THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING KINETICS OF THE LIQUID-PHASE ADDITION REACTIONS INITIATED BY PROPYLENE OXIDE AND METHANOL AND CATALYZED BY SODIUM HYDROXIDEManchiu D. S. Lay A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1958 February 1959 IP-353

Doctoral Committee: Professor Professor Professor Professor Professor Julius T. Banchero, Chairman Leigh Anderson Stuart W. Churchill Joseph J. Martin Robert R. White ii

ACKNOWLEDGMENT The author wishes to take this opportunity to thank the following persons who contributed in one way or another to the completion of this work: Professor J. T. Banchero, for his understanding, advice and the many helpful suggestions during this investigation. The other members of the Doctoral Committee for their continued interest: Professors L. Anderson, S. W. Churchill, J. J. Martin and R. R. White. Mr. H. Maget for many fruitful discussions on this subject and otherwise. The Dow Chemical Company for the propylene oxide and Dowanols used in this work. Miss Bertha Hugh for typing the manuscript and the Industry Program of the College of Engineering for printing this work. iii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS......o oo o........... o....... o........................ iii LIST OF TABLES................................................ vi LIST OF FIGURES..... o o o o o... o....................................... ix NOMENCLATURE... O.. o.. o. o.... o..... o.. a.... o. o............ xi INTRODUCTION.........................o........... o........... 1 LITERATURE REVIEW o.................................. 4 Kinetic and Product Distribution Studies............. 4 Reaction Mechanisms...,................................ 6 Equations Describing Product Distributions.,......... 11 Solvent Effects on the Ratio of Reaction and Product Distribution......................o...o...........o.o 11 EXPERIMENTAL METHODS AND APPARATUS............................ 13 Materials.........................................o... 15 Experimental Apparatus............0...0...00...0...o. 15 Experimental Procedure..o........................ 19 Analytical Methods................ o................ 20 EXPERIMENTAL DATA AND RESULTS.. o..o., o...o..........o.o..ooo 23 Considerations In the Formulation of the Rate Equations......................................o..... 23 Method of Correlation of Single Reactions............ 23 The Individual Reactions........,.. o.. o....o..... 30 Product Distributions..,,.,o............o.....o... 38 Composition Effects..o,.....o................ o..... 47 DISCUSSION OF RESULTS.,o,..o... oo..e.....o o..o............. 54 Uncatalyzed Reactions..o.............o............. 54 Activation Energy of the Catalyzed Reactions......... 57 The Influence of the Medium on the Rate of Reaction.o 58 Equations for the Rate Constants.................... 60 Temperature Influence on Medium Effects............ 64 Polarity of the Reacting Mediums.................... 65 Acidity of the Reactants.......................... 66 Accuracy of Measurements and Errors................. 67 Comparison with Work Reported in the Literature...... 68 iv

TABLE OF CONTENTS (CONT'D) Page CONCLUSIONS o o o o o...........o o o o......... o...................... o.. o o 74 APPENDICES I. PHYSICAL PROPERTIES,............ o o......... 76 Densities o.......o...............o....o......... 76 Refractive Indices................o...........o 76 Infrared Spectrograms....... o.,........... 79 II. ANALYTICAL METHO.DS....... oo oo o o o o o..o o o... 81 Chemical Analysis of Propylene Oxide...o..o... 81 Chemical Analysis of Hydraxyl Group.,............. 86 III. THEORETICAL AND EMPIRICAL TREATMENT OF REACTION RATE IN THE LIQUID PHASE... o.......... o........... o.. 89 Relationship Between Rate Constants and Activity of the Reacting Species............o....o...... 89 Molecular Association and Its Influence on the Kinetics of Liquid-Phase Chemical Reactions..... 95 Medium Effects on the Arrhenius Equation......o 95 IV, MATHEMATICAL DERIVATIONS..e...o.......... o.... o... 99 Equations Describing Product Distribution of Consecutive Reactionso.,,o..,.o...........,o...... 99 Application of the Least Squares Methods to the Arrhenius Equation o...................o. o. 104 V. EXPERIMENTAL DATA................................... 106 VI. SAMPLE CALCULATIONS.....o........................... 117 Single Reactions.,,,... o...................... 117 Product Distributions............o..... o o...... 119 BIBLIOGRAPHY.. o o o o o o o..........o o....o..............o.......... 121 v

LIST OF TABLES Table Page Summary of Experimental Work...................... 14 II Physical Properties of Reactants and Productso........ 15 III Representative Results of Calculated Rate Constants... 31 IV Rate Constants for the Reaction Between Methanol and Propylene Oxide........o..........................5. 35 V Rate Constants for the Reaction Between Dipropylene Glycol Methyl Ether and Propylene Oxide............... 36 VI Rate Constants for the Reaction Between Tripropylene Glycol Methyl Ether and Propylene Oxide.........o.... 37 VII Product Distribution Data; Starting Materials: Propylene Oxide and Methanol. Temperature of Reaction 45 C. o o s * o...*.o o * e * 40 VIII Product Distribution Data; Starting Materials: Propylene Oxide and Monopropylene Glycol Methyl Ether. Temperature of Reaction 60~C..o**.......o*.......*.... 40 IX Comparison of Ratios of Rate Constants Obtained From Single Reaction Experiments with Values Obtained From Product Distribution Data Initiated by the Reaction of Propylene Oxide with Methanol at 45~C............. 45 X Comparison of Ratios of Rate Constants Obtained From Single Reaction Experiments with Values Obtained From Product Distribution Data Initiated by the Reaction of Propylene Oxide with Propylene Glycol Methyl Ether at 60 ~C.......... o o.......o... o e 45 XI Values of the Pseudo-First Order Constants for the Reaction of Propylene Oxide witi a Mixture of Methanol and Propylene Glycol Methyl Ether at 450C............. 52 XII Activation Energies of Individual Reactions......... 57 XIII Successive Approximation for Value of C1 and C2....... 62 XIV Comparison of Experimental Product Distribution Data with Calculated Results for the System of Reactions Initiated by Propylene Oxide and Methanol at 550C and 64 C o0*...oo o..o...................................... 64 vi

LIST OF TABLE& (CONT ID) Table Pg XV Dielectric Constants at 250C.,.......000600o. 65 XVI Autoprotolysis Cosat,.,,....*,,,.. 66 XVII Estimation of Accuracy of Individual Measurements Involved in the Experimental Work...,.................. 6 XVIII Accuracy of the Activation Energies for the Rate Constants of the Individual Reactions..,..,....,..... 68 XIX Variation of Density of Reacting Mixture..oo.,,,...,,. 69 XX Velocity Constants at 250C f or Ethylene Oxide and Propylene Oxide with Various Alcohols Using Sodium Hydroxide as Catalyst........,,...... 0000000*0 70 XXI Comparison of Product Distribution Initiated by the Reaction of Propylene Oxide with Propylene Glycol Methyl Ether at 6o0C,....,..............00......... 72 XXII Methods of Analysis for Propylene and Ethylene )XXIII Analysis of Propylene Oxide in Alcohol-Ether by the Aqueous HCl-CaCl2 Method,..o....... ~....,...o 84 XXIV Analysis of Propylene Oxide in Alcohol-Ether Using the Periodic-Perchloric Acid Method..,,,o........ 87 XXV Analysis of Hydroxyl Group in Alcohol-Ethers by the Acetic Anhydride-Pyridine Method..,,.......,., 88 XXVI Reaction Velocity Constants for Methanol-Propylene Oxide Reaction From Propylene Oxide Concentration Data.,o.,o.,,,,.,.o........,.,...,. 16 XXVII Reaction Velocity Constants for the Dipropylene Glycol Methyl Ether-Propylene Oxide Reaction From Propylene Oxide Concentration Data....,.,o.,,....,..... 107 XXVIII Reaction Velocity Constants for the Tripropylene Glycol Methyl Ether-Propylene Oxide Reaction From Propylene Oxide Concentration Data..,.,,.,....,O.. 111 XXIX Reaction Velocity Constants for Methanol-Propylene Oxide Reaction in Dioxane From Propylene Oxide Concentration Data at 450C. *,.,.***.,. 114 vii

LIST OF TABLES (CONT'D) Table Page XXX Experimental Time-Composition Data and Pseudo-First Order Rate Constants for the Reaction of Propylene Oxide with a Mixture of Methanol and Propylene Glycol Methyl Ether at 45~C.......0.....o......o........ o.. 115 XXXI Raw Data From Run 1 of the Reaction of Tripropylene Glycol Ether with Propylene Oxide at 100~C and a Starting Mole Ratio of Alcohol to Oxide of 9.25/1.... 117 XXXII Results From the Conversion of c.c. Na2S207 to Moles Per Liter of Propylene Oxide for the Data in Table XXXI... o... o.................................. 118 XXXIII Results of the Calculation for the Specific Reaction Velocity Constant Using the Data in Table XXXII...... 119 viii

LIST OF FIGURES Figure Page 1 Glass Reactor Set-Up. o.... o.. o......o. o.. 17 2 Concentration-Time Curves of Propylene Oxide in the Reaction of Propylene Oxide with Dipropylene Glycol Methyl Ether at 85~C O., o o o o o,. o.......... o o o 24 3 Concentration-Time Curves of Propylene Oxide in the Reaction of Propylene Oxide with Tripropylene Glycol Methyl Ether at 85C o......................... 25 4 Effect of Catalyst Concentration on the Reaction Velocity Constants of the Propylene Oxide - Dipropylene Glycol Methyl Ether Reaction..,.... o......... 33 5 Effect of Catalyst Concentration of thel Reaction Velocity Constants of the Propylene Oxide - Tripropylene Glycol Methyl Ether Reaction,...... o.......... 54 6 Effect of Temperature on the Catalyzed Reaction Velocity Constants...........o o.......... o o o. 59 7 Comparison of Experimental Product Distribution with Calculated Values for the System of Reaction Initiated by the Reaction of Propylene Oxide with Methanol at 45OCo,o o, oooooooosoooooeo oooooooo.oooeeoo.,.*o 44 8 Comparison of Experimental Product Distribution with Calculated Values for the System of Reaction Initiated by the Reaction of Propylene Oxide with Propylene Glycol Methyl Ether at 60C o..,................o.o 46 9 Effect of Dioxane on the Rate Constant of the Reaction of Propylene Oxide with Methanol at 45~C..ooo,. 48 10 Concentration-Time Curves of Propylene Oxide in the Reaction of Propylene Oxide with Mixtures of Methanol and Propylene Glycol Methyl Ethers at 45~C....o..o... 50 11 Concentration-Time Curves of Propylene Oxide in the Reaction of Propylene Oxide with Mixtures of Methanol and Propylene Glycol Methyl Ether at 450~C..o.....oo. 51 12 Variation of GA with Methanol Concentration,..,...... 53 13 Effect of Temperature on the Uncatalyzed Reaction Velocity Constants,o,,.o..........o ooo....,...o. o 56 ix

LIST OF FIGURES (CONTD) Figure 14 Variation of the Reaction Velocity Constants, k, and k2, With Methanol Concentration....,...,........ 63 15 Comparison of Experimental Product Distribution - Time Data With Calculated Values at 13500........... 16 Effect of Temperature on the Density of AlcoholEthers.,,,,,,,,,,,,,,..,,*,,,,**.,,,,,* 77 17 Binary Refractive Index of Alcohol Ethers at 250C.... 78 18 Infrared Spectrogram of Dipropylene Glycol Methyl Ether and Tripropylene Glycol Methyl Ether,..oo.... 8o 19 Calculated Product Distribution Curves (C = 1, 0.5 and O.10)....0........,.............. 0..... 0000...00 120 x

NOMENCLATURE A, Moles of component A. [A], Alcohol, moles per 100 gramso A, Pre-exponential factor in the Arrhenius Equation. ABn Moles of alcohol-ethers at any time t. B, Moles of propylene oxide at any time to [B], Propylene oxide, moles per 100 grams. CA. Concentration of the anion of alcohol, moles per liter. CA, Concentration of methanol at any time t, moles per liter, CAo, Initial concentration of methanol, moles per liter. CA, Pure methanol, moles per liter. CABn) Concentration of alcohol-ethers at anytime t, moles per liter. CB, Concentration of propylene oxide, moles per liter. Cn, Constants used in the equation for rate constants. D, Dielectric constant. Do, Dielectric constant of the pure alcohol. E, The measured Arrhenius activation energy, calories per gram-mole, E, The activation energy obtained by extrapolating to l/D = 0, GA GA klCA + k2 B ~ K, Boltzmann constant. K Equilibrium constant. eq. M, Reciprocal of the molal volume of methanol at the temperature of the reaction. N, Avogadro's number, RQ, Anion of the alcohol. xi

NOMENCLATURE (CONT'D) R, The gas constant, 1.987 calories per gram-mole per degrees Kelvin o T, Absolute temperature, OK, V, Volume, liters. Z Charge. aj, Distance of closest approach of another ion to the ith ion. ci, Concentration of the ith ion, moles per liter, c cj, Distribution constant, kn/kl, kj/k1o j,n>l. c, Catalyst concentration, moles per liter. e Electronic chargeo f(CA), A function of methanol concentration. h, PlancK s constant o k Rate constant. kw, Rate constant at infinite dilutiono kc Catalyzed second order rate constant, moles 2liter2min. -. km., Rate constant as function of the reacting medium. kn, Catalyzed second order rate constants corresponding to an excess of alcohol in the reacting medium at unit molar catalyst concen2 2 -1 tration, moles-2liter2 min.-l kn, Second order rate constant at unit molar catalyst concentration, moles 21iter2mino 2 ku, Uncatalyzed second order rate constants, moles 2liter2min.1 ko~ Rate constant referred to the gas phase. nt, Total number of moles per 100 grams of initial charge. n5 Refractive index at 25~C. ra, Radius of molecule a. rA Radius of the activated complex. xii

NOMENCLATURE (CONT 'D) t, Time in minuteso v, Ratio of moles of oxide consumed to moles of initial alcohol. 5, Activity coefficient. Ya,b' Activity coefficient of the reactants. 7i.. Activity coefficient of the ith ion. 7y Activity coefficient of the activated complex. ASr, Entropy of activation. AH, Heat of activationo, Ionic strength = 1/2 Z ciZi

INTRODUCTION The interest in reactions between epoxides and alcohols goes back as far as 1894 when Roithner(64) observed the reaction of ethylene oxide and propylene oxide with phenol. Industrial applications for the reaction products were proposed even then. However, it was not until about thirty years later that these reactions received widespread attention when I. G. Farbenindustrie(20) patented the process for condensing short chain alcohols with ethylene oxide in the presence of acidic or basic catalysts. Since then, the reaction products obtained from the condensation of epoxides with alcohols have been extensively used as solvents, lubricants, wetting, emulsifying and drying agents, and as chemical intermediates, Considerable information is found in the patent and technical literature about these reactions, most of which however, are concerned with the applications of the products. Rate studies of these reactions have received scant attention until recently. (57) Pecorini, in this laboratory, has initiated the investigation of the liquid-phase kinetics of the reaction between propylene oxide and methanol, catalyzed by sodium hydroxide. The reaction gives rise to a system of consecutive addition steps represented as follows: CH OH + CHCHCH -C. CH OCH2CHOH (1) CH3 CH3OCH2CHOH + CH3CH-CH2 k2 CH3(OCH2CH)20H (2) CH3 6 CH3.-, 1

CH3(OCH2CH)2OH + CH CH-CH2 — k C(OC(oCH2)3OH (3) CH3 0 CH3 CH3(0CH2CH)30H + CHCH-RH^ 4 CH3(OCHCCH)H (4) or in general, k CH3(OCHgH)nOH + CHCH-CH-H n CHR(OCH2CH) n+OH (5) CH CCH 3 3 where n = 1, 29 3,... Although different isomeric products are possible for the reactions, it was shown that for the first reaction the product is exclusively a secondary alcohol(57). In the present work, the glycol ethers used and the products formed from the succeeding reactions were assumed to consist of only one isomer. The work of Pecorini was limited to the study of the individual rates of reactions 1 and 2 and of the rates when the two reactions occurred consecutively. Semi-empirical rate equations were derived so that the rate data for reactions (1) and (2) when occurring consecutively could be predicted from the rate constants obtained for the individual reactions. However, most of the work on individual reactions was limited to an alcohol to oxide mole ratio of 5 to 1 and the data obtained from the study of the consecutive reactions are mainly based on a starting mole ratio of alcohol to oxide of 1 to 1. The effect of composition change on the rate constants was therefore investigated only over a limited range. In a consecutive and competitive reaction system, as the one described above, the nature of the distribution of the products is of major importance. Theoretically, if the reaction velocity of each of

-5 - the individual steps is known, the product distribution of the system can be readily calculated. A frequently observed phenomenon concerning reaction systems similar to the one mentioned above is the inability of the individuallydetermined rate of reaction to describe the product distribution of the system. ( 4654 55 > 7 7 ) Although no satisfactory explanation has yet been advanced to explain this behavior, it is generally believed that factors such as solvent effects, ionization equilibria and the different acidities of the reactants may be involved. The present investigation was therefore initiated to extend Pecorini's work as well as to try to gain an insight in to the factors that may influence the reaction velocity of the system under varied conditions and to derive a set of consistent rate equations that can describe the kinetics of the system under all the conditions studied.

LITERATURE REVIEW Most of the fundamental work reported in the literature on the reactions of low molecular weight epoxides with alcohols are mechanism studies. To our knowledge, only the following papers reported rate investigations on the reactions of ethylene or propylene oxide with short (55,57.58,Y76 chain aliphatic alcohols.) On the other hand, extensive, work on the reaction of epoxides with water has been reported.(6 9'l13 41,46,48,65) Kinetic and Product Distribution Studies Natta(55) reported kinetic and product distribution studies of the uncatalyzed reaction of ethylene oxide with methanol and with their products of reaction. From product distribution data, the ratios of rate constants (distribution constants) at constant temperatures were derived and it was shown that the individual second order rate constants can be calculated by a simple substitution if the time, amount of initial reactants and the distribution constants were known. Specific second order rate constants, obtained in this manner, were presented for the uncatalyzed reactions between ethylene oxide and methanol; ethylene oxide and ethylene glycol monomethyl ether. It was observed, however, that the specific rate constants calculated for the reactions ethylene oxide-ethylene glycol monomethyl ether and ethylene oxide-diethylene glycol monomethyl ether from product distribution data initiated by the reaction of ethylene oxide with methanol have values quite different from the rate constants evaluated from product distribution data initiated by the reactions themselves,

-5 -(76) Weibull and Nycander investigated the product distributions initiated by the reaction of ethylene oxide with ethanol and ethylene oxide with ethylene glycol monoethyl ether using sodium as a catalysts The ratio of rate constants (distribution constants) from the product distribution studies were compared with ratios of individually determined rate constants using dilute solutions of ethylene oxide in the respective alcohols, The data presented were limited and the distribution data were obtained at 65~C while the individual rate constants reported were at a temperature of 25~C, Nevertheless, the discrepancies between the distribution constants and the ratio of the rate constants were too large to be attributed to temperature effects alone. Pecorini and Banchero(5 studied the liquid-phase sodium hydroxide catalyzed reactions of propylene oxide with methanol and propylene oxide with propylene glycol monomethyl ether. The individual rate constants were obtained using a starting mole ratio of alcohol to propylene oxide of 5/1. The data obtained covered the temperature range 35-100~C and catalyst concentrations from 0-1.5 weight percent. It was found that normal second order reaction rate constants calculated from data obtained from single reaction experiments do not agree with rate constants derived from time-composition data wherein several additional products were formedo As a result, a semi-empirical rate equation was developed which was shown to correlate all the experimental data. Recently, Satkowski and Hsu(66) reported kinetic data on the addition reaction of ethylene oxide with tridecyl alcohol in the presence of various basic catalysts in a constant pressure reactor. They found that at elevated temperatures (190~-200~C) the rate of addition

of ethylene oxide is constant indicating that the rate constants of each succeeding reaction are equal. The reactions of ethylene oxide and propylene oxide with phenols (7) in alkaline solutions have been investigated by Boyd and Marle(7) and second order velocity constants were obtained for the reactions at one temperatureo Miller, Bann, and Thrower (49) and Patat, Cremer, and Bobleter(56) reported product distributions for the base-catalyzed reactions initiated by ethylene oxide and phenol. Their data indicated that the rate of reaction of ethylene oxide with phenol to form ethylene glycol monophenyl ether is very much faster than the reactions of ethylene oxide with the succeeding products formed. More extensive work on the kinetics of the reactions of ethylene (13,41,46,65) oxide and propylene oxide with water)uncatalyzed and catalized by acids (6,948,65) or bases (34146) has been reported. The similarity of the structures of alcohols and water suggests the usefulness of the hydration data in understanding the alcoholysis of epoxides. Reaction Mechanisms The alcoholysis and hydrolysis of epoxides proceed in three kinetically distinct reactions. Namely, the base-catalyzed reaction, the pH independent reaction, and the acid-catalyzed reaction. Ingold(32) has summarized the probable mechanisms involved in these reactions. The formulated mechanism for the base-catalyzed reaction is an 'S2(substitution, nucleophilic, bimolecular) mechanism as follows:

-7 - V slow (6) OR- + CH CH-CHo CH CHCCHOR (6) CH3-CHCH20R + ROH fas CH3CH-CH20R + ROT (7) 0 O0 H where the rate may be represented as rate = k (epoxide)(RO-). This has been deduced and corroborated by mechanism studies in the hydration of epoxides and from extensive work on the mechanism of the reaction of epoxides with alcohols(3'11'33'69'72) Specific support for the SN2 mechanism has come from the following sources: 1. Structural isomers formed from the reaction It is well known that the base-catalyzed reaction between unsymmetrical epoxides and alcohols gives two isomeric products(2'l'33j' 63,72) although the preferential attack of the anion on the primary carbon atom usually yields a high percentage or near exclusive amount of the secondary alcohol-ethers. For example, the reaction of propylene oxide with methanol, catalyzed by sodium hydroxide, yields exclusively: CH3OH + CH3-CH-CH -Na CH-CH-CH2OCH (8) 3 5 \/2 3`0H5 (8) 0 0 H (63) the secondary alcohol-ether. This has been interpreted as a bimolecular nucleophilic (SN2) attack of the alkoxy ion selectively at the primary carbon atom because of its lower electron density as shown by the configuration denoting the relative charge in the various atonms of the propylene oxide molecule CH3 --- CH -CH2 N56 0

The charge distribution of the propylene oxide molecule as represented is a consequence of the electron-repelling nature of the methyl group and the electronegativity of the oxygen atom. One would therefore expect a nucleophilic attack of the alkoxy ion predominantly on the primary carbon atom of the epoxide ring. This has been shown to be the case experimentally( 11 69) Furthermore, for other unsymmetrical epoxides the ratio of the isomeric products obtained was observed to be constant as the base strength was increased, indicating that the cleavage of both C-O bonds proceed under the same mechanism(3) The type of attacking alkoxy ion was found to have no effect on the direction of ring openings, although the rates of reaction were affected(ll). The type of epoxide, however, has a marked effect on the ratio of isomeric products formed. This can be readily clarified by the charge distribution of the molecule and the possibility of steric hindrances 2. Base-catalyzed reactions Most base-catalyzed homogeneous organic reactions are characterized by two distinct steps (1) The protolytic step in which the acid transfers a proton to the base and, (2) the subsequent reaction of the product of protolysis to form the end product. Both steps are bimolecular processes. 3o Stereochemical considerations The mechanism of bimolecular nucleophilic (SN2) displacement involves backside attack on the carbon atom -- this position of approach, which requires the least amount of energy, would result in the inversion

(28) (30) of configuration, Hammett has pointed out that total inversion is a consequence of a bimolecular nucleophilic substitution. Such an inversion for the case of an SN2 attack of the propylene oxide molecule by an anion may be represented as follows: (9) H3C H _ CH3 H / CHO __ /5 INVERSION OCH3 H H H H Backside attack of the propylene oxide molecule by methoxy ion 4. Isotopic tracer studies More recent work using isotopic oxygen (018) and chlorine (C138) further reinforced the bimolecular nucleophilic mechanisms of the base(42) catalyzed reactions of epoxides with alcohols For the uncatalyzed reactions, the proposed mechanism were not as specific, Ingold(3 listed three possible mechanisms for the spontaneous reaction, They are, in the order of acceptance, as follows: 1. The SN2 substitution of the epoxide base with the alcohol molecule as a substituting agents _ _ /H CH3CH-CHO2CH3 CH 3- CH 2 + 0 -- OH (10) 0 2- HCH >CHHCH OH OCH3 2. The STl substitution of the epoxide base. CH CH-CH slow CHCH-CH + (l 3-H-H2 CH3CH-CH2 +(11) 0 06 H CH CH-C + OCH H -- CH CH-CH OCH3 (l2) 0_ + OH

35 SN2 substitution by the alkoxy ion in the conjugate acid of the epoxide. CH3OH + CH 3-CH-CH2 CH30- + CH3-CH-CH2 3 + 0 0 (13) CHO 3 + CH3 CH-CH2 slo CHoCH-CHOCH (4) 3 3c-/02 3 2 3 H+ The slow rate of reaction for the uncatalyzed alcoholysis of epoxides is one of the reasons for not having a better understanding of the mechanism of the reaction. In the acid-catalyzed alcoholysis of epoxides, the favored mechanism is an SN1 substitution of the conjugated acid 32 42) where a carbonium ion is an intermediate. RCH-CH2 + H > RCH-CH2 equilibrium (15) \O O H+ H RCH-CH2 slow > RC+HCHOH (16) \0 OH+ OR RC HCH2OH + ROH fast > R-CH-CH20H + H (17) Examples in support of this mechanism are the reversla of orientation in the ethyl alcoholysis of propylene oxide on changing from alkaline (11) (42) to acidic condition ) and also from the work by Long and Pritchard( It is quite possible to have several mechanisms operating concurrently. There is actually no sharp dividing line between the SN1 (32) and SN2 mechanism Cases have been known wherein the mechanism for a series of homologous reactions changed from aniSN1 mechanism to an

SN2 mechanism as was the case with the alkaline hydrolysis of alkyl (32) halides Equations Describing Product Distributions For a system, of consecutive additional reactions such as those shown on page 2, the product distribution is proportional to the reaction probabilities of each individual reaction, The general case of the distribution of products in a series of bimolecular competitive reactions at constant temperature, with different rates for each step, in terms of the remaining concentration of the starting (54) material has been derived by Natta and Mantica(5. Less comprehensive treatments have also been considered previously by Abel(, Fuoss () f47) and Martin and Fuchs o Several simplified forms of the general case have also been (25) derived Flory'(3) considered the case where all the reaction probabil-. ities are equal and showed that the Poisson distribution describes the products obtained, Weibull and Nycander76), going a step further, considered the case where only the rate of the first step is different from the rates of all the succeeding steps, the rates of the succeeding steps being all equal, Solvent Effects on the Rates of Reaction and, Product Distribution No results are available in the literature on the effects of solvents and changing compositions on the rates of reaction or product distributions on epoxide-alcohol reactions although speculations have (54,55) (46) been made Maget studied these effects on the sodium hydroxide catalyzed propylene oxide-water reaction and has shown

that these effects may be predicted in terms of the starting concentrations of the reactants or the dielectric constants of the reacting medium,

EXPERIMENTAL METHODS AND APPARATUS The scope of the experimental work may be conveniently divided into three distinct parts: In the first part, the effects of temperature and catalyst concentration upon the rate constants for the homogeneous reaction of propylene oxide with dipropylene glycol monomethyl ether, and the reaction of propylene oxide with tripropylene glycol methyl ether, using sodium hydroxide as catalyst were investigated. Additional rate data on the reaction of propylene oxide with methanol were also obtained at several temperatureso The second part of the experimental work consisted of obtaining product distribution data initiated by the reaction of propylene oxide with methanol and by the reaction of propylene oxide with monoglycol methyl ether. While the first part of the work was primarily performed to obtain reaction rate constants of the individual reactions, the second part was run. to test the applicability of these rate constants under conditions where several consecutive reactions were occurring at the same time, Finally, the remaining part consisted of experimental work done in an attempt to explain the results obtained in the first two parts. They comprised several runs in which the sodium hydroxide catalyzed reaction of propylene oxide with mathanol in dioxane as solvent and the catalyzed reaction of propylene oxide with methanol and monoglycol monomethyl ether were studiedo

TABLE I SUMMARY OF EXPERIMENTAL WORK Re s Temp. Cat. conc. Starting alcohol to oxide Table Reactionle ratio No. ~C mols./lit. mole ratio No. Single Reactions methanolpropylene oxide dipropylene glycol methyl ether - propylene oxide 35-5.5 35-87 0.139 - 0.252 0.0556 - 0.3469 XXVI 5 - 10 XXVII tripropylene glycol methyl ether- propylene oxide 45-100 0.05683 - 0.3495 7 -10.25 XXVIII Product Distribution (Initiating Reaction) -Fj methanolpropylene oxide 45 o.52.305.21-5 -.305 0.645 - 10 0.667 - 3 VII VIII propylene glycol methyl, ether - propylene oxide 60 Mixed Reactions methanol - propylene oxide in dioxane methanol and propylene glycol methyl ether - propylene oxide 0.1839 - 0.234 12.51 - 37-20 0.575 - 6.90 XXIX (dioxane conrT mol./lit.) 0.1625 - 0.266 6.67 -3-5.20(methanol/oxide) XXX 4.06 - 13.50(glycol/oxide)

-15 All experimental data were obtained in batch reactors described in page 17. A tabulated summary of all the experimental work is presented in Table I. Materials The propylene oxide, propylene glycol ether, dipropylene glycol ether and tripropylene glycol ether were Dow Chemical Company commercial grade products and were used without further purification, The methyl alcohol used was reagent grade material. The dioxane used in the solvent experiments was a technical grade product that had been refluxed with sodium hydroxide for two hours and then distilled. A summary of the physical properties and purity of the reactants is tabulated in Table IIo More detailed physical properties of the reactants and products including their infrared spectra are presented in Appendix I. Experimental Apparatus All of the experiments, except for the uncatalyzed runs, were performed in a 500 ml. glass reactor kept at a constant temperature by an oil bath as shown in Figure 1. Heat was supplied to the bath by a 200-watt copper resistance coil heater and controlled through a relay by a Fenwal contact type thermoregulatoro The thermoregulator was sen sitive to a temperature change of + 0.10C in the range of temperatures of the experiments. An air-driven bath stirrer kept the bath temperature uniform. The temperature inside the reactor generally does not vary by

TABLE II PHYSICAL PROPERTIES OF REACTANTS AND PRODUCTS Materials Molecular Density Boiling Refractive Water Ref. Weight 250C Point ~C Index n 5 Content 760 mm Hg. D wt. % Propylene oxide 58.08 0.824 33.9 1.363 0.1 (l0) Methanol 32.04 0.787 64.7 1.3275 0.1 (57) Propylene glycol monomethyl ether 02 0.918 120.0 1.402* (16) monomethyl ether TDipropylene glycol monomethyl ether 206.28 0.965 242.8 1.428* 0.15* (16) Tetrapropylene glycol 2646 0978* 1.42 (16) monomethyl ether Dioxane 88.10 1.041 101.3 1.42(10) H * Values experimentally determined by the author.

I To reLay' and power supply B D oil bath A - 500 ml. round bottom flask B - 5 gal. battery jar C - Fenwal Thermoregulator D - Copper heating coil E - Thermometer F - Mercury-seal stirrer G - Water condenser H - Motor driven stirrer I - Soda-Lime drying tube J - Sample withdrawal tube Figure 1. Glass Reactor Set-Up.

more than 0.20~C. A temperature history of a typical run is shown in Appendix VIo Although the propylene oxide-alcohol reaction is an exo(57) thermic one(57) the addition of about 4 mass percent propylene oxide to start the reaction produces negligible temperature change of the reacting mixtureo The glass reactor was a modified 35neck 500 ml, round bottom flask with a fourth opening added in the form of an 8 mmo Pyrex glass tubing as shown in Figure 1. A water condenser and a calibrated thermometer were inserted in the two side necks while an air-driven, mercury seal, stirrer passed through the center neck, The glass tubing opening was sealed with a serum cap and samples were withdrawn through this cap by means of a hypodermic needle and calibrated syringeo The uncatalyzed runs were performed at 200~C in an autoclave (57) previously described by Pecorini. This was a Monel pressure vessel with a capacity of 2.7 liters and equipped with a magnetically operated agitator. Lines were provided for the introduction of reactants as well as removal of products at any time during the runo Analysis of the products obtained in the product distribution runs was made by distillation using fractionating columns and auxiliary (74) equipment which have been described in the literature Two columns were used, one was a twelve mm.I.D. column packed with 89 cmo of 3/16 single-turn glass helices corresponding to about thirty theoretical plates and having a hold-up of about 5 CoCo The other column was a 4 mm.I.D. column with a continuous Monel wire spiral and corresponding to about ten theoretical plates. The hold-up of this second column is negligible. The second column was primarily used to separate the higher

molecular fractions, The fractionation column had two heating jackets to compensate for any heat losses from the colu to the surroundings, A magnetic reflux splitter actuated by a contro.l.ed timer relay system regulated the reflux- and provided for regular take-off of distilled products o Experiental Procedures In the determination of the rate constants of each of the consecutive reactions (see page l), the time-composition history of propylene oxide was obtaised at predetermined temperatures and catalyst concentrations, An excess of the starting alcohol reactant was necessf ary to insure that no hgher products are formed and also to keep the medium change during the reaction negligible, The degree of dilution of the propylene oxide was dictated only by the 1=iitations of the analytical methods, A starting concentration of about 4 mass percent propylene oxide was used for all runs in the determination of the individual rate constants. This corresponds to alcohol to oxide mole ratios for reactions (3) and (4) of 10 and 7 respectively.An analysis of the reaction products of reactions (3) and (4) using these starting alcohol to oxide mole ratios has shown no detectable amount of higher products formed other than the first additional product, Approximately the same mass concentration of propylene oxide was used for the reaction of propylene oxide with methanol in dioxane and the reaction of propylene oxide with a starting mixture of methanol and propylene glycol ether. In the product distribution studies, various amounts of propylene oxide were reacted to completion with the alcohol and the final. mixture was analyzed.

-20 - The procedure used in conducting the runs in the glass reactor was essentially as follows: A predetermined —amount of the alcohol with a corresponding amount of dissolved sodium hydroxide catalyst was weighed into the glass reactor. The thermometer, water condenser and mercury seal stirrer were then put in. place and the whole reactor placed into the oil bath set at the desired temperature. Propylene oxide was then introduced into the reactor through the capped glass tubing by means of a calibrated syringe and hypodermic needle. The concentration of propylene oxide with respect to time during the reaction was then obtained by analysis of samples taken from the reacting mixture through the capped tubing at frequent intervals. In the case of a product distribution run, no samples were taken. The reactions were run to their conclusion by letting the reaction flask stay in the temperature -at-h for a prol.onged period. A. arnalysis for propylene oxide was made at the end of the run to insure that al.. tfhe propylene oxide was reacted. The resulting mixt;ure was then distilled and the fractions analyzed to determine the concentrations of the va-ious products For the uncatalyzed runs the pressurized tatch reactor, described (f7) previously, was used. The same procedure used by Pecorini.- was followed. An.alytical Methods 1. Analysis of Propylene Oxide Several methods were evaluated for the analysis of propylene oxide in the presence of the reactants and products. Two were chosen as the most desirable for our work,

-21 - (1) The hydrochloric acid-calcium chloride method. This method is essentially based on the fact that hydrogen qhloride adds to the alpha epoxide group to form a chlorohydrin according to the following equation I I 4 s -C ---- C — + + Clr --- -C — c- (18) o0 6H Cl The difference between the amount of acid added and the amount unconsumed, allowing for the presence of catalyst is the measure of the epoxide. (17} (2) The periodic-perchloric acid method The essential feature of tbis method is the hydration of the alpha epoxide group and the subsequent oxidization of the alpha glycol formed. The periodic acid is the specific oxidizing agent. The reactions proceed according to the following equations: I H H -C - C- + H+ + H20 ---- - (19) o / dH OH -C — C + HI04 - - RCHO + RCHO + H20 (20) OH OH + HI03 The free iodine liberated from the excess HIO4 by the addition of an aqueous solution of 10 percent potassium iodide is titrated with standard sqddium thiosulfate. The difference of the amount of thiosulfate used between a blank and the sample is the measure of the epoxide content of the sample. Both of the methods gave satisfactory results although prior calibration of the methods were necessary. A detailed summary of the work performed in reviewing and calibrating various methods are presented in Appendix II.

-22 - 2. Product Distribution Analyses Physical as well as chemical methods were used to obtain a complete product distribution analysis. A charge of about 100 grams of the reaction mixture from a product distribution run was first separated into binary fractions using the distillation columns previously described. By controlling the distillate temperature and operating the column under vacuum, each cut of the distillate from the column was taken such that only one or two components are present in any particular cut. The various fractions were then analyzed for the relative amount of the two components by refractive index measurements. Binary refractive index calibration curves of the reactants and products were prepared for this purpose. The calibration curves are shown in Appendix I. The residue left in the distillation flask which was of the order of ten grams was not amenable to the refractive index analysis. However, by assuming the residue is a binary mixture, an analysis of the hydroxyl group in the residue together with a material balance for the hydrox.yl group results in a complete description of the concentrations of the products. It may be noted that the hydroxyl concentration is invariant throughout,the reaction. The method of acetylation with acetic anhydride in pyridine(50) was used for the analysis of the hydroxyl group. The method was found to be satisfactory and in general gave quantitative results. Details of this method are found in Appendix II.

EXPERIMENTAL DATA AND RESULTS The experimentally determined data consisting of propylene oxide concentration versus time are tabulated in Appendix V. In Tables XXVI~XXYVIII theconcentration-time data of propylene oxide for the single reactions of propylene oxide with methanol, propylene oxide with dipropylene glycol methyl ether, and propylene oxide with tripopylene glycol methyl ether are collected. Table XXIX - tabulates the experimental data for the propylene oxide-methanol reaction in dioxane while Table -XXX.. presents the data for the experiments where propylene oxide was reacted with methanol and propylene glycol methyl ether simultaneously. In Figures 2 and 3 typical concentration curves for the reaction of propylene oxide with dipropylene glycol methyl ether and with tripropylene glycol methyl ether are shown. The product distribution data for the initial reaction of propylene oxide with methanol at 450C and the initial reaction of propylene oxide with propylene glycol methyl ether are tabulated in Tables VII and VIII on page,40o Considerations In the Formulation of the Rate Equations According to all available evidence, the most logical mechanism for the sodium hydroxide catalyzed liquid-phase reactions initiated by propylene oxide and methanol can be represented by the following simple steps: -23 -

-24 - 6 -w -J 0 g 4 z 0 z w3 z 0 0 02 Lu 2 Lu J 0. 0..I 0 0 100 200 TIME - MINUTES 300 Figure 2,. Concentration-Time Curves of' Propylene Oxide in the R~eaction of~ Propylene, Oxide with Dipropylene Glycol Methyl. Ether at 85WC.

-25 - 0...5 10 20 30 W \\ B. Q 6 0.3 \\ v v o P.I 0 0.30.0568 MOLES/LIT.(NoOH) 04 iUz 0.3 M 01134 MOLES/LIT. (NoOH) 0 L0,2 L. L ]0.2256 MOLES/LIT.(NoOH) 0 0.0.1 0.3368 MOLES/LIT.(NoOH) 0 100 200 300 TIME - MINUTES Figure 3. Concentration-Time Curves of Propylene Oxide in the Reaction of Propylene Oxide with Tripropylene Glycol Methyl Ether at 85~C.

Na0H INa+ + OH- (21) CEO H ' CH 0 + O(22) CH 3O + CHZCHCH - CH OCH2CHO- (25) 3~ / 2 CH 0 3 CH 3OCH2CHO_ + CH 3OH -—.CH3OCH2CO + CHO3 (4 CH3OCH2CHO- + CH 3CH-2H2 — ),CH 3OCH29HOCH2CHO- (25) CH5 o CH'5 26u CH 3OCH2CHOH + 0H -~ CH-5OCH2CHO_ + H20 (26) CH5 CH5 or in general CH3(OCH2CH)nOH + O-4kq. H()HC~O + H20 (27') CH3( OCH2gH)niO' + CH3S(OCH2CH)njOH < CH3( OCH2CH)n.0 H3CH3 6H53 + CH (OCH2CH)niOH (28) ni nj 6H3 CH3( OCH2CH)n0 + CH3CH-CH2 CH 3 C2Hn+ - (9 CH3 o 5 C2&3~l(9 and n = 0,1.,2,5,...nthe l'ate-controlling step is denoted by Equation (29). Pecorini(57') has shown that the protolytic step is not the rate-determining step in these series of reactions. In essence, the rate equation for each of the individual reactions of propylene oxide with the alcohol or alcohol-ethers may be represented as:

-27 - rate = k (Propylene oxide)(R0-) where k = constant for constant temperature RO-" = anion of the alcohol such a rate equation is valid only however under restricted conditions wherein intermolecular forces between reactants are kept at a minimum, e.g. in gas-phase reactions at moderate pressures and in dilute solutions in the condensed phase. In liquid-phase reactions where the compositions of reactants and products vary over a wide range of concentrations, the influence of the changing environment usually has to be taken into account, For a bimolecular reaction A + B = Z X- Products (30) activated complex the general rate expression is given by rate = k' CACB -ab (31) -7 where the specific rate constant k = k' (32) and k' = the rate constant at infinite dilution = activity coefficient of the reactants a,b yf = activity coefficient of the activated complex Equation (32) may be written in the equivalent logarithmic form as in k = n k' + in -a-b (33) 7i

The whole problem therefore reduces to the evaluation of the activity coefficients which are functions of temperature, pressure, and compositions, The actual experimental evaluation of these activity coefficients, however, is not only impractical but often times impossible. For example, 7 cannot be evaluated experimentally. Theoretical or empirical calculation of these activity coefficient are possible for some cases but their reliability is not expected to be very good. Appendix III presents some of the theoretical and empirical treatments of reaction rates in solution which are pertinent to this investigation. Method of Correlation of Single Reactions According to the mechanism postulated on page 26, the general form of the rate equation for the base-catalyzed reaction of propylene oxide with an alcohol or an alcohol-ether maybe represented as: B -km C C (34) dt where km = specific rate constant, liter mols. min.The subscript m is used to indicate that it is a function of the reacting medium. CA' = anion of the alcohol, moles per liter. CB = propylene oxide, moles per liter, The concentration of A" in the case where the reactions are confined individually by the use of high alcohol to oxide mole ratio is wholly dependent on the hydroxyl ion concentration.

Depending on the equilibrium constant of Equation (22), the observed kinetics maybe second-order, fir.st order inCA-, and first order inCB in the case when K for Equation (22) is large or for eq. the more usual case when Keq is small the observed kinetics will be third order, first order inCOH',CA, andCB. SinceCOH' is constant, being regenerated by the reaction shown in Equations (22) and (27) the kinetics maybe pseudo-second order or pseudo first order depending on the concentrations ofCA. In the case where A is in great excess CA + COF- -- CA- + CH2O (35) and Keq small,CA is essentially constant and the observed kinetics is a pseudo-first order one, By the use of Equations (21) and (22), Equation 04) may be rewritten as: d A CB - C(NaOH) (36) dt and since (NaOH) is constant in any one reaction, then dCB = - CACB (37) dt where kI is also dependent on the catalyst concentration. For any experimental run the condition of the medium can be kept practically constant through out the duration of the-run by using a great excess of one of the reactants -- in our case, the alcohol. Integration of Equation (37) gives k -(t) 1 A (38) CAo.- CBo CAO CB

-30 - where t = time in minutes CAo = initial concentration of alcohol, moles per liter CBo = initial concentration of propylene oxide, moles per liter CA = concentration of alcohol at time t, moles per liter CB = concentration of propylene oxide at time t, moles per liter Concentration units of moles per liter and a time unit of minutes were used throughout, the correlations forjthe rate equations and rate constants. The use of average density values for the reacting mixtures is not expected to introduce significant error with the dilute solutions used in the single reaction experiments. The errors involved are discussed on page 69 The specific rate constant k" can therefore be evaluated from m experimental concentration-time data of propylene oxide obtained in the individual reaction experiments. We must however keep in mind that these rate constants are dependent on the catalyst concentration and possibly on the composition of the reacting medium. Representative results of rate constants calculated from data obtained in the single reactions experiment using Equation (38) are given in Table III. The Individual Reactions In Tables IV-VI, the values of the rate constants are tabulated for the reactions of propylene oxide with methanol; propylene oxide with dipropylene glycol methyl ether and propylene oxide with tripropylene glycol methyl ether. The values were obtained using Equation (38).

TABLE III REPRESENTATIVE RESULTS OF CALCUILAED RATE CONSTANTS Run No. 1 Methanol-Propylene Oxide Reaction (temp. = 550C, catalyst cone, 0.252 mols./lit.) Initial Mole Ratio, Methanol to Oxide = 48,1 Time Propylene Oxide Cone, k mines. Mols./Lit, moles lit. min. 0 0.465 11 0,580 ooooo8o6 0 0254 0.0000oooo894 55 0.157 o.0ooo0 78 85 00o86 0.0000885 131 o0045 0.0000796 Run No. 6 Dipropylene Glycol Methyl Ether-Propylene Oxide Reaction (temp. = 850C, catalyst conc. = 0.1109 mole/lit.) Initial Mole Ratio, Diglycol Ether to Oxide = 10 Time Propylene Oxide Conc. k mins./, Mols./Lit. _M. moles lit. m.n.-l 0 90 185 270 360 0.5T6 o.1 92 0.109 0.057 0.00111 0, 00107 0.00113 0.00118 Run No. 1 Tripropylene Glycol Methyl Ether-Propylene Oxide Reaction (temp. s 1000C, catalyst cone. = 0.1895 moles/liter) Initial Mole Ratio, TriglycolEEther to Oxide = 9.25 Time Propylene Oxide Cone, k mins..Mols./Lit.. molel lit. min. 0 14.5 26.0 39.0 57.0 69.0 o.457 0.307.271 0.171,0114 0.078 0.o00662 0.oo487 0.00566 0.00625 0.oo644

The experimental data from which the rate constants were calculated are given in Appendix V. The linear dependence of the rate on the catalyst concentration is well known for many reactions involving acid-base catalysis. In the case of the system of reactions now under study, Pecorini(57) has shown that this is so for the NaOH-catalyzed reactions of propylene oxide with methanol, and propylene oxide with propylene glycol methyl ether. In Figures 4 and 5, the dependence of the rate constants on the concentration of NaOH is again shown to be linear for the reaction of propylene oxide with dipropylene glycol methyl ether and the reaction of propylene oxide with tripropylene glycol methyl ether. The temperature dependence of the rate constants presented in Tables IV-VI may be conveniently represented by the Arrhenius Equation Ek = A e RT (39) where k = specific rate constant A = thepre2.eqSpnential factor E = activation energy, calories/gm. mole R = Boltzmann constant, calories/gm mole ~K T = temperature, ~K. To do so, the values of the rate constants in Table IV-VI must all be reduced to one reference catalyst concentration such that the resultant rate constants would be independent of the catalyst concentration. In this case, the reference catalyst concentration is unit molar catalyst per liter.

-33 - 3x1l r 85 ~C LU 7L N.W Iw I',, LU 4 0:.IU) 69 ~C 35~C 0 0.I NaOH CONCENTRA\TION l MOLES PER LTER Figure 4. Effect of Catalyst Concentration on the Reaction Velocity Constants of the Propylene Oxlde-Dropylene Glycol Methyl Ether Reaction.

-34 - z a22Td w I-I 0 Figure 5 o 0J 02 03 0.4 NCO"9 CONCENTRATI0N, MOLES PER LITER Effect of Catalyst Concentration on the Reaction Velocity Constants of the Propylene Oxide -Tripropylene Glycol 1Wthyl Ether Reaction,

-35 - TABLE IV RATE CONSTANTS FOR THE REACTION BETWEEN METHANOL AND PROPYLENE OXIDE k Run Temp. Mole Ratio Cat. Conc. lit. Number 0C Alcohol/Oxide Mols./Lit. mols.mins. -: 1 35 48.1 0.139 o.oooo884 2 45 38.4 0.172 0.000292 3 55 48.8 0.252 0.000852

-36 - TABLE V RATE CONSTANTS FOR THE REACTION BETWEEN DIPROPYLENE GLYCOL METHYL ETHER AND PROPYLENE OXIDE k Run Temp~. Mole Ratio Cat. Conc. lit. Number 0C Alcohol/Oxide Mols./Lit. rnols.mins. 1 87 10 0.1764 0.00179 2 87 10 0.1764 0.001924 3 87 10 0.1764 0.001941 4 87 5 0.1764 0.002265 5 85 10 0.0556 0.000445 6 85 10 0.1109 0.001121 7 85 10 0.1109 0.000987 8 85 10 0.2207 0.002250 9 85 10 0.3295 0.003790 10 69 10.1 0.2746 0.001060 11 60 10 0.1158 0.000194 12 6o 10 0.1195 0.000224 15 6o 10 0.2R27 0.000425 14 60 10 0.2264 o.ooo5o3 15 60 10 0.3380 0.000602 16 55 10 0.1168 0.0000515 17 55 10 0.2525 0.000725 18 55 10 0.5469 0.000908

-37 - TABLE VI RATE CONSTANTS FOR THE REACTION ]IETWEEN TRIPROPYLENE GLYCOL METHYL ETHER AND PROPYLENE OXIDE k Rurn Temp Mole Ratio Cat. Conc, lit, Number 0C Alcohol/Oxide Mols./Lit. mols. mins. 1 100 9.25 0.1895 0.00597 2 100 10.25 o.19o0 0,00612 3 85 7 0.05683 0,00742 4 a5 7 0.1154 0.00133 5 85 7 0,2256 o.0o3o6 6 85 7 0.3368.oo0386 7 60 7 0.05683 o,ooolo6 8 60 7 0.1162 0.000224 9 6o 7 0,2511 0.00050.2 10 60 7 0.345 0.00076 11 45 7.005897 040000276 12 45 7 0,1177 0,0000536 13 45 7 0.2341 oooolo6 14 45 7 0.3495 0.000205

-38 - The constants in the Arrhenius Equation were then evaluated for each reaction by the least squares method (see Appendix IV). The rate constants 1k, kp, k3 and k4 were calculated from experimental runs using an initial alcohol to oxide mole ratio of 40:1, 5:1, 10:1, and 7:1 respectively. The Arrhenius Equation for k was evaluated from data re(57) ported by Pecorini. It is being included here for the sake of completeness. The subscripts on each rate constant refers to the equations on page o For example l refers to the propylene oxide-methanol reaction, etc., 17,200 -2 2. = 1.02 (l09) e RT moles lito min. (40) - 11700 -2 2 -1 k2 = 0.97 (105) e RT moles lit. min. (41) _15,800 -2 2 k3 = 4.75 (107) e RT moles lit. min. (42) - 8,500oo -2 2 -1 = 2.25 (109) e RT moles lit. min. (45) In Figure 6 the four rate constants were plotted versus the reciprocal of the absolute temperature. The significance of these curves is discussed in page 57 Product Distributions The general applicability of the rate constants as represented by Equations (40-43) may be evaluated by the ability of these rate constants to reproduce experimental product distribution data. With this in mind, two sets of product distribution data were obtained experimentally. The first experimental product distribution was obtained by reacting methanol with various amounts of propylene oxide to completion at 45~C, The data are tabulated in Table VII.

-159 - 0.04 0.02 k 0.01 0.008 '1IJwQ006 I~z 20.004 x Su,) 0 0.0008 00004 2.7 Figure 6. lIT X 101 Efftect of' Temperature on the Catalyzed Reaction Velocity Constants.

TABLE VII PRODUCT DISTRIBUTION DATA; STARTING MATERIALS: PROPYLENE OXIDE AND METHANOL. TEMPERATURE OF REACTION 45~Co Catalyst Run Concentration mole ratio methanol monoglycol diglycol triglycol No. moles/liter methanol/oxide mole fractions 1 0.152 10o00 0.90 0.10 2 0o180 6,25 o085 0.15 3 0.325 1.79 0o43 0.52 0.05 4 03550 1.067 0.149 0.736 0.115 5 0.382 0.834 -- 0.78 0.20 0.02 6 0.305 o.645 -- 0.495 0.32 0o185 ~,.,.,,.,.,,.,=,,....., J,,,, L,,,,.,,i,,. r.,,,,,.,,,,, TL,, The second set of product distribution data was obtained experimentally by reacting propylene glycol methyl ether with various amounts Of propylene oxide to completion at 60~C. The results are tabulated in Table VIII. TABLE VIII PRODUCT DISTRIBUTION DATA; STARTING MATERIALS: PROPYLENE OXIDE AND MONOPROPYLENE GLYCOL METHYL ETHER. TEMPERATURE OF REACTION 60 C. Catalyst mole _fractions Run Concentration mole ratio mono- di- tri- tetra- pentaNo. moles/liter alcohol/oxide glycol glycol glycol glycol glycol 1 0.215 3.00 0.75 0.222 0.026 2 0.278 2.00 0.59 0.323 0.087 5 0.272 1.55 0.525 0,343 0.109 0.0174 4 0.253 1.15 0.431 0.362 0.162 0.045 5 0.301 0.855 0.376 0.32 - _ * 6 0.305 0.665 0.255 0.337 0.23 0.16 0.02 *Higher products unrecovered.

-41 - In order to compare experimental with calculated values of product distributions, a set of product distribution equations relating the various product concentrations with the rate constants and concentrations of the initiating reactants are required. In the following derivation we follow closely the treatment presented by previous authors(54' For a system of bimolecular consecutive reactions such as represented in page 1 and briefly abbreviated below A + B = AB AB + B = AB2 AB2 + B = AB3 (44) ABn + B = ABn+l The rate of formation or disappearance of each of the alcohols or alcoholethers may be written as dCA/dt = k1 CA CB dCAB/dt = k1 CA CB k2 CAB CB (45) dCAB/dt = k2 CAB CB k3 CAB2 CB dCABn/dt = kn1 CABn2 CB kn Cn-l CB where CA = alcohol, moles per liter CABn = alcohol-ethers, moles per liter CB = propylene oxide, moles per liter kn = specific rate constants, liter moles-1 min.-l The series of differential Equations (44) can be solved in closed form if the volume is assumed constant and by eliminating the variable time (t). The units of Equations (44) may therefore be reduced to moles per minute instead of the concentration units of moles per liter per minute by the following substitutions:

A = VCa dA = VdCa where A = moles of component A Ca = moles per liter of component A V = volume, liters Equation (44) may be then rewritten in moles units as follows V(dA/dt) = -ki (A)(B) V(d(AB)/dt) = k1 (A)(B) - k2 (AB)(B) V(d(AB2)/dt) = k2 (AB)(B) - k3 (AB2)(B) (46) (47) (48) V(d(ABn)/dt) = knl_ (ABn_2)/dt - kn(ABnl)(B) The advantage of using mole units will become apparent if we choose a value for V such that the number of moles of the initiating alcohol is unity. Since the number of moles of alcohols in the reacting mixture is always constant at any time, if all the epoxide were reacted we have n ABn = 1 (49) 0 where ABo = A by definition. The total number of moles of propylene oxide reacted is necessarily n BT = n (ABn) 0 (50) The solution of the series of differential Equations (48) gives the composition of each of the alcohols in terms of the amount of propylene oxide consumed, the starting amount of the initiating alcohol and the ratios of the rate constants, kn/kl. The solution is k. n+l (A k ABn n n+l ( - 0 =j n ( k( k (51) j=l (kj kk) j=l jk

where A = the number of moles of the initiating alcohol at any time t. Ao = number of moles of initiating alcohol at t = 0. ABn = number of moles of product, kn = rate constants, liter mole1 min.The detailed solution of Equations (48) is presented in Appendix IV. Several cases of product distribution of interest were also developed. These include the situation where the initiating alcohol is a mixture of two alcohols and the case where the initiating rate equation is first order while the succeeding ones are second order. Equation (51) may be used to evaluate the ratios of rate constants when product distribution data and the starting compositions of propylene oxide and alcohol are known. Alternatively, product distributions may be calculated if the ratio of the rate constants and starting amount of propylene oxide and alcohol are available. In Figure 7 we compare the experimental product distribution initiated by the reaction of propylene oxide with methanol at 45~C (Table VII) and the distribution calculated with the use of Equation (51) and specific rate constants obtained from the single reaction experiments in page 38. The difference of these two distributions is quite striking. The ratios of the rate constants obtained from single reaction experiments and those obtained from product distributions initiated by the reaction of propylene oxide with methanol at 45~C are compared in Table IX. It is quite obvious therefore, that specific rate constants calculated from single reaction data are not able to give the product distribution initiated by the reaction of propylene oxide with methanol at 450C.

2 0 U IL cr w -J 0 2 I! Q3 0.4 0.5 06 0.7 0 0.9 LO 1.1 1.2 MOLES PROPYLENE OXIDE REACTED/MOLES INITIAL METHANOL Figure 7. Comparison of Experimental Product Distribution with Calculated Values for the System of Reactions Initiated by the Reaction of Propylene Oxide with Methanol at 45~C.

-45 - TABLE IX OPAISONW TFINTTI S O- RA-TE 'OS' OBTAINED-TROM SbINGLE KREACTION EXPERIMENTS WITH VALUES OBTAINED FROM PRODUCT DISTRIBUTION DATA INITIATED B:THe: -ffiC'l'lN Pfif'f —.CE 0Xl WITH5IDEi L 'iTA TICU'. Cn = kn/kl single reaction product distribution c2 0.571 0.10 C3 0.42T 0.075 c4 0.282 0.075 On the other hand, the rate constants from single reaction experiments are able to reproduce experimental product distribution data initiated by the reaction of propylene oxide with monopropylene glycol methyl ether at 60~C. In Figure 8 the experimental product distribution is compared with the distribution calculated using Equation (124) and the specific rate constants from page 38. The agreement is very good. Table X compares the ratio of the rate constants obtained from single reaction data and those calculated from the product distribution data initiated by the reaction of propylene oxide with monopropylene glycol methyl ether at 60~C. TABLE X COMPARISON OF RATIOS OF RATE CONSTANTS OBTAINED FROM SINGLE REACTION EXPERIMENTS WITH VALUES OBTAINED FROM PRODUCT DISTRIBUTION DATA INITIATED BY THE REACTION OF PROPYLENE OXIDE WITH PROPYLENE GLYCOL METHYL ETHER AT 60~C. cj = " 'singleproduct c.(..../k2 reactions distribution - c3 1.00 lo00 c4 0.933 1.00 c5 - 1.00

-47 - Composition Effects Up to this point, the experimental results seem to suggest the presence of a composition effect on the rates of reaction, possibly, due to the disproportionate nature of the physical properties of methanol as compared with the other alcohol-ethers. For any general rate equations to be valid, such effects must be taken into accounto The knowledge of the manner in which the concentration of methanol might affect the rates of reaction is therefore highly desirable. The extent to which the propylene oxide-methanol reaction is sensitive to solvent change, a change of the dielectric constant of the medium in particular, was investigated using dioxane (D25o = 2.206) as solvent. The results at 45~C are shown in Figure 9. The rate of reaction increases with increasing dioxane concentrationo Although this is an indication of medium effect on the propylene oxide-methanol reaction, we must be cautious in trying to extrapolate it to our system. Figure 9 must therefore be considered only as an indication of a possibility of such an effect also being present in our system. A study of the effects of composition change on the velocity of reaction can be made by limiting the consecutive reactions to only two succeeding reactions and by making runs using different ratios of the two reacting alcohols. The nature of the behavior of the rate constants of reaction 1 (methanol-propylene oxide) and reaction 2 (propylene glycol methyl etherpropylene oxide) when both reactions occur simultaneously was therefore

1.0 Z ^ DIPROPYLENE, 0.6 - V TRIPROPYLENE. TETRAPROPYLENE.. U 0.5 - * PENTAPROPYLENE, 0 0.4 -J~ 0.3 0.2 0., 0 1.2.3.4.5.6.7.8.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 MOLES PROPYLENE OXIDE REACTED/MOLES INITIAL PROPYLENE GLYCOL ETHER Figure 8. Comparison of Experimental Product Distribution with Calculated Values for the System of Reaction Initiated by the Reaction of Propylene Oxide with Propylene Glycol Methyl Ether at 600~C 0N I

-48 - 0.002 Tsw z_ I0,0i i i I D I cn.j 0 a 0.001 mm ir c I - I - I I I I - I-.. I I I I 70 80 90 100 0 10 20 30;40 50 60 MASS PERCENT DIOXANE Figure 9. Effect of Dioxane on the Rate Constant of the Reaction of Propylene Oxide with Methanol at 45'C.

investigated by reacting small amounts of propylene oxide with a mixture of the twoalcohols. We can write for the rate of disappearance of propylene oxide as - dCB/dt = CA CB + k2 CAB C](NaOH) (52) By using excess amounts of methanol and propylene glycol methyl ether, the quantity (kI CA + k2 CAB) may be considered as a constant and Equation (52) reduces to a pseudo-first order equation - dCB/dt = GA CB (NaOH) (53) where GA = kCA + CAB GA is a constant for any run but in general is dependent on the starting concentration of methanol or the ratio of methanol to propylene glycol methyl ether. Equation (53) is easily integrated to give CB t dCB = GA dt (NaOH) (54) CB o in CB/CB = GA (t)(NaOH) (55) If the time composition data of propylene oxide are known, GA can be readily evaluated. Figures 10 and 11 show composition-time curves for propylene oxide corresponding to different starting mole ratios of methanol to propylene glycol methyl ether at 45~C. In Table XI, the respective values of GA are tabulated.

-50 - 0 RUN NO. 3 s iI 7 a I. i 8 A is.I 9 V i, o. 6 i 0.5 a:.i 0!I a 0 0o z wO UJ z 0 0 a 'z 0.3 -a A. 0.0.3 0.1295 MOLES/LITER (NoOH) 0.180 MOLES/LITER (NoOH) 0.176 0.1625 MOLES/LITER 0.2 Figure 10. TIME _ MINUTE$ Concentration.Time Curves of Propylene Oxide in the Reaction of Propylene Oxide with Mixtures of Methanol and Propylene Glycol Methyl Ethers at 45CC.

-51 - D 40 50 60 70 80 90 100 110 120 T!ME - MINUTES Concentration-Time Curves of Propylene Oxide in the Reaction 0~f Propylene Oxide withWMixtures of Methanol and.Propylene Glycol Methyl -Ether at 45'C. Figure 11.

."52 - TABLE XI VALUES OF THE PSEUDO-FIRST ORDER CONSTANTS FQR THE REACTION OF PROPYLENE OXIDE WITH A MIXTURE OF METHANOL AN]) PROPYLENE GLYCOL METHYL ETHER AT 45 oC. Run Methanol Number moci 1 7.40 2 8.61 3 5.2k 4 5.89 5 6.5 6 181 7 9.55 8 9,55 9 17.85 Propylene XLycol Ether CA niols/k'it.6.52 5.95 7.44 7. $9 6.95 2,115 5.65 -5.65 GA (NaCH).(K-CA + K CAB moles/lit 0 os3P 0.0381 0,0305 OO.255 0.0524 0.0479 0.01595 0,01595 0.0447 o.185 0.213 0.1295 0. 266 0,176 0.163 0.190 00190 0,176 In Figure 12 the values of' GA are plotted. versus methanol concentration. The straight line connecting h2 CAB and. A represents values of GA if the rate constants obtained. from single reaction experiments listed in page 158 were used.. The d~ifference between the experimental values and those calculated. using the rate constants listed. in page 38 must essential-~ ly be a result of composition effects.

-53 - A 0.04 k1c 0.03 C) 04 0.02 0.01 0 2 4 6 8 10 12 14 16 Il 20 22 METHANOL CONCENTRATION.MOLES PER LITER Figure 12. Variation of GA with Methanol Cbncentration.

DISCUSSION OF RESULTS Uncatalyzed Reactions The values of the measured catalytic rate constants tabulated in Tables IV, V and VI actually represent the sum of the spontaneous rate constant and the specific catalytic constant k = k + kc (NaOH) (56) The magnitude of the spontaneous rate constant is usually significant only in catalyzed reactions when the catalyst concentration is so low such that ku and kc (NaOH) are of the same order of magnitude, e.g. ku > (- = 0.10 (57) kc (NaOH). (58) Pecorini and Banchero have reported experimental data for the uncatalyzed reaction of methanol with propylene oxide. The temperature dependence of the second order rate constants of this reaction is plotted in Figure 13. The Arrhenius Equation for the uncatalyzed rate constant of the reaction of propylene oxide with methanol is -19,500 k = 1.21 (107) e RT (58) and from Equation (40), the Arrhenius Equation for the rate constant of the catalyzed reaction at unit molar catalyst concentration is -17,200 kc = kl = 102 (109) e RT (59) substituting Equations (58) and (59) into Equation (57), the concentration

-55 - of the catalyst (NaOH) at which the spontaneous rate would become significant can be calculated as follows -19,500+ 17,200 1.21 (107) e RT 0 (NO) 0.10 (NaOH) (S0) oO02 (109) or 0185 (10-2) e > (NaOH) 0.10 at RT = 600 (NaOH) = 0.00255 moles per liter It is also interesting to compare the uncatalyzed rate constant of the propylene oxide-methanol reaction with that of the ethylene oxidemethanol reaction. The Arrhenius Equation for the ethylene oxide-methanol reaction calculated from data reported by Natta(55) is -20,100 ku = 1.0 (108) e RT moles liter min (61) as was expected, the activation energy of both reactions is about the same. The fact that the uncatalyzed rate constant for the ethylene oxidemethanol reaction is slightly higher than that of the propylene oxidemethanol reaction (see Figure 13) may be a result of steric effectso For the reactions of propylene oxide with the glycol ethers, the uncatalyzed rates of reaction are expected to be even slower. When dipropylene glycol methyl ether was mixed with propylene oxide at 85~C for 50 days, no appreciable reaction was observed. The same mixture at 2000C similarly has shown no detectable reaction occurring in 10 hours,

-56 - IR 4X10 2XI1& 2xl63 8xl64 6x 64 4 x10' 4xl64 -4 2x10 -4 - 5 _ 6X10 z x 4xl1 x I-. x X ao 10' oz 8X10 -6xlO 62107 -6 -7 4xlO -7x( PROPYLENE OXIDE METHANOL REACTION (REF. 58) A ETHYLENE i. Io.. f (REF. 55) I I _ I I I I I I I I a 2.1 2.2 2.3 2.4 2.5 2.6 2.7 I/T X IO 28 2.9 3.0 3J 32 Figure 13. Effect of Temperature on the Uncatalyzed Reaction Velocity Constants.

-57 - In view of this, the uncatalyzed rate of reactions for these compounds with propylene oxide may be neglected when studying the catalyzed react ions. Activation Energy of the Catalyzed Reactions The presence of catalysts generally lowers the activation energy of chemical reactions. In Table XII the activation energy of the individual reactions are compared. These values are meaningful only when used in context with the composition of the medium. TABLE XII ACTIVATION ENERGIES OF INDIVIDUAL REACTIONS Initial Reaction Uncatalyzed Catalyzed Mole Ratio.. Alcohol/Oxide Methanol + propylene pxide 19,500* (5/1) 17,200 45/1 Monopropylene glycol methyl ether + propylene oxide 11,700 5/1 Dipropylene glycol methyl ether + propylene oxide 15,800 10/1 Tripropylene glycol methyl ether + propylene oxide 18-500 7/1 * Calculated from Ref, 57. It is interesting to note the variation of the activation energies of the alcohol-ether reactions with propylene oxide. Although the relative values of the rate constants for these reactions are about the same in the temperature range investigated, the values of the activation energy, nevertheless, are not the same the values increasing with increasing molecular weight of the alcohol-ether. However, the collision factors also increase

in thp same direction (see Equation (~40-43.)) compensating for the increaseof the activation energy. The variation -of these quantities is probably due to the increasing complexity of the transition state., The Influence of the Medium on the Rate of Reaction The equation relating the rate constant of an ion-dipolar reaction in a medium having a dielectric constant of unity to that existing in the actual solution, according to Laidler (3)(see Appendix III) is e2Z211 F-1 ln kt =lnI + a r1j LDJ (62) where ko rate constant referred to the gas phase e =electronic charge Z charge K = Boltzmann constant T =absolute temperature 'K ra =radius of molecule a rA= radius of activated complex D =dielectric constant of the medium For any particular reaetioin, e2 Z2[11 K Lr -j constant (63) or ln kv i n k + CJ~QJ- (64~).0in Equation (62), the rate constant referred to the gas phase, maybe eliminated as follows:

let k' = rate constant where the reacting medium corresponds approximately to that of the pure alcohol then from Equation (64) in k' = n ko + C [ (65) TL Do J where Do is the dielectric constant of the alcohol and the rate constants kn are represented by Equations (40o435) At any other dielectric constant, the rate constant will vary according to Equation (65). Subtracting Equation (65) from Equation (64). In k' - in k' _C D- (66) T LD Do or ln k'= ln k'+ C [DD] (67) T Do D In most cases, the quantity, 1/TDo, is approximately constant since, as temperature increases, dielectric constant usually decreases. Equation (67) may therefore be further simplified to (6-D) n k' = In k' + C' [DD (68) __ D An inspection of Equation (68) indicates that a straight line is obtained if in k' is plotted against (l/D). Since the dielectric constant of methanol is always greater than the dielectric constant of a mixture of methanol and alcohol ethers, the effect of the medium on the rate of reaction of propylene oxide with methanol in a mixture of methanol and alcohol-ethers is to accelerate the rate of reaction as the concentration of methanol decreases. On the other hand, the presence of methanol in the mixture would slow down the rate of reaction between propylene oxide and the alcohol-ethers.

-6o The use of Equation (68) presuppose the assumption that the polarity of the reacting mixture is a major cause of the anomalous behavior of the rate constants. At best, Equation (68) would give only a qualitative description of the effect on the rate constants, the uncertainty in the calculation of the various ionic and molecular radii and the fact that ionic radius varies from solvent to solvent makes it necessary that the use of equations of this form be supported with experimental data, Furthermore, experimental values of dielectric constant of mixtures are practically nonexistent and additivity of dielectric constants can be assumed only for a limited range of composi(68) tions. Anomalous behavior of dielectric constants of polar mixtures due to temperature and composition changes and attributed to molecular association has also been observedo It was therefore found expedient to relate the effect of the medium on the rates of reactions with the concentration of methanol in the reacting mixture rather than with the dielectric constant, Equation (68) then takes the following form In k' = n k' + f(CA) (69) where f(CA) = function of methanol concentration Equations for the Rate Constants The choice of the function f(CA) was dictated by the following considerations: 1. It must be consistent with Equation (62) e.g., the rate constant should increase with decreasing polarity of the reacting medium.

61 - 2. For the glycol-ether reaction f(CA) = 0 when CA, the concentration of methanol in the reacting medium is zero. 30 The effect of the concentration of propylene oxide in the reacting medium on the rate of reaction is negligible. 4. The ratios of the rate constant for consecutive reactions should correspond to that obtained in the product distribution experimentso 5. The results in Table XI should be satisfied. 6. The effect of temperature on f(CA) is negligible over the temperature range studied~ The final forms of f(CA) used were f (CA) = C1 ( - ) (70) for the methanol-propylene oxide reaction and f (CA) = -C2 (CA/M) (71) for the alcohol ethers-propylene oxide reactions whaere C1 and C2 = constants CA = concentration of methanol at any time, moles/liter M = reciprocal of the molar valume of methanol at the temperature of the reaction. The final forms of the equations for the rate constants are 1e (1 - CA/M) kz = h (72) n = C2 e (CA/M) for n red= n e (7 and C are constants for n =~2, and kn reduces to kn when CA Oo Here C1 and C2 are constants

-62 - to be determined fram consecutive reaction data in Tables VII and XI. In order to evaluate the Constants in Equations (72) and (73) we shall define an average rate constant which is a function of methanol concentration as M k I ef(CA) dCA kn(avg.) = -n (74) M f dCA CA With the use of Equation (74), the constants in Equations (72) and (73) were evaluated by a successive approximation method as follows: Values of C1 were assumed and the corresponding C2 values calculated from the data in Figure 12. The ratio of the rate constants was then evaluated using Equation (74). The correct values of C1 = 1.42 and C2 = 240 result in the k2/kl value of 0.lO corresponding to the value obtained in the product distribution studies. In this calculation using Equation (74), A was assumed to have been all reacted. Table XIII shows the result of the successive approximations for the values of C1 and C2. In Figure 14 the variation of kl and k2 with methanol concentration according to Equations (72) and (73) is shown. TABLE XIII SUCCESSIVE APPROXIMATION FOR VALUE OF C1 AND C2 C1 C2 (k2/kl) avg. 1.025 0 0.33 1013 0.8 0.212 1.23 1.17 0.172 1.386 2.19 0o108 1.42 2.40 0.10

-C2f I-. z i x cm~ w -J 0 a Wx 0 0.1 0.2 Q3 0.4 0.5 0.6 Q7 Q8S 0.9 1.0 (I -h) Figure 14. Variation off the Reaction Velocity Constants, kandk with Methanol Concentration.

-64 - Temperature Influence on Medium Effects The influence of the temperature on medium effects may vary widely depending on the nature of the medium. For the present system and over the range of temperature studied it may be assumed to be small. Thermal energies of molecules in the temperature range investigated are about 1500 calories per gram mole while energies of associative links attributed to polar substances such as alcohols are of the order of 5000 calories per gram mole or higher(6) In Table XIV, the calculated product distribution using Equations (72), (73) and (74) are compared with some experimental data at 55~C and 64~Co The agreement is quite good. TABLE XIV COMPARISON OF EXPERIMENTAL PRODUCT DISTRIBUTION DATA WITH CALCULATED RESULTS FOR THE SYSTEM OF REACTIONS INITIATED BY PROPYLENE OXIDE AND METHANOL AT 55~C and 64~C. Temper- Mole Ratio Products ature ~C Oxide Consumed Mole Fraction Initial Methanol Experimental Calculated _. -fi..-, —._..- i- - Methanol 55 0o,845 0.235 0.235 Propylene glycol o.696 0.715 methyl ether Dipropylene glycol 0.069 0.050 methyl ether Methanol 64 0.544 0.505 0.505 Propylene glycol 0.453 o.480 methyl ether Dipropylene glycol O0042 0.015 methyl ether This set of data obtained from Ref. 57~

-65 - Polarity of the Reacting Mediums A comparison of the dielectric constants in Table XVI indicates the relative "polarity" of the various reactants and products. The large difference of the dielectric constants between methanol and the rest of the compounds may be a factor affecting the rates of reaction of propylene oxide when several of the alcohols are present at the same time, TABLE XV DIELECTRIC CONSTANTS AT 250C 1. Methanol 2. Propylene oxide 3. Propylene glycol methyl ether 4o Dipropylene glycol methyl ether 5. Tripropylene glycol methyl ether 6. Tetrapropylene glycol methyl ether 32.63 16.0 14 13 12 12 Ref. (53) (68) * * * * 7. Dioxane 2.209 (53) *Estimated values based on Refo 53 and 68. In the present work we have shown that at least for the NaOH catalyzed reaction of propylene oxide with methanol and with the succeeding products the shifting values of the rate constant may be explained in terms of the changing polarity of the reacting medium, primarily caused by the changing concentration of methanol. The manner in which the rate constants vary is explainable qualitatively by the nature of electrostatic forces in the medium. Specifically, it is shown that the variation of the rate constants can be directly related to the concentration of methanol in the reacting medium. This phenomena is best,~,.

brought out by the product distribution data which involve a radical change of the composition of the reacting medium. Methods of treatment where the activities of the reacting species are related to the medium properties such as Equation. (98) are often used. The effect of the medium on the activities of the reacting species is sometimes denoted as the "primary kinetic effect". Another possible effect of the solvent is its influence on the concentration of the reacting species which naturally will reflect on the rate of reaction. This effect of the solvent designated by some authors as the "secondary kinetic effect" is due to the influence of the medium on the equilibrium constants involved in the mechanism of the reaction. A good example of the latter (30) case is the effect of the solvent in protolytic equilibria(3 Acidity of the Reactants The acidity of the various alcohols and alcohol-ether may, to a certain extent be implied from their autoprotolysis constants. The autoprotolysis constant is the product of the concentration of lyonium and lyate ions in the solvent, eog., (RCH2)(RO-) = Ka, This constant determines the range of values of acidity available in these solvents, The autoprotolysis constant of some solvents of interest are listed in Table XVI () The autoprotolysis constant pK of the alcohol-ethers is estimated to be around 22-24, T4BLE XVI AUTOPROTOLYSIS CONSTANTS Solvent Temp. OC pK Water 25 14o0 Water 100 12.3 Methanol 25 16.7 Ethanol 25 19 l

-67 - Of more direct interest is the relative acidity of these alcohols in a common solvent. Generally, ionization is favored in a solvent of high polarity. However, the ionization of these alcohols in a common solvent is of importance only for the uncatalyzed reactions. For catalyzed reactions, the concentration of the alkoxide ion is dependent only on the concentration of the hydroxyl ion. Accuracy of Measurements and Errors In Table XVTI the maximum limits of error of the measurements used in the experimental work are tabulated. TABLE XVII ESTIMATION OF ACCURACY OF INDIVIDUAL MEASUREMENTS INVOLVED IN THE EXPERIMENTAL WORK Accuracy of Measurement Remarks Measurement % Error Weighing reaction charge of 200-300 gm per batch 4.0% propylene oxide 0.05 gm o.6 alcohol 0.5 gm 0.2 Titration HCl-CaC12 method 3.25 analysis periodic-perchloric method 1.10 Side negligible 0.50 reactions Time lag 1 min 0.35 Maximum error in measurements 4.90 Illl I.i.........! |.......,.I.I...,..I.I.I.I..11........I....II.I...I.'.I..I....'.].....!.........I... I. __.I. The maximum deviations from the least~square fit of the individual rate constants are presented in Table XVIII. Here the deviations were assumed to be all due to errors in the activation energy.

TABLE XVIII ACCURACY OF THE ACTIVATION ENERGIES FOR THE RATE CONSTANTS OF THE INDIVIDUAL REACTIONS Activation energy Maximum Reactions from least-square fit deviation calories/gm. mole calories/gm. mole Propylene oxide 17,200 + 60 + methanol Propylene oxide + dipropylene 15,800 - 170 glycol methyl ether Propylene oxide + tripropylene 18,500 - 190 glycol methyl ether The use of average densities in the calculation of the individual rate constants, as was expected contributed comparatively small errors. In Table XIX below, the maximum errors incurred are tabulated. The assumption of constant volume in thp product distribution equations results in larger errors. Comparison with Work Reported in the Literature There are very little quantitative data reported in the literature on the base catalyzed alcoholysis of propylene oxide or ethylene oxide, (76) Weibull and Nycander reported the bimolecular rate constant for the base catalyzed reaction of ethylene oxide with ethanol and ethylene oxide with ethylene glycol monoethyl ether at 25~Co These values are compared in Table XX with those obtained in our work involving methanol and propylene oxide and values calculated from Pecorinis data(57) oxide and values calculated from Pecorini's data

TABLE XIX VARIATION OF DENSITY OF REACTING MIXTURE Initial Initial Tempo Dev. charge Mole Ratio ~C start.f inal average from avg. % Single Reactions Methahol + C propylene Dipropylene glycol methyl ether + propylene oxide Tripropylene glycol methyl ether + propylene oxide Methanol + propylene oxide in dioxane Mixed runs' propylene oxide + methanol + monoglycol ether Product Distribution Methanol + oxide 0 Monoglycol + oxide 0 3/1 5/1 7/1 35 55 55 87 87 45 85 45 0.78038 0.78769 0 76117-T 0 76875 -0.9752 0.94228 o.88460 0.89294 0.87844- 0.89568 0.94228 0.9496o 0.90T7T65.- 0 91559..-. (maximum deviation of.0,78403 0.76496 0'o9587 0,8887 0.8870 O.9459 0- 91162 -all runs) 0.47 0.50 0.38 0.47 o.97 0.39 o.44 0.30 5/1 I 45 (maximum deviation of all runs) 1.70.64 ~67 - 45 6o 0.79 o834 o.924 0o. 9265-.... 0o"957 0.881 7.5 5.0

-70 - TABLE XX VELOCITY CONSTANTS AT 25~C. FOR ETHYLENE OXIDE AND PROPYLENE OXIDE WITH VARIOUS ALCOHOLS USING SODIUM HYDROXIDE AS CATALYST "2 Reactions Starting k, moles2 Reference Mble Ratio liter min 1 I. alcohol/oxide_ Ethylene oxide + ethanol 1.29 x:10 76 Ethylene oxide + * 6010 x 10-4 76 ethylene glycol ethyl ether Ethylene oxide + * 6.10 x 10-4 76 diethylene glycol ethyl ether -4 Propylene oxide + methanol 5/1 3.15 x 10 57 Propylene oxide + methanol 45/1 2.63 x 104 Propylene oxide + propylene glycol methyl ether 5/1 2.58 x 104 57 Propylene oxide + dipropylene glycol methyl ether 10/1 1022 x 10O Propylene oxide + 5 tripropylene glycol methyl ether 7/1 3.95 x 10 * Reported only as dilute solutions While values of the rate constants of some individual reactions of epoxides with alcohols have been reported(55 the reason why some of these rate constants are not valid when several consecutive reactions (54) occur at the same time hps never been fully explained. Natta introduced the idea of the molecules existing in an activated state at the instant in which they are formed; however, such an assumption is too vague and there is no way in which it may be verified. Weibull(76) mentioned the possibility of an effect of the acidity of the alcohols and the changing

condition of the reacting medium on the rate constants but did not pursue the subject further. (57) Pecorini in his work with the base-catalyzed reactions of propylene oxide with methanol, and with propylene glycol ether, introduced the following empirical rate equation which was shown to correlate his experimental data: [dB]/dt = -k [A]tB]/nt (75) where B = Propylene oxide, moles per 100 grams A = Alcohol, moles per 100 grams ~ = Time, hours nt = Total number of moles per 100 grams of initial charge. The Arrhenius Equation for the rate constants of the oxide-methanol reaction (kl) and the oxide propylene glycol ether reaction (k2) were k = 3.24 (10)13 e 17,800/RT hours1 (76) 2 5 3.15 ()10 -14,600/RT -1 k.15 (10) e hours (77) It is possible to use the numerical values of the ratio of the rate constants as a basis for comparison with our correlation since they are dimensionless. In this manner, the calculation of k2/kl at 45~C using Pecorini's correlation yields a value of 0.159. In Figure 15,.resiLts: obtained by the use ot Pecdrini '$ and our correlation are compared with experimental composition-time data of propylene oxide ob(57) tained at 45~C using an initial mole ratio of alcohol to oxide of 1 to 1 When Pecorini's rate equation was used to correlate the data of the glycol ether reactions obtained in the present work, a larger difference

-72 - from our results using the present correlation is obtained. In Table XXI the product distribution from the reaction of propylene oxide with propylene glycol methyl ether at 60~C obtained by various methods are compared. TABLE XXI COMPARISON OF PRODUCT DISTRIBUTION INITIATED BY THE REACTION OF PROPYLENE OXIDE WITH PROPYLENE GLYCOL METHYL ETHER AT 60~C. Initial Mole Products Ratio Experi- This Pecorini's Glycol Ether mental Correlation Rate Equation Propylene Oxide mole fraction Propylene glycol methyl ether 1.15 0.431 0.43 0.43 Dipropylene glycol methyl ether 0.362 0.36 0.40 Tripropylene glycol methyl ether O.161 0.16 0.17 Tetrapropylene glycol methyl ether 0.046 0.050 0.0 Pecorini's correlation therefore predicts the results for the reactions of methanol with propylene oxide and the reaction of propylene oxide with propylene glycol methyl ether fairly well, both when they occur singly and consecutively. However, at the high initial mole ratio of methanol to oxide of 45 to 1, the values predicted by his rate equation are about 40 percent higher than the experimental results obtained in this work. In the case of the reaction of propylene oxide with methanol and propylene glycol methyl ether initially present in the mixture and with consecutive reactions involving glycol ethers only, his correlation is less accurate.

a 7 6 0 0 011 II2. 3 TIME — ---- Figure 15. Comparison of Experimental Time.-Composition Data of Propylene Oxide with Calculated Values at 4150C.

CONCLUSIONS lo The reaction velocity of each of the reactions is directly proportional to the sodium hydroxide concentration. The reaction velocity constant can be expressed as: k = k+ kc (NaOH) (56) where k = the measured rate constant ku = the uncatalyzed rate constant kc = the catalyzed rate constant (NaOH)= catalyst concentration, moles/liter For the methanol reaction, ku becomes significant only at a catalyst concentration of less than 0.0025 moles/liter. For the reactions with the alcohol-ethers, ku is negligible. 2. The reaction velocities of these reactions are sensitive to qomposition changes of the medium which affect the polarity of the reacting mixture. 3. The effect of the reacting mixture on the various rate constants could be directly related to the concentration of methanol in the mixture. The following equations for the rate constants are able to correlate experimental data obtained in this work under varying conditions, e.g., whether the reactions occurred independently or consecutively. a. For the propylene oxide-methanol reaction 1.42 (1-CA/M) k1 = kl e -- 17200 (79) RT, a kl = 1.02 (109) e moles lit min

b. For the propylene oxide-propylene glycol methyl ether reaction -2.40 (CA/M) k2 = k2e (8o) mls-2 1 -1 k2 =0.97 (105) emle it 1 c. For the propylene oxide-dipropylene glycol methyl ether reaction -2.40 (CA/M) k k3 e -15,8o00 (81) 3= 4.75 (107) e RT moles lit mm di For the propylene oxide-tripropylene glycol methyl ether reaction k k4 ee-2.940 (CAJM) l84 (82) -18,500 2 ~2 -l _ = 2.25 (109) e R moles lit min where A = concentration of methanol at time t iLn motes per liter M = the reciprocal of the molar volume of methanol at the temperature of the reaction

APPENDIX I PHYSICAL PROPERTIES Densities The use of concentration units in the rate equations necessitates the accurate knowledge of the densities of the reaction mixtures. (57) Pecorini found that the densities of the reacting mixture are additive with respect to the compositions in mass fractions. Figure 16 presents the densities of the four alcohol-ethers as a function of temperature. The values for the first three alcohol-ethers were obtained from several sources ) while the values for the tetrapropylene glycol methyl ether were extrapolated from an experimental value obtained at 25~C. The densities of propylene oxide and methanol at various temper(57) atures are well investigated. Pecorini has summarized the various values for the densities of these two compounds in his work. Refractive Indices In order to analyze the relative amounts of the two alcoholethers in the binary fractions obtained from distilling samples from the product distribution runs, binary refractive index calibration curves were prepared at 25~Co They were found to be additive with respect to the mass fractions of the pure compounds. The curves are shown in Figure 17. The measurements were obtained using a Bausch and Lomb (57) Abbe-56 refractometer. Pecorini * has reported similar results on the refractive indices of binary mixtures as well as ternary mixtures.

IDO A... "-fts. *Wftwxa. ft-fta "ftft" oftftoft. "%ftft "-.ftft Oft-ft., -TETRAPROPYLENE GLYCOL ETHER -TRIPROPYLENE GLYCOL ETHER U W. OC I >- 0.9 z CM I REF (57),(16) PROPYLENE 0.8 I I I I M. I 8 0 1 0 0 A% ZU 40 60 TEMPERATURE. ~C 80 100 Figure 16. Effect of Temperature on the Density of Alcohol-Ethers.

1.0 0.9 0.8 -e c 0.7 X 0.6 0.5 CIO ' 0.3 IL u,, 0.2 0.1 0 -0 00 REFRACTIVE INDEX 250C Figure 17. Binary Refractive Index of Alcohol Ethers at 25~C.

-79 - Infrared Spectrograms The infrared spectrograms of methanol, propylene oxide, and isomers of propylene glycol methyl ether have been reviewed, analyzed and presented in Pecorini's work. No spectrograms for the dipropylene glycol methyl ether or for the tripropylene glycol methyl ether have so far been reported in the literature. In order to have a permanent record of these two alcohol-ethers used in our work, their infrared spectrogram was obtained using a Baird Model B double beam recording spectrophotometer. The spectrograms are shown in Figure 18.

I 33NVYLUM4NVU iN303d a":2 0 0 ~ONYUNWSNY11 1iMO3d 0 0 I 2 2 a:! — Ln 40 j~rmm ql.0 to I z l - ii z - I z El 4 2 i. 9!9 I % = q. 2 8 - 0 8. -!! i i I; '' I, i 1: i B u ei n. M. I a [L'1 I It rb OG) A -P p~4 ~4O U A rA 0 r4 0 O C', H 1 -H Wo " I 1. _; |: 1 4 1 i 1;'.1 mm' IJ.I _-.:.1 ' I,, 1in1 H-...." Y Ii I I -T- I Ira:''!;. I t,: I ~.: I'. I J - I., T_i _'.;:, l l i I, TT U %A 0i9 I I IOL tg I -^ (i P1 >1 l3NViW4SNYVI iN33Vid 0 0 PA i -j 3ONVPIY4SNYV1 iN33V3d a - I I f1 - I $ 0i w ^ 1J I jj.II -11 i d ^i I Vb W a Q A. IV i t UN 0%~ i J. o a o 4 U e 8 IB o i I Ct -I q d0 U u1-I da d u_ iIF 0u Ta

APPENDIX II ANALYTICAL METHODS Chemical Analysis of Propylene Oxide Numerous methods for the analysis of epoxides have been reported (50) in the literature. Some were specifically developed for the analysis of a particular epoxide compound in the presence of other materials while others are only adaptable to the analysis of low molecular weight epoxides. The effectiveness of the method depends to a large extent on the concentration of the analytical reagent (a factor sometimes overlooked), on the time required for reaction, and sometimes on the temperature. A constant trouble spot is interference by other substances in the sample resulting in side (50) reactions. Mitchell has summarized available methods for analyzing epoxy compounds. Table XXII below presents a condensation of methods for analyzing low molecular weight opoxides. It should be pointed out, however, that this table may be used only as a rough guide. It has been our experience that results vary considerably depending on the condition of analysis and the particular substance analyzed. A description of the two methods used for the analysis of propylene oxide in this investigation is presented below: 1. Aqueous HCl-CaCl2 Method(43'44) Preparation of the Reagent — A saturated aqueous solution of calcium chloride at room temperature was prepared by dissolving reagent grade anhydrous calcium chloride in distilled water. The saturated solution was acidified with hydrochloric acid to make up an acid strength of about

TABLE- XTI METHOD-OFmA LYSTSB FOR 'TPROPYLIEE- -AD E'TH'TCLNE OXIDES.- ~ 1 - ~ Methods Reagents Reaction Reaction Titrant Precision Ref. Temperature Time ~.... -......................... 1. Aqueous MgC12-HCl 2. Aqueous CaC12-HCl 3. Alcohol MgC12-HCl 4. Cellosolve-HUCI 5. EthyI ether-HC1 6. Pyridinum ChloridePyridine 7. Pyridinum ChlorideChloroform 8. Dioxane-HCl 9. Periodic-Perchloric 10. Sodium Thiosulfate 11 Sodium Sulfite 0.1N HCl,sat. soln. MgC12 0.15N HCl, sat. soln. CaC12 0.55 HC1 in ethanol O.2 EHCI in Cellosolve 0 i2T-HCI in anhyd. ether 0.2N HC1 in Pyridine Mix (6) in Chloroform 0.2N HC1 it dioxane IHIf04 in 0.4N HC104 0.2M Na2S203 in 50% acetone sat. soln. of Na2SO3 room temp. room temp. room temp. 65C: room temp. reflux reflux room temp. room temp. 65oc room temp. 30 mins. 30-miins. -"530 mins. 3-hours 3"hours 50 mins. 50 mins. 350" mins. 1 hour 30" mins. 0.1N NaOH 0.1N NaOH O ~ T aOE O.1N NaOH 0.1N NaOH ON Na0H 0.1N NaOH 0.1N NaOH 0,1N NaOH KI, 0.1N Na2S203 -O.2i-a cetic acid -C -C -C ).5.. (15) ).& 8 (43, ).2% (34) (50) (73) ).5%' (18) ).5, (50) ). 5,% (35) ).2% (17) (12) 44) - C - C - C - c ro 30 mins. 0.2N HC1 - 0.5% (71)

0.15 N. The prepared solution was stable over a period of several months. Standard 0.1 N sodium hydroxide was used as the titrant. Procedure —15 c.c. of the analytical reagent was pipetted into an erlenmeyer flask with a glass stopper. The samples to be analyzed were withdrawn from the reacting mixture with a calibrated 2 c.c. hypodermic syringe with exactly 1 c.c. of the sample being delivered into the erlenmeyer flask. The mixture was allowed to stand for thirty minutes and then titrated to neutral with a standard base. The hydrochloric acid consumed, corrected for the catalyst, was the measure of the epoxide in the sample. Calibration —The simple procedure and the stability of the reagent made this method a very desirable one, especially, when a large number of analyses had to be made. Several undesirable effects, however, were uncovered when the method was being calibrated for our materials. One of these is the presence of competing side reactions according to the following equations: H+ IH I I C —C- + HO -— >,C C- (19) \0/ OH OH H+ -C — C- + ROH -- -C —c- (83) OR 6H which are catalyzed by hydrogen ions. This made it impossible to account for all the epoxides by Equation (18) page 21. Furthermore, Equation (19) and (83) indicate that less and less epoxide will react by the way of Equation (18) as the concentration of hydrogen ion is increased. In Table XXIII the percentage of epoxide analyzed by this

TABLE XXIII ANALYSIS OF PROPYLENE OXIDE IN ALCOHOL-ETHER BY THE AQUEOUS HCl-CaCl2 METHOD HCl strength Concentration Oxide Fraction Deviation of reagent of oxide in analyzed analyzed from sample,, gm/gm average 0.15 N 0.0115- 0.0112 0.974 + 0.0065 0. 0125- 0.0120 0.96 - 0.0075 0.0 150-. 0.0150 1.00 + 0.0 525' 0.015-2* 0-.0150 0.-987 + 0.0195 0.0160 0.-0 158 0. 989 + 0.0215 0.025' 0.02~4 0.972 + 0.0045 0.0264* 0.024o0 0.909 -0.0585 o.o~67 0.0262 0.981 + 0.Q1355 0.0~9O 0.0282 0.972 + 0.0045 0.03150* 0.0310 0.939 - 0.0285 0.044o 0.0425 0.966 - 0.0015 0.0500 0.0465 0.93 - 0.0575 0.0500 o.o485 0.97 + 0.0025 0.0520* 0.0500 0.962 - 0.0055 0.0550 O-o54o 0.982 + 0.0145 0.0875* 0.0760 0.968 + 0.0005 0.0875 o.o845 0.966 - 0.0015 0.0940 0.0920 0.979 + 0.0115 0.1040 0.1015 0.976 + o.oo85 average 0.967, 0.25 N 0.0260 0.0230 o.885 - o.oo48 0.0555 0.0295 0.881 - o.oo88 o.o565 0.0500 o.885 - o.oo48 0.0975 o.o885 0.908 + 0.0182 average 0.889, CZo - a rn-n anL + n-P -n nnr y.L n1.L n -,r A, ~U a LJ. + 44J -n~r Jnr l~ 9= ~ ( A 2. ether. glycol e The rest are mixtures of propylene oxide and dipropylene ~ther.

-85 - method are tabulated. Fairly consistent results were obtained and the actual concentration of the epoxide in the sample can be obtained by using the necessary correction factor. This method was used for Runs 1 to 14 inclusive, for the dipropylene glycol methyl ether - propylene oxide runs. 2. Periodic - Perchloric Acid Method( 7) Preparation of Reagent —The analytical reagent was prepared by dissolving 1 weight percent periodic acid in an aqueous solution of a 0.4 N perchloric acid. Iodine is liberated from the excess periodic acid by the addition of 10 c.c. of 15 percent potassium iodide solution. The free iodine was titrated with a 0.1 N standard sodium thiosulfate solution. The periodic acid reagent was found to be stable over a period of one month. Procedure —25 c.c. of the reagent was pipetted into an erlenmeyer flask fitted with a glass stopper. Samples to be analyzed were withdrawn from the reacting mixture with a calibrated 2 cL.c. hypodermic syringe and exactly 1 c.c. of the sample was introduced into the flask. The mixture was allowed to stand for one hour after which 10 c.c. of 15 percent potassium iodide solution was added to the mixture together with 1 c.c. of concentrated acetic acid. The free iodine liberated in the mixture was then immediately titrated with standard 0.1 N sodium thiosulfate. The difference of sodium thiosulfate used between a blank and the sample is a measure of the propylene glycol present in the sample. From this, the concentration of propylene oxide can be calculated.

Calibration —Results using the periodic-perchloric acid method on known samples are tabulated in Table XXIV. As can be seen, low values are obtained when an insufficient amount of the reagent was used, The results in Table XXIV agree quite well with values reported (17) (22) by Latremouille7) for pure ethylene oxideO Fleury() reported that methanol and acetic acid are reactive with the periodic reagent, However, blanks with and without these two compounds had failed to indicate that this is so, It may be pointed out here also that this method is (50) known to be specific only for adjacent hydroxyl groups o Chemical Analysis of Hydrpxyl Group(50) Acetylation with Acetic Anhydride in Pyridine —As mentioned in page 22, the analysis of the hydroxyl concentration is necessary to give a complete description of the experimental product distribution, The analytical method used was the acetylation of the hydroxyl group using acetic anhydride in pyridine. This method is essentially that described by Mitchell(5 with slight modification. Preparation of' reagentc —The analtyical reagent consisted of 10 percent acetic anhydride in reagent grade pyridineo Standard 0.5 N NaOH was used as a titrant with phenolphthalein as indicator, This reagent is not too stable and should be prepared fresh, Procedure —A sample of about 500 mg. was weighed into a glass stoppered erlenmeyer flask with 25 cc, of the reagent. The glass stopper was moistened with pyridine and seated loosely on the flask, The flask was then placed on a steam bath and heated for one hour. After the heating

TABLE XXIV ANALYSIS OF PROPYLENE OXIDE IN ALCOHOL-ETHER USING THE PERIODIC-PERCHLORIC ACID METHOD c.c. of Concentration Oxide Fraction Deviation reagent of propylene analyzed Analyzed.. from used oxide in sample average gm/gm 15 0.03565* 0.0342 0.96 - 0.0066 0.03565 0.034 0.954 - 0.0126 0.03565 0.0544 o.965 0.0oo16 0.0254 0.0241 0.9488 - 0.0178 0.0294 0.0288 0.9799 + 0.0133 0.05495 0.0338 0.9668 + 0.0002 0.01527 0.01504 0.985 + 0.0184 0.0286* 0.02748 0.9608 - 0.0058 0.03858 0.0374 0.9699 + 0.0033 0.01293 0.01233 0.955 - 0.0136 0.0586* 0.0378 0.978 + 0.0114 0.0386* 0.0378 0.978 + 0.0114 0.0386 0.0576 0.972 + o.0054 0,0386 0.05714 0.961 - 0.0056 average 0.9666 25 0.05565 0.05547 0.995 - 0.0017 0.05565* 0.03558 0.998 + 0.0015 o.0386 0.0388 1.005 + o.oo83 0.0386* 0.0382 0.99 - 0.0067 0.0155 0.01558 0.992 - 0.0047 0.0270 0.02727 1.01 + 0.0133 0.0129* 0.01277 0.99 - 0.0067 0.0456* 0.0451 0.989 -0.0077 0.0456 0.04596 1.008 + 0.0115 0.0245 0.03426 0.99 - 0.0067 average 0.9967 * Samples consist of propylene oxide and tripropylene glycol ether. The rest are mixtures of propylene oxide and dipropylene glycol ether.

-88 - period, about 50 c.c. of distilled water was added to the mixture to hydrolyze the unreacted anhydride. The mixture was then titrated with the standard base. Simultaneously, a blank was also prepared and titrated. The difference in the titrating base between the blank and the sample is a measure of the hydroxyl group concentration of the sample. This method was found to be satisfactory and in general, gave quantitative results. Care should be taken that the acetic anhydride concentration in the reagent should be at least 10 percent, as low results will be obtained at lower concentrations. In Table XXV results of this method on pure glycol ethers are tabulated. TABLE XXV ANALYSIS OF HYDROXYL GROUP IN ALCOHOL-ETHERS BY THE ACETIC ANHYDRIDE-PYRIDINE METHOD Theoretical Molecular weight by molecular weight analysis of OH group dipropylene glycol 148.25 148.16 methyl ether 148.30 tripropylene glycol 206.8 206.24 methyl ether 206.0 I

APPENDIX III THEORETICAL AND EMPIRICAL TREATMENT OF REACTION RATE IN THE LIQUID PHASE Theoretical treatment of chemical reaction kinetics in the liquid phase has always been hampered by the fact that the theories of liquids and solutions are still in the developmental stage. The extension -of gas kinetics methods to the liquid phase has met with relatively little success except in systems that can be considered as ideal solutionsO For non-ideal systems, the common approach is to relate some bulk properties of the solution to the activity of the reacting specieso For reactions involving ions and polar molecules, the important parameter is the ionic atmosphere or electrostatic potential between the reacting species. A summary of this treatment is presented below. The inherent simplifying assumptions involved, however, make such a treatment valid only as a rough guide. Sometimes, the results obtained are not too consistent ( 239). For non-electrolytes in general, the recent extension of strictly regular solution theory to kinetics in the liquid phase indicates some promising results(29 52) Relationship Between Rate Constants and Activity of the Reacting Species By considering the electrostatic forces among ions and assuming complete dissociation of strong electrolytes in solution, Debye and Huckel (14) satisfactorily solved the problem of calculating activity coefficients of ions and electrolytes, expressing them in terms of the ionic strength of -89 -

the solution: z2 A;,l - lnyi = i (84) 1 + i A where ai = distance of closest approach of another ion to the ith ion 7i = activity coefficient of the ith ion = ionic; strength = 1/2 E CiZi Z charge ci = concentration of the ith ion and A e3 2IN (85) DKT 1000 DKT 8iNe (86) D 1000 DKT where e = electronic charge N = Avogadro's number K = Boltzmann's constant D = dielectric constant T = absolute temperature ~K The activity coefficient for the electrolyte defined as Y+ = z+ + Y_ (87) is then related as follows: Z+Z A.. - - in + = f- (88) 1 + Pai Ah The above equations hold rigorously for very dilute solutions or very low ionic strengths; for moderately higher ionic strengths or a change of the dielectric constant of the solution, additional terms had to be

-91 - added to Equation (84) to account for deviations (2) For reactions involving ions only and where the dielectric constant of the reacting medium is unchanged, the Debye and Huckel expression for the activity coefficients may be used. For a bimolecular ion-ion reaction in solution, the substitution of the Debye and Huckel terms for the activity coefficients in Equation (33) yields the following expression for the specific rate constant: in k = in k' + e Zb ( e) (89) DKT 1 + where 2 8N e2 K (90) =1000 DKT The assumption of a double-sphere activated complex was made to facilitate the calculation of Ir. In the case where one of the reactants is a neutral molecule, ZaZb = 0, and according to Equation (89), the specific rate constant is independent of the ionic strength of the reacting medium. In the above treatment, the dielectric constant of the reacting medium was considered to be unchanged. In reactions in the liquid phase the dielectric constant of the reacting medium may play an important role. The dielectric constant of the medium affects markedly the ability of reactant particles to contact each other. This is especially true with ion-ion and ion-dipole reactants. The work required to separate two unlike charges varies inversely as the dielectric constant of the medium. The Debye and Huckel theory predicts activity coefficients for ions as less than unity in the range where the theory holds. This implies

-92 - that the variation of activity coefficients is attributed to forces of attraction between the oppositely charged ions, which are more important than the repulsions between the like charged ions. By the same reasoning a decrease in the dielectric constant of the medium leads to an increase in the activity coefficient of the ion. The effect of the dielectric constant of the medium on the rate of ionic reactions may be similarly treated by the method of Debye and Huckel( By relating the rate constant at infinite dilution, k', in Equation (89) to that in the gas phase k' = ko (91) where ko = is a true constant independent of the dielectric constant and ionic strength a, b = activity coefficient of reactants relating the infinitely dilute solution to the ideal gas or n k' = inko + in -a (92) Following Scatchard's treatment (67) where the concentration of the activated complex was calculated in terms of the concentration of A ions, the concentration of B ions at a distance r from A, and the electrostatic potential, the following relationship is obtained: n- - = ab (1 1( - 1n K(93) on K T r - D

substituting this into Equation (92) gives ink' = inko + e2Za) (94) K T r, D where r = ionic radius of the activated complex which relates the rate constant in solutions of different dielectric constants. Equation (94) may be written in a more useful form d in k' = e Za () d (1/D) K T r Laidler and Eyring(39) treating the activated complex as a sphere instead of a double sphere, arrived at a similar equation for the effect of the dielectric constant on the rates of ionic reactions 0 2KT D / ra rb r in kt = in ko + e ( _a Z (Za + —,-) ) (96) or kt e2 2 Zb2 (Za + Zb)2 dIn k' e (a + 4 _ (Za+Zb) ) (97) d(l/D) 2KT ra rb rt Equations (97) and (95) are identical when ra = rb = r/. An examination of Equations (97) or (95) shows that the effect of the dielectric constant on the rate of ion-ion reactions is dependent on the charge type of the reactants. For the reaction of an ion with a polar molecule, Equation (94) is not applicable. Equation (97), however, reduces to d n k' e _ (98) d(l/D) 2KT ra r

-94 - Since the radius of the activated complex r?, is always greater than that of the ion ra, the effect of the dielectric constant of the medium on ion-dipolar reactions is to decrease the rate of reaction as the dielectric constant increases. Deviations from Equation (98), frequently found at low dielectric constant, have been attributed to the tendency of the more polar component to cluster around ions such that the bulk dielectric constant is very much lower than the dielectric constant around the ions. Here the rate constant should conform more to that of a medium of a higher (27) dielectric constant than to the apparent one7) Recently, Landskroener(40) presented an improved version of Equation (98) which was applied to reactions such as the hydrolysis of esters, reactions which have failed to be treated satisfactorily by Equation (98), The final form of the Landskroener equation is in k = in ko +...) 2KT D ra rb r. 3 5e2( \ a Gb G () + 3 ( + - I ) (99) a b Here Gi is the distance separating the two point charges of the aolecule formling the dipole. For an ion, G = 0 and evaluation of G is possible if the configuration of the activated complex is known. Additional terrms may be added to Equation (99) to account for higher multipole momenenlts of the molecule(36) Equation (99) is equivalent to Equation (98) except for the last term on the right hand side. It was pointed out that for ion-ion rieactlons the final term of Equation (99) might be negligible while for

-95 - dipole-dipole reactions the effect of the solvent is solely given by the last term. For ion-dipole reactions the final term may be more important than the second term thereby accounting for the failure of Equation (98) in its application to some reactions. Molecular Association and its Influence on the Kinetics of Liquid-Phase Chemical Reactions Associative phenomena occur widely in non-ideal liquid mixtures and when hydroxylic compounds are involved, hydrogen bonding is invariably the cause. The result of such interaction is the formation of stable complexes which definitely affects the rate of reaction of such a system. (45) (57) Lutskii5) and Knorre(37) have studied organic reactions in solutions and the effect of hydrogen bonding on their rates. Anomalous behaviors on the rates of reaction were observed and some of the data were shown to be explainable in terms of the dielectric constant of the solutionso In general, it was observed that the activation energy is decreased by hydrogen bonding. In another direction, Prigogine(61) has summarized recent efforts in calculating activity coefficients of associated solutions (due to hydrogen bonding) from spectroscopic data. Medium Effects on the Arrhenius Equation According to the transition state theory and thermodynamics, the specific rate constant k is expressable as k = K T e /R e -,/RT (100) h and since for reactions in the liquid state E = MBf + RT (101) k eK T ASf/R eE/RT (102) h

-96 - ~Tlfh - " 'Y Y - lr 1 rmrl t r% — ' c? +r+.T - *U Ji- }. ~f~''.......

-97 - following equation(75) d in k = lnn k + lnk d (104) dT T.JD J dT leads to E = E + 2.3 RT2 logk dD (105) C WDJ dT wher EE is the apparent energy of activation measured in media of constant -composition and ED is the activation energy at constant dielectric constant. Harned and Samaras(3 derived equations relating the work required to displace a solvent by another of different polarity in the presence of an electric field and showed that the specific rate constant can be represented as -w/KT k =k c'e (106) where k = is the velocity constant in the medium in question k = velocity constant in the original medium before the change was effected c/ = concentration of the catalyst ~w/KT e = a Boltzman factor, where w is the work term (22) Evans and Jenkins have shown that the activation energies of some organic reactions in solvents of different dielectric constants can be correlated by the simple relationship E = EB + E/D200 (107)

-98 -where E = the measured Arrhenius activation energy EB = the activation energy obtained by extrapolation to 1/D = 0 Ex/D = E - EB, the repulsion energy, characteristic of the solvent.

APPENDIX IV MATHEMATICAL DERIVATIONS Equations Describing Product Distribution Of Consecutive Reactions Case 1: All the steps are bimolecular and volume change is assumed negligible.. The rate equations are V dt = - k (A)(B) (48a) V = k1 (A)(B) - k (AB) (B) (48b) dt 2 2 d(AB2) V dB2 = k2 (AB)(B) - k3 (AB2)(B) (48c) dRt where the ABns' and B are in number of moles and the units of kns' are in liter mole min.~1. Dividing: qi-ationi 48a by 48b. (A) = k (A) (108) d(AB) k1 (A) - k2 (AB) rearranging, d(AB) - 2 (A) d(A) = - d(A) k1 (A) Equation (108) is a linear equation of the first order whose solution is ___ 1 (kk2 (AB) k1 (A) {kk + kik k } (109) similarly, by dividing Equation 48a by Equation 48c and substituting the values of (AB) obtained from Equation (109), a similar first order linear equation is obtained, and the solution is -99 -

-100 - (AB2) = kl k2 (A) (k2 - 1)(k1 1 2/ 12 ^ / kl )(k3 k^) kl-k2 (kl k2)(k3 - k2) A ki-k + 1 l r (kl - k3)(k2 - k3)L A J J (110) repeating this procedure, it can be shown that the solution is symmetrical and can be written in terms of the mole ratio ABn/Ao, as n+l (A _n = II k nAT --- (51) j=l I (kj - kk) In terms of distribution constants c, the general solution may be written as n+l ABn jn n 1 A = (-i) n cn L 0 j=l j =1 A cA (A ) A0 n+l n (cj - ck) -=1 jyk llU) Equatiors (111) do not hold when two or more alcohols are present at the start of the reaction. For the case where both (Ao) and (AB), are present at the start of the reaction, the boundary condition[(A) = (Ao);(AB) =(AB)o; at t = 0O must be satisfiedo Equation (109) then becomes k2 kAB -kl (A) + (AB) O) k1 k2Pk1 ki (A k I/kI k' 1 0 i i 1o) (112)

-101 - and Equation (ilo) becomes 3 1 - kB1 k2 [(A) — A = (k2 - k9)(k5 - kl) LA' k 5k1 (1115) klk2 - 2((AB)o)(k2-k1):F A1 -k/1 A1O' 3 -+ kik)(k2 k2 L /ki~ A k3/klj ~he number of moles of the higher products can be obtained by the same procedure. In the case where k1,~ kn; n,l kn =kn+; n>-l Equation (ill) reduces to ABn n ~1r/A\ n-iJ (c l)njA(\A) 7n T 3=0 (114) where cn =k1 n l k1 Case 2:. Distribution of products of consecutive second order reactions with equal velocities. The system of differential equations is identicE with Equations (48) except that k = k2 = o.* = kn., The rate of change of B may be written as k An)(B) =-k (B) j~ (ABn)(15 0n We note also that n I(ABn) =A0, the initial concentratioM of the pro.pagatting alcohol(16

-102~ substituting Equation (116) into Equation 115) gives ) = - k Ao (B) (117) dt solving Equation (117) in the following manner: B t d (B) = A k (B) dt (118) Bo 0 or t Bo B = k (B) dt (119) Ao 0 Letting B - B v = -, the mole ratio of oxide consumed (120) Ao to that of the initial alcohol we have dv = k (B) dt (121) from Equation (45a) d(A) = -k (A)(B) dt = -A dv (122) similarly from Equation (45b) and (121) (AB) = k (A)(B)- k (AB)(B) (123) dt d (AB) = k (A - AB)(B) dt (124) (A - AB) dv The general solution to Equations (45) is (Ao)vn e-v AB = (A..."e- (125) 11 n'

-103 - or in terms of the mole ratio of the product to that of the initial alcohol, Equation (125) becomes ABn vn e-v Ao n (126) This equation is the well-known Poisson distribution equation. The amount of B at any time t may be obtained from Equation (119). The result is B = e k(A)t (127) An interesting result is obtained by differentiating ABn/Ao (Equation (126)) with respect to v and equating the expression to 0,. e.g., d (ABAo) - l vn (-ev) + e- (nvn1) ]= 0 (128) dv n L simplifying, we have v = n (129) implying that the maximum mole fraction of any ABn is reached at v = n. Case 3: The initiating reaction is first order and the succeeding reactions are second order. The system may be represented by the following rate equations assuming negligible volume change. V dA/dt = kl (B) (130a) V d(AB)/dt = k (B) - k2 (AB)(B) (150b) V d(AB2)/dt = k2 (AB)(B) - k3 (AB2)(B) (130c) V d(AB )/dt = k3 (AB2)(B) - k4 (AB3)(B) (130d) and so on

where the ABns and B are in number of moles and the units of the kn's '-l are in liter mole' sec.. 1 -n > 1 and the units of kl is sec. dividing Equation(530a) by Equation (130b) k dA/d(AB) kl - k2 (AB) (151) or kl dA - k2(AB) dA = kl d(AB) (132) Equation (132) is a linear differential equation of the first order, solving the equation for AB in terms of A and kl/k2 we have (AB) = kl/k2 - (k/k2)e(-kl/k2 A (133) likewise, using Equation (130a and c) the relationship of AB2 in terms of the rate constants and the concentration of the starting alcohol (A) is 2) / k1 -(k2/kl)(A) k2 e (-k3/k)A (AB.) = ke/k2 (134) k3 - k2 k5(k5 - k2) similarly, (AB5, AB4,..) can be obtained. Application of the least Squares Method to the Arrhenius Equation The Arrhenius Equation for the reaction velocity constant is k = Ae-E/RT (9) This equation may be written in the logarithmic form as in k = in A + E/RT = 0 (135)

-105 - The method of least squares specifies that the sum of the square of deviations of Equation (135) by a minimum or (ln k - In A + E/RT)2 = minimum (136) Let the left hand side of Equation (136) be represented by cp, then to evaluate the two constants A and E we partial differentiate cp with respect to the two constants and equate the two equations to zero, resulting in two equations in two unknowns. 6(p/)A = (ln k In A + E/RT)(-1/A)-= 0 (157) 6cp/6E = (In k - in A + E/RT)(1/RT) = 0 (138) or In k + Z E/RT in A = i (139) i Z In A/RT Z in k/RT E = i /R2T2 (140) Z 1/R2T2 i where i is the number of experimental observations. From these two equations, the constants A, and E can be readily calculated~

.AP.LPENDIX V EXPERIMENTAL -DATA TABLE XXVI REACTION VELOCITY CONSTANTS FOR tAETHANOL-PROPYLENE OXIDE REACTION FROM PROPYLENE OXIDE CONCENTRATION DATA Run Temp. Mole Ratio Cat. Conc. Time Oxidie k Number 0C methanol/oxide mols/lit. min. conc. lit. 1 35 2 45 48,1l 38.,4 0,139 0,172 0 15 85 150 205 295 365 0 25 65 95 150 235 370 O.488 O o.470 O.410 0.357 0.262 0,,228 0.0000879 O0,oooo894 O0,o0oo84o 0.0094 0,0000895 average o~oooo884 0.595 0. 489 0~ 380 0,,314 0.216 0.142 0.075 0oooo344 0.000300 0.0O0295 0.000296 0.0O0268 0.000248.average 0.000292 3 55 48.8 0.252 0 11 30, 55 131, o. 465 0o.38o 0 ~,2539 0,1569 o.o856 0o.0447 0o0ooo8o6 0.000894 0.oo0878 O.ooo885 0.000796 average 0.000852

-107 - TABLE XXVII REACTION VELOCITY CONSTANTS FQR THE DIPROPYLENE GLYCOL METHYL ETHERPROPYLENE OXIDE REACTION FROM PROPYLENE OXIDE CONCENTRATION DATA Run Mole Ratio Temp. Cat. Conc. Time Oxid~e k Number alcohol/oxi'de 0C mols/lit. mins. conc. lit.mols/lit mol~min. 1 10 87 0.1764 0 20 4o 75 155 195 0.573 O.487 O0.364 00 240 0.172 o~o89 0.00202 0.00210 O0.00163 O0.00177 - average 0.00179 2 10 87 0.1764 0 50 95 145 215 0.575 O.340 O0.218 0.129 0.050 0.001l86 0.00184 -0.00189) 0.00212.average 0.00192 5 10 87 0.1764 0 20 48 95 145 215 0.573 0. 495 0.352 0.215 0,,124 0.049 o.ooi8i O.OO191 0.00196 O I O0l.average 0.00194 -5 87 0.1764 0 45 106 167 261 1.102 - o.683 0.00200 0.342 0.00226 o.16o 0.00257 0.050 0.00249.average 0.00227

TABLE )QCVII (CONT ID) Runi Mole Ratio Temp. Cat. Conc. Time Oxid~e k.Number alcohol/oxide 0C mols/lit. mins. co~c. lito mols/lit mol~minl. 5 10 85 0.0556 0.70 150 190 290 0.578 0. 491 0. 410 0.540 0.288 0.000594 0.0oo464 0.000494 0.000429 average 0.000o445 6 10 85 0ll09 0 90 185 270 560 0.576 o —.341 0.246 0.109 0.057 0 *003r07 0.00l10 0.00118 average 0.00112 7 10 85 0.1109 0 90 150 240 0.576 0.347 0.246 0.169 0.00100 0.00102 0.00093.average 0.00099 8 10 85 0.2207 0 25 60 120 i8o 0.575 0.388 0.252.0.121 o.o48 0.00278 0.00247 0.00257 0.00257 9 10 85 0.3295 0 20 6o 145,average 0.00255 0.570 -- 0.579 0.00365 0.165 0.00578 o.o68 0.00577 0.027 0.00598 average 0.00579

-109 - TABLE XXVII (CONTID) Run Mole Ratio Temp. Cat. Conc. Time Oxide k.Number alcohol/oxide 0C inols/lit. inins. conc. lit. mols/lit mol.Min. 10 10.1 69 0.2746 0 43 115 145 191 0.575 0. 438 0.575 0.50o6 0.256 0. 185 0.00120 0.00097 0.00105 0.00104 0.00110 average 0.00106 11 10 6o 0.11578 0 105 195 515 0.591,0,529 0. 474 0. 427 0.000181 0.000199 0.000199.average 0.000194 12 10 60 0.1195 0 185 245 296 58o 0.599 0.,478 0. 420 0.599 0,577 0.000205 0.000246 0.000256 0.000210.average 0.000224 15 10 60 02,2227 0 125 158 295 0.583 0.56o 0.525 0.220 0.000429 0.0004531 0.000415 10 60 0.2264 0 60 105 165 245 average 0,000425 o.588 0.469 o.ooo646 0.,441 o~ooo455 0.590 0.000451 0.502 0.000476 average 0.000505

-110 - TABLE XXVII. (CONT'D) Run Mole Ratio Temp. Cat~ oc Tm xd k Number alcohol/oxide 0 moIs,/1it. mins. conc. lit. mols/lit mnol.niin. 15 10 60 0.338o 0 60 a,4o ~~70 560 0.585 o. 490 0,558 0.226 0, 152 0.000506 0.000612 -0.000624 0.0006-71 average 0.000602 16 10 355 0,1168 0 550 140 577 1070 0. 667 0.566 o.546 0.547 0. 495 average 0.604 0.582 0.,554 0.526 0.,432 0.0000528 0.0000594 0.0000297 17 10 355 0.2323 0 60 210 515 755 0.0000515 0.,ooo681 0.000725 0.000768.average 0.000725 10 355 0.3469 0 120 180 515 0o.6oo o.563 0.542 0.507 0.000878 0.000950 0.000897.average O.OOOWo8

-111 - TABILE XXVIII REACTION-VELOCITY CONSTANTS FOR THE TRIPROPYLENE GLYCOL METHYL ETHERPROPYLENE OXIDE REACTION FROM PROPYLENE OXIDE CONCENTRATION DATA Run Mole Ratio Temp. Cat. Cone. Time Oxide k Number alcohol/oxide 0C mols/lit. mins. cone, lit. mols/lit mols.mino' 9.25 100 0. 1895 0 14.5 26.0 159.0 57.0 69.0 0. 457 0.3507 0.271 0.171 0. 114 0.078 0.00662 0.00487 O0.oo566 0.00625 0.0 IL),4 2 10.25 100 0.1900.average 0.00597 0 o.414 -- 9 0.3521 0.0067 19 0.264 0.0057 29 0.1935 o.oo64 62 0.100 0.00568,average 0.00612 15 7 85 0,056835 0 45 1150.190 1505 o. 6o5 0. 494 0.411 0,1568 0.1508 0.00108 0.000728 0.0006155 0.0005159.average 0.00742 4 7 85 0.111540 0 150 90 150 270 o. 6o4 0. 475 0,1568 0.2615 0,1515 0,001915 0.001158 0.00129.average 0.001151

-112 - TABLE XXVIII (CONT'D) Run Mole Ratio Temp. Cato Conc. Time Oxide k Number alcohol/oxide ~C mols/lit mins. cone. lito mols/lit mols.min......,.,,..... _.......... 5 7 85 0.22560 0 45 150 o.604 0.336 o.104 0.00312 0.00300 average 0.00306 6 7 85 0.33684 0 30 75 105 135 0.598 0.361 0 191 0.135 0.075 0.00415 o oo386 0.00364 o oo4oo average 0.00386 7 7 6o 0 05683 0 30 180 365 995 1665 2480 0 620 0.571 0.549 0.506 0.407 0 336 0.278 0.0000ooo64 0.000150 0.000130 0.000103 o.ooo88 0.000078 average 0.000106 8 7 6o 0.11620 0 575 84o 1040 1370 0.619 0.345 0.28o 0.239 o 181 0.000326 0.000229 0.000223 0.000224 9 7 6o 0.23114 0 120 285 4o5 690 average 0.000224 0.616 - 0.474 0.000515 0.342 o.oo000496 0.267 0.000500 0.150 0.000510 average 0.000502

TABLE XXVIII (CONT'D) Run Mole Ratio Temp. Cat. Conc. Time Oxide k Number alehol/oxide ~C mols/lit mins. conc.. lit. mole/lit molsmin. ' t,,, |..... i....__. _l,..... I, _ _. J_......._. i _ ~_.H,_. _......._ _ _1 _ IJL ____>____ 10 7 6o 0.34505 0 110 180 410 0.612 0.425 0.347 0.177 0.00079 000075 0.00075 average 0.00076 11 7 45 0.05897 0 585 1115 2100 363o 4445 0.628 0.578 0.545 0.493 0.436 0.371,000032 0.000030 0.0000266 0.0000254 0.0000278 average 0.0000276 12 7 0.1177 0 840 1110 2085 2655 0. 0.511 0.476 0.410 0.343 0.000056 0,000057.oooo000048 0.0000535 average 0.0000536 13 7 45 0,23413 0 300 1120 1410 0.564 0.361 0.504 average o.oooo8i 0,000116 0.000120 0.000106 o.ooolzo 0.000127 0.000190 0.002020 0.000212 0o.ooo00208 7 0.35495 0 6o 155 275 550 68o 0.620 o.6oo 0.543 0.,489 0.386 0.343 average 0.000205 rrr ~- I - -- - - - - -w - - __ _. _ _ C - --- i - - --

-114 - TABLE XXIX REACTION VELOCITY CONSTANTS FOR METHANOL-PROPYLENE OXIDE REACTION IN DIOXANE FROM PROPYLENE OXIDE CONCENTRATION DATA AT 4150C. Run Mole Ratio Cat. Conc. Dioxane Time Oxide k Number Methanol/Oxide Mols/Li-t. Cone. Mine'. Cone. lit., Mcols/Lit. Mols/Lit Mols.Min 1 12.51 0.202.6.90o 0 10 40 92 1315 190 0.677 0.645 o.585 0. 445 0.0390 0.1505 0.000555 0.00042-9 0.000487 O0.ooo464 0.ooo476.average 0.000482 2 47.00 0.2154 0.18159 1,988 0 150 50 8o 110 140 0.4157 0.1595 0.1529 0.000279 0.282 0.000268 0.222 0.0001500 0.191 0.000290.average 0.000284 35 157.20 0.575.0 20 50 100 140 170 225 0.571 - 0.492 0.000157 0.416 0,000197 0.1578 0.000202 0.1511 0.000209 0.270 0.000211 0.207 0.000215.average 0.0001985

-115 - TABLE XXX EPE-RIMENTAL TIME-COMPOSITION DATA AND PSEUDO-FI.RST ORDER RATE CONSTANTS FOR T~EREACTION OF PROPYLENE OXIDE WITH A MIEXTURE OF METHANOL AND PROPYLENE GLYCOL METHYL ETHER AT 450C. Run Mole Ratio Number Methanol/Oxide Mole Ratio Monoglycol/Oxide Cat0, Cono. Mols/Lit Time Oxide Mins. Conc. Mols/Lit.5-03)llog-. t gB~ 1 2 3 12.8 11355 0.185 0 10 50.65 95 170 7.78 0. 2125 10 20 4o 70 100 150 160 0.574 0.542 0. 475 0.393 0.305 0.215 0.765 0.687 0. 625 0.559 0.4355 0.525 0.288 00245 o.6o8 0.518 00 479 0. 407 0.562 0.295 0o.583 0.536 00,454 0.551 0.292 0.256 0.00557 0.00622 0.oo583 0. oo666 o.0058o 0o.oio43 0.01117 o.oo868 0.01271 0.00859 0o00751 0.00714 0.00589 0.00550 0.00598 O.oo4o5 o.oo346 0.003555 0.00412 O.0056o 0.00622 0.00610 -0o.oo633 8.62 6.67 12.25 15.50 0.1295 0 15 50 6o 100 150 205 0.266 0 20 53 91 115 145A 4

TABLE XXX (CONTtID) Run Mole Rat io Mole Rat io.Number Methanol/Oxi'de Monoglycol/Oxide Cat. Cono, Mols/Lit Time Oxide 1 Bo Miris. Conc. (2.3o5)'tlog~-. Mols/Lit 5 6 11086 355.20 16.00 7 12.70 4.12 9.47 90,47 4. o6 0.1755 0 20 43 81 111 136 0. 1625 0 20 4o 8o 100 0.190 0 15 50 75 105 127 0.190 0 8 25 37 - 90 1126 0.547 00 494 0.385 0.342 0.262 00218 0.517 0.444 0.576 0.275 00246 0.596 0.524 0. 414 0.344 0.272 0.238 0.597 0.549 0. 498 0. 446 00 4ol 0.512 0.257 0oool83 0o.oo815 o,oo058o 0ooo684 0.00679 0.00762 0.00797 0,oo541 0,oo484 0.00875 0.00750 0.00746 0.00721 0.01020 0.00795 0.00781 0.00707 0.,00712 0.00755 0.-00785 0.00760 0.00788 0.00755 8 16.00 0.176 9 52.70 o.0,,48 5 0.528 25 o. 453 45 o.384 69 0.520 95 0.270

APPENDIX VI SAMPLE CALCULATIONS A. Single Reactions In the following sample calculations, the steps involved in the conversion of experimental raw data to the final rate constants are presented. The raw data used here were taken from Run 1 of the reaction of tripropylene glycol ether with propylene oxide (see TableXXVIII), TABLE XXXI RAW DATA FROM RUN 1 OF THE REACTION OF TRIPROPYLENE GLYCOL ETHER WITH PROPYLENE OXIDE AT 100~C. AND A STARTING MOLE RATIO OF ALCOHOL TO OXIDE OF 9.25/1 Reactor Charge Tripropylene Glycol Ether 248,3 grams Propylene Oxide 8033 grams NaOH 2.08*grams Total Charge 258.63 grams Reactor Time Na2S207 used Temperature Minutes per sample,c.c 0C 100ol 0 99.9 1 100.0 14,5 102.0 100.1 26.0 102.5 100.2 39.0 103.9 100.0.557o0 104.7 100o.0 69.0 105.2 * Dissolved in the glycol-ether. For this particular run, the weight of each sample was 0.94 grams and 25 co. of the periodic-perchloric reagent was used (see analytical methods in page 81). The blank titration of 25 c.c. of this -117 -

-118 - periodic-perchloric reagent corresponded to 10653 C.Co of the sodium thio= sulfate solution used. The normality of the thiosulfate titrant was 0.149 N. The amount of propylene oxide in the sample may now be calculated from Table XXXIo The differences of the amount of thiosulfate solution used in the blank and that used on the sample, properly adjusted by the correction factor in Table XXIV, is a measure of the propylene oxide content of the sample. Conversion of the number of c.c of sodium thiosulfate to grams of propylene oxide may be effected by the following relationship: (c.c. Na2S207)(Normality) = Milli-equivalents (141) grams propylene oxide = 58o08.02904 (142 milli-equivalents 2000 Table XXXII gives the result of the calculation for the concentration of propylene oxide in the samples reported in Table XXXI. TABLE XXXII RESULTS FROM THE CONVERSION OF c.C NaS 20 TO MOLES PER LITER OF PROPYLENE OXIDE FOR THE DATA IN TABLE XXXI. Time Na2S207 Propylene Oxide Mins. (c.c. Blank Moles per Litero oCco for Sample) 0 0.457 14.5 4.3 0.307 26.0 308 0.271 59.0 2~4 0.171 57.0 1o6 0.114 69.0 1.1 0.078

-119 - The time-composition data of propylene oxide shown in Table XXXII can now be used to calculate the specific rate constant according to Equation (38a). 1 CA CB k = In.o. (38a) t (CAo-CB) CA CB The results of the calculation are tabulated in Table XXXIII. TABLE XXXIII RESULTS OF THE CALCULATION FOR THE SPECIFIC REACTION VELOCITY CONSTANT USING THE DATA IN TABLE XXXII Time CA, Triglycol CB, Oxide k Minutes Moles per Liter Moles per Liter Liter Moles Min. 0 4.22 0,457 14.5 4.07 0.307 o.oo66 26.0 4.04 0.271 0,00487 39.0 3.94 01ol71 0.00566 57.0 3.88 0o114 0.00625 69.0 3.85 0o078 0.00644 B. Product Distributions In the case when the distribution constants are to be calculated from experimental distribution data, the calculational steps involve a successive approximation of the distribution constants until the calculated product distribution matches the experimental results. On the other hand, if the values of the distribution constants are already known, the product distribution maybe immediately calculated using Equations (111)(114) and (126). The calculations, although a bit tedious, are straightforward. In Figure 19, calculated product distrubution results using Equation (114) and various values of c (c = 1, 0,5 and Ool0) are plotted.

jmi CD H 'I' O C '3 0 0 O CD O PII H 0 fr) t1 t-i6 w CfI rCD 1-&s II z 2 4 -49 0 a I I MOLES OXIDE REACTED / INITIAL MOLE OF METHANOL

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