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Hydration of ketones in mixtures of water and dipolar aprotic solvents Van Dyke, John D. 1970

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THE HYDRATION OF KETONES IN MIXTURES OF WATER AND DIPOLAR APROTIC SOLVENTS BY JOHN D. VAN DYKE B.Sc, University of Alberta, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1970 I n p r e s e n t i n g 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 o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada ABSTRACT Supervisor: Professor Ross Stewart The hydration of a series of a,a,a-trifluoroacetophenones has been studied in sulfolane-water and dimethyl sulfoxide-water solvent systems 19 and their extents of hydration measured by F N.M.R. spectroscopy and U.V. spectroscopy. In order to quantitatively determine the equilibrium constants for the very readily hydrated ketones in this series and at the same time to study the effect of a dipolar aprotic solvent on the ab i l i t y of an aqueous medium to hydrate a ketone, a function W q (analogous to the Hammett acidity function H ) was developed for the systems sulfolane-water and dimethyl sulfoxide-water. Nine substituted a , a , - a - t r i f l u o r o -acetophenones were used to establish the W 'scale for sulfolane-water: o ' two were used to establish the'scale for dimethyl sulfoxide-water. The a b i l i t y of a medium to reduce the extent of ketone hydration is indicated by an increase in the medium's W function. In sulfolane-J o water, W values increase continuously as sulfolane is added to the o medium, ranging from 0 in pure water to about 2.7 in 99 mole % sulfolane. The corresponding function in dimethyl sulfoxide-water decreases i n i t i a l l y as dimethyl sulfoxide (DMSO) is added reaching a minimum of -0.42 at 40 mole % DMSO. As more DMSO is added, the function rises and reaches a value of about 1.1 in 99 mole % DMSO. The differences between the W functions in DMSO and sulfolane o are accounted for by differences in the behavior of the water activity terms and the activity coefficients of the ketone hydrates in the two solvent systems. From considerations of the effect of the dipolar aprotic solvents on the hydrate molecules, i t appears that the activity - i i i -coefficients of the hydrates are affected in the same manner as the activity coefficients of water but to a greater degree. Data on the hydration of s-dichloroacetone in dioxane-water and acetonitrile-water (supplied by Professor R.P. Bell) allowed the development of functions in these solvents. A comparison of W Q functions shows the following order for effectiveness of a solvent in decreasing the extent of hydration: sulfolane > acetonitrile > dioxane > DMSO. The pK^ (d = dehydration) values for the nine substituted cx,a,a-trifluoroacetophenones determined in sulfolane-water vary from -0.86 for the 4-dimethylamino derivative to 3.15 for the 3-nitro derivative. A plot of log versus the Hammett substituent constants (a +) for these compounds yields a p"*" value of -1.62. Measurements of the kinetics of hydration in sulfolane-water mixtures containing no acid indicate that three water molecules are intimately associated with the hydrating ketone in the transition state for the water-catalyzed mechanism. In sulfolane-water mixtures containing acid, the same measurements do not indicate conclusively the number of water molecules associated with the transition state. The heats of reaction (AH) and entropies of reaction (AS) for the dehydration of a,a,a-trifluoroacetophenone hydrate and i t s 4-methoxy derivative were determined in sulfolane-water mixtures. AH values range between 7 and 10 kcal/mole and AS values between 19 and 25 e.u. Changes in solvent composition and ketone structure appear to have relatively l i t t l e effect on AH and AS. - iv -TABLE OF CONTENTS Page INTRODUCTION 1 A. Historical Interest 1 B. Investigations into the Equilibria of Hydration ... 2 1. Experimental Methods 2 2. Results 9 C. Investigations into the Kinetics of Hydration 12 1. Experimental Methods 12 2. Results 15 D. Dipolar Aprotic Solvents 21 E. Acidity Functions in Dipolar Aprotic Solvents 23 OBJECT OF THE PRESENT STUDY 27 METHODS OF APPROACH 28 EXPERIMENTAL 29 A. Purification of Compounds ... . 29 B. Preparation of Compounds 29 C. Purification of Solvents . 34 D. Preparation of Solvent-Water Mixtures 35 E. Equilibrium Measurements by N.M.R. Spectroscopy.... 36 F. Equilibrium and Kinetic Measurements by U.V. Spectroscopy 39 G. Treatment of Data 43 1. N.M.R. Data • 43 2. U.V. Data 43 (a) Equilibrium Studies 43 (b) Kinetic Studies 45 - v -Page RESULTS 48 A. The W Function ... 48 o B. U.V. and N.M.R. Spectroscopy for Equilibrium Studies of Hydration 50 C. The Equilibria of Ketones in Sulfolane-Water Mixtures 55 1. Results 55 2. Errors .... 72 D. The Equilibria of Ketones in DMSO-Water Mixtures... 73 E. Equilibria of s-Dichloroacetone in Dioxane-Water and Acetonitrile-Water Mixtures ................... 79 F. Heat of Reaction and Entropy of Reaction in Sulfolane-Water Mixtures 79 G. The Kinetic Treatment of Hydration in Dipolar Aprotic Solvents , 84 1. The Spontaneous Reaction 85 2. The Hydrogen-Ion Catalyzed Reaction 88 (a) Kinetic Treatment .. 88 (b) Effect of Acid"on the Forward and Reverse Rate Constants 89 H. Kinetics of Hydration in Sulfolane-Water Mixtures Containing no Acid 92 I. Kinetics of Hydration in Sulfolane-Water Mixtures Containing Varying Amounts of Methanesulfonic Acid. 96 1. Kinetics of Hydration . ... 96 2. Determination of Acidity 100 3. Analysis of Kinetic Results 101 - v i -Page DISCUSSION . 104 A. U.V. and N.M.R. Spectroscopy for Hydration Studies. 104 B. Validity of the W Function ". . 106 J o C. A Comparison of pK^ Values . . 108 D. A Comparison of W q Scales I l l E. The W Function in Sulfolane-Water 114 o F. - The W Function in DMSO-Water 124 o G. Heat of Reaction and Entropy of Reaction in Sulfolane-Water Mixtures 129 H. Kinetics of the Spontaneous Hydration Reaction in Sulf olane-Water Mixtures 131 I. Kinetics of the Hydrogen-Ion Catalyzed Hydration Reaction in Sulfolane-Water Mixtures 137 SUGGESTIONS FOR FURTHER RESEARCH . . . . 141 Appendix I: Computer Program for the Calculation of Mole Percentages Water in Solvent-Water Mixtures 143 Appendix II: Ultraviolet Data for a,a,a-Trifluoroaceto-phenone and Derviatives 144 BIBLIOGRAPHY . 145 - v i i -LIST OF TABLES Table Page I Rate Constants for Hydration of Some Carbonyl Compounds 16 II Test of Repr o d u c i b i l i t y of N.M.R. Results 52 III N.M.R. Results: Experimental Values of log [Z]/[ZH 0] for the A r y l Substituted a,a,cx-Trif luoroacetophenones i n Sulfolane-Water (0.1 molar methanesulfonic acid present) 57 IV U.V. Results: Experimental Values of log [Z]/.[ZH20] for the A r y l Substituted a,a,a-Trifluoroacetophenones i n Sulf olane-Water (no acid present) 61 V U.V. Results: Experimental Values of log [Z]/[ZH 0.]' fo r 4-CHo0C^H.C0CFo i n Sulfolane-Water (0.1 molar 3 6 4 3 methanesulfonic acid present) 61 VI The pK d Values of the Ketones Used to E s t a b l i s h the W Scale i n Sulf olane-Water 65 o VII Least Squares Data for Plots of log [Z]/[ZH 0] versus W for X-C,H.C0CFo i n Sulfolane-Water 65 o 6 4 3 VIII W q Values f o r the System Sulfolane-Water Containing 0.1 molar Methanesulf onic Acid 66 IX U.V. Results: Experimental Values of log [Z]/[ZH 0] for s-Dichloroacetone i n Sulfolane-Water (0.1 molar methanesulfonic acid present) 70 X Least Squares Data for a Plot of log [Z]/[ZH 0] versus W for s-Dichloroacetone i n Sulfolane-Water 72 o XI Experimental Values of log [Z.]/[ZH20] for Substituted a,a,a-Trifluoroacetophenones i n DMSO-Water Mixtures.... 74 XII W Values for the System DMSO-Water 76 o - v i i i -Table Page XIII Least Squares Data for Plots of log [Z]/[ZH20] versus W for X-C,H,COCF., in DMSO-Water 79 o 6 4 3 XIV Experimental Values of log [Z]/[ZH 0] for s-Dichloro-acetone in Dioxane-Water and Acetonitrile-Water Mixtures Plus the Calculated W Values Based on pK, = 0.674 80 o d -XV Heat of Reaction and Entropy of Reaction for the Dehydration of 4-CH30C6H4C(OH)2CF3 and CgH C(0H) CF 3 in Sulfolane-Water Mixtures 83 XVI Rate Constants, k , , for the Hydration of 4-CH.OC,H.C0CFo obs J 3 6-4 3 in Sulfolane-Water Mixtures (no acid present) . .. 94 XVII Analysis of Rate Constants for the Hydration of 4-CH_0C,H.C0CFo in Sulfolane-Water Mixtures Where No 3 6 4 3 Acid was Present 95 XVIII Rate Constants, k. ^  and k^+, for the Hydration of 4-CHo0C,H.C0CFn in Sulfolane-Water Mixtures Containing 3 6 4 3 Varying Amounts of Methanesulfonic Acid 98 XIX Average Acidity (h ) of Sulfolane-Water Mixtures o Containing Various Amounts of Methanesulfonic Acid .... 102 XX Analysis of Rate Constants for the Hydration of 4-CHo0C,H.C0CFo in Sulfolane-Water Mixtures Containing 3 6 4 3 Methanesulf onic Acid .... 103 XXI Analysis of the W q Function in Sulfolane-Water 115 XXII Analysis of the W^  Function in Sulfolane-Water 121 XXIII Analysis of the Wq Function in DMSO-Water 126 XXIV Thermodynamic Parameters for the Hydration of Carbonyl Compounds at 25°C 130 - i x -LIST OF FIGURES Figure Page 1 Test of Reproducibility of N.M.R. Results (two independent determinations of ^ CH^OC^H^COCF^ i n sulf olane-water) 53 2 Test of Reproducibility of N.M.R. Results (two separate determinations of solutions of A-CH^CgH^COCF^ i n sulfolane-water) 54 3 Comparison of U.V. and N.M.R. Results for 4-CH3OC6H4COCF3 . i n DMSO-Water Solutions 56 .4 Plots of log [Z]/[ZH 0] versus Mole % Water for Substituted a,a,a-Trifluoroacetophenones i n Sulfolane-Water Mixtures 59 5 Plots of log [Z]/[ZH 0] versus Mole % Water for 4-(CHn)nNC,H.C0CF. and 4-CHo0C,H.C0CFo i n Sulfolane-3 2 6 4 3 3 6 4 3 Water Mixtures (no acid present) 62 6 Effect of Acid on Equilibrium Results for 4-CH 0C,H.C0CFo 3 6 4 3 i n Sulf olane-Water Mixtures 63 7 Plot of W versus Mole % Water for Sulfolane-Water o Mixtures Using Substituted a , a , a - T r i f l u o r o a c e t o -phenones as Indicators 67 8 Plot of log [Z]/[ZH 0] versus W q for Substituted a ,a ,a-Trifluoroacetophenones i n Sulfolane-Water Mixtures 69 9 Plot of log [Z]/[ZH 0] versus Wq for s-Dichloro-acetone i n Sulfolane-Water Mixtures 71 - x -Figure Page 10 Plots of log [Z]/[ZH 0] versus Mole % Water for X-C,H,C0CF_ in DMSO-Water Mixtures 75 6 4 3 11 Plot of W versus Mole % Water for DMSO-Water o Mixtures Using Substituted a,a,a-Trifluoroacetophehones as Indicators 77 12 Plot of log [Z]/[ZH.O] versus W for X-C^H.C0CFo in I o 6 4 J DMSO-Water Mixtures 78 13 Plot of W versus Mole % Water Using s-Dichloroacetone o ° as Indicator for Dioxane-Water and Acetonitrile-Water Mixtures 81 14 Typical Rate Plot: Kinetics of the Hydration of 4-CHo0C,H.C0CFo in a Sulfolane-Water Mixture Contain-3 6 4 3 ing 65.02. Mole % Water 93 15 Typical Rate Plot:. Kinetics of the Hydration of 4-CH„0C,H.C0CFo in a Sulfolane-Water Mixture Contain-3 6 4 3 ing 49.51 Mole % Water and .04874 molar Methane-sulf onic Acid . 97 16 Hammett Correlation of Equilibrium Constants for the Dehydration of Substituted a,a,a-Trifluoroaceto-phenone Hydrates 109 17 Plot of W versus Mole % Water for Sulfolane-Water o and DMSO-Water Mixtures Using a,a,a-Trifluoroaceto-phenones as Indicators • .. 112 18 Plot of W versus Mole % Water for Sulfolane-Water, o Acetonitrile-Water and Dioxane-Water Mixtures Using s-Dichloroacetone as Indicator 113 - x i -Figure Page 19 Plot of f I T rtf„/f_„ . versus Mole % Water for "2 Z 2 Sulfolane-Water Mixtures Using a , a , a-Trifluoroaceto-phenones as Indicators 117 20 Plot of f f / f versus Mole % Water f or H 2 0 Z Z n ^ C J Sulfolane-Water Mixtures Using s-Dichloroacetone as Indicator 122 21 Plot of A c t i v i t y of Water versus Mole % Water f or Sulfolane-Water and DMSO-Water Mixtures 123 22 Plot of f H 0 f z / f Z H 0 versus Mole % Water f or DMSO-Water Mixtures Using a,a,a-Trifluoroacetophenones as Indicators 127 23 Plot of w versus Mole % Water for DMSO-Water Mixtures o 24 Using a,a,a-Trifluoroacetophenones as Indicators.... 128 Plot of log versus log [R^O] for the Water-Catalyzed Hydration of 4-CUjOC H^COG^ •. . 134 25 Plot of log versus log [H^O] for the Water-Catalyzed Hydration of 4-CH 3OC 6H 4COCF 3 135 - x i i -To you i t is given to know the mysteries Luke 8:10 - • x i i i -ACKNOWLEDGEMENT The author is indebted to Professor Ross Stewart for his suggestion of this project and his patience, guidance and encouragement throughout this work. Gratitude is extended to Dr. John M. McAndless for suggestions made during the preparation of this thesis. The technical assistance of Mr. Roland Burton is acknowledged. The generous financial assistance of the H.R. MacMillan Foundation and the National Research Council is gratefully acknowledged. INTRODUCTION A. H i s t o r i c a l Interest The study of the hydration of aldehydes and ketones has been gaining momentum ever since Ramsay and Young discovered that acetaldehyde and water mix with considerable heat and diminution of volume."'" 2 Perkin observed that t h i s evolution of heat occurred over a period of several minutes. These observations were a t t r i b u t e d to the formation of a p a r t i c u l a r l y strong association between acetaldehyde and i t s solvent. Whether the association was very strong hydrogen bonding or an actual chemical addition of water to the carbonyl double bond was a 3 matter of some conjecture at that time. Soon a f t e r , Brown and Pickering conducted quantitative experiments on the heat of mixing of aldehydes, 4 and Homfray measured the density of aqueous solutions of these. The r e s u l t s showed that the degree of a s s o c i a t i o n varied with temperature and d i l u t i o n , and indicated that a considerable proportion of aldehyde remained unassociated except where water was i n large excess. Brown and 3 Pickering also observed that heat was evolved more r a p i d l y when ammonia'..was present. This was f i r s t a t t r i b u t e d to the intermediate forma-t i o n of an aldehyde-ammonia complex, but l a t e r r e s u l t s showed that i t was due to c a t a l y s i s by hydroxide ions. With the advent of u l t r a v i o l e t spectroscopy, i t was possible to show that hydration involved a chemical reaction between water and - 2 -5 6 the carbonyl compound, rather than strong hydrogen bonding. Schou ' as well as Herold and Wolf ^  observed that the carbonyl (^C=0) absorption was almost zero in aqueous solution, whereas i t was of normal intensity in non-polar solvents such as hexane. More recently, i t has been possible to isolate certain solid aldehyde and ketone hydrates containing several electronegative substituents. Some d i - and triketone hydrates have also been isolated. The study of these hydrates has added further proof that a chemical bond i s formed between the carbonyl compound and water. In the case of g chloral hydrate, for example, proton magnetic resonance measurements 9 and Raman spectra provide direct evidence for the gem-diol formula CClyCHCOH) . In recent years, the study of hydration has assumed both a scie n t i f i c interest and a practical importance. This is because many investigations of carbonyl group reactions carried out in aqueous media have been affected by hydration of the aldehyde or ketone sample. In addition, studies of the equilibria and kinetics of hydration have increased the knowledge of carbonyl group reactions. The hydration of aldehydes is particularly interesting in this regard because of the simple nature of the reaction and i t s sensitivity to acid-base catalysis. Recently, two excellent reviex^s"*"^'summarizing many important investi-gations have been published on the hydration of aldehydes and ketones. B. Investigations into the Equilibria Of Hydration 1 . Experimental Methods The hydration equilibria of aldehydes and ketones have been studied - 3 -using a variety of techniques. Spectroscopic methods used have included ultraviolet, infrared, nuclear magnetic resonance, and Raman spectroscopy. Other methods including polarography, use of chemical scavengers, cryometry, measurement of the index of refraction, and the measurement of densities have also been employed. Generally, these methods yield results of the same order of magnitude for each compound. The two most widely used methods, ultraviolet (U.V.) and nuclear magnetic resonance (N.M.R.) spectroscopy, have yielded the most reliable results and their use is described herein in more detail. U.V. spectroscopy has been used extensively since Schou^ measured the hydration of acetaldehyde in water. In the U.V. method, the con-centration of free carbonyl compound is measured by means of the n—IT absorbance of the ^C=0 group, which occurs in the neighborhood of 260-300 my. It is assumed that the hydrate does not absorb in this region. This assumption holds f a i r l y well for aliphatic aldehydes and ketones, but care must be taken when applying i t to heteroaromatic aldehydes. For these, -rr-band absorptions of the aromatic ring can * 12 13 appear in the carbonyl region, often masking the weaker n—u band. ' The equilibrium for dehydration may be written as follows: (1) Assuming that the equilibrium is measured under standard conditions, - 4 -i.e. in pure water, the equilibrium constant can be expressed as [carbonyl] [hydrate] .w 'CO (2) .w - E . .W e 'CO o where the terms e and represent the molar extinction coefficients of the carbonyl compound in water measured before and after hydration takes place. Under the usual experimental conditions employed in the U.V. technique, £ W is d i f f i c u l t to measure directly owing to the fast rate 10 15 w of hydration. ' In many studies, e Q was assumed equal to the molar extinction coefficient of the carbonyl compound measured in cyclohexane (e ), based on experiments with acetone (which does not hydrate measurably"*"^). These experiments indicated that the molar extinction coefficient of acetone did not vary from solvent to solvent. "^ More recent work, however, has shown these observations to be invalid; several examinations of acetone, pinacolone, hexamethylacetone, and some cyclic ketones in a wide range of solvents has resulted in £ values 17-22 which are far from solvent independent. w Many investigators have concerned themselves with determining E Q . Four main methods have been developed. One method used by Bell and In this thesis, the symbols [ ] and x are used to denote concentration on the molar and mole fraction scales, respectively. The term a denotes activity and the activity coefficient f is defined from the relation-ship a = f[ ], except where otherwise specifically noted. - 5 -23 Clunie combines calorimetric data with U.V. spectroscopic data. In this method, the heat of hydration, AH, is determined by calorimetry and compared to the AH calculated from a plot of In vs 1/T according to the equation AH 1 . AS ... l n K d - - -R- T + T 0 ) w The values of used are determined by assuming a value for C q and w measuring e as a function of temperature. By adjusting the value CO W of £ q and assuming i t to be temperature independent, i t is possible to obtain a value of AH equal to that obtained by calorimetric means. The w value of e thus obtained is said to correspond to the true value, o w Using this method, Bell and Clunie calculated c^ = 17.0 for acetaldehyde whereas the value determined in cyclohexane (e ) is equal to 16.2 for the same compound. A second method used to obtain e W has been to choose e W so as to o o produce a linear plot of In vs 1/T. This has proved much less satisfactory, since a large variation in produces only a slight change in the linearity of the relationship. In the case of s-dichloro-acetone, when two markedly different values of (40.7 and 26.0) are used and the calculated "In values are plotted versus 1/T, a good linear dependence (correlation coefficients 0.996 and 0.999, respectively) is w obtained for both values of E q . However, the corresponding values differ by a factor of 1.7. In this thesis, thermodynamic parameters of the hydration reaction are reported assuming that the reaction is written as in equation (1). - 6 -A third, and much more reasonable method in principle, has been 2^\ 25 26 the kinetic method suggested by Herold ' ' and used by Bloch and 27 Rumpf. It can be applied to hydration reactions which are not instantaneous. For these reactions, the term In (A -A^) can be plotted as a function of time according to the relationship In (A.-A ) = ^ln (A -AJ - k t (4) t 0 0 o 0 0 obs which is derived from a f i r s t order kinetic treatment"*"* of the hydration reaction. Here A , A and A refer to the optical density at time o. 0 0 t zero, at equilibrium, and at time t, respectively. Extrapolation back to zero time yields A , from which the equilibrium constant K, = o n d A /(A -A ) can be calculated. co o 0 0 One problem associated with this method is that the reactions are often too fast to obtain satisfactory extrapolations. Accordingly, ways w have been sought to overcome this. Assuming to be temperature 112 independent, the kinetic run can be carried out at lower temperatures 28 111 112 where the hydration rate is slower. ' ' Alternatively, the 28 w hydration can be carried out in D„0. Here the e determined is valid 2 o for the heavy water solvent. A slight solvent correction in going from D^ O to H^ O i s required. A fourth way to obtain has been to correct the extinction coefficient (e) obtained in a non-hydroxylic solvent by using non-hydrating ketones as model compounds. The correction is based on a factor calculated from the variation in e for the model compound 29 obtained in going from the non-hydroxylic solvent to water. Here, one assumes that the optical behaviour of the carbonyl compound studied - 7 -is identical to that of the ketone standard. Greenzaid,Rappoport and 17 Samuel have used this method with great success by plotting the e values obtained in many solvents for two carbonyl compounds against w one another. In general, the result i s a linear relationship. If is known for one of the compounds, an appropriate extrapolation or interpolation w i l l yield for the other compound. Greenzaid et al have shown that the results obtained are much closer to the true ones (as determined by N.M.R.) than those previously obtained. By extending this method, they have also shown that there exists an approximate * c w * linear relation between Ea and e -e , where Ea is the sum of the o aliphatic polar substituent constants. Their work has yielded the most accurate values for determined by U.V. spectroscopy. It must be emphasized that many of the early reported hydration equilibrium constants determined by U.V. spectroscopy are invalid w due to the d i f f i c u l t y in obtaining e^. It is only recently that results have been obtained which approximate those determined by N.M.R. The N.M.R. method of determining the equilibrium constant, K^ , is a much more recent development. Since i t s inception, however, i t has gained acceptance as being the most reliable method for determining K..^'^ Its u t i l i t y depends on the two molecules R.,R„CO and R_R„C(OH)„ d r 1 2 1 2 2 having different N.M.R. spectra due to the change in structure brought about by the addition of water to R^^CO. The advantage of this method is that each species is represented by a different resonance. Thus the calibration which is necessary for most spectroscopic methods is not necessary here. Many hydration studies have already been carried out 30-47,111,114-116 using this method. In the case of acetaldehyde, the proton - 8 -magnetic resonance (P.M.R.) spectrum of the neat compound contains a doublet due to the methyl group and a quartet from the hydrogen of the aldehyde group. Neutral aqueous solutions of acetaldehyde give these same two peaks with reduced intensities and also two additional peaks due to CH 3CH(OH) 2 3 1' 3 2' 3 3' 3 8 a' b By studying the effects of solvents and temperature on the position and intensity of the N.M; R. peaks, i t is possible to assign the peaks to one or the other of the compounds present in solution. In P.M.R., i t is found that the resonance due to protons bonded to the gem-diol carbon atom in the hydrated species i s shifted 4.6 to 5.0 ppm upfield relative to the aldehydic hydrogen in the unhydrated form. Similarly, a-protons in both hydrated aldehydes and ketones are found to be shifted +0.7 to 0.9 ppm relative to the corresponding unhydrated compounds. 3-Protons are also found to shift upon hydration but to a lesser extent (+0.14 to +0.20 ppm). 17 30 Using 0 nuclear magnetic resonance (O.M.R.) , i t is found 17 that the 0 resonances of neat aldehydes and ketones f a l l in the 17 17 range -530 to -595 ppm relative to the 0 peak, while the 0 resonances due to the hydroxyl groups on the hydrate occur near the water resonance (-50 to -70 ppm). Quantitative determinations of by O.M.R. have not been as accurate as those determined by P.M.R., because the "^0 spectra are usually recorded as the derivative of the absorption mode. A disadvantage of the N.M.R.' technique is i t s relative insensitivity compared to U.V. The result is that f a i r l y concentrated solutions of carbonyl compounds must be used. Concentrations usually range in the order of 1 to 3 molar. r-. 9 -2. Results Much of the literature published on the hydration of carbonyl compounds has dealt with perfecting techniques involved in determining the equilibrium constant. Therefore, accurate results are known for only relatively few aldehydes and ketones. Many of these results have been tabulated in the reviews by B e l l " ^ and Le Henaff.^ A comparison of results for various compounds shows a number of factors affecting the equilibria of h y d r a t i o n . ^ E l e c t r o n e g a t i v e substituents reduce the stability of the carbonyl compound and increase i t s reactivity towards water. Bulky groups tend to decrease the stability of the diol by steric strain and thus push the equilibrium towards the carbonyl compound. Any substituent which is conjugated with the carbonyl group stabilizes the carbonyl group against hydration. Hydroxyl substitution on a carbon of an alkyl substituent stabilizes the carbonyl form despite the electronegativity effect of the oxygen. This i s most likely due to intramolecular hydrogen bonding of the hydroxyl proton with the carbonyl. Various attempts have been made to correlate these effects into a..single expression. B e l l " ^ has proposed an expression (see equation (5)) linking polar and steric effects to the equilibrium constant but restricted the correlation to non-conjugated aldehydes and ketones. * It i s based on the polar and steric substituent constants a and E r s derived by T a f t ^ from the rates of acid and alkaline hydrolysis of log K, = 2.70-2.6Ea - 1.3ZE (5) d s - 10 -aliphatic esters. The summations involve both substituents in R^R^CCOH) The methyl group is considered to be the standard (a =0, E = 0). Experimentally, the agreement is f a i r despite the use of the term EE g which sums the steric effects for two groups attached to the same 30 carbon atom, a procedure not normally valid. Greenzaid et al have improved on this correlation by using more accurate values for (determined by P.M.R.). They obtained the following: log Kd = 2.10 - 2.12E0 - 1.12ZE (6) In addition to improving on Bell's correlation, Greenzaid et a l produced another correlation (equation (7)) which they feel represents the hydration reaction more explicitly. It, too, is restricted to non-conjugated aldehydes and ketones. The steric term, EE^, is eliminated, and a parameter, A, which indicates the number of aldehydic protons on the carbonyl compound, is introduced. The basis for this is the assumption that steric effects have a relatively small effect compared to the specific effect of substituting a C-H bond by a C-C bond upon going from aldehydes to ketones. log K d = 2.81 - 1.70Ea - 2.03A (7) Greenzaid's relation appears much more linear than Bell's. An example of this is with pivalaldehyde which has a very large E g and, according to Bell's correlation (equation (6)), should give a log value of 2.03. The experimental value is only 0.6. Much better agreement is - 11 -obtained with Greenzaid's correlation (equation (7)) where the calculated value for log is 0.4. Studies undertaken on aromatic and other conjugated systems have been limited; however, i t has been shown that aromatic carbonyl compounds are affected by polar substituents in the same way that 53 aliphatic ones are. These compounds f a l l on a correlation line lying above and roughly parallel to the one for aliphatic compounds. It is useful to examine some of the other results which have been published on the hydration of carbonyl compounds. The thermodynamic ^ , j • , „ T , N , « , j - 10,12,15,16,28 heat of hydration (AH) has been examined by a number of authors and found to range from 2 kcal/mole for monochloroacetone to 14.6 kcal/mole for formaldehyde."''''"''" The entropy changes (AS) for the dehydration of the hydrates of these same compounds varied from 7.7 e.u. to 30.8 e.u., the relative magnitudes following those of AH. The effect of isotopes on hydration equilibria has also been examined. Gruen and McTigue"''^  have concluded that for five aliphatic aldehydes at 25°C is 16% to 25% smaller in B^O than in ^ 0 , the differences between the various aldehydes being probably within experimental error. This has been ascribed mainly to an entropy effect. The effect of inert solvents on the equilibria of hydration has also been a subject of some interest. In this case, the equilibrium constant, K^ , can no longer be expressed in terms of equation (2). The change in activity of water and the change in the activity coefficients of the carbonyl compound (Z) and hydrate (ZH^O) must also be considered. Therefore, the equilibrium constant is expressed as follows: - 12 -K, [Z] [ZH20] ZH20 [Z] H20 [ZH20] "ZH20 [ H2°- ] fH 20 (8) where f , f and f refer to the activity coefficients of the carbonyl compound, the hydrate, and water, respectively, and a refers H „ ( J 16 54 to the activity of water. Bell and coworkers ' studied the hydration of s-dichloroacetone in dioxane-water mixtures and attempted to calculate the equilibrium constant, K^ , at various solvent compositions. In one approach, they'ignored any change in the ratio f„/f and Z H 2 ° determined from the product of the observed [Z]/[ZB.^O] ratio and a^ Q . The result was values of which varied throughout the solvent range. In another approach, they determined from tie product of [Z]/[ZH 0] and x , the mole fraction of water. The result was a 2 H 20 f a i r l y constant value for at a l l solvent compositions. This last result indicates that the ratio f 1 T *f /f is f a i r l y constant, which r ^ U L Z n 2 U is attributed to the fact that the activity coefficient of the hydrate, containing the group J^C(0H) 2, is similar to that of water, thus leading to cancellation of terms in the equilibrium expression. C. Investigations into the Kinetics of Hydration 1. Experimental Methods There are two phenomena characteristic of hydration that need to be considered when undertaking kinetic studies of hydration. First of a l l , in most instances water is present in large excess, which leads to pseudo-first-order kinetics. Secondly, most techniques measure the approach to equilibrium, and any method which does this yields - 13 -an overall rate constant consisting of the sum of the rate constants for the forward and reverse reactions (i.e. k , = k, + k, ).~^ obs d h The individual rate constants, k^ and k^, are obtained from the equilibrium constant which is equal to k^/k^.^^ Determining the first-order rate constants for hydration reactions is generally less d i f f i c u l t than determining the equilibrium constants, since the first-order nature of the reaction renders i t unnecessary to know the exact amount of carbonyl compound present i n i t i a l l y . A 56 wide variety of methods can thus be used, some of which are dilatometry, • -, _ . 54,63-66 ultraviolet spectroscopy , nuclear magnetic resonance spectro-34,36,38a,b,45-47 , . , . 36,67-70 18_ , 71,72 scopy, chemical scavenging, 0 exchange, 73 58—62 polarography, and a thermal method. A brief description of the more useful methods follows. The dilatometric method was applied by Belland coworkers"^'^ to the hydration of acetaldehyde. Use is made of the fact that a considerable volume change accompanies the hydration reaction. This volume change is measured as a function of time. In applying this method i t has been necessary to slow the reaction to a measurable rate, either by carrying out the reaction at low tempera ture"*^ or 56 by using a solvent pair such as acetone and water. The thermal method can be used for faster reactions, and a method developed by Bell and Clunie"'8 ^ allows reactions with half-lives of a second or less to be measured.^ Here the maximum temperature observed, T , rather than the time, t , at which the maximum ' m m' temperature occurs, is used to determine kinetic rates. For slower 62 reactions, the thermal method can be used in another way. Experimental - 14 -rate constants can be obtained from slopes of plots of log (T^-T ) versus time, where and T refer to temperatures at inf i n i t e time and time t, respectively. 54 63—66 A third technique is U.V. spectroscopy, ' where the rate of reaction i s determined by following the rate of disappearance of the 63 carbonyl absorption. In a detailed study by Bell and Jensen using this method, i t was necessary to slow the reaction to a measurable rate by carrying out the reaction in a mixture of 95% dioxane and water. Although water was present in large excess yielding first-order kinetics, i t was necessary to keep i t s amount accurately constant, since the concentration of water sharply affected the rate of reaction. In several other s t u d i e s ' ^ 3 ' k ' ^ ' ^ using this method, the reaction was carried out at 0°C to allow measurement of the reaction rate. N.M.R. spectroscopy can be used in two ways to determine kinetic 45 rates. For relatively slow reactions (where the h a l f - l i f e for reaction is longer than 1 to 2 minutes), the rate can be determined 46 47 from peak area measurements as a function of time. ' For fast reactions, when the reaction rate (in sec ^ ) exceeds the N.M.R. line width (in rads/sec), line broadening of the N.M.R. signals occurs, A C - l , ' -A-U • . j . 34,36,38a,b,40a,b,45 and from the excess widths i t is possible to derive rates. Use of the chemical scavenger m e t h o d " ^ ^ to determine reaction rates is dependent on the ab i l i t y of a suitable carbonyl reagent (e.g. hydrazine, phenylhydrazine, semicarbazide, hydroxylamine, or bisulfite) to react with the unhydrated carbonyl compound in solution at a rate far in excess of the rate of hydration or dehydration. It is found that the reaction i s independent of the nature and concentrations - 15 -of the reagent, and dependent only on the rate of dehydration of the hydrate. S ince the reaction no longer tends towards equilibrium in this case, only the rate constant for dehydration, k^, is obtained. 2. Results Most of the work undertaken on the kinetics of hydration has been spent on determining the catalytic effects of various acids and bases. It has been established that hydration is subject to general acid and general base catalysis as well as catalysis by hydrogen and hydroxide ions. In addition, there exists a spontaneous reaction that proceeds in the absence of added catalysts. Due to the various catalytic effects, the first-order kinetic rate constant, k , , is the sum of a number of terms, obs kobs " ko + V [ H + ] + k0H- [ 0 H _ ] + W ^ 1 + V [ A _ ] ( 9 ) In equation (9), k^ is the rate constant for the spontaneous reaction, and the symbols, k^+, k - , k^, and k _, represent the catalytic con-stants for hydrogen ions, hydroxyl ions, the general acid HA, and the general base A . Usually, significant proportions of both HA and A are present, and so the system is buffered. The rate constant, k , , is then often represented as follows: obs r + - V kobs = ko + k H + t R ] + k0H- [ 0 H ] + (kHA + IT> ™ ( 1 0 ) where R = [HA]/[A ], the buffer ratio. Bell and Darwent have developed - 16 -a method to obtain a l l the rate constants involved. It consists of running a series of plots of k^g versus [HA]. The buffer ratio, R, i s kept constant for each plot but is varied for each successive plot. An analysis of the slopes and intercepts of the plots gives the various catalytic constants. The magnitude of the catalytic constants involved for three compounds in a series is indicated in Table I. Table I. Rate Constants for Hydration of some Carbonyl Compounds Formaldehyde Acetaldehyde Acetone k +, (M "'"sec ri 5400 560 33 k A c O H ( M " l s e C _ 1 ) 86 0.28 3 x 10~3 k O A c - ( M " l s e C _ 1 ) 44 0.094 0.0 k Q H-(M 1sec 1) 3.2 x 10 6 4.8 x 10 4 110 k (sec "S o 10 4.7 x IO- 3 <? 2 x 10"5 The rate constants are given for the hydration reaction (k^) k See Greenzaid, Luz and Samuel, Trans. Farad. Soc. bk_, 2780 (1968). It is noteworthy that a l l the rate constants decrease in passing from formaldehyde to acetone. This corresponds to the order of sta b i l i t y of the respective hydrates. Thus, for the hydration of carbonyl compounds, rates parallel equilibria, i.e. the more stable the hydrate, the faster i t is formed. Studies of various acid and base catalysts for the hydration of 74 carbonyl compounds show that the Brjzkisted relation, which relates the acidic and basic catalytic constants, k and k^, to the pK of the 0 - 17 -catalyst, is valid over a wide range of pK. In the case of acetaldehyde, the Br0nsted coefficient for acid - catalysis, a, is equal to 0.54; for base catalysis, the Br^nsted coefficient, 3 , is equal to 0.45. The corresponding numbers for formaldehyde are 0.24 and 0.40 and for s-dichloroacetone, they are 0.27 and 0.53. It appears that the coefficient a is more influenced by the structure of the carbonyl compound than is g . This can be partially explained by mechanistic considerations. The mechanisms for acid- and base-catalyzed hydrations listed below were f i r s t suggested by Bell and Higginson"^ and have been , 1 . _ . 10,38a,58,75,76 supported by more recent investigations. Acid Catalysis RoC0 + Ho0 + HB — ^ R„C(0H)0~H„ + B (i) z z — z z + RoC(0H)0H. + B — ^ RoC(0H)„ + HB ( i i ) ( I D Base Catalysis R„C0 + Ho0 + B — ^ RoC(0H)0 + HB ( i i i ) z z ^ — z R„C(0H)0" + HB — ^ RoC(0H)„ + B _ (iv) z ^ — 2. z The rate-limiting steps in these mechanisms are steps (i) and ( i i i ) which involve much greater structural changes than steps ( i i ) and (iv). Both (i) and ( i i i ) are formally termolecular reactions in one direction, and attempts"*^ to reduce them further to two consecutive bimolecular processes leads to predictions which contradict experimental results. Supporting evidence for the mechanism is obtained from solvent deuterium isotope effects in phosphate, diethylmalonate and imidazole buffers. The observed k n values of 1.7-4.2^^a'^ agree with a 2 2 rate-determining proton transfer in HO and a deuteron transfer in DO. - 18 -The behavior of the BrjzJnsted coefficients from one carbonyl compound to another further substantiates the above mechanism. The fact that 3 is less influenced by the structure of the carbonyl compound than is a can be explained i f the catalyzing acid acts on the carbonyl group i t s e l f , while the base catalyst acts on the reacting water molecule. It has recently been suggested by Eigen'''' that a more reasonable mechanism for hydration reactions can be obtained when more than one water molecule is pictured in the transition state. The steps (i) and ( i i ) or ( i i i ) and (iv) can be replaced by a concerted process involving a hydrogen-bonded transition state. The resulting cyclic transition state for the water-catalyzed spontaneous reaction is pictured in Structure I, where i t is assumed that three water molecules are R R ? H - - G T I H present. This mechanistic proposal resulted from estimates of the absolute rates of the individual processes in Equation (11), which in some cases led to impossibly large rate constants for the reverse of reactions (i) and ( i i i ) . 78 Kurz and Coburn have recently obtained evidence which substantiates Eigen's proposed mechanism at least for the water-catalyzed spontaneous pathway. Two anomalies were observed for the water-catalyzed rate term which were not present in the hydrogen-ion and hydroxide-ion catalyzed terms. First of a l l , the Br^nsted correlation for acid catalysis based on carboxylic acids and phenols predicts a value for log k + tl which is within 0.2 of the observed value. Similarly the Br^nsted correlation ' for base catalysis based on carboxylate and phenolate ions predicts a value lying close to the observed value. However, for the water-catalyzed term, the observed value of log k Q is 1.6 units higher than that predicted by the general acid BrjzSnsted correlation and more than 2 units higher than the value predicted by the general base BrjzSnsted correlation. Secondly, the water-catalyzed mechanism t exhibits an extremely low value of AS (-38 e.u.) when compared to the corresponding AS^ values for • hydrogen and hydroxide ion-' catalysis (-4 and -7 e.u., respectively). The very large loss in entropy of activation as well as the anomalous rate for k Q can only be explained by a major reorganization of solvent structure into a more ordered structure in the vic i n i t y of the hydrating molecule. The transition state that Kurz and Coburn suggest is the Eigen-type transi-tion state pictured in Structure I. They also conclude that the reactions catalyzed by'vhydrogen and hydroxide ions do not proceed by an Eigen-type mechanism. The hydrogen-iori catalyzed reaction is presumed to involve a rate-determining proton transfer step while catalysis by hydroxide ions involves simple addition by the hydroxide ion to the carbonyl compound. 54 Bell et a l have recently attempted to obtain direct evidence for the number of water molecules involved in the transition state of the carbonyl hydration reaction by varying the concentration of water dissolved in a non-reactive solvent. Using dioxane and aceto-n i t r i l e as solvents, they investigated the order of reaction with respect to water in the presence and absence of catalysts. They found - 20 -that, for the spontaneous reaction, the orders with respect to water were close to 3 and 2 for the hydration and dehydration reactions, respectively. This strongly suggests that the Eigen-mechanism is followed; the transition state, similar to that in Structure I, would involve the cooperation of two extra water molecules. When catalysts are present, the reaction orders with respect to water are not the same. For instance, when the reaction is catalyzed by triethylamine in aqueous dioxane, the order is approximately 2 and 1 for the hydration and dehydration reactions, respectively. This suggests that the catalyst can replace one of the water molecules in the transition state. Benzoic acid acting as a catalyst causes the order to drop to one and zero for the hydration and dehydration reactions. The simplest explanation here is that the two oxygen atoms of the benzoic acid molecule replace two of the three water molecules in the transition state. It is surprising that the integral orders of 3 and 2 for the water-catalyzed reaction would be maintained for those systems where the concentration of water is such that thermodynamic treatments of both freezing point and vapour pressure measurements reveal large deviations from the laws of dilute solutions. This suggests that as the concentration of water increases, the activity coefficient of 3 the hydrate varies similarly to f . The parallel behavior of the term H2° \ O^-'VIZ^O] i n equilibrium studies implies that the activity coeffic-ient of the hydrate RjT^CCOH^ (referred to zero concentration of water in the same solvent) varies similarly to f^ n . This similarity in behavior::seems reasonable since a l l these species exhibit non-ideal behavior due mainly to hydrogen bonding to other molecules. - 21 -D. Dipolar Aprotic Solvents The usefulness of inert solvents in the study of hydration has been amply demonstrated. By introducing dioxane to an aqueous solution of s-dichloroacetone, the extent of hydration has been reduced from 90% to 70%. In addition, dioxane has been effective in reducing the rates of very rapid reactions. To study more highly hydrated compounds i t would be desirable to investigate solvents which can more efficiently reduce the extent 0 f hydration. Solvents which have potential in this regard are the dipolar aprotic solvents. Dipolar aprotic solvents as a class are distinguishable from those solvents such as water, alcohols and carboxylic acids which can act as proton donors. Dipolar aprotic solvents are characterized by dielectric constants £>15, and dipole moments P > 3D. 79 (arbitrary limits set by A.J. Parker ), as well as an inability to act as proton donors. They are noted for their a b i l i t y to dissolve many inorganic and organic compounds. Examples of this class of solvent are tetramethylene sulfone (sulfolane), dimethyl sulfoxide (DMSO), acetonitrile, nitrobenzene, and hexamethylphosphoramide. Interest in the a b i l i t y of dipolar aprotic solvents to solvate water extensively and thus reduce i t s activity resulted largely from investigations into highly basic systems composed of a dipolar aprotic solvent, a hydroxylic solvent such as water, and a hydroxylic base such as tetramethylammonium hydroxide. The presence of a dipolar aprotic solvent in the system can cause the basicity of the system to rise by as much as fourteen powers of ten over that of aqueous solutions of 80 hydroxide ion. The postulated reason for this is that these solvents compete for the water in the medium and, by doing so, reduce the - 22 -abili t y of water to solvate the hydroxide ion. The result is that the activity of the hydroxide ion increases drastically. The majority of work on highly basic systems has been carried out using the dipolar aprotic solvents sulfolane and DMSO. Both of these solvents are. very effective in increasing the basicity of these media; however, examination of these two solvents reveals very pronounced differences in the manner in which they solvate water. DMSO appears 81 82 to form strong hydrogen bonds with water molecules ' as indicated 79 83 by thermodynamic, dielectric and viscometric data. ' Indeed, the value of the partial heat of mixing of water term at in f i n i t e dilution co 84 AH °°, in DMSO, -1.28 kcal/mole, indicates that the sulfoxide group is w 85 a strong acceptor of protons. Data for the activity of water at 70°C in DMSO-water mixtures show that, as the water content decreases and the DMSO content increases, both the activity of water and the activity coefficient of water, f , steadily decrease. This indicates negative H2° deviations from Raoult's law (AG < 0). Thus DMSO-water interactions are stronger than the intermolecular association of water. It has been suggested that one molecule of DMSO preferentially associates with two molecules of water as shown in II: II However definite complex formation could not be detected by cryoscopic investigations. Sulfolane interacts quite differently with water. vHere the partial CO heat of mixing at in f i n i t e dilution, AH , is +1.6 kcal/mole. The OH. (CH ;>S=0. .H-O-H - 23 -a c t i v i t y c o e f f i c i e n t of water, f , increases rather than decreases H 20 as water i s replaced by sulfolane i n the so l u t i o n . Thus, there are p o s i t i v e deviations from Raoult's law (AG > 0) i n sulfolane-water solutions. Cryoscopic i n v e s t i g a t i o n s of sulfolane-water systems show that ! water i s dimeric over the concentration range 0.01 to 0.1 molal. No evidence can be found f o r the monomer or any higher polymers. 87 A possible structure of the solvent system i s shown i n I I I : / ° H 0 o H^-'' rr Y The preceding treatment has dealt only with the e f f e c t of dipolar aprotic solvents on the a c t i v i t y of water, and"' from these considera-tions alone i t would seem that DMSO i s by far the better solvent to i n h i b i t hydration. However, the e f f e c t of solvents on the a c t i v i t i e s of the carbonyl compound and the hydrate must not be ignored. This i s e s p e c i a l l y important since the presence of two hydroxyl groups i n the hydrate uiakes i t very s e n s i t i v e to changes i n the solvent composition. E. A c i d i t y Functions i n Dipolar Aprotic Solvents The fact that dipolar aprotic solvents are e f f e c t i v e i n increasing the b a s i c i t y of an aqueous hydroxide medium has made i t possible to 88 study the d i s s o c i a t i o n of very weak acids. Using a procedure - 24 -113 developed by Hammett and Deyrup the thermodynamic acid dissociation constants can be obtained, i.e. the dissociation constants related to pure water at in f i n i t e dilution. The application of this treatment to weak acids w i l l be dealt with in the following paragraphs. The dissociation of the Brjzinsted acid HA occurs according to the following equilibrium: HA — ^ H + + A (12) X — and the acid dissociation constant is defined as a H+a A _ [ A - 3 a H + £ A - V " AHA ~ ™ FHA ( } When the negative logarithm is taken of each side of the equation, the following is obtained: PKRA •" ~ L O G THAT " L O S -J—  ( 1 4 ) H A The Hammett acidity function H_ for protonation of a negatively charged base i s defined as H = -log " (15) HA For two acids, HAN and HA0, in the same solution - 25 -[HA 1] [HA 2] fHA x fA 2 The success of the Hammett treatment depends on the l a s t quantity i n equation (16) being zero or, i n other words, on the r a t i o f ^ - / £ j j A i n a given s o l u t i o n being independent of the in d i c a t o r acid. In th i s case, the function H i s also independent of the i n d i c a t o r . This has 89 become known as the Hammett a c t i v i t y c o e f f i c i e n t postulate. In the event that t h i s postulate holds, equation (16) reduces to [HA 1] [HA 2] " p KHA 2 = l 0 S l A j F " 1 0 8 l A p - ( 1 7 ) and the r e l a t i v e pK's for two acids that are p a r t i a l l y ionized i n the same so l u t i o n can be obtained by measuring the two quantities on the rig h t side of equation (17). This i s usually done spectrophotometrically -4 -6 so that concentrations of the in d i c a t o r acid (about 10 to 10 molar) that do not measurably change the medium can be used. If the Hammett postulate holds, then the r e l a t i v e pK's obtained from equation (17) fo r two acids should be the same when measured i n a serie s of solutions of varying a c i d i t y . Consequently, such constancy i n the r e l a t i v e pK's f f -i s regarded as experimental proof that the quantity log HA^ A 2 i s f _ f a c t u a l l y zero. A^ HA2 To determine the thermodynamic pK^'s for several weak acids i t i s necessary to determine the pKj^ for one acid i n d i l u t e aqueous s o l u t i o n where equation (14) reduces to - 26 -P ^ A = - l o s i r k f + P R ( 1 8 ) since f^-> f j j ^ and f^t- a l l approach unity as concentration approaches zero i n aqueous solution. Using r e l a t i v e pK's determined by equation (17), the thermodynamic for a second indicator can be obtained. The procedure can be applied to a t h i r d acid HA^ i f both HA^ and HA^ are p a r t i a l l y ionized i n the same solution. By a choice of indicator acids with suitably spaced pK's the dissociation constants of acids with a wide range of pK's can be determined. This stepwise procedure allows measurement of the dissociation of increasingly Tweaker acids i n increasingly more basic media. From the same measurements of IHA]/[A ] that are used to determine the pK's of the weak indicator acids, the Hammett a c i d i t y function, H_, can be determined for the solutions i n which the measurements were made. Combining equations (14) and (15) we obtain H - = % + C 1 9 ) For an acid that obeys the Hammett postulate i t can be seen from equation 0 -9) that the pK^ of the acid i s equal to the value of H_ for the solution i n which i t i s half ionized. Furthermore, a plot of IA~J log versus H_ gives a straight l i n e of unit slope. OBJECT OF THE PRESENT STUDY This research was undertaken to study the hydration of substituted a,a,a-trifluoroacetophenones. I t i s known that the extent of hydration i n t his series varies over a wide range. For example, no evidence of free unhydrated ketone can be observed i n pure water for the parent compound, cx,a,a-trifluoroacetophenone. For the 4-dimethylamino-substituted compound, however, the extent of hydration i n pure water 90 i s only about 20%. Dipolar aprotic solvents, p a r t i c u l a r l y sulfolane and DMSO, w i l l be used i n an attempt to vary the extent of hydration for these ketones. A Hammett treatment similar to the one applied i n determining the a c i d i t i e s of weakly acidic amines w i l l be applied to the series of substituted a,a,a-trifluoroacetophenones i n an attempt to determine the thermodynamic pK^ values of this complete series. The attainment of the pK^ values for this series w i l l y i e l d insight into two areas. F i r s t , the effect of aromatic substitution on the extent of hydration w i l l be established. Secondly, i f the Hammett treatment i s successful, a function, W , can be developed, which indicates the a b i l i t y of a part i c u l a r dipolar aprotic solvent to reduce the extent of ketone hydration. The ki n e t i c s of hydration w i l l also be examined i n this study with pa r t i c u l a r emphasis placed on the effect of dipolar aprotic solvents. The ki n e t i c s w i l l be carried out both i n the presence and the absence of added acid catalysts. METHODS OF APPROACH Both ultraviolet and nuclear magnetic resonance techniques are useful in the study of equilibria and kinetics of hydration. The 19 i F N.M.R. resonance of the -C-CF^ group should exhibit a chemical shift between the hydrated and unhydrated form. The size of this 91 chemical shift should be larger than the corresponding proton chemical 30 shift which has been shown to be from 0.7 to 0.9 ppm. Ultraviolet spectroscopy can be used in the study by determining the decrease of the carbonyl absorption band under conditions of hydration. Care must be taken to ensure that no n-band absorptions from the aromatic ring l i e near the n—rr band. In addition, for equilibrium studies i t is important that known values for the extinc-tion coefficient of the unhydrated compound in the solvent mixture be used. EXPERIMENTAL A. Purification of Compounds Sublimation as a purification technique was found very useful in the purification of solid compounds. Sublimations were generally carried out at temperatures close to the melting points of the compounds and under o i l pump pressure. Most of the liquid compounds were purified by gas-liquid chromatography. The chromatographic column used for this purpose was an 8 foot by 1/2 inch Apiezon MNW on Chromosorb A Column. Reasonable retention times were generally obtained when the column was heated to 150-175°C, and a flow rate of 75 ml/min was employed. Generally, sample volumes of 0.1 ml were introduced successively into the column. The purity of collected liquid compounds was checked by running the samples on two other chromatographic columns. These were a Carbowax 20 M and a Silicon Gum Rubber Column. In some cases thin layer chromatography was used to check the purity. The identity of the compounds was checked by infrared and nuclear magnetic resonance spectroscopy. B. Preparation of Compounds Many of the compounds used in this study were obtained from commercial sources; the others were prepared by known methods. - 30 -A l l melting points were obtained on a Buchi melting point apparatus and are uncorrected. 1. 4-Dimethylamino-a,a,a-trifluoroacetophenone 3.3 ml (5 gm, 0.0236 moles) of reagent grade trifluoroacetic anhydride were added dropwise over a period of 30 minutes to 6 ml (5.71 gm, 0.0472 moles) ice-cold reagent grade N,N-dimethylaniline. The mixture was stirred vigorously throughout the addition. I n i t i a l l y , the reaction mixture turned a very dark green; then i t formed into a solid mass. The excess N,N-dimethylaniline was fi l t e r e d out and the remaining solid recrystallized from petroleum ether. The solid was then sublimed and recrystallized once again, m.p.: 75.5-77°C ( l i t : 92 75-4°C). Analysis C H F calc. 55.30 4.64 26.24 found 55.39 4.85 25.92 Attempts to carry out the reaction using aluminum trichloride as catalyst were unsuccessful, as the reaction mixture became tarry. 92 A different procedure was previously used to synthesize this compound. 2. 4-Methoxy-a,a,a-trifluoroacetophenone This ketone was obtained from Aldrich Chemicals Co. and purified by gas-liquid chromatography. 3. 4-Methyl-a,a,a-trifluoroacetophenone A crude mixture of this ketone, prepared previously in this 93 laboratory , was purified by gas-liquid chromatography. - 31 -4. 3-Methyl-cx ,a, a - t r i f luoroacetophenone 94 3-Methyl-a,a,a-trifluoroacetophenone was prepared by the reaction of trifluoroacetic acid with 3-tolyl magnesium bromide in an ether 93 solution according to the procedure of Stewart and Van der Linden for the preparation of 4-methyl-a,a,a-trifluoroacetophenone. The product was isolated by fractional d i s t i l l a t i o n and further purified by gas-liquid chromatography. Analysis C H F calc. 57.45 3.75 30.29 found 57.61 3.92 30.05 5. 4-Fluoro-a,a,a-trifluoroacetophenone This ketone was obtained from K.& K Laboratories and purified by gas-liquid chromatography. 6. a,a,a-Trifluoroacetophenone This ketone was obtained from K & K Laboratories and purified by gas-liquid chromatography. 7. 3-Methoxy-a,a,a-trifluoroacetophenone 3-Methoxy-a,a,a-trifluoroacetophenone was prepared by the same Grignard procedure used to prepare 3-methyl-a,a,a-trifluoracetophenone. The product was isolated by fractional d i s t i l l a t i o n (b.p. 60°C at 2 Torr) and further purified by gas-liquid chromatography. Analysis C H F calc; 52.95 3.45 27.92 found 52.74 3.49 28.1 - 32 -8. 3-Fluoro-a,a>a_trifluoroacetophenone This ketone was obtained from K & K Laboratories and purified by gas-liquid chromatography. 9. 3-Nitro-a,a,a -trifluoroacetophenone This ketone, previously prepared in this laboratory by the method 93 of Stewart and Van der Linden, was purified by sublimation. 10. s-Dichloroacetone s-Dichloroacetone was obtained from Eastman Organic Chemicals and 95 purified by sublimation, m.p.: 42-44°C. ( l i t : 45°C). 11. 2-Trifluoromethyl-2-(4'-methoxyphenyl)-l,3-dioxolane (IV) CH9 I 2 H 3 C ° ^ ^ ) V * 2 CF, This compound was prepared by a modification of a procedure for 96 the preparation of cyclic ketals. 1 gm (0.00490 moles) of 4-methoxy-a,a,a~trifluoroacetophenone, 0.78 gm (0.0126 moles) ethylene glycol and 0.22 gm (0.00128 moles) 4-toluenesulfonic acid were heated together at 110°C in a flask fi t t e d with a total reflux separating head. When droplets of water were observed to form in the column, high boiling petroleum ether (60-110°C) was introduced, and the mixture was refluxed for 24 hours. The refluxing was then discontinued and - 33 -0.22 gm sodium acetate was introduced. After stirring for one hour, the solution was fil t e r e d and concentrated. The precipitated crystals were collected and recrystallized twice from petroleum ether, m.p. : 52-3°C. The purity was checked by dissolving the compound in ether and analyzing the solution by gas-liquid chromatography. The identity of the compound was established by I.R. and N.M.R. Analysis C H F calc. 52.23 4.43 22.96 found 53.35 4.63 22.72 12. 4-Methoxyacetophenone This ketone was obtained from Aldrich Organic Chemicals and purified by recrystallization from petroleum ether, m.p.: 38.5-39.5°C ( l i t : 38-9°C). 13. 4-Dimethylaminoacetophenone This ketone was prepared from N,N-dimethylaniline, acetic acid, and 97 phosphoric oxide by the method of Nineham with the following modifica-tion. When attempting to d i s t i l l the crude product, only N,N-dimethyl-aniline could be collected. Therefore, the remaining solid was sublimed. The sublimed material was recrystallized from high-boiling petroleum ether yielding the pure product, m.p.: 105-6°C ( l i t : 103-103.5°C 9 7 (corr.)). - 34 -14. 2,3-Dichloroaniiine This compound was obtained from Aldrich Chemical Co. and purified in this laboratory by D. Dolman. m.p.: 26-26.5°C. 15. 2,4-Dichloroaniline This compound was obtained from Eastman Organic Chemicals and purified in this laboratory by D. Dolman, m.p.: 61.5-62.5°C. 16. 2,5-Dichloroaniline This compound was obtained from Aldrich Chemical Co. and purified in this laboratory by D. Dolman, m.p.: 49-50°C. C. Purification of Solvents Commercial.grade sulfolane, purchased from Shell Development Co., was allowed to stand over sodium hydroxide pellets for two weeks. The liquid which did not solidify at 23°C was poured off. The remaining solid was melted and d i s t i l l e d from powdered sodium hydroxide 87 98 according to the procedure of Langford. ' A large forerun was discarded. The remaining d i s t i l l a t e was stirred i-h a closed vessel over calcium hydride, then d i s t i l l e d at reduced pressure (b.p. 88°C at 0.57 Torr.) using a 34 cm Vigreux Column. The f i r s t and last 10% of the d i s t i l l a t e was discarded. A Perkin Triangle was used to cut fractions allowing nitrogen to be introduced directly on top of the d i s t i l l e d sulfolane. It was found that passing water at 30°C through the water condenser and heating the Perkin Triangle with a heat lamp prevented the sulfolane from solidifying inside the condenser and the - 35 -Perkin Triangle. The purified sulfolane was stored over Fisher Type 4A Molecular Sieves in glass-stoppered flasks. DMSO was purified by d i s t i l l a t i o n from calcium hydride by the 88 method of Dolman. The centre fractions collected were stored over Fisher Type 4A Molecular Sieves in glass-stoppered flasks. Water that was used for preparing sulfolane-water and DMSO-water solutions was d i s t i l l e d before use. Methanesulfonic acid, used as an acid catalyst in this study was obtained from Eastman Organic Chemicals and purified by reduced pressure d i s t i l l a t i o n , b.p.: 115°C at 0.55 Torr. D. Preparation of Solvent-Water Mixtures The following description of the preparation of sulfolane-water mixtures is applicable to the preparation of any other mixture of inert solvent and water. Sulfolane-water mixtures were prepared and stored in ordinary reagent bottles f i t t e d with rubber serum caps which prevented excess moisture from entering the bottles. The bottles were kept in a desiccator. Care was taken hot to splash the solvent mixtures against the rubber serum caps. These rubber caps could be penetrated several times by syringe to withdraw liquid. When preparing solutions, the amounts of sulfolane and water needed to prepare a known volume of solution at the desired composition were f i r s t calculated. The bottles and their stoppers were weighed, and the appropriate amounts of sulfolane were introduced. The bottles were weighed again and the calculated amount of water was introduced. A third weighing was made at this stage. When acid was desired in the - 36 -solution, the amount of methanesulfonic acid required to yield a 0.1 molar solution was introduced and a fi n a l weighing made. The high viscosity of sulfolane made i t d i f f i c u l t to introduce this solvent by syringe. Therefore, a l l additions to the bottles were made by briefly removing the stopper from the bottles. Any variations in the f i n a l composition of the solutions were detected by a Karl Fischer T t i t r a t i o n . Analysis of the solutions by the Karl Fischer method required that the density and the approximate weight percent of the solutions be known. The density was determined by weighing known volumes of each solution using a calibrated syringe. Approximate weight percent values for each solution were determined from the weighing data. An aliquot of each solution was removed using a calibrated syringe (fitted with a Chaney Adapter) and titrated with standardized Karl Fischer Reagent. The mole percentages of water, sulfolane and acid were calculated with the aid of a computer program which employed a loop to correct the approximate value supplied for the weight percent. In this way i t was possible to obtain the correct mole percentages water for solutions which were kept for some time and whose compositions had changed some-what. The computer program is lis t e d in Appendix I. E. Equilibrium Measurements by N.M.R. Spectroscopy Solutions of substituted a ,a ,a-trifluoroacetophenones in various solvent mixtures were prepared in N.M.R. tubes and measured on a Varian 19 HA-100 N.M.R. Spectrometer employing a F variable temperature probe. Concentrations of ketones were approximately 0.1 molar. Solutions of solid ketones were prepared in small vials before being introduced into -37 -the N.M.R. tubes. The solvent mixtures contained 0.1 molar methane-sulfonic acid except where the 4-(CH ) N compound was used. (Here no acid was present, since the dimethylamino group became protonated.) The measurement of the 4-CH^ O compound is described as a typical run. A set of N.M.R. tubes was f i r s t prepared by extending them with 3 inch pieces of Pyrex tubing. These were then cleaned with a chromic acid solution, thoroughly rinsed and dried at 200°C. While hot they were transferred to a nitrogen-flushed dry box and allowed to cool. Tight f i t t i n g plastic caps were placed on each tube. A minimum amount of moisture was thus introduced into the N.M.R. tubes. To introduce the substrate and solution, the caps were briefly removed, and 10 mg A-CH^OC^H^COCF^ (the amount required to give 0.5 ml of a 0.1 molar solution) was introduced by means of a 50 y l syringe equipped with a 6 inch needle. This was followed by 0.5 ml of an appropriate solvent mixture introduced by means of a 2 ml syringe equipped with a 5 inch needle. Care was taken that no liquid came in contact with the top of the N.M.R. tube. Immediately after the solvent was added, the N.M.R. tube was re-capped and the solvent analyzed for i t s water content on the Karl Fischer Aquameter. After a number of N.M.R. tubes were prepared, they were withdrawn from the dry box and sealed with a flame. The sealed N.M.R. tubes were equilibrated at various temperatures for two days. This length of time was well in excess of the time required to achieve equilibration as determined by qualitative kinetic When reference is made to a specific derivative, the aromatic substitution derivative of a,a,a-trifluoroacetophenone i s implied. - 38 -measurements. In most cases, the equilibrating temperature was 19 31.4°C. This corresponds to the temperature maintained by the F spectrometer probe at room temperature as measured by a chromel-alumel thermocouple. To study the temperature dependence of equilibria, the N.M.R. tubes were equilibrated at various temperatures above room temperature. The temperature of the probe was determined in each case by means of the chromel-alumel thermocouple. Measurement was made by removing the N.M.R. tubes one by one from the constant temperature bath and inserting them into the spectro-meter probe. The following settings were required on the HA-100 spectrometer in order that measurement could be made. Output: Max Receiver Gain 2 Sweep Rate 100 x 100 x 1 Frequency Response 5 R.F. Attenuator 70 d.b. Sweep Time 250 sec. The spectrum consisted of two sharp peaks separated by 12.7 ppm. That these peaks corresponded to the -CF^ resonances for the ketone and the hydrate was verified by changing the composition of the solvent. The upfield peak proved to be due to the hydrate. The resonances were easily located in a l l cases by f i r s t adjusting 19 the f i e l d so that i t was centred on the F resonance of CF . J C O 2 H . It was not necessary to spin the N.M.R. tubes as the peaks were very sharp and widely separated. Integrals of the peaks were taken in the forward and reverse directions. This was intended to cancel errors introduced by d r i f t , since i t was d i f f i c u l t to find a suitable standard onto which the N.M.R. spectrometer could be locked. (Spectrometer d r i f t was minimized in a manual fashion.) -Care was taken to ensure that the resonances observed were not saturated. To check that they were not saturated, the amount of power supplied to the R.F. Attenuator was varied. The integrals of the peaks, determined generally six times for each solution (three times in each direction) and then averaged, provide direct indication of the amount of ketone and hydrate present in solution. There was a slight variation in the preparation of solutions containing solid ketones such as 4-(CH„)„NC,H.COCF„ and 3-N0„C,H,COCF^ 3 / 6 4 3 2 6 4 3 Here the appropriate amount of indicator was weighed into small clean glass vials f i t t e d with screw caps. In the dry box, various solvent mixtures were introduced into the vials and the resultant solutions were withdrawn by syringe and introduced into the N.M.R. tubes. In the case of the 4-(CH3)2N compound, where very l i t t l e hydrate was found to be present, time-averaging (28 scans) was carried out in order to obtain the relative proportions of ketone to hydrate. It was found that the ratio of ketone to hydrate obtained by this means very closely approximated the value obtained by U.V. spectroscopy. F. Equilibrium and Kinetic Measurements by U.V. Spectroscopy To undertake measurements by U.V. spectroscopy, a stock solution of the ketone to be studied was prepared, and 30 y l of this solution was - 40 -added to a 1 cm U.V. c e l l containing 2.5 ml of a solvent mixture. Absorbance measurements were made on this solution at the carbonyl absorption maximum. A matched c e l l containing the solvent mixture but no ketone was used as reference. The large extinction coefficients of the ketones necessitated _3 the preparation of a stock solution. Concentrations (2-6 x 10 molar) of these were chosen so that upon dilution into the U.V. c e l l a carbonyl band absorbance of 0.9 to 1.0 would result i f the ketone was unhydrated. To prepare the stock solution, the ketone was weighed directly into a volumetric flask and the correct amount of the inert solvent was added. This was always the same solvent as that used in the solvent-water mixtures. After the ketone dissolved, part of the solution was transferred to a small bottle fi t t e d with a rubber serum cap. When these solutions were not being used, they were stored in a desiccator. Despite the precautions taken, i t was found impossible to totally prevent moisture from entering these solutions; therefore, the stock solutions were seldom kept for longer than two weeks. When acid was desired in the f i n a l mixture, a second stock solution was prepared. This contained methanesulfonic acid dissolved in the same inert solvent. In this case, the concentration varied according to the fi n a l concentration of acid desired in the U.V. c e l l . A l l U.V. measurements were made on a Cary 16 U.V. spectrophotometer equipped with a Cary Sample-Changer Accessory (Model #1641500). An input and outlet line on this accessory allowed the passage of water from a constant temperature bath to control the temperature of the c e l l compartment. The equilibrating temperature of the cells in this c e l l holder was not necessarily equal to that of the constant temperature - 41 -bath. This was particularly true at temperatures above or below room temperature. Thus, the temperature inside the cells was monitored by means of a special c e l l containing polyethylene glycol 400 into which was inserted a standardized chromel-alumel thermocouple. To attain a certain c e l l temperature, the constant temperature bath was adjusted u n t i l the thermocouple registered the desired reading. The f i n a l solutions for measurement were prepared and measured in the following manner. Using a 5 ml syringe equipped with Chaney adapter, approximately 2.5 ml of a solvent mixture (prepared as described in part D) were introduced into two matched 1 cm s i l i c a cells containing ground glass stoppers. The solvent mixtures used . did not contain acid. Therefore, when acid was desired, 10-100 ul of a stock solution containing methanesulfonic acid was added by means of a "Sampljector" (Cole-Parmer) syringe fit t e d with standardized adapters. One c e l l was inserted into the sample beam and the other into the reference beam of the spectrophotometer, and at least 15 minutes were allowed for thermal equilibration. The two cells were electrically balanced at the X of the carbonyl band and 30 ul of J max J the stock solution containing ketone was added to the sample c e l l by means of a Hamilton 50 ul syringe fit t e d with a Chaney adapter. Absorbance readings were taken at various times at the carbonyl absorption maximum. An attempt was always made to obtain absorbance readings as soon as possible after mixing. The reaction was monitored until equilibrium was achieved. The absorbance at equilibrium, A , was noted. After equilibrium had been attained the proportion of water present in the U.V. c e l l was checked by withdrawing an aliquot and - 42 -titrating i t oh • the Karl Fischer Aquameter. This provided an accurate measurement of the water content in the actual solution in which measurements were made. To obtain the ratio of ketone to hydrate in the f i n a l equilibrated solution, i t was necessary to know E q of the ketone in the solvent mixture. For the slower reactions, i t was possible to obtain an absorbance reading closely approximating that of the unhydrated compound. However, when this was not possible, E q was obtained through the use of a model compound (one which did not hydrate). The procedure involved in determining E ^ consisted of f i r s t measuring the carbonyl absorbance of the ketone in 100% inert solvent. This was always done soon after preparing the ketone stock solution so that small amounts of water that might be present would not be able to hydrate the ketone and give an anomalous reading of the ketone absorbance in 100% solvent. (The rate of reaction is slow in 100% solvent.) Then the absorbance of the model compound was measured both in 100% solvent and in the solvent mixture in which E q was desired; the change in absorbance was then noted. Assuming the same relative change to be applicable to the ketone, the ketone absorbance measured in 100% inert solvent was corrected to give E q for the solvent mixture. The relative absorbance of the model compound in the two solvent compositions was readily obtained when a stock solution of this compound was prepared in 100% inert solvent. Thirty ul of this solution was introduced in turn into 2.5 ml of the two solutions to be measured and the relative absorbances measured. When the solvent system contained acid, the acidity of the medium - 43 -was measured by an independent method. Three different amine indicators 88 with known pK + values were used to measure the acidity. Thirty ul of a stock solution containing the amine indicator were added to a portion of the solvent mixture in which hydration experiments were to be carried out. The absorbance measured corresponded to the absorbance of the unprotonated base. Acid was,then added in the same proportions as that used in the hydration studies and the absorbance remeasured. From these measurements, i t was possible to determine the relative amounts of unprotonated and protonated amine present in the solution and from this to determine the acidity of the medium. G. Treatment of Data 1. N.M.R. Data Using the N.M.R. technique, i t is possible to determine the concentrations of both ketone (Z) and hydrate (ZR^O) directly by measuring the integrals of the respective peaks. I = IZ] [ZH20] (average integral of ketone peak) (average integral of hydrate peak) (20) The hydration data for various indicators have been .recorded in Tables III and XI. In these tables the log [Z]/[ZH 0] values are recorded versus solvent composition. 2. U.V. Data (a) Equilibrium Studies In the U.V. method, the ratio of ketone to hydrate is obtained by - 44 -u t i l i z i n g the following relationship. If the solutions are dilute 99 enough that Beer's law is followed, then i = m = J J L _ ( 2 1 ) where e is the molar extinction coefficient of the unhydrated ketone o at the carbonyl absorption maximum in a specific solvent mixture , e is the molar extinction coefficient, at the same wavelength, 0 0 for the same solution containing an equilibrium mixture of ketone and hydrate. Since the value of e is directly measurable only in solutions o where the kinetics of hydration are slow, the model compound correction was applied in the following manner: e - e'x ) (22) o O S £M s where e is the molar extinction coefficient of the unhydrated ketone o in pure inert solvent at the carbonyl absorption maximum, s is the molar extinction coefficient of the model compound in pure inert solvent at the wavelength of maximum absorption, e,, is the molar extinction coefficient of the model compound in M the solvent mixture at the wavelength of maximum absorption. In most cases, the same ketone stock solution was used to measure both s e (or e ) and e . The molar extinction coefficient, e, was then o o 0 0 replaced by the absorbance A. Similarly, the same stock solution of model - 45 -g compound was used to measure e and e . These could then be replaced by the corresponding absorbances. Hydration data obtained from U.V. measurements have been recorded in Tables IV, V, IX, and XI. Log [Z]/[ZH 0] is once again recorded versus solvent composition. (b) Kinetic Studies The hydration reaction of ketones proceeds to an equilibrium, and therefore the kinetic treatment for opposing reactions is applied. Generally, a reaction of this type is formulated k f B — C (23) ^k and the rate expression becomes = k f[B] - k r[C] (24) If substitution for C is made in terms of B, B and B , where B is o 0 0 o the i n i t i a l amount of B, and B^ is the amount of B present at equilibrium, and the resulting expression is integrated, the following equation is obtained: [B] " [ B J l n <[B .]- [B ] } " " ( k f + \ } t ( 2 5 ) o 0 0 A plot of ln([B] - [B^]) versus time results in a straight line with slope equal to - (k^ + k^), i.e. a slope equal to the negative sum of - 46 -the forward and reverse reaction rate constants. In> the case of hydration, the solvent water enters into the reaction. The reaction i s then formulated k2 Z + H„0 — ^ - ^ ZHo0 (26) k d and the rate expression becomes = k 2[Z][H 20] - k d[ZH 20] (27) where k 2 is the second-order rate constant for the hydration reaction and kj i s the first-order rate constant for the dehydration reaction, d However, since the solvent i s present in large excess, equation (27) reduces to equation (28) = k h[Z] - k d[ZH 20] (28) where k^ is now the pseudo-first-order rate constant for the hydration reaction. In the integrated rate expression, [Z] - [ Z J ^ ( [ z ] _ [ z j ) = - ( \ + k d ) t (29) values of [Z ], [Z^] and [Z] are proportional to the molar extinction coefficients of the solution at zero time, at equilibrium, and at time t. However, these can be replaced by absorbances, A, since the solutions are sufficiently dilute to ensure that Beer's law holds. The - 47 -rate expression i s then given by the equation A - A CO In (• A -A •) = - (k h + k d ) t (30) o CO Thus, a p l o t of In (A - A ) versus time w i l l give a s t r a i g h t l i n e with slope equal to - (k^ + k^) and intercept equal to In (A q - A^). A l l k i n e t i c data were treated i n the above manner. The method of l e a s t squares was employed to obtain the best l i n e . The equations used for t h i s are those given by Jaf f e. "*"<""") RESULTS A. The W Function (3 The application of the Hammett stepwise technique to the hydration of ketones can be carried out in a manner analogous to that applied to the ionization of weakly acidic amines. The equilibrium constant for dehydration, K^ , i s written as K"" ' 4^' v <31) and i f the negative logarithm of each side of the equation is taken the following expression i s obtained: P K d " " l 0 S { z H j d " l 0 g I ^  ' ( 3 2 ) From this, W and w can be defined as follows: o o «0 - - K > « ^ • V l f z w = -f • a H . (34) fZH 0 H2° Thus, for two ketones, Z^ and Z^, in the same solution - 49 -Z l Z2 [ Z 2 ] [ Z 1 ] fZ 2 fZ 1H 20 PKJ " PK, = log ,„ „ n 1 - log r_ „ .-, + log d - d — [Z 2H 20] [ Z ^ O ] ~ * \ * 2 0 \ (35) If the Hammett treatment i s successful for ketones in mixtures of water and dipolar aprotic solvents, the last quantity in equation (35) w i l l be zero regardless of the solvent composition, and equation (35) w i l l reduce to \ z 2 [z 2] [ z 1 ] PK d - pKd = log [ Z ^ Q ] - log f z ^ o j - (36) The relative pK-d's for two ketones that are partially hydrated in the same solution can be obtained by measuring the two quantities on the right-hand side of equation (36). If the thermodynamic pKd value for one ketone i s known, the pKd values for ketones with a wide range of pKd's can be determined depending on how effective the inert solvents are at reducing the extent of hydration. The function, W , i s determined from the same measurements of o [Z]/[ZH20] that are used to cetermine the P K d's of the ketones. From equations (32) and (33) wo = p Kd + l o g i l b ] ( 3 7 ) It can be seen that a plot of log [Z]/[ZH20] versus W q w i l l give a straight line of unit slope. This fact w i l l be used to test the validity of the Hammett postulate for ketones in dipolar aprotic solvents, - 50 -B. U.V. and N.M.R. Spectroscopy for Equilibrium Studies of Hydration Values of log [Z]/[ZH20] were obtained using both N.M.R. and U.V. spectroscopy as described previously. It was necessary to decide which of the two methods was most advantageous to use in each experiment. N.M.R. spectroscopy at the outset appeared to be suitable for a l l of the substituted a, a, a-trifluoroacetophenones (X-C,H,C0CF„); however, O 4 -J solubility problems were encountered at water concentrations greater than 80 mole %, where for many ketones i t became impossible to attain the necessary 0.1 molar solution. In the case of the 4-(CH3)2N compound, values of log [Z]/[ZH20] could not be measured at a l l by N.M.R., since significant amounts of both ketone and hydrate occur only at water concentrations exceeding 80 mole %. U.V. spectroscopy was advantageous in this region because only low concentrations of sample were necessary to allow measurement to be made. However, the use of U.V. for measurement of the hydration equilibria of substituted a,a,a-trifluoroacetophenones was deliberately restricted. For sulfolane-water mixtures, the nethod was confined to the range 80-100 mole % water and to the 4-(CH3>2N and A-CE^O derivatives, since for many compounds the carbonyl absorption lies close to or beyond the cut-off point of sulfolane (220 my), (see Appendix II.) In addition, for many compounds carbonyl absorptions occurring at low wavelengths often are complicated by aromatic absorptions also present in this region. For DMSO-water mixtures, the use of U.V. spectroscopy was also confined to the 4-(CH3)2N and 4-CH^ O compounds; however, U.V. measurements were made in the range 10-100 mole % water. These were checked by comparing them with the N.M.R. results. A check was made of the N.M.R. results to see that they were - 51 -reproducible. Two independent determinations of log [Zj/IZR^O] for the indicator 4-CH^ OC^ H.COCF,, in sulfolane-water mixtures are recorded 3 6 4 3 in Table II A and plotted in Figure 1. Note that both runs yield values f a l l i n g essentially on the same line. In Table II B the results of a second experiment to determine the reproducibility of N.M.R. results are recorded. A series of sulfolane-water solutions containing the indicator 4-CH„C,H.COCF,, were run once on the N.M.R. spectrometer and 3 6 4 3 values of log [Zj/tZH^O] determined. Then they were run once again at a later date. The results for the two runs are plotted in Figure 2. Again the points f a l l essentially on the same line. For U.V. spectroscopy, the procedures used were designed to yield the most accurate results possible. An attempt was made to use model compounds structurally similar to the ketone which was being studied. The model compounds for the 4-CH30 and 4-(CH3)2N compounds were 4-methoxyacetophenone and 4-dimethylaminoacetophenone, respectively. These compounds represent a minimal structural change ; yet, they do not hydrate. For the 4-CH30 compound, an experiment was conducted to see i f any significant t a i l i n g of the small aromatic absorptions at 277 and 271 my lay at 299 my, the position of carbonyl absorbance. For this purpose, the ethylene glycol ketal of 4-CH3OC6H^COCF3 (2-trifluoro-methyl-2-(4'-methoxyphenyl)-l,3-dioxolane) was prepared in order to simulate i t s hydrate (see Structure IV). For the dioxolane compound, zero absorbance was observed at 299 my with retention of absorbance at 277 and 271 my. Thus, i t could be assumed that for the 4-CH30 compound a l l absorbance at 299 my in various solutions was due only to the ketone. For the 4-(CH„)9N compound, the carbonyl absorbance occurs far removed - 52 -Table II. TEST OF REPRODUCIBILITY OF N.M.R. RESULTS A. Two Independent Determinations of 4-CH30CgH4C0CF3 in Sulfolane-Water Mixtures Mole % Water log [Z][ZH20] Mole % Water log [Z]/[ZH20] 2.22 1.220 3.36 1.048 4.09 0.915 4.23 0.940 6.40 0.725 6.38 0.724 7.85 0.594 7.83 0.630 10.01 0.524 9.94 0.520 15.15 0.318 14.20 0.354 19.87 0.152 19.15 0.199 25.12 0.061 23.34 0.104 31.01 -0.023 28.74 -0.003 40.42 -0.212 39.25 -0.188 50.33 -0.321 49.45 -0.290 60.13 -0.362 60.05 -0.370 70.24 -0.446 69.02 -0.421 80.26 -0.526 80.08 -0.500 89.90 -0.559 89.93 -0.599 B. Two Separate Determinations of Solutions of 4-CH3C ,H.C0CFo in 6 4 3 Sulfolane--Water Mixtures log [Z]/[ZH20J Mole % Water Run I Run II . 3.36 0.461 0.465 4.23 0.342 0.318 6.38 0.111 0.146 7.83 0.037 0.048 9.94 -0.100 -0.087 14.20 -0.281 -0.303 19.15 -0.433 -0.449 23.34 -0.550 -0.532 28.74 -0.611 -0.592 39.25 -0.830 -0.793 49.45 -0.910 -0.900 60.05 -0.955 -0.996 69.02 -1.081 -0.991 80.08 -1.092 -1.047 89.93 -1.119 -1.146 Figure 1. Test of Reproducibility of N.M.R. Results - two independent determinations of A-CH^OC^H,COCF in sulfolane-water (shown by X and A). IT) 0 i n m oo o D. I in o . i a . i 0.0 12.5 25.0 37.5 50.D Mole % Water 62.5 75.0 87.5 100.0 ID Figure 2. Test of Reproducibility of N.M.R. Results i ~l 1 1 1 r 1 i 1 1 O.u 12.5 25.0 37.5 50.0 62.5 75.0 87.5 10 Mole % Water - 55 -from the phenyl absorptions rendering i t unnecessary to prepare the comparable ketal. Experimental results determined by U.V. were compared with N.M.R. results wherever possible. In one experiment with the 4-(CHg) compound, 28 time-averaging N.M.R. runs carried out on a weak solution of the ketone in 80 mole % water yielded a value of 15 for [Z]/[ZH 20]. This can be compared to the U.V. result of 14.5 taken from Table IV and Figure 5. Further supporting evidence for the compatibility of the two methods is obtained by comparing the U.V. and N.M.R. results in Tables III and IV. Nearly identical results are obtained in the 80 mole % region for the 4-CH^ O compound in sulfolane-water mixtures. In DMSO-water mixtures this compatibility i s also confirmed. Log [Z]/[ZB.^0] values determined by both U.V. and N.M.R. on the 4-CH^ O compound over a wide range are listed in Table XI and plotted in Figure 3. Even though log IZJ/IZH^O] values less than -1 are plotted, there is a very good correlation between the two methods. Note that the presence of 0. 1 molar acid in the N.M.R. solutions does not affect the correlation. C. The Equilibria of Ketones in Sulfolane-Water Mixtures 1. Results Relative pK^ values of substituted a,a,a-trifluoroacetophenones were obtained by Hammett's method of comparing log [Zj/tZH^O] values of overlapping indicators in the same solution. The log [Zj/fZH^O] values obtained by N.M.R. measurements for a l l ketones in this series except for the 4-(CH,j)2N compound are listed in Table III. For each ketone, thellog [Zj/lZH.O] values were plotted against the solvent CD I ro o . i o C M S3 Nl CM 60 O to i CO a . I 1 in •—g . I Figure 3. Comparison of U.V. and N.M.R. Results for 4-CH OC H COCF in DMSO-Water Solutions (See Table XI). X N.M.R. values (0.1 molar methanesulfonic acid present) A U.V. values (no acid present) O . D Ln 12.5 25.0 — I — 1 37.5 50.0 Mole % Water 62.5 75.0 87.5 100.0 - 57 -Table III. N.M.R. RESULTS Experimental Values of log [Z]/[ZE^O] for the Aryl Substituted a,a,a-Trifluoroacetophenones in Sulfolane-Water (0.1 molar methanesulfonic acid present) Mole % 4-CH30 4-CH3 3-CH3 H 4-F 3-CH30 3-F 3-NO Water 1.05 -0.428 1.24 0.535 0.108 2.13 -0.917 2.17 0.254 -0.246 2.22 1.220 3.13 -1.184 3.36 1.048 0.463 0.086 3.89 -1.324 4.09 0.915 4.23 0.940 0.330 -0.076 4.42 0.025 -0.202 4.71 -0.130 -0.730 4.78 -0.010 -0.258 4.99 -1.440 6.38 0.724 0.129 -0.303 6.40 0.725 6.63 -0.207 -0.418 6.84 -0.331 -0.959 7.83 0.630 0.043 -0.398 7.85 0.594 7.91 -0.261 -0.498 8.12 -0.421 -1.010 9.94 0.520 -0.093 -0.502 10.00 -0.394 -0.633 10.01 0.524 10.29 -0.553 -1.135 14.20 0.354 -0.292 -0.740 14.30 -0.586 -0.810 14.60 -0.757 -1.317 15.15 0.318 19.15 0.199 -0.441 -0.854 19.30 -0.903 19.37 -0.747 19.87 0.152 23.34 0.104 -0.541 -0.955 23.45 -0.836 23.66 -1.034 25.12 0.061 28.47 -0.967 28.74 -0.003 -0.602 -1.027 - 58 -Table III (Continued) Mole % 4-CH30 4-CH3 3-CH3 H 4-F 3-CH30 3SF 3-N02 Water '  28.79 -1.094 31.01 -0.023 39.10 39.25 -0.188 -0.811 -1.208 39.48 -1.108 40.42 -0.212 48.76 -1.268 49.45 -0.290 -0.905 -1.328 50.33 -0.321 60.05 -0.370 -0.975 -1.398 60.13 -0.362 69.02 -0.421 -1.036 70.24 -0.446 80.08 . -0.500 -1.070 80.26 -0.526 89.90 -0.559 89.93 -0.599 -1.132 i n Figure 4. Plots of log[Z]/[ZH 20] versus Mole % Water for Substituted a , a , o t - T r i f l u o r o -acetophenones i n Sulfolane-Water Mixtures (see Table III) - 0.1 molar methanesulfonic acid present - numbers refer to those i n Table VI a 3 50.0 Mole % Water 75.0 100.0 - 60 -composition, and a smooth curve drawn through the points, as indicated in Figure 4. (Note that the curve for the 4-F compound was omitted for the sake of c l a r i t y ) . The numbers on the plots refer to those of the ketones listed in Table VI. Where successive curves overlapped, differences were taken at regular intervals and the results averaged. Wherever possible, differences were taken for log [Zj/tZR^O] values between -1 and +1 corresponding to only that part of the hydration curve for which the ketone is between 10 and 90% hydrated. However, this was impossible for the more highlyi.hydrated ketones, which did not begin to dehydrate unt i l the composition of water f e l l below 10 mole %. The relative pK^ values were determined with the use of equation (36). Since the hydration of the 4-(CH3)N compound could not be measured by N.M.R,, log [Z]/[ZH20] values for both the 4-(CH3)2N and 4-CH^ O compounds were measured by U.V. The experimental values are lis t e d in Table IV and are plotted in Figure 5. ApK^ was determined by taking differences at regular intervals and applying equation (36). Note that these U.V. results were carried out in solutions containing no acid. Therefore, care was taken to ensure that. equilibrium had been reached before any value was recorded. A check was made to see whether the absence of acid would affect the comparing of U.V. and N.M.R. results. The data for the 4-CH^ O compound from Tables IV and V were plotted in Figure 6. It is seen that the presence of 0.1 molar acid does not affect the correlation between these two runs. The reference ketone, the one for which the thermodynamic pK^ is known,was 4-CH3OCgH^COCF3. An average pK^ value determined by U.V. spectroscopy was 0.84. The determination was made by diluting 30 ul. - 61 -Table IV. U.V. RESULTS Experimental Values of log [Z]/[ZH20] for the Aryl Substituted a,a 5a _ Trifluoroacetophenones in Sulfolane-Water (no acid present) 4-(CH ) N 4-CH30 Mole % Water log [Z]/[ZH20] Mole % Water log [Z]/[ZH20] 79.59 1.161 79.59 -0.520 81.73 1.159 81.86 0^.530 83.52 1.140 82.80 -0.552 85.55 1.130 84.17 -0.569 87.13 1.101 87.56 -0.598 89.87 1.066 ' 89.75 -0.631 90.42 1.042 90.42 -0.646 91.53 1.033 91.80 -0.670 92.82 1.025 92.38 -0.677 93.20 1.008 93.25 -0.699 95.17 0.977 94.52 -0.740 95.77 0.961 95.68 -0.763 96.73 0.919 96.78 -0.774 97.83 0.822 97.83 -0.837 98.73 0.833 98.19 -0.825 Table V. U.V. RESULTS Experimental Values of log [Z]/[ZH20] for 4-CH30C6H4C0CF3 in Sulfolane-Water (0.1 molar methanesulfonic acid present). Mole % Water log [Z]/[ZH 0] 79.54 -0.514 81.81 -0.525 82.75 -0.544 84.12 -0.558 87.51 -0.596 89.71 -0.626 90.38 -0.638 91.76 -0.661 92.34 -0.677 93.20 -0.690 94.48 -0.730 95.64 -0.771 96.74 -0.781 97.79 -0.829 98.15 -0.822 rsi i o o ID D . i rvi T—t . s I Figure 5. 75.0 PlotSBof log [Z]/[ZH 0] versus Mole % Water for 4-(CH3>2NC6H4COCF3 (1) and 4-CHo0C,H,C0CFn (2) in Sulfolane-Water Mixtures (See Table IV). 3 6 4 3 - no acid present ~&~ ~A A-79.0 82.0 — i r 85.0 88.0 Mole % Water 31.0 34.0 37.0 100.0 ID O CN 33 Ml O O. 1 in in o . i LD Q . I i n ID o . ] CD . I i n r -D . I oo o . I 7 6 . 0 Figure 6 E f f e c t of Acid on Equilibrium Results f or 4-CH_0C,H.C0CF„ 3 6 4 3 i n Sulfolane-Water Mixtures (see Tables IV and V) X no acid present A 0 .1 molar methanesulfonic acid present 7 9 . 0 8 2 . 0 i r 8 5 . 0 6JI .0 Mole % Water 9 1 . 0 9 4 . 0 9 7 . 0 ON LO 1 0 0 . 0 - 64 -of a stock solution of this ketone in 20% sulfolane with 2.5 ml water. The resulting solution was 99.90 mole % water. This procedure was carried out six times. In each case, the Cary 16 U.V. spectrophotometer was used to obtain E . Experiments were conducted to extrapolate the pK^ value obtained in 99.90 mole % water to pure water. In each case the difference between the extrapolated value and the value observed in 99.90 mole % water was less than 0.003. Thus the pK^ value of 0.84 is valid for pure water. The model compound 4-methoxy-acetophenone was used to obtain e^. The validity of the value 0.84 in water is thus somewhat dependent upon the accuracy of the model compound correction. However, the good agreement obtained between U.V. and N.M.R. results in other solutions indicates that this value is likely to be f a i r l y accurate. Thus, this pK^ value was used in conjunction with the relative pK values of the other,ketone indicators to calculate their thermodynamic pK^ values. Table VI l i s t s the indicators used to establish the W scale as well as their pK, values o r d obtained in this work. The W values for the sulfolane-water mixtures were then o calculated from the pK^ values of the ketones listed in Table VI and the values of log [Zj/IZH^OJ obtained from Figures 4 and 5, using equation C37). W q values were calculated at those integral values of -mole'% water where several log [Zj/tZH^O] determinations had been made. Table VIII l i s t s the average W q values for the sulfolane-water •mixtures determined with substituted a ,a ,a-trifluoroacetophenones. Each value is generally an.average value obtained from two or more ketone indicators. The standard deviation of the individual values - 65 -Table VI. The pK Values of the Ketones (X-C H COCFj Used to Establish s W o Scale in Sulfolane--Water X P Kd 1. 4-(CH3)2N -0.86 2. 4-CH30 0.84 3. 4-CH3 1.46 4. 3-CH3 1.77 5. H 1.89 6. 4-F 1.91 7. 3-CH30 1.99 8. 3-F 2.50 9. 3-N02 3.15 Table VII. Least Squares Data for Plots of log [Z]/[ZH20] versus W for X-C,H.C0CFo in Sulfolane-Water o 6 4 3 Error X Slope in Slope Intercept P Rd 1. 4-(CH3)2N 1.01 + .04 0.85 -0.85 2. 4-CH30 0.97 + .01 -0.82 0.82 3. 4-CH3 0.98 + .01 -1.44 1.44 4. 3-CH3 1.02 + .01 -1.79 1.79 5. H 0.99 + .01 -1.87 1.87 6. 4-F 0.97 + .03 -1.89 "•1.89 7. 3-CH3 0.99 + .02 -1.98 1.98 8. 3-F 1.01 + .01 -2.51 2.51 9. 3-N02 1.02 + .02 -3.21 3.21 - 66 -Table VIII. W q Values for the System Sulfolane-Water Containing 0.1 molar Methanesulfonic Acid. Mole % W Value Standard Deviation Ketone Water from the Mean Indicator 1.05 2.72 - 9 2.0 2.31 - 8,9 3.0 2.03 .025 6,8,9 4.0 1.83 .025 3,5,8,9 6.0 1.63 .021 2-8 8.0 1.48 .017 2-8 10.0 1.36 .008 2-8 15.0 1.16 .01 2-7 20.0 1.00 .01 2T6 25.0 0.90 .008 2-5 '30.0 0.81 .01 2-4 .40.0 0.66 .01 2,3 50.0 0.55 .01 2,3 60.0 0.47 - 2,3 70.0 0.41 .014 2,3 80.0 0.31 .014 1,2 85.0 0.27 .005 1,2 90.0 0.21 .01 1,2 95.0 0.12 .01 1,2 100.0 1 0 (by definition) The presence of 0.1 molar methanesulfonic acid does not affect the value of WQ at solvent compositionsccontaining greater than 10 mole % water; however, when the water composition is lower than this, i t is likely that the presence of acid affects W . The numbers refer to those in Table VI. o oi' in CM" Figure 7. Plot of Wq versus Mole % Water for Sulfolane-Water Mixtures Using Substituted a,a,a-Trifluoroacetophenones as Indicators (see Table VIII) o CM' in in CD ' o 0.0 , 12.5 25.0 _! | 37.5 50.0 62.5 Mole % Water 75.0 87.5 ON 100.0 - 68 -from the mean is also given as well as the indicators used to determine the for a particular solution. Figure 7 shows the graphical representation of the adata in Table VIII. It can be seen from a plot of W versus solvent composition that W rises as water is r o r o removed from the medium. At either end of the concentration scale, i.e. between 0-10 and 90-100 mole % water, Wq is seen to rise sharply. From equation (37) i t is evident that a plot of log [Zj/tZH^O] versus Wq should give a straight line with unit slope and intercept equal to the pK^ of the ketone. Figure 8 is such a plot for the ketones in Table VI. The W values corresponding to each solvent composition were taken from Figure 7. The slopes and intercepts of these points were determined by least squares f i t t i n g and are listed in Table VII. The nearness of the slopes to unity is a measure of the validity of the Hammett technique as applied to the hydration of substituted a,a ,a-trifluoroacetophenones inssulfolane-water mixtures. The hydration equilibria of the ketone s-dichloroacetone were studied in sulfolane-water mixtures, but this ketone was not used to establish the W scale. Rather, measurements were carried out o ' primarily to detect whether the Wq scale based on substituted a , a , a -trifluoroacetophenones is applicable to other ketones, particularly aliphatic ketones. U.V. spectroscopy was used to measure the concentra-tion of this ketone in sulfolane-water mixtures, but no model compound was used to correct for any change in E q in going from sulfolane to water. The reason is the following. In 100% sulfolane £ q was measured 7 times, and the average yalue was found to be 26.0. Greenzaid et al^ have recently determined e in water for s-dichloroacetone to - 70 -be 26 ± 1. In kinetic attempts to extrapolate to zero time for solutions containing up to 25 mole % water in this work, the value of 26 1 1 was consistently obtained. Thus, for s-dichloroacetone was assumed to be equal to 26 for a l l sulfolane-water mixtures. The experimental values of log [Zj/fZH^O] determined at various compositions for this ketone are listed in Table IX along with Wq values taken from Figure 7 corresponding to these compositions. The log [Zj/fZH^O] values are plotted versus Wq in Figure 9 and the least squares data for this plot are listed in Table X. The nearness of the slope to unity indicates whether the Wq scale can be applied to s-dichloroacetone. The pK^ value for s-dichloroacetone lis t e d in Table X was estimated from the W value of the solution for which equal amounts of ketone and o ^ hydrate were present. This is easily obtained from the intercept of a plot of log JZj/JZH OJ versus W . The literature, value for pK, is also / O a listed. Table IX. U.V. RESULTS Experimental Values of log [Z]/[ZH 20] for s-Dichloroacetone in Sulfolane-Water (0.1 molar- methanesulf onic acid present) Mole % log [Z]/[ZH_0] w0 Water (taken from Fig. 7) 11.56 0.937 1.29 16.68 0.759 1.10 21.02 0.652 0.98' 25.70 0.549 0.88 35.17 0.371 0.73 44.60 0.228 0.61 55.15 00.108 0.51 65.22 -0.003 0.44 74.87 -0.127 0.37 85.22 -0.282 0.27 94.78 -0.523 0.12 99.74 -0.700 - 72 -2. Errors It is d i f f i c u l t to estimate the uncertainty in the W q values for sulfolane-water mixtures and in the pK^ values of the ketone indicators used to determine them. The larger the Wq function becomes, the greater the likelihood of errors because of the stepwise procedure used to establish i t . The errors can be minimized by using a large number of overlapping indicators so that the W q value for a given solution i s not dependent on the data for one indicator, and by using indicators of the same structural type to ensure that the Hammett activity coefficient 89 postulate is obeyed as closely as possible. The pK^ values in this work are recorded to two decimal places. The uncertainty in relative pK^ values for indicators which are less than one pK unit apart is probably ± .01, as determined from A (log[Z]/[ZH^O]) measurements over the complete solvent range. The uncertainty in the thermodynamic pK^ values, however, is li k e l y to be significantly greater than this. This is particularly true of the higher pK^ values. Table X. Least Squares Data for a Plot of log [Z]/[ZH 0] versus W o for s-Dichloroacetone in Sulfolane-Water Slope Error in Slope Intercept p K d ( l i t . ) a 1.24 + .05 -.58 0.58 0.66 a Obtained by interpolation to 31.4°C of results in ref. 17. - 73 -D. The Equilibria of Ketones in DMSO-Water Mixtures The equilibria of hydration in DMSO-water mixtures were determined using the 4-(CH3)2N and 4-CH^ O substituted a, a, a - t r i f luoroacetophenones. The values of log [Z]/[ZH^O] at various solvent compositions are listed in Table XI. These values are plotted in Figure 10. For the 4-011^ 0 compound, the U.V. values are plotted in the region 10-100 mole % water. This is due to the fact that less scatter exists in the U.V. values as compared to the N.M.R. values (see Figure 3). In the region 0-10 mole % water, the N.M.R. values are plotted, since no U.V. values were available in this region. For the 4-(CH3)2N compound, only U.V. values were available; these are plotted in Figure 10. The pK^ of the 4-CH.jO compound was assumed to be 0.84 as before,. Determination of ApK for the 4-CH^ O and 4-(CH3)2N compounds was carried out as for sulfolane-water mixtures. A(log [Zj/IZH^OJ) was found constant only where the water composition was less than 70 mole %. Therefore, ApK for these two ketones was determined with solutions containing less than 70 mole % water. The pK^ value determined for the 4-(CH3;)2N compound was -1.08, a value significantly different from that determined in sulfolane-water mixtures (see Table VI). Using the pK, values for the 4-(CH„)„N and 4-CH„0 compounds, W d 3 z 3 o values were calculated according to equation (37). This led to the W values lis t e d in Table XII. These W values are the result of only o o J two indicators and thus are inherently less accurate than those determined in sulfolane-water mixtures. A plot of W versus mole % r o water in DMSO-water mixtures is given in Figure 11. Log IZj/IZH20i; values for the 4-CH^ O and 4-(CH3)2N compounds are - 74 -Table XI. Experimental Values of log [Z]/IZH20] for Substituted a ,a ,a -Trifluoroacetophenones in DMSO-Water Mixtures 4-CH30 N.M.R. RESULTS (0.1 molar methanesulfonic acid present) Mole % log IZJ/IZH 0] Water 1.02 0.251 1.91 0.023 3.65 -0.253 5.61 -0.436 7.82 -0.542 10.52 -0.670 14.92 -0.824 19.93 -0.928 24.95 -1.025 30.11 -1.046 41.34 -1.244 50.16 -1.244 60.20 -1.222 69.91 -1.137 80.51 -1.125 90.55 -0.935 U.V. RESULTS (no acid present) Mole % log [Z]/[ZH 0] Water z. 10.11 -0.690 18.64 -0.926 29.96 -1.107 39.48 -1.191 49.50 -1.241 59.30 -1.266 68.83 -1.228 78.85 -1.154 89.30 -1.028 99.71 -0.866 4-(CH3)2N U.V. RESULTS (no acid present) Mole % Water 11.01 19.29 29.55 39.36 49.65 59.69 69.15 78.93 89.25 99.71 log [Z]/[ZH20] 1.224 1.017 0.810 0.726 0.691 0.681 0.682 0.675 0.724 0.783 Figure 10. Plots of log [Z]/[ZH 0] versus Mole % Water for X-C H COCF. in DMSO-Water Mixtures (see Table XI) , P 4-(CH3)2N values by U.V. (no acid) x 4-CH^ O values by U.V. (no acid) A 4-CH^ O values by N.M.R. (0.1 molar methanesulfonic acid) 1 r 37.5 50.0 Mole % Water 0.0 12.5 25.0 62.5 75.0 87.5 100 - 76 -plotted versus Wq in Figure 12, and the least squares slopes and intercepts are given in Table XIII. The scatter which exists in the plot for the ^-(CE^)^N compound results from log [Z]/[ZR^O] values obtained at water concentrations exceeding 70 mole % (which were not used to determine W ). These values l i e below the line and reduce o the value of the least squares slope. Table XII. W Values for the System DMS0-Water&' o J Mole % Water W Value o Standard Deviation From the Mean Ketone c Indicator 1.02 1.09 2 5 0.46 - 2 10 0.15 .01 1,2 20 -0.11 .01 1,2 30 -0.27 - 1,2 40 -0.36 .01 1,2 50 -0.40 .01 l',2 60 -0.42 .01 1,2 70 -0.40 .01 1,2 80 -0.31 - 2 90 -0.18 - 2 100 0 (by definition) a With the ketone 4-CH3OC6H4COCF3 no difference in log [Z]/[ZH 0] values exists between N.M.R. values (containing 0.1 molar methanesulfonic acid) and U.V. values (no acid present) for solvent mixtures contain-ing greater than 10 mole % water. k WQ values between 10-100 mole % were determined from U.V. measure-ments; WQ values at 1.02 and 5 mole % water were determined from N.M.R. measurements in the presence of acid. C 1. 4-(CH_)„NC,H.C0CF„ 3 2 6 4 3 2. 4-CH^0C,H,C0CF^ Figure 11. Plot of WQ versus Mole % Water for DMSO-Water Mixtures Using Substituted a,a,a-Trifluoroacetophenones as Indicators x U.V. values (no acid present) A N.M.R. values (0.1 molar methanesulfonic acid present) 0.0 12.5 25.0 i r 37.5 50.0 Mole % Water 62.5 75.0 87.5 100 - 79 -Table XIII. Least Squares Data for Plots of log [Z]/[ZH.O] versus W I o for X-GVH.C0CFo i n DMSO-Water 6 4 3 X Slope Error Intercept pK^ i n Slope 1. 4-(CH 3) 2N 0.82 ±.19 2. 4-CH30 0.99 +.01 -0.82 0.82 E. E q u i l i b r i a of s-Dichloroacetone i n Dioxane-Water and A c e t o n i t r i l e - Water Mixtures Experimental values of log [Z]/[ZH 20] for s-dichloroacetone i n dioxane-water and acetonitrile-water mixtures at 25°C have been obtained from R.P. B e l l . 5 4 ' 1 0 1 These are l i s t e d i n Table XIV along with the calculated W values for dioxane-water and acetonitrile-water mixtures o based on the assumption that pK^ for s-dichloroacetone equals 0.674 (the value of -log [Zj/fZt^O] obtained by B e l l i n pure water^''). The W^  values are plotted versus solvent composition i n Figure 13. I t must be noted that since only one ketone indicator has been used to set up the Wq scale i n these cases, the accuracy of the values w i l l be limited. They w i l l be used only to compare the shape of the Wq function i n dioxane-water and acetonitrile-water to the same i n other solvent mixtures. F. Heat of Reaction and Entropy of Reaction i n Sulfolane-Water Mixtures For the dehydration of a,a,a-trifluoroacetophenone hydrates, the heat of reaction (AH) and the entropy of reaction (AS) can be obtained by applying equation (3) to l n data at different temperatures. In pure water i s easily determined from the ra t i o of concentrations of ketone and hydrate. However, i n solutions composed of water and an inert - 80 -Table XIV. Experimental Values of log [Z]/[ZH20] for s-Dichloroacetone a b in Dioxane-Water Mixtures (no acid present) ' c d Plus the Calculated W Values Based on pK, = 0.674 ' o d Mole % Water log [Z]/IZH20] W o 2.13 1.179 1.85 4.68 0.670 1.34 12.6 0.225 0.90 19.4 0.076 0.75 34.0 -0.119 0.56 49.5 -0.209 0.47 53.7 -0.321 0.35 66.6 -0.420 0.25 82.0 -0.523 0.15 91.4 -0.592 0.08 100.0 -0.674 0 Experimental Values of log IZ]/[ZH 0] for s-Dichloroacetone ~ a b in Acetonitrile-Water Mixtures (no acid present) ' c d Plus the Calculated W Values Based.-on pK, = 0.674 ' o d Mole % log [ZJ/JZH20] WQ Water 20.2 0.428 1.10 22.6 0.335 1.02 28.3 0.407 1.08 42.0 0.019 0.69 53.0 0.057 0.73 55.3 -0.002 0.67 57.5 -0.018 0.66 61.8 -0.031 0.64 Results graciously-furnished by Professor R.P. Bell, k Results determined by U.V. spectroscopy. C:. Based on a value of -0.674 assigned to log [Z]/[ZH20] in 100% HO. d Determined at 25°C. Figure 13. Plot of W versus Mole % Water Using s-Dichloroacetone as Indicator o . - values derived from results furnished by R.P. Bell - x Dioxane-Water Mixtures - A Acetonitrile-Water Mixtures - results determined at 25°C 101 L2.5 37 .5 50.0 Mole % Water 5 2 . 5 1 0 0 - 82 -solvent, K, is the product of this ratio and the term w . Thus, when d r o equations (3), (31) and (33) are combined, the following is obtained: 1 n o [Z] „ = -AH 1 AS . . S [ZH.O] o 2.303R " T 2.303R K ' It i s evident from equation (38) that both log [Z]/[ZH 0] and WQ must be determined as a function of temperature in order to determine AH and AS in mixtures of water and inert solvents. The temperature dependence of Wq in sulfolane-water mixtures was determined by measuring the equilibrium of the 4-CH^ O compound and it s hydrate in solutions ranging from 70-100 mole % water. For a given solution, values of Wq varied by no more than 0.03 units over the range 30-70°C. When log [Zl/tZH^Oj values over the whole solvent range were plotted versus 1/T for this same compound, a linear behavior was obseryed in a l l cases. This, when combined with the previous result, implies that Wq is relatively constant over the whole solvent range. Hence the thermodynamic parameters AH and AS were determined by plotting log [Z]/[ZH20] values versus 1/T yielding slopes s = -AH/2.303R and intercepts r = (AS/2.303R + W ). o The AH and AS values for the 4-CH^ O compound and the unsubstituted compound in various mixtures of sulfolane-water are listed in Table XV'. For the 4-CH^ O compound these values were determined both by N.M.R. and U.V. spectroscopy. For the unsubstituted compound the values were obtained only by N.M.R. It w i l l be noted that the data are considerably more accurate when determined by U.V. spectroscopy. An examination of the data in Table XV shows that AH values range - 83 -Table XV. A. Heat of Reaction and Entropy of Reaction for the Dehydration l of 4-CH-0C,H.C(0H)nCFo In Sulfolane-Water Mixtures J O H z j N.M.R. RESULTS Mole % AH Error AS Error Water (kcal/mole) ' (%) (e.u.) (%) 6.40 7.9 1. 21.8 1. 7.85 8.3 22. 23.4 25. 10.01 8.4 12. 23.8 12. 25.12 9.2 6. 26.3 7. 50.33 9.0 5. 25.5 5. 60.13 8.0 5. 22.5 5. 70.24 7.9 8. 22.0 9. 80.26 8.3 4. 23.1 4. 89.90 7.1 3. 19.8 3. U.V. RESULTS Mole % AH Error AS Error Water (kcal/mole) (%) (e.u.) (%) 68.13 7.1 0.3 19.4 0.3 78.64 7.0 0.3 19.0 0.4 89.40 6.9 0.5 19.0 0.6 99.59 6.7 0.5 18.0 0.6 B. Heat of Reaction and Entropy of Reaction for the Dehydration of C6 H5 C(0H) 2CF 3 in Sulfolane-Water Mixtures N.M.R. RESULTS Mole % AH Error AS Error Water (kcal/mole) (%) (e.u.) (%) 3.27 8.4 4. 19.1 4. 4.13 9.4 3. 22.1 3. 6.24 9.7 4. 23.1 4. 7.66 9.4 5. 22.1 5. 9.73 9.0 7. 21.3 7. 13.92 9.5 8. 22.6 8. 18.80 9.6 4. 23.0 4. 22.97 9.8 5. 23.8 5. 28.35 9.4 3. 22.6 4. 38.73 9.5 3. 22.6 3. 48.86 9.0 8. 21.0 10. 59.36 9.0 3. 21.2 4. 68.56 8.9 14. 20.6 17. 79.47 8.9 7. 20.8 9. 89.46 7.2 9. 16.1 11. - 84 -between 7 and 10 kcal/mole and AS values between 18 and 25 e.u. A change in solvent composition appears to have remarkably l i t t l e effect on AH and AS, with the exception that at higher water concentrations there is a trend towards smaller values for both AH and AS. In addition, no striking difference is observable for values of AH and AS from one ketone to the other. G. The Kinetic Treatment of Hydration in Dipolar Aprotic Solvents The observed rate constant for hydration has been shown to be the sum of several terms (see equation (9)). These terms correspond to a spontaneous reaction mechanism, a hydrogen-or hydroxide-ion catalyzed mechanism, and a general-acid or general-base catalyzed mechanism. Each term is composed of a contribution by the forward (hydration) reaction and the reverse (dehydration) reaction. When these reactions are carried out at the standard state (i.e. in pure water), ^ Q ^ s is easily s p l i t into k^ and k^ by application of the relation: K d = k d/k h (39) In this work, rate constants have been observed for hydration in the absence of acid and in the presence of various concentrations of methanesulfonic acid. Various solvent mixtures have been used. The departure from the standard state by the addition of dipolar aprotic solvents is shown to greatly affect the rates of reaction. In what follows, the kinetic treatment for opposing reactions w i l l be re-applied - 85 -to determine the relation of observed rate constants in solvent mixtures to the standard state. 1. The Spontaneous Reaction In the spontaneous reaction, the hydration reaction is represented by the following scheme: Z + Ho0 ZHLO l — 2 -1 (see equation (26)) The rate of reaction is given by 102 , fZ 3H 0 fZH 0 I r 1 - V z i - r 2 - - k - i [ Z H 2 0 ] — - (40) where -d[Z]/dt i s the rate of reaction, is the second-order rate constant for the forward (hydration) reaction, k_^ the first-order rate f constant for the reverse (dehydration) reaction, and f is the activity coefficient for the transition state. If k = k a , the equation 1 Z H^O reduces to (41) where k^ is now the pseudo-first-order rate constant for the forward (hydration) reaction. Using the relation [ZH 0] = [Z 1 - [Z] z o (42) - 86 -where [Z q] is the amount of Z i n i t i a l l y present and substituting for [ZH^O] as well as gathering terms, the following equation results: ^ = dt f Z k l + fZH 90 k-l fZH,0 k-l C43) ( A 2 — ) [ Z J " — I t I z o ] This equation can be simplified by considering the condition at equilibrium where the rate of reaction becomes zero. In this case, the following equation holds: k f k - l f Z H 0 - T T " [ Z J = — r ~ ( I V - [ Z J > ( 4 4 ) By rearranging the terms in equation (44) the following relationship results: fZH 0 k - l I Z J " I Z o J k f + k f ( 4 5 ) *1 Z -1XZH20 When equation (45) is substituted into (43), equation (46) is obtained. , m f Z k l + fZH„O k-l [zj - [ z j ~f d t <46> Integration of equation (46) yields equation (47) [Z] - [Z .] C f Z k l + fZH 2O k-l } l n [ z j - iz°°] = Tt fc ( 4 7 ) O «= f The observed rate constant is thus - 87 -f Z k l + fZH O k-l k Q b s = -( ) + (48) Note that k , is the sum of a contribution from the forward and obs reverse reactions. To separate k^g into the two contributing terms i t is necessary to rearrange equation (44). When such is done, we obtain [ z 1 - [z ] R f K' = — 2 !L_ = J L ? . ( 4 9 ) [ Z J k-l fZH 20 ( 4 9 > where K* is the ratio of hydrate to ketone at equilibrium in the solvent mixture under study. Application of equation (49) to (48) yields equations (50) and (51). f7 k 1 f7 K' kh = 7r- =7aH2ok2 = k ° b s W ( 5 0 ) fZH.O k-l k, = = k . (-^—) (51) d f t obs K,..+1 Inspection of the preceding two expressions shows that variations which occur in k, and k, when the reaction is carried out in other h d 4- 4-solutions w i l l be due to changes in the ratios a cS If. and f /f H20 Z Zri20 for the hydration and dehydration reactions, respectively. In addition, the rate constants k^ and k^ reduce to k^ and k when the reaction i s carried out at the standard state. Here, equation (49) reduces to K' = V k - i (52) - 88 -where K'' is now equal to 1/K^ . Thus, equations (50) and (51) relate the rate constants for the forward and reverse reactions to the standard state. 2. The Hydrogen-Ion Catalyzed Reaction (a) Kinetic Treatment The treatment of the reaction for the hydrogen-ion catalyzed mechanism i s essentially the same as for the spontaneous mechanism. The difference now is that the reaction is represented as + 3 + Z + Ho0 + H T ZH_0 + H T (53) ¥ — 2 -2 The reaction rate is given by _ d r z 1 fZ aH 0 aH + fZH„O aH + - 1 ^ = k 3[Z] ^ - k_ 2[ZH 20] ^ (54) f TT+ f -4-H H + When the same treatment that was applied to equation (40) is applied to equation (54), the integrated rate expression becomes: [Z] - [ Z J ( fZ k2 + fZH 20 k-2 ) 1 1 1 [Z ] - [ Z J - " aH + A t ( 5 5 ) o 0 0 f J. H where k = k a . Application of equation (49) yields equations (56) / j H2U and (57). f Z a H + K' kH +lV = k2 — f - = kobs ( } ( 5 6 ) H,h. 2 fT obs , H - 89 -= k fZH 2O aH + -2 = k obs K , + 1 (57) (b) Effect of Acid on the Forward and Reverse Rate Constants Because the hydration reactions in this work are not carried out in pure water, the acidity of the medium cannot be accounted for by a simple concentration term. To correct for the acidity, i t would be desirable i f the term a + could be determined in each solution. However, H a + cannot be determined alone; instead, i t must be incorporated into H an acidity function. Because different species are protonated in the forward and reverse reactions, a separate acidity function must be developed for each case. The protonation of the carbonyl oxygen in the hydration reaction is l i k e l y to follow an acidity function based on the following equilibrium: ZH+ — ^ Z + H + (58) ^ The equilibrium constant for such a reaction is Z t t IZH-J £ZH + If the negative logarithm of each side of the equation is taken the following is obtained; - 90 -PK + = -log - log (60) ^ [ZH+] *ZH+ ket ket From this, H , the acidity function for ketone protonation, and h o ' o can be defined as follows: H k C t = -log (61) fZH + ,ket aH + fZ h = ~~?—T- (62) 0 fZH + The dehydration reaction w i l l follow an acidity function based on the following equilibrium: ZH.0+ ^ ZHo0 + H + (63) J ^ 2 The equilibrium constant for this reaction is [ZH 0] aH + fZH 0 K 7 H 0+ = —T- • ~l 4— (64) Z H 3 ° * [-ZH30+] fZH 30 + Taking the negative logarithm of the equation, we obtain [ZH 0] aH + fZH 0 PK 7 H n+ = - log - log — — (65) Z H 3 ° [ZH 30 +] fZH 30 + and H*1^ and h* 1^ for protonation of the hydrate are defined as o o c J , , aH+fZH.O = - log f - (66) fZH 0 + - 91 -a + f , DH ZHO0 and h h y d = (67) F Z H 3 0 + It i s d i f f i c u l t to estimate how closely these two acidity functions w i l l approximate one another, as one function relates to protonation of a carbonyl oxygen whereas the other relates to protonation of a hydroxylic oxygen. Using the derived acidity functions and expressions for and k + , (equations (56) and (57)), the following relationships can H, d be obtained. From equation (56): f 7 a + a„+f„ £'7v& k +, . = k. -^ -5— = k 9 - f - 4 - • (68) H' 1 1 2 -f++, 2 F Z H + f++ If equation (62) is substituted into the above expression, k^+^ becomes V A similar treatment can be applied to equation (57) , and i f equation (67) is used, kg^Kj becomes FZH,0 + u A V d = k 9 j ~ • *h7d (70) It is seen that i f h k e t and h ^ d are kept constant, any changes in o o k +-, and k + -, caused by changing the solution w i l l be due' to changes H , n H , d t t in the ratios aTT „f_TT+/f , and f„TT n+/f . , respectively. It is not H^ O ZH JJ T 3 H + possible to detect changes in the ratios a „f„/f and f /f , by n_U L A. Ztuu TJ ' 2 H 2 ti this method. - 92 -H. Kinetics of Hydration In Sulfolane-Water Mixtures Containing No Acid The hydration of 4-CH-0C,H.COCF„ was observed kinetically in 3 6 4 3 sulfolane-water mixtures ranging from 16.99 to 83.55 mole % water. Treating the absorbance versus time data in the manner previously described for the U.V. method gave very good straight line graphs. A typical rate plot is illustrated in Figure 14. The least squares slopes as well as the correlation-coefficients and student test T values are listed in Table XVI. It was possible to reproduce the values listed quite accurately. The values of k , for the spontaneous reaction are separated into obs the forward and reverse components, k^ and k^, in Table XVII. The formulas used to accomplish this are also listed. Values of K' were obtained for each solvent mixture, by treating the log [Z]/[ZB.^O] data for 4-CH„0C,H.C0CFo listed in Tables III and V. From this data, the 3 6 4 3 corresponding values of [ZH 0]/[Z] were calculated. These were plotted versus the solvent composition, and values of K ' were interpolated from this graph. It should be noted that values of k, and k, decrease steadily as h d the proportion of water decreases. From the preceding kinetic treatment. t the change in k is due to change in the ratio f„u '/f (see equation Cl Zn^U (51)). For k , i t is due to .a decrease in both a and in the ratio n n„U t f ^ / f (see equation (50)). Thus, for comparison with k^ values, values of k, /aTT „ were calculated and are lis t e d along with k, . The h R^O n data for a were obtained from an interpolation of the data published H (J 84 by Benoit and Choux (see Figure 21). i n i I i r I i 1 . 0.0 40.0 80.0 120.0 1C0.0 200.0 240.0 280.0 320 TIME (SEC) - 94 -Table XVI. Rate Constants 3, k , , for the Hydration of 4-CH^ OC^ H,COCF obs J 3 6 4 in Sulfolane-Water Mixtures (no acid present), k Mole % obs Error (%) Correlation Student Water (s e c - 1 x 10^) Coefficient, r Test, T 16.99 0.398 .55 .99927 175 21.80 0.818 .10 .99996 1019 26.28 1.695 .19 .99989 515 30.78 2.987 .21 .99984 477 32.89 3.989 .21 .99983 487 35.94 5.896 .10 .99997 1006 40.27 9.32 .13 .99993 761 45.67 16.44 .11 .99995 896 50.07 26.08 .22 .99981 455 54.53 41.05 .13 .99995 747 60.59 60.5 .21 .99992 . 475 65.02 95.3 .15 .99998 701 69.91 143.3 .15 .99998 667 75.01 238. .59 .99984 167 79.71 390. .54 .99993 186 83.55 553. .30 .99999 348 Si Measured at 31.4°C. \ - 95 -Table XVII. Analysis of Rate Constants for the Hydration of 4-CH„0C,H.C0CFo in Sulfolane-Water Mixtures Where No 3 6 4 3 Acid was Present Mole % Water [ZH.O] k h  C obs k h V a H 2 0 ' k d (x 104) (x 104) (x 104) (x 104) 16.99 0.480 0.54 0.398 0.140 0.291 0.258 21.80 0.560 0.73 0.818 0.345 0.616 0.473 26.28 0.618 0.90 1.695 0.803 1.300 0.892 30.78 0.661 1.10 2.987 1.565 2.368 1.422 32.89 0.686 1.19 3.989 2.166 3.158 1.823 35.94 0.710 1.35 5.896 3.384 4.766 2.512 40.27 0.744 1.58 9.32 5.70 7.67 3.62 45.65 0.781 1.83 16.44 10.64 14.62 5.80 50.07 0.810 2.02 26.08 17.45 21.54 8.63 54.53 0.831 2.16 41.05 28.08 33.79 12.97 60.59 0.864 2.33 60.5 42.4 49.0 18.1 65.02 0.875 2.48 95.3 67.9 77.6 27.4 69.91 0.894 2.70 143.3 104.6 117.0 38.7 75.01 0.904 2.96 238. 178. 196.8 60. 79.71 0.910 3.28 390. 299. 328. 91. 83.55 0.925 3.62 553. 434. 469. 119. a Values of a„ H ^ were obtained from reference 84 . and plotted in b c Figure 21. The values listed were interpolated from Figure 21. Taken from Tables III andVV and Figures 4 and 6. The following relationships should be noted K' , , • 1 k , = k, + k,; k, = k , (— ); k = k (— ) obs ti d' h r.obs d obs „ r , i IS. t l JX T l - 96 -I. Kinetics of Hydration In Sulfolane-Water Mixtures Containing Varying Amounts of Methanesulfonic Acid 1. Kinetics of Hydration Kinetics of hydration for 4-CH„0C,H,COCF„ in various sulfolane-3 6 4 3 water mixtures were carried out in the presence of methanesulfonic -4 acid. Acid concentrations ranged from 9.918 x 10 molar to 9.566 x -2 10 molar. The method used has been described previously. A typical rate plot (Figure 15) shows that very good straight line plots were once again obtained. The least squares slopes as well as the correlation coefficients and student test T values are listed in Table XVIII. The values obtained were very reproducible. Also lis t e d are values of k Q, the observed rate constant for the spontaneous reaction. These are obtained by interpolation of a plot of k^ versus solvent composition using values taken from Table XVI. Using the interpolated values of k , k + (the first-order rate constant for the acid_catalyzed o n mechanism) can be obtained from equation (71). k = k + k + (71) obs o H Known concentrations of acid were obtained by introducing aliquots of a methanesulfonic acid stock solution into the U.V. c e l l . A standardized "Sampljector" syringe was used for this purpose. In several instances, the resulting concentration of acid was checked by titrating an aliquot of this solution with standardized base. In a l l cases, the concentration.-was found to be within 1% of the calculated value. C Q o . I CM t—I . I to t — I I Figure 15. Typical Rate Plot Kinetics of the' Hydration of 4-CH3OP6H4COCF3 in a Sulfolane-Water Mixture Containing 49.51 Mole % Water and .04874 molar Methanesulfonic Acid. vo c r CM. i CM. I CO CM. I CM tn. I 0 . 0 4 0 . 0 SO.O 1 2 0 . 0 1 6 0 . 0 TIME 2 0 0 . 0 (SEC) 2 4 D . 0 2 B 0 . O - 98 -Table XVIII. Rate Constants, k , and k+, for the Hydration of obs H 4-CH^0C,H.C0CF„ in Sulfolane-Water Mixtures Containing 3 6 4 3 Varying Amounts of Methanesulfonic Acid a Mole % k Error Correlation Student k k + Water " ° ^ s (%) Coefficient, Test T - 1 4 - l 4 (sec xlO ), J: (sec xlO ) (sec xlO ) 1. [CH3S03H] = 0.9918 x 10~3 m/1 21.79 1.972 .25 0.99990 433 0.818 1.154 30.39 4.05 .22 0.99987 446 2.86 1.19 39.61 10.05 .09 0.99998 1005 8.80 1.25 49.52 25.44 .16 0.99993 555 24.5 0.9 59.94 62.10 .11 0.99997 834 58.4 3.7 69.39 145.3 .21 0.99997 474 133.4 11.9 2. [CH 3S0 3H] = 4. 888 x :10' 3 m/1 21.56 7.43 .40 0.99968 214 0.79 6.64 30.43 8.80 .23 0.99994 455 2.87 5.93 39.38 14.60 .14 0.99997 711 8.62 5.98 49.28 29.80 .17 0.99994 535 23.9 5.9 59.39 65.5 .15 0.99996 678 56.2 9.3 69.15 149.1 .27 0.99995 358 127.8 21.3 3. [CH 3S0 3H] = 0. 9889 x 10~ 2 m/1 21.68 14.06 .28 0.99987 354 0.80 13.26 30.30 15.64 .13 0.99998 831 2.82 12.82 39.64 20.94 .14 0.99994 648 8.84 12.10 49.71 37.33 .16 0.99996 608 25.0 12.3 59.72 76.71 .09 0.99999 1108 57.4 19.3 69.77 163.3 .25 0.99996 387 141.8 21.5 4. [CH3S03H] = 2. 4602 x 10~ 2 m/1 21.61 34.4 .29 0.. 99985 321 0.79 33.6 30.44 34.8 .29 0.99987 354 2.87 31.9 39.68 40-. 3 .20 . 0.99995 535 8.86 31.4 49.53 57.56 .10 0.99998 1047 24.5 33.1 59.93 98.8 .10 0.99998 777 58.2 40.6 69.83 174. .98 0.99943 103 142.2 32. - 99 -Table XVIII (Continued) a b Mole % Water obs -1 4 (sec xlO ) Error (%) Correlation Coefficient, r Student Test T k o -1 4 (sec xlO ) V (sec 5. [CH3 S03H] = 4.874 x 10"2 m/1 21.43 67.0 .30 0.99981 293 0.79 66.2 30.14 66.2 .15 0.99996 676 2.77 63.4 39.28 71.6 .28 0.99990 387 8.54 63.1 49.51 87.7 .10 0.99998 890 24.5 63.2 58.92 133.0 .30 0.99993 330 54.6 78.4 69.28 216. .74 0.99971 132 130.4 86. 6. [CH3 S03H] = 7.242 x 10"2 m/1 21.20 97.3 .31 0.99990 328 0.75 96.6 29.90 99.6 .20 0.99994 422 2.69 96.9 39.15 101.1 .20 0.99997 586 8.36 92.7 48.96 119.7 .17 0.99997 563 23.1 96.6 59.02 168.6 .30 0.99995 363 54.8 113.8 68.56 259. .54 0.99988 182 119.2 140. 7. [CH3 S03H] = 9.566 x 10"2 m/1 21.02 130. .62 0.99970 168 0.73 129. 29.60 132.3 .38 0.99988 257 2.60 129.7 38.67 132.3 .30 0.99994 363 8.04 124.3 48.79 151.9 .33 0.99992 295 22.6 129.3 58.89 193.3 .26 0.99997 414 54.4 138.9 68.78 290. .97 0.99967 103 122.6 167. k Q values are taken from values in Table XVI interpolated to the water concentration at which k , was measured. obs When acid is present, k , = k + kT,+ . obs o H - 100 -2. Determination of Acidity As indicated, a separate acidity function for both the hydration and dehydration reactions needs to be determined. However, experiment showed this to be impractical. For hydration, i t was not possible to find a ketone which became protonated in the range of acidity used. For dehydration, there i s , i n general, no spectral change accompanying protonation of alcoholic oxygens. For these reasons, a single acidity function was developed based on the protonation of aromatic amines. The acidities of sulfolane-water mixtures containing varying amounts of methanesulfonic acid were measured using the 2,3-, 2,4-and 2,5-dichloroanilines. For these anilines, the pK + values are BH 103 known. The acidity function (h^) for the protonation of aromatic amines which ionize according to equation (72) is defined in equation (73). The [BH+]/[B] ratio was determined in each case by following the BH+ ^ B + H + (72) ho - -ilr ' KBH + <73> decrease in absorbance of unprotonated amine as acid was added. Concentrations of acid measured were 0.02472 molar, 0.04896 molar, 0.0725 molar and 0.09609 molar. These closely approximated the acid concentrations for four of the kinetic runs. For a specific sulfolane-water mixture, the h values determined o at different acid concentrations for each indicator were plotted against [CH^SO^H], From these graphs, values of h Q corresponding to - 101 -the acid concentrations used in the kinetic runs were calculated. These values were averaged for a l l three indicators. The average values of h for methanesulfonic acid in sulfolane-water mixtures are list e d o in Table XIX. Acidities were not determined for the three lowest acid concentrations used to carry out kinetic runs. For these runs, the acidity was too low to accurately determine h Q using the three aniline indicators. 3. Analysis of Kinetic Results In Table XX, the k + values determined at four acid concentrations H are analyzed. F i r s t , k^ + is separated into the forward and reverse components (k +, and k + , ). Values of K' used to accomplish n , n H , Q this were obtained in the same way as described previously. Secondly, each of the and k^+d values i s divided by the h Q value correspond-ing to the concentration of acid and the proportion of water present. These h values were obtained by plotting the h data in Table XIX o J v ° o versus mole % water. A separate line was drawn for each concentration of acid used. The h values used-in Table XX were determined by o J interpolation of these graphs. As in the spontaneous reaction, the forward reaction component contains a contribution from aTT ^ . For comparison with k„+. ,/h , H^ O r H,d. o values of k +, /h a were calculated and are listed along with the I I ) ' ! . O n^\J k„+i /h values. The data for aTT n were once again obtained from an H» n o H„0 84 interpolation of the data published by Benoit and Choux (see Figure 21) It w i l l be noted that values of kTT+, /a„ Ai and kTT+, ./h generally H,n H^ O o H,d o - 102 -Table XIX. Average Acidity (h ) of Sulfolane-Water Mixtures Containing Various Amounts of Methanesulfonic Acid. - acidities determined using the 2,3-, 2,4-, and 2,5-dichloro-substituted anilines Mole % Water Acidity (h Q) 4. [CH3S03H] = 2.4602 x 10 2 m/1 Mole % Water Acidity (h Q) 5. [CH3S03H] = 4.874 x 10 2 m/1 19.72 29.61 39.36 49.21 60.04 70.17 0.00319 0.00192 0.00136 0.00112 0.00104 0.00117 19.55 29.37 39.09 48.90 59.72 69.86 0.00721 0.00397 0.00271 0.00217 0.00201 0.00225 [CH3S03H] = 7.242 x 10 -2 i / l [CH3S03H] = 9.566 x 10 2 m/1 19.38 29.14 38.81 48.60 59.41 69.55 0.01115 0.00598 0.00403 0.00321 0.00297 0.00331 19.21 28.91 38.54 48.30 59.10 69.25 0.01502 0.00796 0.00532 0.00422 0.00391 0.00435 decrease as the proportion of water decreases regardless of the concentration of acid present. According to the transition state + treatment, this i s due to a decrease in the ratios f +/f + and Z H H + f r , T T r , + / f t i + •> i f i t i s assumed that the h values used approximate the Z H 3 U r i o theoretical values h k e t and h* 1^ o o - 103 -Table XX. Analysis of Rate Constants for the Hydration of 4-CH„0C,H.C0CF„ 3 6 4 3 in Sulfolane-Water Mixtures Containing Methanesulfonic Acid. Mole % Water H20 K (xlO 4) (xlO 4) kHth-(xlO 4) kHth kHth  aH 20 ho V d (xlO 4) 4. [CH SO H] = 2.4602 x 10 2 / i m/1 21.61 0.558 0.72 28.9 33.6 14.1 .49 0.87 19. 5 0.68 30.44 0.657 1.08 18.5 31.9 16.6 .90 1.36 15. 3 0.83 39.68 0.741 1.55 13.5 31.4 19.1 1.41 1.92 12. 3 0.92 49.53 0.808 2.00 11.2 33.1 22.1 1.97 2.45 11. 0 0.99 59.93 0.862 2.31 10.4 40.6 28.3 2.72 3.16 12. 3 1.18 69.83 0.893 2.69 11.6 32. 23. 1.98 2.25 9. 0.75 5. [CH SO H] = 4.874 -2 x 10 m/1 21.43 0.555 0.72 63.5 66.2 27.6 .43 0.78 38. 6 0.61 30.14 0.655 1.07 38.4 63.4 32.8 .85 1.30 30. 6 0.80 39.28 0.739 1.53 26.9 63.1 38.2 1.42 1.92 24. 9 0.93 49.51 0.808 1.99 21.0 63.2 42.1 2.00 2.48 21. 1 1.00 58.92 0.856 2.28 20.1 78.4 54.5 2.71 3.17 23. 9 1.19 69.28 0.890 2.67 22.3 86. 63. 2.82 3.12 23. 1.04 6. [CH3 S03H] = 7.242 -2 x 10 m/1 21.20 0.553 0.70 99.2 96.6 39.8 0.40 0.73 56. 8 0.57 29.90 0.653 1.06 57.2 96.9 49.9 0.87 1.34 47. 0 0.82 39.15 0.738 1.52 39.9 92.7 55.9 1.40 1.90 36. 8 0.92 48.96 0.804 1.97 31.9 96.6 64.0 2.00 2.50 32. 6 1.02 59.02 0.857 2.29 29.7 113.8 79.2 2.67 3.11 34. 6 1.16 68.56 0.889 2.64 32.6 140. 101. 3.10 3.49 39. 1.18 7. [CH3 S03H] = 9.566 x 10~2 m/1 21.02 0.550 0.70 : 131.8 129. 53. 0.40 0.73 76. 0.58 29.60 0.650 1.04 76.4 129.7 66.1 0.86 1.33 63. 6 0.83 38.67 0.735 1.50 53.0 124.3 74.6 1.41 1.92 49. 7 0.94 48.79 0.803 1.96 42.0 129.3 85.6 2.04 2.54 43. 7 1.04 58.89 0.856 2.28 39.1 138.9 96.5 2.46 2.88 42. 4 1.08 68.78 0.890 2.65 43.2 167. 121. 2.80 3.15 46. 1.06 b c Values of aTT were obtained from reference 84 and plotted in Figure 21. rl2U The values listed were interpolated from Figure 21. Taken from Tables III and V. Values of h Q are interpolated from plots of h D versus solvent composi-tion for each acid concentration using the data in Table XIX. The following relationships should be noted K -k1T+ = k-K + kT7+ • kTT+, = k (— ); k + H H,h H,d..' 11,h obs K - r + 1 H,dt = k -(-^-) ° b s K'+l DISCUSSION A. U.V. and N.M.R. Spectroscopy for Hydration Studies In terms of log [Z]/[ZH20] values, both N.M.R. and U.V. methods yield comparable results. In general i t i s possible to obtain greater precision by U.V. spectroscopy and better accuracy by N.M.R. spectroscopy. That comparable results are obtained by both methods is indeed satisfying since the accuracy of a U.V. result is always a matter of some question, and one must resort to comparison with N.M.R. results to ensure the validity of a result. The accuracy inherent in the N.M.R. method results from the fact that both hydrated and unhydrated species can be measured together in 19 the same solution. For F N.M.R. spectroscopy, this fact i s particularly pronounced, since large chemical shifts exist between both species; therefore,there i s no interference between resonances of either the ketone or i t s hydrate. By judicious choice of method, the advantages of both U.V. and N.M.R. spectroscopy were utilized in the study of the hydration of ketones. Some of the specific advantages that either of these methods present are now list e d . The N.M.R. method i s advantageous i f one does not know the exact i n i t i a l concentration of the ketone. This results from the fact that the concentrations of both ketone and hydrate are - 105 -measured relative to one another. For this same reason, i t is not as necessary to have the ketone stringently pure as in the U.V. method. An advantage of the U.V. method is the need for only very small concentrations of sample. Thus, no solubility problems are encountered and the character of the solution is not perturbed by the presence of a large amount of ketone. ' Another advantage of U.V. is i t s sensitivity (resulting in greater precision) which allows one to measure ketones hydrated to only a small extent. A further advantage of this method is that the Karl Fischer ti t r a t i o n can be carried out directly on the sample solution. This also allows for greater precision in the results. The choice of catalyzing acid and the model compounds used in U.V. studies require explanation. Methanesulfonic acid was generally used for equilibrium studies in this work. A desirable characteristic of this acid is i t s solubility in both water and dipolar aprotic solvents. In addition, i t does not absorb significantly above 230 my in the U.V. The concentration of acid used (0.1 molar) was chosen .to be great enough to allow fast equilibration between ketone and hydrate. Generally, solutions were, equilibrated in fifteen minutes time. The acetophenones are excellent structural models for the a , a , a -trifluoroacetophenones in that replacement of a fluorine atom by a hydrogen atom does not affect the shape of the molecule due to the small size of the fluorine atom. For this reason, fluorinated cyclo-hexanes have been used as models for conformational studies of cyclo-94 17 hexanes. Greenzaid et al have recently shown that there is a straight line correlation between e values for monochloroacetone and - 1 0 6 -s-dichloroacetone in several solvents. A similar correlation between acetophenones and a,a,a-trifluoroacetophenones is expected. B. Validity of the W Function o The validity of a Wq function can be checked in two ways. One is to show that A(log [Z]/[ZE^0]) values are constant between indicators over a wide range of solvent composition. A second i s to show that plots of log [Z]/[ZE^0] versus Wq yield slopes of unity, as required by equation ( 3 7 ) . In sulfolane-water mixtures, A(log [Z]/[ZU^0]) values were taken at regular intervals of solvent composition for a l l nine indicators used to derive the W scale. Between successive indicators of increasingly o ° J larger pK^ values, the standard deviation of A(log [Zl/CZH^O]) values varied between 0 . 3 3 % and 2 . 7 5 % (except in one case where a standard deviation of 9.1% was observed). The constancy of A(log [Zj/tZH^O]) values over a wide range of solvent composition proves the validity of the W function i n sulfolane-water solutions. The second test for the o validity of this Wq function was applied in Figure 8, and the slopes of the plots are list e d in Table VII. For a l l nine indicators used to set up the W q scale, the slopes of plots of log [Zj/fZH^O] versus are within 3% of unity. This ensures the validity of the W scale in o sulfolane-water mixtures. For s-dichloroacetone, plotting log [Zj/fZH^O] versus Wq for sulfolane-water mixtures yields a slope deviating 2 4 % from unity. This shows that s-dichloroacetone cannot be considered an indicator of the same type as substituted a,a,a-trifluoroacetophenones. More - 107 -generally, this indicates that the W function in sulfolane-water cannot be applied to a l l ketones. In order to test the applicability of the function to a particular ketone, a plot of log [Zj/tZR^O] versus W must be undertaken, o In DMSO-water mixtures only two ketones were used to determine the W function. In spite of this, there is evidence that the W function o o is valid. This is indicated by the constancy (standard deviation 0.52%) of A(log [Z]/[ZH 0]) between 0 and 70 mole % water and the unit slopes of plots of log [Z]/[ZH„0] versus W when the values for 2 o 4-(CH_)„NC,H.C0CF_ between 70-100 mole% water are disregarded. It is 3 2 b 4 J like l y that the inconsistencies noted for this ketone in the region 70-100 mole % water are due to experimental errors. The applicability of the W function in DMSO mixtures to aliphatic ketones has not been o tested; however, i t is l i k e l y that similar behavior w i l l be observed with s-dichloroacetone in DMSO-water mixtures as was observed in sulfolane-water mixtures. The W values in dioxane-water and acetonitrile-water mixtures, o listed in Table XIV, were determined with only one indicator, s-dichloro-acetone. The pK^ value used to anchor these scales was that determined by Bell at 25°C in pure water. L i t t l e can be said about the validity of these scales. At best, the W function in these solvents is o applicable to ketones closely resembling s-dichloroacetone. Agreement of pK^ values measured in different solvent systems is a test of the validity of W q functions. In the case of 4-(CH3) ^NCgH^ COCF.^  the determination of pK^ in sulfolane and DMSO systems results in a difference of 0.24 pK units. This difference is d i f f i c u l t to explain - 108 -in terms of the Hammett postulate. Recently, however, differences of 104 up to one pK unit have been noted between pK's determined from one solvent system to another in acid-base systems. This was found to be particularly true when the indicators had widely varying absorption maxima. The anomaly was attributed to dispersion effects. It is possible that somewhat the same effect i s operating between 4-(CH„)0NC,H.C0CF_ 3 2 6 "> 3 and 4-CH„0C,H.C0CFo. J 6 4 3 C. A Comparison of pK^ Values By applying the Hammett stepwise technique i t is possible to determine the thermodynamic pK^ values for a l l the indicators used to set up the scale. A wide range of pK^ values has been provided by introducing various substituents onto the benzene ring. A widely used method to examine the sensitivity of a reaction to substituent effects is the Hammett ap correlation. In this method, the log K values for the compounds studied are plotted versus the appropriate a values for the substituents present in the ring. The effect of substitution is expressed as a function of a. ' The slope of the plot, p, is determined by least square a n a l y s i s a n d the correlation coefficient, r, is calculated to measure the f i t . The pK^ values listed in Table VI were found to correlate well with a+ values,^"^^ which are based on the solvolysis of substituted 2-phenyl-2-propyl chlorides. This correlation, illustrated in Figure 16, gives a straight line of slope, p + , equal to -1.62 and a correlation coefficient, r, of 0.997. A l l the substituted a,a,a-trifluoroaceto-phenones studied were used in the correlation. o+ values used range from - 110 --1.7 for the 4-(CH 3)compound to 0.710 for the 3-N02 compound. An attempt to correlate the pK^ values with a values resulted in a much poorer f i t (p and correlation coefficient, r, equal to -2.61 and 0.976, respectively). The fact that the f i t i s much better with o + values than with a values is related to the availability of direct resonance between electron supplying substituents and.the carbonyl function in the ketone. This type of resonance interaction between substituent and reaction centre is illustrated by (V). Upon hydration, a species is formed V which i s incapable of resonance interaction. It might be reasoned that the resonance interactions operating on substituted ketones involved in the hydration reaction are similar to those involved in the ionization of benzoic acid, which upon ionization forms a species incapable of resonance with ring substituents. If this were the case, the hydration of substituted a,a,a-trifluoroaceto-phenones would correlate with a values. However, the fact that the reaction correlates much better with a + values indicates that resonance interaction in substituted a,a,a-trifluoroacetophenones is much more important than in the case of benzoic acids. Generally speaking, other carbonyl addition reactions are also found to correlate with a"*" or some combination of a and a + (using the - I l l -Yukawa and Tsuno equation^ 7 log k/k = p (a + rAa + ) ) . The addition o R of both hydrogen cyanide and bi s u l f i t e to benzaldehyde follow a +, and the addition of semicarbazide to benzaldehyde is best correlated by Yukawa and Tsuno's method with an r-value of 0.4. The magnitude of p + for the hydration of substituted a , a , a-trifluoro-acetophenones gives a quantitative estimate of the sensitivity of hydra-tion to substituents. A p + value of +1.62 for the hydration reaction (a positive value of p + is obtained i f log = -log is correlated with 0 + ) can be compared with a p + value of +1.11 for cyanohydrin addition to benzaldehyde and with a p value of +1.81 for the addition of semicarbazide to benzaldehyde."'""'"7 For the addition of p-nitrophenol to benzylidineaniline a p + value of -0.5 is observed. It is interesting to note that the p + value observed for the dehydration of substituted a,a,a-trifluoroacetophenone hydrates very closely approximates the p value (-1.70) for aliphatic aldehydes and 30 ketones determined by Greenzaid et a l . Thus the similarity that 53 exists between aliphatic and pyridine aldehydes can be extended to include aromatic ketones. D. A Comparison of W Scales _ o The W scales in sulfolane-water and DMSO-water mixtures are o plotted for comparison in Figure 17. Comparing the magnitudes of Wq at specific compositions, i t can be seen that sulfolane is much more effective at reducing the extent of ketone hydration than DMSO. A comparison between Wq scales in sulfolane-, dioxane-, and acetonitrile-water mixtures is shown in Figure 18. The Wq values for CM' Figure 17. Plot of Wq versus Mole % Water (using substituted a,a,a-trifluoroacetophenones) X Sulfolane-Water Mixtures • A DMSO-Water Mixtures CM I D O I CO I 0.0 T 12.5 25.0 37.5 50.0 62.5 Mole % Water 75.0 87.5 100.0 Mole % Water - 114 -sulfolane-water were taken from Table XXII where the indicator s-dichloroacetone is used to determine w' . This allows direct o comparison between a l l three solvents, since the same indicator i s used in each case. It can be seen from this graph that sulfolane is the most effective solvent for inhibiting hydration and dioxane the least effective. It should be noted that W in a l l three of these o solvent systems does not assume negative values, as i t does in DMSO-water (see Figure 17). E. The W Function in Sulfolane-Water o The W function in sulfolane-water, indicated in Figures 7 and 17, o rises continuously as water is removed from the medium. The rise is f a i r l y gentle except in the regions 0-10 and 90-100 mole % water. According to equation (37), this indicates that adding sulfolane is effective in decreasing the extent of ketone hydration. To examine the factors influencing the rise in W , the expressions for W and w are repeated below, and the various terms in these o o c equations are calculated. The results are recorded in Table XXI. In this table a^ Q and f^ Q data were taken from published values by Benoit and W = -log w (74) o ° o " " t ^ ' v * % • V 'V <75) 84 Choux. The activity coefficients of water are based on the mole fraction concentration unit, i.e. a u = f x, n . The f „ / f T ^ and 2 "2 n^U Z Zn^U - 115 -f T T .f„/f„77 _ values are c a l c u l a t e d from the l i s t e d W , x , and a u r i ^ U Z Z H ^ O O n ^ U n ^ U values. In sulfolane-water mixtures i t has been shown that the value of f r i s e s as water i s removed; thus, the a c t i v i t y of water does not decrease as f a s t as the concentration of water. Despite t h i s , i t can be •. seen i n Table XXI that w decreases considerably f a s t e r than x„ o H20 This i s due to the very r a p i d decrease of the term f / f as water Z Z H ^ U i s removed from the medium. Table XXI. A n a l y s i s of the W Function i n Sulfolane-Water f Mole % f n a ' b a„ n C W d w 6 £z fH n fZ " a t e r X ° 10 3.074 0.307 1.36 0.044 0.14 0.44 20 2.684 0.537 1.00 0.10 0.19 0.50 30 2.177 0.653 0.81 0.15 0.24 0.52 40 1.858 0.743 0.66 0.22 0.29 0.55 50 1.621 0.811 0.55 0.28 0.35 0.56 60 1.436 0.862 0.47 0.34 0.39 0.57 70 1.278 0.895 0.41 0.39 0.44 0.56 80 1.141 0.913 0.31 0.49 0.54 0.61 90 1.047 0.942 0.21 0.62 0.65 0.68 100 1.000 1.000 0.00 1.00 1.00 1.00 H 20 a b A c t i v i t y c o e f f i c i e n t of water data at 30°C obtained from r e f . 84. Values of f bear no u n i t s , s i n c e f o r the a c t i v i t y c o e f f i c i e n t of water the d e f i n i t i o n i s made a = f x . c H2U 2 2 These data are p l o t t e d versus mole % water i n Figure 21. d e Taken from Table V I I I . The f o l l o w i n g r e l a t i o n s h i p s apply: W = - l o g w ; w = f„/f 7 l 7 • a = t Ji • f • x o o o Z ZH 20 H 20 Z ZH^O H^ O R^O This term has no u n i t s , since the l i t r e s / m o l e u n i t s of f and f Z ZH2U cancel i n the r a t i o . In a d d i t i o n f bears no u n i t s , s i n c e i t n 20 i s based on mole f r a c t i o n . - 116 -The change in f /f may be due to a decreasing f term, an Z Z r i ^ U Z increasing f term, or a combination of these. It is lik e l y that Z H ^ U changing the solvent from water to sulfolane decreases the f^ , term, since ketones are generally more soluble in sulfolane than water; however, the drastic decrease in f /f can not be accounted for by Z Z r l ^ U this alone. A large increase in f is also necessary. Z H ^ U Large increases in f can be accounted for by considering the ZH20 effect of sulfolane on the activity coefficient of water, f . This term rises with the addition of more sulfolane to the system, indicating that sulfolane is less able to solvate water than water is able to solvate i t s e l f . Since the hydrated species has two hydroxyl groups present, i t bears a great resemblance to water, and f might be expected to behave quite similarly to f . Thus the removal of water from the medium would result in the hydrate being less solvated. The resulting decrease in sta b i l i t y would shift the equilibrium towards the carbonyl compound. It is lik e l y that removing water from the medium affects f to a much greater extent than f^. The two hydroxyl groups on the hydrate molecule are expected to require much more extensive solvation than the carbonyl group. The term f f /f in Table XXI is determined by dividing w H ^ U L, Z H ^ O O values by the corresponding x values. The behavior of this term as a function of solvent composition is illustrated in Figure 19. There is an i n i t i a l rapid decrease as water is removed from the medium, followed by a leveling off. Between 10 and 90 mole % water, the function decreases only slightly. Since W q is the product of x^ ^  and 03 LO O CN txl O CN cn o' CM o a a Figure 19. Plot of f R Q f z / f Z H Q versus Mole % Water for Sulfolane-Water Mixtures Using a,a,a-Trifluoroacetophenones as Indicators. 0.0 12.5 25.0 ! . ! 3 7 . 5 50.0 Mole % Water 52.5 75.0 87.5 100 - 118 -f T T „/:£„,, i t is evident that w decreases faster than x despite ti^y Z Lti^j o 2 the rise in f as water is replaced by sulfolane. In fact, since f f /f „ continues to decrease as water is removed, the rate of n ^ O Z Z n ^ U decrease in w becomes greater as xTT „ becomes smaller, o ° H20 It should be noted that the decrease in f f /f between 10 H 20 Z Z H ^ O and 90 mole % water is almost linear. The least squares equation for this portion of the curve is f f HO Z ~ = .23x + .44 (76) fZH 0 H2° The slope of the line is not. very great despite large changes which occur in f and f /f . Thus, a cancelling of terms is occurring HrjO Z Z H 2 O probably between f and f . H 20 Ln^j It w i l l be recalled that a similar linearity was noted in dioxane-water s o l u t i o n s . ^ ' ^ 4 In these solutions, however, the correlation was not as good. In addition, linearity was.reported only up to 50 mole % water. ' The increased correlation with sulfolane-water mixtures w i l l be due, in part, to the use of a number of ketones. Only one ketone was used to obtain the results in dioxane-water mixtures. Since the addition of sulfolane to water does not i n i t i a l l y change the values of f and aTT n very greatly, the rapid decrease of H 2 U H 2 U f„ -f ^ / f ^ . , and thus in w in the 90-100 mole % region is due to a r l 2 U Z Z r l 2 U O large increase in f . Thus, i t appears that small amounts of sulfolane are effective in breaking up the structure of water conglomerates. This conclusion is arrived at in the following way. In pure water the - 119 -two hydroxyl groups of the hydrate allow this species to f i t into the water structure without greatly perturbing i t . Therefore, i t can be,effectively solvated by water without breaking down the solvent structure. As sulfolane is added a large increase in f results, Z t ^ O implying that this special solvation is decreased, resulting,probably from breakdown in the solvent structure. Supporting evidence for a breakdown in water structure is obtained from cryoscopic studies of water dissolved in sulfolane. These studies 87 indicate that water is dimeric over a wide concentration range. „ - 40a,b,111,115 j . , , c Several authors studying the hydration of pyruvic acid in highly aqueous mixtures of water and pyruvic acid have also observed that an i n i t i a l decrease in water concentration drastically affects the extent of hydration. In these cases, however, a decrease in the extent of hydration, as pyruvic acid was added to the mixture has been attributed to a third power dependence on the concentration of water. It i s postulated that the hydrate is associated with three more water molecules than the unhydrated ketone. The variation in the activity coefficient of the hydrate i t s e l f was not considered. Studies of the hydration of aliphatic aldehydes^ "'"2'''"''"4 have shown that the addition of large quantities of NaCl significantly lowers the activity coefficient ratio f /f . This has been interpreted in Z Z H ^ O terms of different hydration numbers for the aldehyde and i t s hydrate. The hydrate is presumed to have two more water molecules intimately associated with i t than the aldehyde. In the hydration of a,a,a-trifluoroacetophenones, the rapid change of w between 90-100 mole % water in sulfolane-water mixtures can o also be explained by postulating a greater than unit dependence of W Q - 120 -upon the concentration of water. This is demonstrated by the fact that a plot of log [Z]/[ZH20] versus log [H^O] in this region yields a curve with an average slope of greater than unity. The slope increases as the concentration of water increases. Throughout the remainder of the solvent range, however, a plot of log [Z]/'[ZH^O] versus log [H20] yields a line with slope 0.7 while a plot of log [Z]/[ZH 0] versus log x yields a line with slope 1.15. From this i t i s H20 concluded that the hydrate contains one more water molecule than the ketone. Since this i s not expected to change between 90-100 mole % water, the rapid change of w in this region is most easily attributed o to a specific effect on the activity coefficient of the hydrate. It is most lik e l y that this is due to a change in the structure of water and consequent change in i t s a b i l i t y to solvate the hydrate. Originally, s-dichloroacetone was used to test the applicability of the W scale in sulfolane-water to other ketones. It was noted o that was not entirely general as shown in Figure 9 where a plot of log [Z]/[ZH20] versus Wq does not yield a unit slope for s-dichloro-acetone. In the light of the preceding treatment of W , i t is interesting to examine the behavior of a function in sulfolane-water mixtures based on the indicator s-dichloroacetone. Values of W'~ can be calculated from log [Z]/IZH„0] values listed in Table IX O 2 i f i t is assumed that pK^ = 0.700 for s-dichloroacetone (the value measured in 99.74 mole % water at 31.4°C in this work). W1 values are o listed along with f , aT1 .., and. the calculated values of w. , f„/f„TT . and 2 2 ° "^-20 ^O^Z^ZH 0' Table XXII. These values are based on. only one indicator and thus are not as accurate„as those calculated from W values. It can be seen .• o - 121 -Table XXII. Analysis of W' Function in Sulfolane-Water o a b f fH 0O fZ 11.56 0.351 1.64 0.023 0.065 0.20 16.68 0.475 1.46 0.035 0.073 0.21 21.02 0.550 1.35 0.045 0.081 0.21 25.70 0.613 1.25 0.056 0.092 0.22 35.17 0.706 1.07 0.085 0.12 0.24 44.60 0.776 0.93 0.12 0.15 0.26 55.15 0.834 0.81 0.15 0.19 0.28 65.22 0.876 0.70 0.20 0.23 0.31 74.87 0.903 0.57 0.27 0.30 0.36 85.22 0.930 0.42 0.38 0.41 0.45 94.78 0.968 0.18 0.66 0.68 0.70 100 1.000 0.00 1.00 1.00 1.00 Mole % Water 3 . Activity of water data interpolated from a R data in Table XXI (see Figure 21). 2 k The following relationships apply: W - -log w o ° o f z f z ° fZH 20 H2° fZH 20 H2° V CD a' o C N t o o. o CN CN a' a a' Figure 20. Plot of f R Q^Z^ZYL 0 v e r s u s M o l e % Water for Sulf olane-Water Mixtures Using s-Dichloroacetone as Indicator. .X X" 0.0 12.5 25.0 i I I 37.5 50.0 52.5 Mole % Water 75.0 87.5 100 Figure 21. 'Plot of Activity of Water versus Mole % Water. X Sulfolane-Water Mixtures (see Table XXI) Q DMSO-Water Mixtures (see Table XXIII) N> Mole % Water - 124 -that the f /f values follow much the same course as they do when Z Z H 2 O substituted a,a,a-trifluoroacetophenone indicators are used. A difference can be noted, however, i n the behavior of the f f /f H ^ U Z 2 term. A plot of this term versus mole % water is given in Figure 20. The least square equation for the data in the region 10-70 mole % water i s given in the following equation: HO Z -=-=• =0.20 x u . + .17 (77) fZH 20 H2° With s-dichloroacetone, i t is noted that f f /f decreases more H 2 O Z LYL^J slowly than with a ,a ,a-trifluoroacetophenone indicators. This contributes to the difference between the W and W' functions. o o F. The W Function in DMSO-Water o The W q function in DMSO-water, shown in Figures 11 and 17, i n i t i a l l y decreases as water is replaced by DMSO and reaches a minimum of -0.42 at 60 mole % water. After this i t begins to rise and crosses the mole % axis at approximately 15 mole % water.. In . the region 15-100 mole % water, ketones are more readily hydrated in DMSO-water mixtures than in pure water i t s e l f . An examination of the data in the DMSO-water system with a view towards explaining the W results has been undertaken. In table o XXIII W , w , f„ „ and aTT n values are listed along with the calculated o o H^ O H^ O values of f^f^ Q and f R 0 f z / f Z H 0' ( V a l u e s o f a H 0 a r e t a k e n f r o m ^85 2 2 2 published results at 70°C adjusted to 31.4°C using a set of relations 108 kindly supplied by Professor R.L. Benoit. These values are plotted - 125 -in Figure 21.) In DMSO-water mixtures, the term f„/f„ u increases Z Z H ^ U as water is removed from the medium. This effect is opposite to that observed in sulfolane-water systems; however, this increase parallels a decrease in f as water is replaced by DMSO. If i t is assumed, H^ O as before, that changes in f„/f„TI are mainly due to changes in f , Z 2 Z n ^ U an increase in i Ii must be due to a decrease in f . Z Z n ^ O Z n ^ O ' • -Since w is the product of the term a and f /f , i t is o 2 2 evident that there are two opposing effects operating on w^ . As water is removed, the term a decreases more rapidly than x , since f also decreases. However, the term f /f increases throughout H 2 0 Z Z r ^ O the solvent range, and in the range 15-100 mole % water effectively negates the decrease in a . This results in values of w greater H2° ° than unity. Below 15 mole % water, the activity of water drops to a point where i t s effect is greater than f /f . Z Z n ^ O The behavior of the term i Ii can be explained once again in Z Z H ^ O terms of the behavior of f . The decrease in f as water is "^2 H ^ O removed indicates that DMSO is more effective in solvating water than water is in solvating i t s e l f . Negative values for the partial heat of 84 mixing of water in DMSO also indicate this. Assuming that hydrated a,a,a-trifluoroacetophenones behave like water, then DMSO w i l l also solvate the hydrate better than water does. Therefore, as water is replaced by DMSO, the activity coefficient of the hydrate w i l l decrease. This effect w i l l increase the tendency of the ketone to hydrate in these solutions. Consequently, in the region 15-100 mole % water a ketone is hydrated to a greater extent than in pure water. In Table XXIII i t can be seen that, for DMSO-water mixtures, the - 126 -Table XXIII. Analysis of the W q Function in DMSO-Water a,b,c d e f f fH 0fZ Mole % f a u . W w -= -=-± Water H2° H2° ° ° fZH 20 fZH 20 10 0.473 0.047 0.15 0.71 15.0 7.1 20 0.545 0.109 -0.11 1.29 11.8 6.4 30 0.592 0.178 -0.27 1.86 10.5 6.2 40 0.675 0.270 -0.36 2.29 •8.5 5.7 50 0.769 0.385 -0.40 2.51 6.5 5.0 60 0.871 0.523 -0.42 2.63 5.0 4.4 70 0.957 0.670 -0.40 2.51 3.8 3.6 80 1.054 0.843 -0.31 2.04 2.4 2.6 90 1.062 0.956 -0.18 1.51 1.6 1.7 100 1.000 1.000 0.00 1.00 1.0 1.0 9. Activity coefficient of water data at 31.4°C. k Values of f are based on the relationship a = f x . Values of f valid for 70°C were obtained from ref. 85. They have 108 been adjusted to 31.4°C by application of the following relation where AH^ Q is the partial heat of solution of H^ O in DMSO. 2 6 1 n fH 20 \ o ST RT2 108 The necessary data were supplied by Professor R.L. Benoit. d These data are plotted versus mole % water in Figure 21. £ Taken from Table XII. ^ The following relationships apply: F 7 F 7 a o i ' i n O i " o CM" i n Figure 23. Plot of w versus Mole % Water for DMSO-Water Mixtures Using a,a,a-Trifluoro-acetophenones as Indicators. experimental points (see Table XXIII) graphical representation of equation (79) 00 i n o o 0.0 12.5 25.0 37.5 50.0 62.5 75.0 87.5 100.0 Mole % Water - 129 -term f i Ii is not constant but increases as the water concentra-tion decreases. Thus the addition of DMSO affects the activity coefficient of the hydrate much more than that of water. This behavior is graphically represented in Figure 22. The points, although describing a slight curve, follow the linear regression line with a correlation coefficient of 0.990. The least square equation is fH 0fZ -=-± = -6.8xH + 8.1 (78) fZH„0 H2° Since w is the product of x and f f /f , the following O 2 Zn^U quadratic equation relating Wq to x R ^ results: w = -6.8x72T n + 8.1x (79) o H20 H20 The behavior of w as a function of water concentration can thus be o explained in terms of equation (79) , which describes a parabola with a maximum at 60 mole % water. In Figure 23, experimental values of w o taken from Table XXIII are plotted versus mole % water along with the graphical representation of equation (79) to test the extent of their agreement. It is seen that the agreement between experimental points and equation (79) is quite good. G. Heat of Reaction and Entropy of Reaction in Sulfolane-Water Mixtures The heat of reaction and entropy of reaction data lis t e d in Table XV suggest that these parameters are very l i t t l e affected by changing the solvent from water to sulfolane in the hydration of - 130 -Table XXIV. Thermodynamic Parameters for the Hydration of Carbonyl Compounds at 25°C.a'^ AH° AS° (kcal/mole) (e.u.) Formaldehyde 14.6 30.8 Chloral 12.7 30.2 Pyruvic acid 7.8 26.8 4-Methoxy-a,a,a-trifluoroacetophenone 6.7 18.1 s-Dichloroacetone 5.7 14.8 as-Dichloroacetone 5.5 16.4 Acetaldehyde 5.1 16.4 Diacetyl 4.5 12.7 4-Pyridinecarboxaldehyde 4.2 13.9 2-Pyridinecarboxaldehyde 3.8 13.8 Monochloroacetone 2.0 .7.7 Si A l l values except those determined taken from Pocker, Meany, Nist and 2879 (1969). in the present study Zadorojny, J. Phys. were Chem. 73, k The values of AH°and' AS°are listed for the dehydration of the hydrates of the carbonyl compounds lis t e d . - 131 -4-CH-0C,H.C0CFo and C,HcC0CFo. This is in line with the observation 3 6 4 3 6 5 3 16 made by Bell and McDougall that both AH and AS are l i t t l e affected by the proportion of water in dioxane-water solutions for the hydration of s-dichloroacetone. In pure water the dehydration of 4-CH OCgH^C(OH)2CF3 yields AH° =6.7 kcal/mole and AS° = 18.1 e.u. These values were obtained by U.V. spectroscopy for which the estimated error from the plots of log [Z]/[ZH20] versus 1/T was less than 1%. In Table XXIV, values of AH° and AS0 are lis t e d for the hydration of a number of carbonyl compounds along with the values obtained from the present study. AH° and AS° values for 4-CH„0C,H.COCF_ have approximately the same magnitude as values obtained for acetaldehyde, s-dichloroacetone, and as-dichloroacetone. H. Kinetics of the Spontaneous Hydration Reaction in Sulfolane-Water  Mixtures In the kinetic treatment previously applied to hydration (see RESULTS: Section G), i t was assumed that the reaction was first-order with respect to water for the forward (hydration) reaction and zero order with respect to water for the reverse (dehydration) reaction. Changes in k^ and k^ have thus been attributed to variation of the terms a R Q^/f and. f Z R Q / f , respectively. When consideration is given to the possibility that more than one water molecule is involved in the transition s t a t e , ^ 4 ' 7 7 ' 7 ^ the reaction is formulated as in equation (80): Z + (n + l)H.O ^ [Z...n + 1(H„0)] + * ZH.O +, nHo0 (80) Z "v! Z V Z Z - 132 -Application of transition state theory to this reaction yields new expressions for and k^ (equations (81) and (82)) analogous to equations (49) and (50) but containing the terms a^+^ and a^ . H _ U H - 0 '2 2 K' fZ n+1 k , ( ) = k, = — • k_ ' a„ " (81) obs K , + 1 Ti f t 2 H20 , fZH 0 kobs W = kd = — ' k - l ' aH 20 ( 8 2 ) Using these equations, i t is possible to attribute changes in k^ and k^ to variation in the terms f /f^, f ^/f^, a „ + i and a„ . 109 Recent work on the acid-catalyzed hydrolysis of esters shows that two molecules of water may be involved in the transition state for ester hydrolysis. When the logarithm of the rate data was plotted versus log a for this reaction, a straight line was obtained with slope equal to the number of water molecules involved in the transition state. The straight line obtained from this plot showed that the ratio of activity coefficients of the protonated ester and the transition state was constant throughout the range of water activity investigated. Thus, for this reaction, changes in the rate were due to variations in the activity of water alone. In systems where protona-tion of a substrate is followed by a reaction involving no additional species, such as in the acid-catalyzed hydrolysis of sucrose,^® there is often an excellent correlation between the rates in increasingly acid solution and the.acidity function for these solutions. Therefore, an increase in the acid concentration has a similar effect on the rates of reaction and the ionization equilibria of uncharged monoacid bases. - 133 -In terms of transition state theory, this indicates that the equilibrium between reactants and activated complex, whose position determines the rate of reaction, approximates an ionization equilibrium of the correct charge type. This suggests that the activity coefficients for protonated substrate and the activated complex are equal. In the light of these observations, i t is interesting to examine whether the ratios f„/f and f /f are actually constants in the Z Zn^O hydration reaction with the result that a l l changes in the rate are due to the a^ +^ and a^ terms. A plot of log k, versus log a w i l l yield a straight line with d H„0 t slope equal to n i f the ratio f /f is a constant. When the k, Zt^O u data in Table XVII were treated in this way, a straight line did not resu Instead, a curve sloping^upward towards higher-a values resulted. Thu changes in k^ as the solvent composition is varied cannot be accounted for solely by a R ^ . A similar treatment applied to the k^ data 2 + yielded the same result indicating that the term f z / f is not constant in sulfolane-water mixtures either. 54 With the ketone s-dichloroacetone in dioxane-water mixtures, Bell discovered that plots of log k^ and log k^ versus log [H^O] yielded straight lines indicating there was a cancellation taking place between n+1 + f u and f . This treatment was applied to the data in Table XVII for the hydration of 4-CH„0C,H.COCF„ in sulfolane-water mixtures. Plots 3 6 4 3 of log k^ and log k^ versus log [H^O] yielded very good straight lines with slopes of 3.1 and 2.4 and correlation coefficients of 0.9990 and 0.9998, respectively. These plots are indicated in Figures 24 and 25. When the log k^ and log k^ data were plotted versus log x R ^, the - 136 -c o r r e l a t i o n c o e f f i c i e n t s were somewhat decreased because of a s l i g h t curvature which appeared i n the p l o t s . B e l l ' s work i n dioxane-water mixtures resulted i n the suggestion that three water molecules are involved i n the t r a n s i t i o n state of the water-catalyzed spontaneous hydration reaction. The present r e s u l t s strongly r e i n f o r c e B e l l ' s conclusions, since the values produced here over a very wide range of water composition agree with h i s observations. f t Since the r a t i o s f„/f and f , Ji vary as the solvent L 2 composition i s changed, d i r e c t proof of the number of water molecules involved i n the t r a n s i t i o n state i s not obtained. (A d e f i n i t e answer would be gained i f a p l o t of log k, or log k, versus log aT. _ n d n^ '-' produced a s t r a i g h t l i n e . ) In t h i s study, we must r e l y on a c a n c e l l a -t i o n occurring between the a c t i v i t y c o e f f i c i e n t of water raised to a power equal to the number of water molecules taken into the t r a n s i t i o n state and ..the a c t i v i t y c o e f f i c i e n t of the t r a n s i t i o n state, i t s e l f . A c a n c e l l a t i o n of t h i s type can be v i s u a l i z e d i f the a c t i v i t y c o e f f i c i e n t of the t r a n s i t i o n state i s affected independently by each water molecule associated with i t . Indeed, i t was observed i n equilibrium studies that a c a n c e l l a t i o n occurred between f u and f . If t h i s behavior can be extended to a species containing three water molecules intimately associated with the structure, there would be a 3 t c a n c e l l a t i o n between f and f . It w i l l be noted that while the observed value for the order of re a c t i o n with respect to water for the forward r e a c t i o n i n equation (80) i s close to the i n t e g r a l value three, the value for the reverse reaction i s s i g n i f i c a n t l y d i f f e r e n t from two. Thus the difference - 137 -between these two values i s not the expected value of one. I f i t i s assumed from the r e s u l t s that three water molecules are inv o l v e d i n the t r a n s i t i o n s t a t e f o r h y d r a t i o n , the value of 2.4 obtained f o r the reverse r e a c t i o n can be r a t i o n a l i z e d by c a l c u l a t i n g values f o r the t t r a t i o f / f w i t h :n equal to 2. When the r a t i o f / f i s compared Zn„U. ZH_0 2 2 2 to f , i t i s noted that a complete c a n c e l l a t i o n does not take place between these terms. Thus the slope of a p l o t of l o g k^ versus l o g [H^O] i s adjusted to account f o r t h i s v a r i a t i o n . The f a c t that a d i f f e r e n c e of one i s not observed between the orders of r e a c t i o n w i t h respect to water f o r the forward and reverse r e a c t i o n s i s a r e f l e c t i o n of the r e l a t i o n s h i p between l o g K' and lo g [H^O] f o r the e q u i l i b r i u m r e s u l t s of the 4-CH30 compound. A p l o t of l o g K' versus l o g [H^O] r e s u l t s i n a slope of 0.7. This i n d i c a t e s that when the a c t i v i t y c o e f f i c i e n t of water i s based on the molar conc e n t r a t i o n of water, a complete c a n c e l l a t i o n does not occur between the a c t i v i t y c o e f f i c i e n t of water and the hydrate. A more complete c a n c e l l a t i o n i n the term f f / f occurs when the a c t i v i t y c o e f f i c i e n t of water i s c a l c u l a t e d from the mole f r a c t i o n of water. Thus, a p l o t of l o g K' versus l o g x y i e l d s a l i n e of slope 1.15. I. K i n e t i c s of the Hydrogen-Ion Catalyzed Hydration Reaction i n Sulfolane-Water Mixtures -Examination of the terms kT1+ / a , n and k. +Jh i n Table XX H,h/ H Ooo • H,d' o. t t shows that the v a r i a t i o n i n the terms f +/f + and f +/f + (from Z H H Z H ^ U H equations (69) and (70)) f o r the a c i d - c a t a l y z e d r e a c t i o n i s not ne a r l y as great as the v a r i a t i o n i n f„/f^ and f /f^ (from equations (49) and Z Z H 2 O - 138 -(50)) shown in Table XVII for the spontaneous reaction. This indicates that for acid-catalyzed hydration, the binding of water in the transition state is not as extensive relative to the reactants as in the spontaneous reaction. . A comparison of water-catalyzed and acid-catalyzed reactions is not truly valid, however. In acid-catalyzed hydrations the reactants are considered to be the protonated ketone and'protonated hydrate for the forward and reverse reactions, respectively. On the other hand, the reactants are considered to be the unprotonated ketone and hydrate in the spontaneous reaction. It is likely that the protonated reactants are more extensively solvated than the unprotonated reactants. In Bell's work on the acid-catalyzed hydration of s-dichloro-54 acetone, the acidity correction was made by dividing the observed rates by the concentration of acid present in'.the medium. In an attempt to determine the order of reaction with respect to water for the hydrogen-ion catalyzed reaction, i t was found that the rates decreased for both forward and reverse reactions as the water concentra-tion increased. This behavior was attributed to changes in the solvation of the hydrogen ion as the solution composition was varied. It was not possible to determine the order with respect to water in this reaction. In the present work, i t was observed that dividing the rate constants by the concentration of acid present produced the same result as Bell observed for the reverse (dehydration) reaction. In this latter reaction, the resulting rate constant decreased as the water concentration increased. However, the same treatment for the forward - 139 -reaction yielded rate constants which continued to increase as the water concentration was increased. This phenomenon results from the fact that the true acidity of the medium (measured by h Q) decreases as the water concentration increases (see Table XIX). For the hydration reaction, this i s overcome by the effect on k^-r^ of an increase in the activity of water. It i s fe l t that compensating for the acidity of the medium by use of h is in t r i n s i c a l l y more valid than the use of the concentration o term, since the solutions in which the measurements take place deviate widely from the standard state. Although the acidity function used in the present work is not the true acidity function applicable to hydration, i t s use is deemed more valid than use of the concentration term. When the acidity is accounted for by h^, the problems associated with changes in the solvation of the proton no longer exist. The extent of protonation in the ionization equilibrium, from which h o is calculated, takes into account any changes in solvation which occur. However, the expressions relating the rate constants k + and kTT+, to ' H , h - H, d the standard state contain not the ratios of the activity coefficients of unprotonated ketone and hydrate to the activated complex, but rather the ratios of activity coefficients of the- protonated species to the activated complex. An attempt to determine the order of reaction with respect to water for the forward and reverse reactionsof acid-catalyzed hydrations was carried out by a treatment similar to that applied to the spontaneous reaction. When the log k^ +, and log k + data were plotted versus H,n Hsd - 140 -log [H 20], straight line plots were not obtained. Instead, curves sloping - downwards towards higher log [EO"]-values were obtained for a l t concentrati of acid. The average slopes were approximately 1 and 0.3 for the forward and reverse reactions, respectively. The curvature i n these plots can be due to a number of factors. First, an error may result from using the incorrect acidity function. Secondly, complete cancellation w i l l probably not occur in a term of f the type f f +/f +, since there are two charged species present which can lead to various spurious effects. Due to the inaccuracy of the method, the values of 1 and 0.3 obtained for the forward and reverse reactions of the acid-catalyzed mechanism can not be used with certainty. However, in conjunction with other results, they may assume some significance. As mentioned • 78 i in the introduction, Kurz and Coburn noted large negative AS values for the water-catalyzed hydration of acetaldehyde but only small negative A s values for the acid-catalyzed reaction. In addition, they observed that rates measured for the water-catalyzed reaction exceeded those predicted by Bro'nsted correlations, whereas rates measured for the acid-catalyzed reaction were in line with those predicted by a BrySnsted correlation. They inferred that the water-catalyzed mechanism involved a major reorganization of the solvent (water) into a more highly organized structure (a cyclic transition state), whereas the acid-catalyzed mechanism involved relatively l i t t l e reorganization of the solvent. The results of the- present research also suggest that the number of water molecules in the transition state for the acid-catalyzed mechanism is less than in the water-catalyzed mechanism. SUGGESTIONS FOR FURTHER RESEARCH Experiments show that sulfolane and DMSO vary widely in their abilities to inhibit hydration. It would be of interest to extend the study by examining some of the many other dipolar aprotic solvents available. Preliminary qualitative experiments were carried out on the ketone 4-CH„0C,H,COCF„ in a number of these solvents to test the 3 6 4 3 extent of their abilities to inhibit hydration. At compositions of 20 mole % water in these solvents, the following approximate order was observed (solvents which were the most effective at inhibiting hydration are listed f i r s t ) : 3-methylsulfolane > sulfolane > formamide > dioxane > N-methylacetamide > N-methylformamide >> N,N-dimethyl-formamide > N,N-dimethylacetamide > hexamethylphosphoramide > DMSO > tetramethylene sulfoxide. It is evident that a high dielectric constant does not necessarily indicate that a solvent w i l l be effective in inhibiting hydration. For example formamide has a much higher dielectric constant (e = 109) than sulfolane (e = 44), yet is less effective at inhibiting hydration. Similarly, 3-methylsulfolane (e = 29.2) is more effective than sulfolane but has a lower dielectric constant. A comparison of data obtained from hydration studies to water activity data in the same solvents may yield interesting properties of these solvents. Furthermore, since 3-methylsulfolane appears more effective than sulfolane, the - 142 -equilibrium constants of more highly hydratable ketones could be determined. It would be interesting to study the hydration of pyruvic acid in sulfolane-water mixt ures. A third power dependence of [Zj/fZH^O] on the concentration of water was observed in highly aqueous solutions. At lower water concentrations this may change, and a linear dependence on the concentration of water may be observed, as was observed for a,a,a-trifluoroacetophenones. The kinetics of hydration in dipolar aprotic solvents present many interesting possibilities for further study. For example, i t would be of interest to do a careful study of the rates of hydration in DMSO-water solutions. In mixtures of water and this solvent, negative values of are observed between 15-100 mole % water. It would be of interest to examine whether the rates of hydration w i l l . parallel the equilibria. If such were to happen, the rates of reaction would increase as DMSO was added to the mixture. Another kinetic study of interest would be a study of hydration at various temperatures in various mixtures of water and dipolar t + aprotic solvents. This would provide the AH and AS values for reaction in the presence of these solvents. Large negative values of *f 78 AS have been observed for the hydration of acetaldehyde in water. It would be interesting to see whether these values change as dipolar aprotic solvents are added. - 143 -Appendix I: Computer Program f o r the C a l c u l a t i o n of Hole Percentages Water i n Solvent-Water Mixtures C C TO COMPUTE THE MOLE P E R C E N T A G E S WATER AND S O L V E N T IN S O L V E N T -C WATER M I X T U R E S C C THE SYMBOLS N,PGE R E F E R TO THE E X P E R I M E N T A L BOOK NO. AMD PAGE NO. £ FROM WHICH THE DATA WAS T A K E N C WTCAT IS T H E WEIGHT OF C A T A L Y S T CONT. IN 0.5 ML. OF SOLN A N A L Y S E D C WTSUB IS THE WEIGHT OF S U B S T R A T E CONT. IN 0.5 ML. OF SOLN ANALYSED C Sl»S2 tS3 ALLOW T E N S P A C E S INTO WHICH THE S O L V E N T NAME IS PUT C VOLS IS THE VOLUME OF S O L U T I O N A N A L Y S E D , DENS I S THE D E N S I T Y OF IT C WTPCTS IS THE APPROX. WT. P C T . OF S O L V E N T CONT. IN THE S O L U T I O N C T H I S PROGRAM EMPLOYS A LOOP WHICH COR R E C T S WTPCTS AND P R I N T S I T C AMWS IS THE MOLECULAR WT. OF THE S O L V E N T C A K F T IS THE KARL F I S H E R T I T R E FOR THE SOLN, A K F S T D I S THE STANDARD C FOR THE K . F . RGNT C TCONSC IS THE TOTAL CONC OF S U B S T R A T E AND C A T . IN SOLN C M IS THE NUMBER OF RUNS AT A S P E C I F I C WTCAT AND WTSUB C , 41 READ 5, N, P G E , WTCAT, WTSUB, M 5 F O R M A T ( I I , F 5 . 1 , F 9 . 0 , F 1 0 . 0 , 3X, 12) P R I N T 1,N,PGE 1 FOR MA T ( 1 X , 6 9 H M 0 L E P E R C E N T A G E S WATER AND S O L V E N T IN SOLVENT-WATER M 1 ! Y'!' UP.»rS j S E E PG £ : ' * . ; ! ! * I H—» F-K , 1 / / / / ) P R I N T 4 ' ' ' ' 4 FORMA T ( 1 X , 1 0 H S O L V . US ED,7X, 10HPCT• WATER,5X,10HPCT. S O L V . , 4 X , 1 2 H P C I T S 0 L V - 0 T H , 2 2 X , 14HWT. P C T . S O L V . / / ) DO 31 1=1,M READ2, S I , S 2 , S 3 , V O L S , DENS, WTPCTS, AMWS, A K F T , A K F S T D , TCONSC 2 F O R M A T ( 2 A 4 , A 2 , 7 F 1 0 . 0 ) 21 AMOLS = ( V O L S * D E N S * W T P C T S ) / ( A M W S * 1 0 0 . 0 ) AMOLW = (A K F T * A K F S T D ) / 1 ti 01 5 . 3 AMOLO = V 0 L S * T C 0 N S C / 1 0 0 0 . 0 TMOL = AMOLS + AMOLW + AMOLO PCTW = (AMOLW*100.0)/TMOL PCTS = ( A M O L S * 1 0 0 . 0 ) / T M 0 L PCTS 0_ =_ ( (AMOLS + _AMOLO )_*100 ._0J_/ TMOL WTS = AMOLS * AMWS WTW = AMOLW * 1 8 . 0 1 5 3 TWT = WTS + WTW + (WTCAT + W T S U B ) # V 0 L S / 0 . 5 AWPCTS = (WTS * 1 0 0 . 0 ) / T W T I F ( A B S ( A W P C T S - W T P C T S ) . L T . 0 . 0 0 1 ) GO TO 31 WT PCTS_ E_A WPC TS GO TO" 21 31 P R I N T 3, S I , S 2 , S 3 , PCTW, P C T S , P C T S O , WTPCTS 3 F 0 R M A T ( 1 X , 2 A 4 , A 2 , 3 F 1 5 . 2 , 2 OX,F 1 5 . 2 / ) C O N T I N U E GO TO 41 _._ END , . , . . - 144 -cL Appendix II: Ultraviolet Data for a ,a,a-Trifluoroacetophenone and Derivatives X-C6H4COCF3 Sulfolane Water Cyclohexane X e X e X e max max max 4-(CH3)2N 369 30,800 376 4-CH 0 299.5 17,840 298 277 270 4-CH 271 10,200 269(sh) 265 259 254(sh) H 258 9,040 266 259 24,000 348 32,300 341(sh) 31,700 254(sh) 4,750 245 7,030 2,090 297(sh) 16,500 1,450 287 19,100 1,340 231(sh) 9,300 225 10,800 500 264 15,700 550 530 400 330 288 1,420 430 252 13,700 254 370 249(sh) 280 di Data measured at 30°C. - 145 -BIBLIOGRAPHY 1. W. Ramsay and S. Young, Phil. Trans. 177, 71 (1886) 2. W.H.Perkin, J. Chem. Soc. 51, 808 (1887) 3. H.T. Brown and P.S.U. Pickering, J. Chem. Soc. 7_1, 774 (1897). 4. I.F. Homfray J. Chem. Soc. 87, 1435 (1905). 5. S.A. 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