constant t o t a l volume, while the H + concentration and the r e a c t i o n r a t e i n the regions increase i n p r o p o r t i o n to the a c i d concentration i n i n i t i a l s o l u t i o n s ; the observed order i n H + i s then u n i t y . On the other hand, at high a c i d concentrations the s o l u t e i n the r e a c t i o n regions i s e s s e n t i a l l y a l l HC1 at the highest p o s s i b l e c o n c e n t r a t i o n . Any f u r t h e r increase i n a c i d concentration i n i n i t i a l s o l u t i o n s only increases the volume of l i q u i d regions i n the frozen s o l u t i o n . The c o n c e n t r a t i o n = ~r C, remains constant, the h 2 n r e a c t i o n r a t e t h e r e f o r e remains constant, and the r e a c t i o n appears to 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 order f o r glucose does not occur. Although the c o n c e n t r a t i o n of glucose i n l i q u i d regions 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 to i n i t i a l glucose 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 concentrations of other s o l u t e s , the k i n e t i c order i s independent of glucose 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 . I f A sV g = A^V^ then dA s/dt = ^k^B^Ag and when B^  i s constant throughout a run (as i n a c a t a l y t i c r e a c t i o n ) , the r e a c t i o n order i s seen to be independent of A g. However, the observed r a t e constant k^ = k2B^ w i l l depend on the i n i t i a l c o n centration of a l l s o l u t e s ( i n c l u d i n g A). Therefore, as a l l s o l u t e s are i n v o l v e d i n determining the t o t a l volume of r e a c t i o n r e g i o n , the observed r a t e constant depends on the i n i t i a l glucose c o n c e n t r a t i o n . A gre a t e r number of moles of glucose r e s u l t s i n a grea t e r volume, V^, and, f o r the same number of moles of a v a i l a b l e a c i d , the concentration H* must be more dilute,. At a constant i n i t i a l HC1 concentration of 0.10 M, the decrease i n observed r a t e constant w i t h increase i n glucose concentration (see Figure 20) r e s u l t s from such changes i n r e a c t i o n volume. At the lowest glucose concentration a maximum r a t e constant, corresponding to a maximum a c i d concentration of H* = should be obtained. At high concentration of glucose the minimum r a t e constant i s obtained when the s o l u t i o n contains too much glucose to allow f r e e z i n g at -4° ( i . e . , when V, = V ). h s The e f f e c t of 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 of 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 greater volume of t o t a l r e a c t i o n r e g i o n s , the reactants are made more d i l u t e and slower r a t e s of r e a c t i o n are observed (see Figure 22). The changes i n observed r a t e with temperature may a l s o be explained i n terms of concentrations and volumes of l i q u i d r e a c t i o n regions. With constant i n i t i a l concentrations of HC1 and of glucose, a decrease 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 solvent i s frozen out. A corresponding increase i n concentration C n 78 occurs. As long as the increase i n concentration outweighs the decrease i n second-order r a t e constant, k^, an o v e r a l l increase i n observed r a t e i s obtained (see eq.9). A maximum r a t e i s reached, however, when f u r t h e r decreases i n temperature f a i l to increase enough to compensate f o r decreases i n the second-order r a t e constant. This e f f e c t i s i l l u s t r a t e d i n Figure 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 of eq 9, the rate constant f o r uncatalyzed mutarotation, k^, and the second-order r a t e constant f o r a c i d c a t a l y z e d mutarotation, k 2> may be obtainec 1 by e x t r a p o l a t i o n of data obtained i n normal s o l u t i o n s 30 down to 0°. The value of i s obtained from the temperature-composition phase r e l a t i o n s h i p f o r the glucose-water system. The value of at any temperature was taken from the w e l l e s t a b l i s h e d glucose-water phase 29 diagram r a t h e r than from the HCl-water system which d i f f e r s i g n i f i c a n t l y below -5°. Freezing p o i n t s of glucose-HCl-water s o l u t i o n s , w i t h the r a t i o of glucose to HC1 near that used i n the frozen k i n e t i c runs, showed that the glucose-water phase r e l a t i o n s h i p i s s i m i l a r , down to ca. -13°, to that f o r glucose-HCl-water when r e l a t e d i n terms of t o t a l s o l u t e concentration. The curved l i n e of Figure 20 shows the c a l c u l a t e d v a r i a t i o n of observed r a t e constant w i t h glucose concentration f o r runs at constant a c i d c o n c e n t r a t i o n o f 0.10 M. The values p r e d i c t e d by eq 9 as kobs = (- 1* 9 2 X 1 0 _ 5 - ) + (' 4" 2 5 X 1 0 ~ 4 ) ( l - 6 4 j 0.1 are very c l o s e to 0.2 + G s the experimentally obtained values. In a l l supercooled l i q u i d s o l u t i o n s , as i n a s o l u t i o n more concentrated than ca. 1.4 M glucose at -4°, the same r a t e constant o f ca. 6.2 x 10 "* sec. 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 of 1.6 M no i c e can form at -4° (see Table X I I ) . At 79 concentrations lower than 1.4 M, the rat e constant i n frozen s o l u t i o n s increases as p r e d i c t e d by eq 9. The broken l i n e s i n Figure 19 show the 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 to H* (from eq 9 i n the form k Q b s = (1.92 x I O - 5 ) + (4.25 x I O - 4 ) (1.64) H e at two d i f f e r e n t glucose c o n c e n t r a t i o n s , G = — s G + 2 H + s s 0.051 a n d 0.555 M) . At the highest a c i d concentrations 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 values. This d e v i a t i o n of p r e d i c t e d and observed l i n e s i s s m a l l , but apparently r e a l , as such d e v i a t i o n occurs only at concentrations corresponding to high a c i d concentration i n the r e a c t i o n regions ( i . e . , l a r ge H*) . In the equation k , = k, + k„ H v , at high a c i d concentration only the k_H* term i s obs 1 2 n 2 h important, and as an e r r o r i n the value of k^ would s h i f t a l l the 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 Figure XI) must be due to an increase i n e f f e c t i v e c a t a l y s t concentration as HC1 concentration i s increased. The observation that the r a t e of 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 of glucose increases f a s t e r than the a c t u a l a c i d concentration 28 ( f o r HC1 > 0.4 M) was reported by Lowry and Smith and discussed i n terms of a " c a t a l y t i c c o e f f i c i e n t of u n d i s s o c i a t e d molecules of HC1 greater than that of the hydrogen ions derived from them". In o r d i n a r y s o l u t i o n s t h i s g reater c a t a l y t i c e f f e c t 1 becomes important only when the mutarotation i s 34 too f a s t f o r convenient measurement; i n frozen s o l u t i o n s the e f f e c t , although complicated by the two phase system, may be more a c c e s s i b l e i At -4.0° the r a t e constants observed at high a c i d concentrations are not as great as would be the case i f the r e l a t i o n k Q b = + k„ (h ) were fol l o w e d where log h = -H Q, the Hammett a c i d i t y f u n c t i o n at 25^35 and the values of H 0 used correspond to the HC1 concentrations of the r e a c t i o n regions i n the frozen system). 80 f o r study. At 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 frozen sample can be s u f f i c i e n t l y slowed by thawing so that analysis may be c a r r i e d out at room temperature. The c a l c u l a t e d e f f e c t of temperature on the a c i d c a t a l y z e d mutarotation i n i c e a l s o shows that the observed r a t e constants are greater than p r e d i c t e d . The broken l i n e s of Figure 21 show the temperature v a r i a t i o n according to eq 9. For these two s e r i e s of runs at constant reactant concentrations, the rate maximum a r i s e s from the decrease i n k 2 and an increase i n as the temperature i s made lower. The experimental p o i n t s l i e above the 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 discussed above, the d i f f e r e n c e could 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 at the higher concentrations encountered at lower temperatures o r , p o s s i b l y , from inexact values of ( e s p e c i a l l y at lower temperatures) as obtained from the glucose-water phase diagram. Summary., I t i s apparent that the mutarotation of glucose i n frozen aqueous s o l u t i o n s i s w e l l accounted f o r by the concentration e f f e c t . The k i n e t i c treatment of t h i s e f f e c t , as summarized by the equation k , = k, + k„C, H+/C , c o r r e l a t e s the experimental observations f o r obs 1 2 h s s v changes i n reactant 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 oncentration and i n temperature. At the concentrations used i n t h i s study, any e f f e c t of the s o l i d i c e i s n e g l i g i b l e and the r e a c t i o n i n the remaining l i q u i d regions i s normal. 81 I I I . Reactions i n Organic S o l i d s A r e a c t i o n of a s o l i d which i s accompanied by melting of the s o l i d might behave i n a manner s i m i l a r to that described above f o r r e a c t i o n s i n frozen s o l v e n t s ; even before the presence of the melt normally becomes v i s i ^ l f c considerable r e a c t i o n may take place i n t h i s l i q u i d 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 that some r e a c t i o n s which have been thought to proceed i n the s o l i d phase might a c t u a l l y have had a melted phase present which would a f f e c t the observed r e a c t i o n . As f a r as we know h i s suggestion has not been i n v e s t i g a t e d . The authors of recent papers on r e a c t i o n s i n organic 37 38 39 s o l i d s i n which melting occurs ' ' have not attempted to separate the c o n t r i b u t i o n of r e a c t i o n i n the l i q u i d phase. I t would seem that such a separation i s necessary before v a l i d conclusions about the k i n e t i c s and mechanism of the r e a c t i o n can be drawn. In the f o l l o w i n g s e c t i o n s are presented our attempts to take i n t o account r e a c t i o n i n the melt f o r the thermal mutarotation of p o l y c r y s t a l l i n e a-glucose and the 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 Mutarotation of Glucose. A study of the mutarotation of molten glucose has r e c e n t l y been reported i n which a s o l i d s t a t e mutarotation at lower temperatures was 40 suggested . Since the mutarotation r e a c t i o n occurs r a p i d l y i n the melt and s i n c e samples of glucose e v e n t u a l l y melt i f held a few degrees below 82 the m elting p o i n t , i t i s reasonable to take i n t o account r e a c t i o n i n the melted phase which should be present i n s o l i d samples h e l d at temperatures above the e u t e c t i c o f the reactant-product system. Results Weighed samples of dry, 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 lumetric f l a s k s were heated i n a constant temperature bath. The f l a s k s were cooled to quench the r e a c t i o n and the contents d i s s o l v e d i n dimethyl s u l f o x i d e i n which no mutarotation occurs at room temperature. O p t i c a l 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 of glucose i n the sample. The observed s p e c i f i c r o t a t i o n s at v a r i o us times f o r runs at s e v e r a l temperatures are p l o t t e d i n Figure 23. The curves obtained were independent of sample s i z e f o r samples of 0.2 to 1.2 g. and l a r g e l y independent of 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 of Standards dextrose (standard sample No. 41) gave n e a r l y i d e n t i c a l curves. The r e a c t i o n proceeds normally at 130° but does not seem to go at 110°. The presence of small amounts of water have a f a i r l y large o e f f e c t . At 143 undried glucose reaches 50% r e a c t i o n n e a r l y one t h i r d f a s t e r than an i d e n t i c a l sample d r i e d at 100° under vacuum. The presence of 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 while 3% anthracene speeds i t up by ca. 10%. Added B-glucose does not seem to 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 s i n c e 6-glucose i s a l s o j . Extensive g r i n d i n g of the samples caused the r a t e to increase somewhat. 83 60 L , . 0 100 200 300 TIME (Min.) Figure 23. S p e c i f i c r o t a t i o n (e) of s o l i d glucose samples versus time at various temperatures. 84 o p t i c a l l y a c t i v e . Paper chromatography of a sample which had gone to mutarotation e q u i l i b r i u m showed the presence of only a very small amount of m a t e r i a l other than a- and 8-glucose (ca. 1%); the many r e a c t i o n s which give r i s e to very complex mixtures occur l a t e r . 4 * D i s c u s s i o n As w i t h frozen solvent r e a c t i o n s the r a t e of r e a c t i o n i n the melted phase of a s o l i d sample would be a f u n c t i o n of both the concentration of reactants i n the l i q u i d phase and the t o t a l volume of the l i q u i d phase. I f r e a c t i o n occurs only i n the melt the r e a c t i o n can be represented by A .. , **- A,. T3 >- B,. ... I m p u r i t i e s or 8-glucose i n the s o l i d l i q u i d . l i q u i d * 6 c r y s t a l l i n e a-glucose create l i q u i d regions at temperatures near the i d e a l m e l t i n g p o i n t . As B-isomer i s formed i n these regions they grow i n volume by melting more of the a-glucose. Before the sample has completely melted phase e q u i l i b r i u m keeps the concentrations (A^ and B^) of a- and 6-glucose i n the l i q u i d regions constant, while the t o t a l volume of the l i q u i d phase increases i n p r o p o r t i o n to the moles of product, i . e . , = mg / B^. The i n i t i a l p a r t of the r e a c t i o n then takes the form of a f i r s t - o r d e r a u t o - a c c e l e r a t i n g r e a c t i o n , d mB/d t ... (kA. h - W V h = ( k a A h / B h - k g ) m B (10) The observed r a t e constant is k , = (k A,/B, - k n. ,. , . , , obs a h h 8) which could be obtained from a p l o t of log mg versus time. The concentrations A^ and B^ as w e l l as k^ and kg are f u n c t i o n s only of temperature. For the f i r s t few p o i n t s of each run p l o t s of log (a-e) versus time were s t r a i g h t (see Figure 24); a i s the s p e c i f i c r o t a t i o n of the purest a-glucose while 85 e i s the 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 to the moles of product. Values of k Q ^ s at various temper-atures are l i s t e d i n Table XIV. Table XIV Observed Rate Constants f o r Mutarotation o f S o l i d Glucose Temp. °C k Q b s x 10 4 s e c . " 1 140 1.7 141 2.2 142 4.4 143 8.2 144 11. The r e a c t i o n continues to a c c e l e r a t e u n t i l the s o l i d phase i s consumed. When the glucose i s completely l i q u i f i e d the s i t u a t i o n s regarding changes i n volume and i n conc e n t r a t i o n are reversed; the volume of melt, V^, remains constant and the conc e n t r a t i o n s , and B^, now vary. The k i n e t i c form i s then that of 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 to be completely melted a f t e r the s p e c i f i c r o t a t i o n of ca. one hundred was passed, such a r e l a t i o n s h i p occurs i n the lower p a r t of the r o r a t i o n - t i m e curve at 143° shown i n Figure 23. The e f f e c t s of a c c e l e r a t i v e m e l t i n g and then the f u r t h e r approach to e q u i l i b r i u m account f o r the S-shape of the curve. 86 0 I 1 '. . : _ J ; _ i _ 0 100 200 300 TIME (Min.) Figure 24. P l o t s of log (a-0) versus time at various temperatures f o r the mutarotation of s o l i d glucose. 8,7 The unusually l a r g e v a r i a t i o n o f k Q b s with temperature (a seven-fold increase over only a f o u r degree range) seems unreasonable f o r any true r a t e constant f o r mutarotation of glucose and a composite, apparent r a t e constant o f the type found i n frozen 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 grea t e r , a t h i g h e r temperatures not only because the tr u e r a t e constant, k . i n c r e a s e s w i t h temperature, but f o r a given number of moles o f 8-glucose the volume of melted glucose i s a l s o greater (Le. decreases w i t h an increase i n temperature). The r a t e constant k Q may vary normally w i t h temperature while the observed r a t e constant i s unusually s e n s i t i v e to 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 the r e a c t i o n i s d i f f i c u l t to p r e d i c t because thorough and uniform mixing i s d i f f i c u l t or impossible to achieve w i t h s o l i d glucose. I f the o-glucose could be melted and the i m p u r i t i e s d i s s o l v e d i n the melt and then the mutarotation experiments 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 melt, the i m p u r i t i e s would supposedly only c o n t r i b u t e to the 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 the l i q u i d phase. The e f f e c t would be to increase the observed r a t e s i n c e the volume of the l i q u i d phase, V^, would be increased. The large e f f e c t o f sodium c h l o r i d e i s probably due to c a t a l y s i s r a t h e r than to 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 to the high r a t e of r e a c t i o n i n completely molten glucose neigher the tr u e r a t e constants k and k , nor the phase r e l a t i o n s h i p of a- and 8-glucose ( i . e . the values of A h and B h at various temperatures) could be measured. The absence o f any r e a c t i o n at 110°, however, may be because the e u t e c t i c i s above that temperature. No q u a n t i t a t i v e e v a l u a t i o n o f the observed r a t e constant can be made. In more fav o r a b l e cases the k i n e t i c s of decomposition of 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 with observations. 42 Some thermal r e a c t i o n s of systems s i m i l a r to that described above f o r thermal mutarotation of glucose 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 the growth o f c r y s t a l l i n e defects i n tr u e '43 s o l i d s t a t e r e a c t i o n s . The "sigmoid" shaped curves of s o l i d s t a t e r e a c t i o n s are s i m i l a r to those observed i n melting s o l i d s (see r e f . 42 and Figure 23), but a p p l i c a t i o n of the same k i n e t i c treatment can only 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 ) . For mutarotation of c r y s t a l l i n e a-glucose, the k i n e t i c treatment f o r the growth of a l i q u i d phase and with r e a c t i o n only i n t h i s l i q u i d phase accounts at l e a s t q u a l i t a t i v e l y f o r the a v a i l a b l e observations. 89 B. I s o m e r i z a t i o n of 5-Norbornene-2,3-endo-dicarboxylic Anhydride The thermal i s o m e r i z a t i o n of 5-norbornene-2,3-endo-dicarboxylic anhydride to the exo-isomer i s b e t t e r than the mutarotation of glucose f o r an i n v e s t i g a t i o n of a thermal r e a c t i o n i n organic s o l i d s . The endo-isomer i s r e a d i l y endo exo a v a i l a b l e and easy to p u r i f y , the r a t e i n the melt can be measured and a 44 phase diagram of the endo-exo system i s a v a i l a b l e . The approach was s i m i l a r to that followed i n frozen s o l u t i o n r e a c t i o n s . F i r s t , r a t e constants were determined i n the melt above the normal melt 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 values 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 obtained by e x t r a p o l a t i n g . The 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 conjunction w i t h the phase diagram were then compared with experimental r a t e s measured below the normal melt i n g p o i n t . Results Reaction i n the Melt: The r e a c t i o n was s t u d i e d by s e a l i n g ca. 0.1 g. samples i n one ml. v i a l s and thermbstating at the d e s i r e d temperature. 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 to be e s t a b l i s h e d the f i r s t sample was withdrawn and quenched by dipping i n t o c o l d water. 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 90 and the contents d i s s o l v e d i n chloroformed. The per cent exo-isomer i n the sample was determined by comparing the i n t e g r a l o f the p.m.r. peak at 3.6 x (due to the o l e f i n i c protons of both isomers) to the peak at 7.0 T (due to the protons adjacent to the carbonyl groups i n the exo-isomer). The,reaction was. f i r s t - o r d e r up to 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. The r a t e constants obtained from p l o t s GO t of log (% exo - % exo ) versus t i r e are summarized i n Table XV. The r a t e constants i n the melt were about twice as great as those i n d e c a l i n 47 _5 _ i s o l u t i o n determined by Baldwin and Roberts (14 and 38 x 10 sec. at 175 and 187° r e s p e c t i v e l y ) . Table XV ' Rate Constants f o r I s o m e r i z a t i o n of Molten 5-norbornene-2, 3-endo-d i c a r b o x y l i c Anhydride. Temp. °C k o b s x 10^ sec. * 185 '•" ' 64 175.3 26 165 9.8 160.3 5.7 155.0 3.1 A p l o t of log k versus */T was 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 a c t i v a t i o n parameters f o r the forward r e a c t i o n : of AH = 38 kcal/mole and A S * =6.6 e.u;. The values c a l c u l a t e d from the data of Baldwin and Roberts t ± assuming the same e q u i l i b r i u m constant, were A H =33 kcal/mole•and = -5.0 e.u, The e q u i l i b r i u m p o s i t i o n was studied by heating samples of 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 usual way. I t was found that heating an equimolar. mixture 91 of the 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 studied,. 130 to 195°j the composition of the e q u i l i b r i u m mixture was 44% exo-isomer. Reaction i n the S o l i d ; The method was the same as that described above f o r the melt except th a t . t h e samples were melted i n a 175° o i l bath and then cooled to room temperature before thermostating at the temperature of the run. In Figure 25 are presented data f o r runs at four d i f f e r e n t temperatures below the melting p o i n t . Values f o r the slopes of the s t r a i g h t p o r t i o n s of the p l o t s o f (moles of exo-isomer/mole of sample) versus time are summarized i n Table XVI. ,"• Table XVI Slopes of P l o t s of F r a c t i o n o f Product Present versus Time f o r Isomerization o f 5-Norbornene-2, 3-endo-dicarbOxylic Anhydride at Various Temperatures. Temp. °C, Slope x 10 6 s e c . " 1 ; 150 • ••. 6.9 .145- '' •' 3.8 . 141 :' 2.7 135 0.89 A f t e r 5 days at 118° a sample of pure endo-isomer contained 12% exo-isomer, while a sample of pure exo-isomer h e l d at the same temperature f o r the same length of time contained only 2-3% endo-isomer; a f t e r 10 days at t h i s temperature the sample of exo-isomer contained 5T7% endo-isomer. Samples of the endo-isomer thermOstated at 100°, which i s below the e u t e c t i c temperature of the endo-exo system, a l s o reacted s l o w l y . A f t e r 12 days there were 6% exo-isomer i n the sample. On the other hand a sample of Figure 25. Isomeriz.ation-.of -5T-Norbornene-2, 3 - endo - d i carboxy l i e Anhydride i n the S o l i d . 93 exo-isomer h e l d at 100° f o r 12 days contained no endo-isomer. D i s c u s s i o n I f r e a c t i o n occurs o n l y , i n the melted p a r t of the sample the observations f o r endo-exo-isomerization should be s i m i l a r to those made on glucose i n the preceeding s e c t i o n . Before melting i s complete the ra t e equation would be the same as eq 10 and the observed f i r s t ' o r d e r r a t e constant would be given by, k , - (k„ A,/B, - k ). As can be seen . . 1 obs f h h r from Figure 25 the curves do not resemble those found f o r the mutarotation of glucose (see Figure 23); r a t h e r they are steeper near the beginning of the r e a c t i o n . The r a t e constants c a l c u l a t e d from e x t r a p o l a t e d values of r a t e constants and A^/B^ obtained from the phase diagram are too small to account f o r the observed r a t e of production of exo-isomer. For example at 145° kf = 0.49 x 10" 5 s e c . " 1 , k = 0.63 x 10" 5 s e c . " 1 and k./B^ = r r • . . h h 78/22 = 3.55; then k & b . = (1.74 - 0.63) x 10" 5 =-1.11 x 10" 5 s e c . " 1 and the 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. I f there were 1% k exo-isomer present at the beginning of the run there would be 2% a f t e r 1040 min.; however, as can be seen from Figure 25 there would be more than 20% exo-isomer present a f t e r t h i s time at 145°. However, i f a concurrent s o l i d phase r e a c t i o n i s considered the r e s u l t s can be explained. The s o l i d phase r e a c t i o n should be i r r e v e r s i b l e k A s o l i d A l i q . — - £ — > - B l i q k r A i • j ^s B , . s o l i d *»- l i q k I t i s u n l i k e l y that 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 present s i n c e the melting p o i n t o f the endo-isomer used was 164-165° ( l i t . 165°). 94 since a l l the product, j u s t as any other i m p u r i t y , should go i n t o the l i q u i d phase. I f the r e a c t i o n occurs only i n the melt the shape of the curve should be s i m i l a r to those observed f o r glucose, i . e . slow at f i r s t and speeding up as the r e a c t i o n proceeds. I f the r e a c t i o n occurs only i n the s o l i d the shape of the curve would be steep at f i r s t and then l e v e l o f f as the s o l i d phase disappears by me l t i n g . I f both processes are going on at once the shape of the curve would be between these two extremes, the exact shape depending on the r e l a t i v e s i z e s of k_, k and k . f r s One of the i n t e r e s t i n g features of the r e a c t i o n as formulated i s that the two processes are not independent. As exo-isomer i s produced by the s o l i d phase r e a c t i o n , endo-isomer must melt to maintain the concentration of the l i q u i d regions. As the l i q u i d regions increase i n s i z e more r e a c t i o n occurs i n them. This i n t e r a c t i o n e x p l a i n s why the 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. I t may a l s o e x p l a i n why the p l o t s curve more at lower temperatures (see Figure 25). As the temperature i s lowered the l i q u i d phase r e a c t i o n may become l e s s important since the l i q u i d phase would be s m a l l e r and have a higher concentration of exo-isomer i n i t ; the curves would then be more l i k e those expected f o r r e a c t i o n only i n the s o l i d phase. rat e i n the melted p a r t , the s o l i d part and the 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 : For concurrent r e a c t i o n i n both a s o l i d and a l i q u i d phase, the dm B (k, - k ) v f Bh r B dt melt dm s o l i d dt s o l i d 95 dm C—) dt , N , s o l i d k ) mD + k m . rJ B s A (11) t o t a l Eq 11 can be made i n t o an equation w i t h only one v a r i a b l e by s u b s t i t u t i n g f o r m ^ ^ ' i n terms of mfi. The moles of A i n the s o l i d phase at any time are equal to the t o t a l moles of A i n the sample ( m t 0 t = m ° r 1 ^ - mg) minus the moles of A i n the melt (m™ e l t = A u ^ ) . S u b s t i t u t i n g f o r 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 , A - [Ck f A L - V " ( f c s t ^ mB + k s m r 8 ( 1 2 ) d t t o t a l h h A l l the terms i n s i d e the square brackets depend only on temperature, and so are constant during any one run. For the s t r a i g h t p o r t i o n s of the curves of Figure 25, (d mg/dt) ^ i s constant and so cannot depend on mg, the moles o f product present. According to eq 12 the only way t h i s c o n d i t i o n can ho l d i s i f (k^A^/B^ _ k^) -(k +k h) i s c l o s e to zero. In t h i s case (dm n/dt). . = k , the r a t e s s — *• B ' t o t s' h constant f o r the s o l i d phase r e a c t i o n (since the a n a l y s i s i s always on the bas i s of one mole m ^ r i ^ 'is u n i t y ) . An i n d i c a t i o n that the slopes are a c t u a l l y p r o p o r t i o n a l to a rate constant of the form k = Aexp(-a/T) i s the l i n e a r i t y of a p l o t of log k versus 1/T (see Figure 26). The a c t i v a t i o n parameters obtained from the p l o t are AH* = 43 kcal/mole and AS+ = 18 e.u. Many organic molecules 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 g l o b u l a r molecules, e x h i b i t a higher temperature s o l i d " r o t a t o r " phase i n which the 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 3/T Figure 26. Arrhenius P l o t f o r S o l i d Phase Reaction of 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 easily deformed than the lower temperature c r y s t a l l i n e 47 46 48 phases. Both endo - and exo- 5-norbornene-2, 3-dicarboxylic anhydride are such globular molecules and the endo-isomer has such a phas e. The t r a n s i t i o n temperature for the endo-isomer i s f a r below the melting point 48 while that for the exo-isomer i s very near i t s melting point. I f rotation i n such phases i s easier then perhaps isomerization i s also easier. The fact that the s o l i d - s o l i d t r a n s i t i o n temperature for the endo-isomer i s lower may explain the different rates of reaction reported above. In summary, i t may be said that although reaction only i n the melted part of the system studied here cannot account for the observations, the system cannot be treated without considering reaction i n the melt. In any case, i n s o l i d materials above the eutectic temperature of the reacting 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 reaction can only be d e f i n i t e l y established by separating out any reaction which may occur i n such a l i q u i d phase. 98 IV. General Remarks A. A Demonstration Reaction. As shown by the d i s c u s s i o n above many aspects of r e a c t i o n s i n frozen s o l u t i o n s may be c o r r e l a t e d , by the general k i n e t i c treatment of the concentration e f f e c t . One of•'...the...aspects not yet d e a l t w i t h i s the e f f e c t of f r e e z i n g on equilibrium...Any r e a c t i n g system which has a g r e a t e r order of r e a c t i o n i n one d i r e c t i o n than i n the other should experience 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 of the s o l v e n t . The d i r e c t i o n and magnitude of 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 concentration e f f e c t . 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 forward d i r e c t i o n and second-order i n the reverse 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 of reagent, should hol d . B + C B C s s K = — f — • = m B mC 1 eq A s * -m. s r> n 'h h B h C h = mB mC 1 x A h mh V h According to t h i s equation, i f the r e a c t i o n volume i s decreased by f r e e z i n g out solvent (V > V^), the number of moles of B and C must decrease and those of A increase. The e q u i l i b r i u m would s h i f t to the l e f t by a f a c t o r r e l a t e d to the r e l a t i v e s i z e s of the r e a c t i o n volume before and a f t e r f r e e z i n g . 99 That such e q u i l i b r i u m s h i f t s do occur was shown by measuring the absorbance of samples of a s o l u t i o n , o f hydroiodic.and a r s e n i c 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 frozen at -5°. In t h i s case the s h i f t was to the r i g h t , i . e . , i n the H 3As0 4 + 3 I " + 2H + — HjAsOj '+ 1^ + R e -d i r e c t i o n of fewer species. The absorbance at 475 my of the 1^ i n t h e unfrozen sample was only 0.015 w h i l e that i n the frozen sample ( a f t e r thawing) was 0.724. The 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 was 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 brought about when more concentrated samples were f r o z e n . C o l o r l e s s samples 0.01 M i n each r e a c t a n t , which were sealed i n 5 ml. v i a l s , changed w i t h i n two minutes to y e l l o w , then organe, and f i n a l l y to a yellow-brown c o l o r when placed i n a dry ice-acetone bath at -80°. Upon thawing by h o l d i n g under hot tap water the c o l o r was completely discharged w i t h i n a few minutes. The c y c l e could be repeated as o f t e n as. d e s i r e d , thus being u s e f u l as a simple demonstration 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 . B. Review of Published R e s u l t s . I t i s of i n t e r e s t to reconsider some of the evidence which has l e d to suggestions of s p e c i a l e f f e c t s i n frozen systems. The r a t e increases 3-13 upon f r e e z i n g which have been observed by various workers (see Part I) are probably consequences of the. concentration e f f e c t . However, these authors have not separated out the e f f e c t of concentration and r a t e enhancements due to other f a c t o r s may be present. Many of these s y s t e m s * * ' 1 0 , 1 1 are r a t h e r complicated due to the large number of s o l u t e s 100 or the r e a c t i o n i t s e l f and such a.separation of e f f e c t s would be d i f f i c u l t . In the case of the r e a c t i o n s of amino a c i d e s t e r s w i t h hydroxylamine i n i c e as reported by Grant and Alburn**, the observed i n h i b i t i o n brought about by the presence o f amino acids and other 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 , the r a t e decreases u s u a l l y observed when " i m p u r i t i e s " are added to frozen s o l u t i o n s (see e.g., Figure 22.). 49 These same authors i n a very recent paper have reported the p o l y m e r i z a t i o n of s e v e r a l N-carboxyamino a c i d anhydrides (NGA) to polyamino acids i n frozen dioxane. T h e i r observations 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 constants of r e a c t i o n while i n d i v i d u a l runs remain f i r s t - o r d e r , and higher rate: constants when using lower i n i t i a l c oncentrations of NCA's. They conclude that the most l i k e l y e x p l a n ation of the observations i s a s p e c i a l e f f e c t of the frozen solvent i n that "...alignment may occur i n a channel of molecular dimensions during the simultaneous c r y s t a l l i z a t i o n of solvent and s o l u t e . The phenomenon could resemble c l a t h r a t e formation, w i t h the solvent a c t i n g as host and template p a r t i a l l y or f u l l y e n c l o s i n g s o l u t e molecules." T h e i r observations, however, appear to be c o n s i s t e n t w i t h expectations f o r the concentration e f f e c t i f i t i s assumed that the solvent they used contained a d v e n t i t i o u s i n i t i a t o r s . This assumption i s not u n l i k e l y s i n c e the authors s t a t e that they used commercial dioxane (Matheson Coleman and B e l l , S p e c t r b q u a l i t y ) without f u r t h e r p u r i f i c a t i o n . In t h e i r f i r s t paper on r e a c t i o n s i n frozen s o l u t i o n s , B u t l e r and B r u i c e ^ reported s t u d i e s on the h y d r o l y s i s of a c e t i c anhydride, 6-propio lactone and p_-nitrophenyl acetate and on the dehydration of 5-hydro-6-hydroxydeoxyuridine. Although they were not able to make q u a n t i t a t i v e p r e d i c t i o n s , they concluded that the observations 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 reactants i n regions between the 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 paper, on the r e a c t i o n of t h i o l a c t o n e s with morpholine i n i c e , 6 they were o f the op i n i o n that "the conce n t r a t i o n e f f e c t ... appears to. b e . e n t i r e l y inadequate to e x p l a i n the e f f e c t s a s s o c i a t e d w i t h the two systems examined". Bruice and B u t l e r ' s 6 observation that the r a t e o f r e a c t i o n o f t h i o l a c t o n e s w i t h morpholine i n i c e was a f u n c t i o n o f the morpholine co n c e n t r a t i o n and not the square o f i t as i n unfrozen s o l u t i o n s can a l s o be explained on the b a s i s o f the co n c e n t r a t i o n e f f e c t . In o b t a i n i n g the experimental r e s u l t s , the morpholine c o n c e n t r a t i o n 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 simply by d i l u t i o n o f a standard b u f f e r s o l u t i o n . The volume o f the l i q u i d regions of frozen s o l u t i o n s would then be p r o p o r t i o n a l to morpholine concentrations i n thawed s o l u t i o n s , i . e . = K"N s, while the 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 regions would be the same constant value i n a l l the frozen runs. 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 to 2 N, . When measured i n thawed s o l u t i o n s the a c t u a l r a t e i s modified so that h 2 2 the observed r a t e constant i s k . = KN, V./V which i s equal to KN, K"N /V . obs h h s M h s s As i s constant and the volume V g i s always i n terms o f one l i t e r , the ra t e constants are p r o p o r t i o n a l to N^, i . e . k 0 D S = ^'^ s a s experimentally observed. The odd change i n k i n e t i c order f o r r e a c t i o n i n i c e a r i s e s only from the v a r i a t i o n i n r e a c t i o n volumes f o r runs at d i f f e r e n t i n i t i a l c o n c e ntrations. The d i f f e r e n c e i n solvent k i n e t i c isotope e f f e c t which they observed can l i k e w i s e be explained. They found k^/k^ = 4.2 i n unfrozen s o l u t i o n at 30° and k^/k^ =1.6 i n fr o z e n s o l u t i o n at -10°. Since the f r e e z i n g p o i n t of D_0 i s +3.8° the con c e n t r a t i o n o f reactants i n the l i q u i d regions o f 102 heavy water at -10° would be greater, than that i n the l i q u i d regions of normal water at the same temperature and the observed rate constant, k^, correspondingly greater. 8 Home's study of the Fe ( I I ) - Fe ( I I I ) electron exchange reaction i n frozen aqueous perchloric acid i s especially interesting i n that he carried out rate Studies both above and below the eutectic temperature (-58°) of the HC104-H20 system and found no discontinuity. This fact seems to indicate that the mechanism i s the same i n both cases. He was not able to observe the segregation of a concentrated solution upon freezing a mixture of HCIO^ and ^ 0 , corresponding to the eutectic composition, containing Fe(III) . Nevertheless, such a l i q u i d , phase may have been present below -58° i n the frozen reaction mixture; since the phase relationships i n the system HCIO^-^O would not be expected to be the same as those i n the HC10^-H20-FeCl3 system. This author, appears to be the f i r s t to have attempted to make a correction i n the rate equation for concentration of reactants upon freezing. Unfortunately, the reaction i t s e l f and the phase relationships are very complicated and so his conclusion that the reaction 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 Mazur^ were able to show the water-thymine eutectic to be at -0.2° and that photochemical dimerization occuring i n frozen solutions below t h i s temperature proceeds i n a s o l i d phase i n 12 12 agreement with the conclusion of Wang. Wang's conclusion that the photochemical reaction of 1,3-dimethyluracil with methanol i n frozen aqueous solutions 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 solutions take place i n highly concentrated l i q u i d regions present among the crystals of frozen solvent. 103 While many features o f fr o z e n s o l u t i o n r e a c t i o n s are a c t u a l l y p r e d i c t e d by a general treatment o f the concentration e f f e c t , the existence of other e f f e c t s cannot be discounted. However, no c l e a r evidence of such other e f f e c t s has been presented i n any case. I t i s c l e a r t h a t , f o r r e a c t i o n s known to proceed i n normal l i q u i d s o l u t i o n s near the f r e e z i n g p o i n t , any d i s c u s s i o n o f r a t e s i n a frozen s o l u t i o n which does not separate the c o n t r i b u t i o n o f the concentration, e f f e c t must be i n e r r o r . Q u a n t i t a t i v e s e p aration o f r e s u l t s due t o t h i s e f f e c t from those a r i s i n g from any other p o s s i b i l i t y i s not e a s i l y c a r r i e d out when the system contains many s o l u t e s , when the r e a c t i o n i s not w e l l known under normal ( i . e . , unfrozen) c o n d i t i o n s , • t or when the 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 not a v a i l a b l e . • V C. Conclusion. In the course o f t h i s research some new features 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 found, i n c l u d i n g a maximum i n the r a t e -temperature dependence curve, up to 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 order 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 . A general method o f t r e a t i n g the e f f e c t o f co n c e n t r a t i o n , brought about by f r e e z i n g out pure s o l v e n t , on r e a c t i n g systems has been developed. This treatment not only explained our own observations but a l s o some of those obtained by other i n v e s t i g a t o r s . The a p p l i c a t i o n o f t h i s treatment should allow the d e t e c t i o n o f any other p o s s i b l e e f f e c t s o f f r e e z i n g besides the c o n c e n t r a t i o n e f f e c t . . The ideas o f fr o z e n s o l u t i o n k i n e t i c s have been extended to r e a c t i o n s of organic s o l i d s i n which melting occurs during the r e a c t i o n . Separation o f r e a c t i o n i n the melt from p o s s i b l e r e a c t i o n i n the s o l i d has been demonstrated. 104 This work has r e s u l t e d i n a b e t t e r understanding of the e f f e c t s of f r e e z i n g on r e a c t i n g systems. The ideas developed here may f i n d p r a c t i c a l a p p l i c a t i o n to problems encountered i n the f r e e z i n g o f foods, the low temperature p r e s e r v a t i o n of organs f o r surgery and the d e s a l i n i z a t i o n of sea water. For a d i s c u s s i o n o f f r e e z i n g on some aspects of these problems see reference 51. 105 V. Experimental M a t e r i a l s Reagents. Methyl i o d i d e (Eastman Organic Chemicals, reagent grade) was washed with 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 with water. A f t e r d r y i n g over anhydrous calcium c h l o r i d e and d i s t i l l a t i o n (b.p. 44°, l i t . * 43°) through a column packed with glass beads, the product was stored i n a brown b o t t l e over a drop of mercury. Triethylamine was r e f l u x e d over and d i s t i l l e d (b.p. 89°, l i t . 89-90) from barium oxide. 23 t-Butylperoxy formate was prepared as described by Pincock from t - b u t y l hydroperoxide and formic a c e t i c anhydride. The product was stored i n polyethylene b o t t l e s at ca. 0° to avoid the slow decomposition caused by g l a s s . 2,6-Lutidine (Eastman Organic Chemicals, 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_-toluenesulfonate then d i s t i l l e d and r e d i s t i l l e d 52a from barium oxide. 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 barium oxide. Ethylene c h l o r o h y d r i n (Eastman Organic Chemicals, p r a c t i c a l grade) was d i s t i l l e d through a 75cm. Vigreux column. 1 A f t e r d i s c a r d i n g a large f o r e r u n , a center f r a c t i o n with b.p. 128.5 - 130 ( l i t . 128°) was c o l l e c t e d . Sodium hydroxide s o l u t i o n s were made up from B r i t i s h Drug Houses concentrated vol u m e t r i c s o l u t i o n s or 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 values of p h y s i c a l constants were taken from the "Handbook of Chemistry and P h y s i c s " , F o r t y - S i x t h Ed., The Chemical Rubber Co., Clevland (1965) unless otherwise noted. 106 were standardized against potassium a c i d p h t h a l a t e . Glucose used f o r frozen 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 reagent grade a-D-glucose. For the neat r e a c t i o n , i n a d d i t i o n to t h i s glucose 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 of Standards dextrose, standard sample No. 41 was used. 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 were made up from B r i t i s h Drug Houses concentrated vo l u m e t r i c s o l u t i o n s . . 5-Norbornene-2, 3-endo-dicarboxylie anhydride ( A l d r i c h Chemical Co., m.p. 1 5 4 - 1 5 5 ° ) was p u r i f i e d by twice r e c r y s t a l l i z i n g from benzene and then once more from petroleum ether (b.p. 65-110°). The melti n g p o i n t of the a : e 4 4 m a t e r i a l used was 164-165 ( l i t . 165 ). The exo-isomer was prepared 44 by the method of C r a i g . Crude endo-isomer was heated at 190° f o r 2 h r . , cooled and the crude mixture 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 mixtures o f benzene and petroleum ether (b.p. 6 5 - 1 1 0 ° ) to a constant mel t i n g p o i n t , m.p. 141-143° ( l i t . 143° 4 4). 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 or Merck a n a l y t i c a l reagent grade A s ^ . Hydroiodic 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 reagent grade v i a l s o f the constant b o i l i n g mixture. Solvents Reagent grade benzene was r e c r y s t a l l i z e d three times by slow f r e e z i n g of ca. 75-85% of the t o t a l volume. Benzene which had been d r i e d over anhydrous magnesium s u l f a t e , d i s t i l l e d , then 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 methyl i o d i d e w i t h t r i e t h y l a m i n e . Benzene used had f.p. 5.6° ( l i t . 5.53° 5 3). p_-Xylene (Eastman Organic Chemicals, White Label 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 of the t o t a l .volume of 107 l i q u i d three times. The £= xylene was then r e f l u x e d and d i s t i l l e d from sodium, This 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 impurity concentration was l e s s than 0.1 mole pes- cent. Deionized 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 te 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. Freezing Point Depression Diagrams Fr e e z i n g p o i n t depression diagrams were constructed 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 ofknown c o n c e n t r a t i o n . About 21 ml. of 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 of a thermometer p l a c e d i n i t , The s o l u t i o n was then slowly eooled (l=2 e/min). i i n e e the s o l u t i o n s always supercooled before 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 three 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 of a degree. 108 K i n e t i c s Methyl Iodide with Triethylamine A. I n f r a r e d Method. S o l u t i o n s of equal (or n e a r l y equal) concentrations of methyl i o d i d e and of t r i e t h y l a m i n e were prepared, equal volumes of these combined, and.the r e s u l t i n g s o l u t i o n shaken v i g o r o u s l y to thoroughly mix the r e a c t a n t s . This mixture (some product immediately begins to 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 large s y r i nge and d i v i d e d i n t o a number of samples h e l d i n 1 ml. v i a l s , the v i a l s were sealed and plunged i n t o a Dry Ice-acetone or l i q u i d n i t r o g e n bath. When the s o l u t i o n s i n the 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 to a constant temperature bath at the d e s i r e d temperature. ; A f t e r a l l o w i n g the samples to warm up to the bath temperature, the f i r s t v i a l (time zero) was removed and placed i n a Dry Ice-acetone bath. A f t e r a l l the samples of a run had been c o l l e c t e d i n t h i s manner,; they were thawed and analyzed by measuring the change i n absorbance at 1240 cm. * due to methyl i o d i d e . 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 solvent i n the reference c e l l . The sodium c h l o r i d e c e l l s used had path lengths of 0.5 mm. The observed r a t e constant, f o r r e a c t i o n s with equal reactant c o n c e n t r a t i o n s , were obtained by p l o t t i n g ( A Q - A ^ / A^ - A ^ ) against :.time i n minutes and m u l t i p l y i n g the slope of ; t h i s l i n e by 2.303/60. A q , A^ and A ^ are the values of sample absorbance, measured against pure benzene i n the reference c e l l , at time zero, 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 . In a l l cases i n which the absorbance of an i n f i n i t y sample was measured i t was found to. be zero. 109 B. T i t r a t i o n Method. S o l u t i o n s of the reactants having twice the des i r e d c oncentration o f the run were made up, then two or three ml. 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 of ca. 6 ml. v i a l s . An equal amount of the second s o l u t i o n was p i p e t t e d i n t o the f i r s t v i a l which was then immediately shaken, sealed and f r o z e n i n a Dry Ice-acetone or l i q u i d n i t r o g e n bath.. A f t e r a l l the v i a l s had been prepared i n t h i s manner they were placed i n the constant temperature bath. 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 immediately a f t e r withdrawing from the bath by shaking under warm tap water. The s o l u t i o n was washed i n t o excess standard h y d r o c h l o r i c a c i d (0.1 N) and the excess a c i d back t i t r a t e d to the methyl red end p o i n t with standard 0.1 N sodium hydroxide s o l u t i o n . Some l i t t l e s c a t t e r i n the p o i n t s of a run seemed due to the use of i n d i v i d u a l l y prepared samples, r a t h e r than a l i q u o t s of a s i n g l e s o l u t i o n . For runs w i t h unequal reactant concentrations (A and B Y the observed r a t e constants were obtained s sJ by p l o t t i n g log (A sB s) against time i n minutes and m u l t i p l y i n g the slope of 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 to the 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 that i t s concentration was twice as great as i n the f i n a l r e a c t i o n mixture. For runs with p_-xylene present the r a t e constants were obtained from a p l o t of 2 l o g ( A S / A Q ) -Im 12. 303 A against time, s s C. Nuclear Magnetic Resonance Method. 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 prepared and about 1 ml. was q u i c k l y t r a n s f e r r e d w i t h a syringe to a normal n.m.r. sample tube. The sample was frozen i n Dry Ice-acetone and then placed i n a Varian A-60 n.m.r. spectrometer equipped w i t h v a r i a b l e temperature c o n t r o l . The temperature 110 of -5° was measured by the separation of the peaks of a methanol sample. A f t e r the sample came up to -5° the i n t e g r a l curve f o r the broad benzene peak was run about every 15 min. The peak width at h a l f height was ca. 50 cps, 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, prepared as above f o r the s i n g l e sample used i n the run, had been h e l d at -5° overnight and gave an i n t e g r a l curve only 2% as high as that given by the i n i t i a l zero time i n t e g r a l curve. A p l o t of log ( i n t e g r a l value i n mm.) against time was a good s t r a i g h t l i n e over 80% r e a c t i o n , the slope of the l i n e m u l t i p l i e d by 2 x 2.303 gave the value - 4 - 1 of k„C, as 3.5 x 10 sec. . 2 h t-Butylperoxy Formate i n Frozen 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 prepared s o l u t i o n of 2 , 6 - l u t i d i n e (or p y r i d i n e ) i n p_-xylene t o a weighed q u a n t i t y of 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 d i v i d e d i n volumes of 1-2 ml. i n t o about ten to f i f t e e n g l a s s ampoules. The ampoules were sealed under a i r at atmospheric pressure 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 or three unfrozen samples were r e t a i n e d f o r c o n t r o l s as described below. No s p e c i a l techniques f o r sample p r e p a r a t i o n were, necessary. There was no d i f f e r e n c e i n r a t e of TBF decomposition i n frozen-samples which d i f f e r e d i n any of the f o l l o w i n g ways; presence of 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 of s o l u t i o n , degassed or not degassed, and samples frozen by placement i n baths at 8 or 0° (with seeding), at -70 or at -195°. The frozen samples were placed i n a constant temperature bath 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 "zero time" sample was withdrawn. This 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 shaking I l l under tap water at room temperature.; Other samples were c o l l e c t e d s i m i l a r l y at various times and a l l were st o r e d at room temperature u n t i l a n a l y s i s as described below. In runs at high base concentrations the decomposition at room temperature was s u f f i c i e n t l y f a s t to 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 , or storage at ca. -70° u n t i l c o l l e c t i o n was complete and the a n a l y s i s of a l l the samples could be c a r r i e d out over a few minutes. In every run separate samples were stored frozen at -70° (or -195°), unfrozen at room temperature and, i f p o s s i b l e , at the temperature of the run. The p_-xylene s o l u t i o n s could be o f t e n r e t a i n e d as supercooled l i q u i d samples at 0° f o r longer times than r e q u i r e d f o r the run and the a n a l y s i s . These samples were analyzed a f t e r the a n a l y s i s of k i n e t i c run samples was completed and, except at the highest base co n c e n t r a t i o n s , were l e s s decomposed than the "zero time" sample of the run. The d e f r o s t e d samples were analyzed by measurement of the i n f r a r e d 23 carbonyl absorption of TBF as described by Pincock . In every case p l o t s of log P/P -vs.' time f o l l o w e d u s u a l l y to 80-90% decomposition were s t r a i g h t . Since i n f i n i t y samples taken a f t e r 8-10 h a l f - l i v e s f o r various runs showed no absorption f o r TBF, the 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 to be zero. Observed f i r s t - o r d e r r a t e constants f o r completely independent runs at s i m i l a r concentrations sometimes v a r i e d by 10%, but there was no s c a t t e r of 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 Ethylene 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 weighing out the m a t e r i a l , and d i l u t i n g w i t h water. The req u i r e d amount of t h i s s o l u t i o n was mixed with the appropriate volume of sodium hydroxide s o l u t i o n and then d i l u t e d w i t h Water to give the concentration d e s i r e d f o r a run. A f t e r thorough mixing, the 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 v i a l s . Freezing of these i n d i v i d u a l samples o f a run was u s u a l l y accomplished simply by p l a c i n g the samples i n t o a Dry Ice-acetone bath. Sometimes the samples were supercooled to the temperature of a run and then dipped q u i c k l y i n t o a Dry Ice-acetone bath to i n i t i a t e c r y s t a l l i z a t i o n . At various times i n d i v i d u a l - samples were removed from the constant temperature bath and q u i c k l y thawed by shaking under hot tap water. A n a l y s i s of the samples was c a r r i e d out by t i t r a t i o n with standard 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) with phenolphthalein as i n d i c a t o r . Microburets o f 5 and 2 ml. c a p a c i t y were used, the 2 ml. buret being equipped with a micrometer plunger. For runs at low concentrations of base pH measurements on i n d i v i d u a l thawed samples were made using a Radiometer Model 4 pH meter which was standardized against pH 10 b u f f e r . No c o r r e c t i o n was made f o r the d e v i a t i o n of the 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 . For example, a run with 0.001 M reactants gave the f o l l o w i n g pH readings at the given times; 10.967 at 0 min., 10.848 at 46 min., 10.718 at 99 min., 10.681 at 150 min., 10.698 at 188 min., 10.632 at 239 min., 10.493 at 409 min. and 10.385 at 607 min. K i n e t i c data were t r e a t e d according to normal second-order k i n e t i c equations. Rate constants were c a l c u l a t e d from the slopes of the l i n e s i n p l o t s of 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 time or p l o t s of 113 log[ClCH2CH2OH]/[OH"] against time. Runs at the lowest concentration showed some scatter. This seemed due to experimental d i f f i c u l t i e s i n measuring low concentrations of base rather than to r e a l variations i n the amount reacted. As indicated by changes i n pH, t h i s reaction i n frozen solutions proceeds even with i n i t i a l concentrations less than _3 10 M, but individual thawed samples gave very e r r a t i c pH readings at these low concentrations of base. The values of k 2 at one degree intervals were calculated 26 -1 -1 (IBM 7040 computer) from the equation k 2 ( 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 that our method of analysis gave rate constants i n agreement with McCabe and Warner 2 6 (at -1.4° found, 2.06 x 10" 4 l i t e r mole" 1 sec." 1; at -1.0° ' •• -4 . - _ i _ i ' calculated 2.04 x 10 l i t e r mole sec. ). Mutarotation of Glucose i n Ice Solutions were made up by dissolving a weighed amount of a-D-glUcose i n a volumetric f l a s k , then adding the appropriate amount of HC1 solution, and making up to the mark. After thorough mixing the solution was divided into ca. 15 ml. aliquots held i n test tubes which were then supercooled to the temperature of the run. Freezing was i n i t i a t e d by dipping the tubes for a few seconds into a Dry Ice-acetone bath. The f i r s t sample was withdrawn from the constant temperature bath approximately ten minutes after freezing. Analysis of samples having 0.25 M glucose or higher was carried out by f i r s t d i l u t i n g the sample immediately after thawing with an NaOH solution containing buffer (Coleman pH4 buffer t a b l e t s ) . The resulting solution was about pH4, and the mutarotation near the slowest possible rate. The angle of rotation (+_ 0.05°) was then measured with a 114 Bellingham and Stanley Model D p o l a r i m e t e r . Samples having l e s s than 0.25 M glucose were analyzed by use of a Bendix type 143A Automatic Polarimeter equipped w i t h a mercury f i l t e r . The 40 mm c e l l was f i t t e d with a syphon arrangement so that samples could be q u i c k l y exchanged i n the c e l l without removing i t from the o p t i c a l u n i t . Samples could be thawed and analyzed very q u i c k l y , the r o t a t i o n (+ 0.001°) was taken when the meter needle was at maximum d e f l e c t i o n . M u tarotation i n the thawed samples continued as the sample was warmed, of course, but thawing s u f f i c i e n t l y slowed the r e a c t i o n to allow the r a p i d a n a l y s i s described above. The r o t a t i o n s of the i n f i n i t y samples were taken a f t e r a l l o w i n g the s o l u t i o n to stand at room temperature ca. 24 hr. Observed r a t e constants ware obtained from the slopes of p l o t s of log (a - ot^/a .'- a j against time (where a i s observed r o t a t i o n ) . The best s t r a i g h t l i n e was drawn v i s u a l l y through the p o i n t s . The r a t e constants 30 f o r spontaneous" mutarotation, k j w e r e c a l c u l a t e d from -30 to +20° by the equation log k j = -lo g 60 + 10,785 - 16900/2.303 RT (at -4.0° ^ = 1.92 x 10 1 sec. ^ . The r a t e constants f o r second-order a c i d c a t a l y z e d r e a c t i o n were c a l c u l a t e d from log k^ = - l o g 60 - log 0.04 + 12.111 -18600/2.303 RT (at -4.0° k 2 = 4.25 x l O - 4 l i t e r mole" 1 s e c ; 1 ) . Mutarotation of P o l y c r y s t a l l i n e Glucose Weighed samples of glucose which had been d r i e d at 100° under vacuum were heated i n i n d i v i d u a l 25 ml. volumetric f l a s k s i n a constant temperature o i l bath. The f l a s k s were withdrawn at various times, cooled and the contents d i s s o l v e d i n dimethyl s u l f o x i d e i n which no mutarotation takes place 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 first 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%. Nevertheless reasonably consistent results were obtained. 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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