THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING SOLUTION THERMODYNAMICS FROM GAS LIQUID CHROMATOGRAPHY Raymond E. Pecsar A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Science in the University of Michigan Department of Chemical and Metallurgical Engineering 1964 December, 1964 IP-690

Doctoral Committee: Professor Joseph J. Martin, Chairman Associate Professor Richard E. Balzhiser Professor Edward E. Hucke Professor Edgar F. Westrum Professor G. Brymer Williams ii

ACKNOWLEDGEMENTS The author would like to express his appreciation to the following persons and organizations for their assistance and support in this work. Dr. J. J. Martin -- for his interest and encouragement in all phases of the work. The members of the doctoral committee: Dr. R, E, Balzhiser, Dr. E. E. Hucke, Dr. E. F. Westrum, and Dr. G, B. Williams -- for their cooperation and contributions. Mr. F. B. Drogosz -- for many helpful discussions concerning the experimental work, The Industry Program staff -- for their aid in the publishing of this dissertation. The Allied Chemical Corporation -- for their support during part of this work, The California Research Corporation -- for their support and encouragement during part of this work. The Horace H. Rackham School of Graduate Studies -- for a predoctoral fellowship during part of this work~ My parents -- for their encouragement and support to continue in my educational pursuits. Above all my wife -- for her patient helpfulness, understanding, and encouragement through my undergraduate and graduate studies, for her invaluable assistance in the preparation of this manuscript, and most of all just for being my wife. iii

LIST OF TABLES Table Page I Infinitely Dilute Activity Coefficients for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP at 200, 30~ and 40~C...................... 86 II Partial Molar Excess Free Energy (cal/mole) for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP at 200, 300 and 40~C,......,,,.,,. 87 III Partial Molar Excess Enthalpy (cal/mole) for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP from 200 to 40C,...................&.......... 89 IV Partial Molar Excess Entropy (cal/mole ~ ~K) for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP at 200, 300 and 40~C................ 90 V Correlation Constants for Infinitely Dilute Activity Coefficients.......................................... 121 VI Athermal Contribution to the Activity Coefficient at Infinite Dilution for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP...........................**** 124 VII Thermal Contribution to Nonideality Using Hildebrand's Formulation for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP......................................126 VIII Thermal Contribution to Nonideality Using Van Arkel's Formulation for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP..................... a........o.129 IX Thermal Contribution to Nonideality Using Martire's Formulation for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP.........................................131 X Thermal Contribution to Nonideality Using the Theory of Intermolecular Forces for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP..............................134 XI Theoretical Determination of Infinitely Dilute Activity Coefficients for Various Solutes in Water, 2 Pentanone and 2,3,4 TMPa.................&*a........ 137 XII Geometric Contribution to the Partial Molar Excess Entropy for Various Solutes in Water, 2 Pentanone and 2,3,4 TMP...............................148 vi

LIST OF TABLES (CONT'D) Tab e Page XIII Energetic Contribution to the Partial Molar Excess Entropy for Various Solutes in Water, 2 Pentanone and 2,534 TMP..............................................150 XIV Chromatographic Column Properties...................... 163 XV Solute Retention Values............................ 165 XVI Physical Properties of Materials.....,..,.............180 vii

LIST OF FIGURES Figure Page 1 Schematic Diagram of Equipment....................... 71 2 Activity Coefficient of Ethanol in Water as a Function of Concentration in the Dilute Solution Region at 30~C............................,. 98 3 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in Water at 20~C...... 108 4 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in Water at 300~C...., 109 5 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in Water at 40~C...... 110 6 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2 Pentanone at 20~C 111 7 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2 Pentanone at 300C 112 8 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2 Pentanone at 400C 113 9 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2,3,4 TMP at 200~Co 114 10 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2,3,4 TMP at 300C,, 115 11 Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2,3,4 TMP at 40~Co. 116 12 Elution Progress in a Column Composed of Plates,...,.. 194 viii

NOMENCLATURE Upper Case Letters A Helmholtz free energy Bij Second virial coefficient Cj Arbitrary constant D Hydrocarbon radical E Intermolecular potential energy F Carrier gas flow rate Total partition function AGE Partial molar excess Gibbs free energy ASHE Partial molar excess enthalpy Hvap Enthalpy of vaporization I Ionization potential J Martire's specific interaction factor K Henry's law constant L Column length M Molecular weight of solvent NG Molar density of gas NL Molar density of liquid 2%7 Number of molecules?o0 Avogadro's number P Total pressure P Mean column pressure Q Configurational partition function ix

R Gas constant ASE Partial molar excess entropy T Temperature U Configurational potential energy VG Gas phase volume VL Liquid phase volume VR Retention volume VR Specific retention volume X Generalized physical property Y Functional group Z Generalized molecular force Lower Case Letters d Cluster product term e Mathematical constant f Fugacity fo Vapor fugacity f Fraction of time solute is in gas phase g Combinatorial partition function h Planck's constant j Martin's pressure correction factor k Partition coefficient k Boltzmannxis constant Number of methylenic groups m Mass of solvent in column

n Total number of moles p Partial pressure p0 Vapor pressure qint Partition function for internal degrees of freedom r Ratio of molar volumes, r > 1 s Cell theory parameter tR Retention time u Linear velocity v Partial molar volume v~ Molar volume w Interaction energy x Liquid mole fraction y Gas mole fraction z Number of nearest neighbors Greek Letters ca Polarizability a Cubical coefficient of expansion Y Activity coefficient?Y Infinitely dilute activity coefficient ath Athermal contribution to 7 Ith Thermal contribution to y Solubility parameter Dielectric constant I-1 Dipole moment xi

v Characteristic vibration frequency T1 Mathematical constant e Solvent density Cr..j Intermolecular distance T Generalized coordinate'P Generalized coordinate Volume fraction Relative volatility w Dipole interaction parameter Subscripts AB,Co., Components E Energetic contribution G Geometric contribution f Final condition i Inlet condition o Outlet condition s Initial condition u Unretained component 1 Solvent 2 Solute Superscripts E Excess G Gas L Liquid M Mixing co Infinite dilution xii

ABSTRACT The purpose of this study is the determination and prediction of thermodynamic properties of two component volatile nonelectrolyte solutions essentially at infinite dilution by gas-liquid chromatography. This technique is to be preferred to static equilibrium techniques as no analysis of the liquid phase is needed and a very rapid equilibration is established. The components to be studied were chosen on the basis of hydrogen bonding and intermolecular forces so as to encompass all types of solution behavior. The solvents utilized in this work were water, 2 pentanone and 2,3,4 trimethylpentane. In each of these solvents homologous series of alkanes, chlorinated methanes, alkyl formates, aldehydes, amines and alcohols were studied at 20~, 30~ and 40~C. At these temperatures from experimental measurements the values of the activity coefficient, the partial molar excess free energy, the partial molar excess enthalpy and the partial molar excess entropy were determined. The overall average accuracy of the results was + 5% based on repetitive measurements. These results show excellent agreement both with data available in the literature and anticipated properties deduced from possible solute-solvent interactions. The prediction of the experimental results took one of two forms depending on whether hydrogen bonding was the primary solution interaction. For water solutions, as hydrogen bonding was the predominant solution force, no theoretical method of representing xiii

the experimental data quantitatively could be formulated. Rather an empirical correlation providing a linear relation between the partial molar excess free energy and the number of methylenic groups in the solute was employed which fit the data very well. This technique can be justified based on a semi-theoretical group interaction scheme. For the other binary systems studied the nonelectrolyte solution theories based on Van der Waals forces and molecular geometry can be used to predict deviations from ideality. The cell theory of liquids may be employed to ascertain the athermal contribution to the activity coefficient while a modification of Hildebrand's work is used to obtain the thermal contribution. The product of these two contributions represents the experimental data of the 2,3,4 trimethylpentane solutions within 18% and the results for the 2 pentanone systems within 39%. This agreement is quite remarkable considering the fact that the predictive method utilizes only the physical properties of the pure components. A development is also presented based on the lattice theories of statistical mechanics. The relations evolved allow an evaluation of the geometric and energetic terms of the partial molar excess entropy. A number of qualitative conclusions are reached concerning nonelectrolyte solution behavior. Thus the technique of gas liquid chromatography has been proven to be a valid method of obtaining infinitely dilute equilibrium properties of two component volatile systems and methods have been developed for predicting and correlating these properties. xiv

I. INTRODUCTION As this thesis is concerned with the determination of thermodynamic properties of solutions utilizing gas-liquid chromatography, it would seem advisable to define the general concepts of chromatography to a slight extent so as the thermodynamic implications can be more fully appreciated. Chromatography has been defined as a physical method of separation in which the components to be separated are distributed between two phases, one of these phases being stationary with large surface area, the other being a fluid that percolates through or moves along the stationary phase. The phase equilibria for different components will differ due to the varying intensity of the force by which the stationary phase retains each component, whether the nature of this force be absorption, solubility, chemical bonding, or related phenomena, Because of the phase equilibrium differences, the sample components will tend to separate by repeated equilibration between the stationary and mobile phases as they move through the stationary phase. This operation is analogous to that of an equilibrium still and this analogy has been carried over through such factors as Height Equivalent to a Theoretical Plate, Relative Volatility, and other common expressions, While the above definition speaks in terms of a multicomponent mixture and its resolution, the principle can be equally well applied to a single pure component. The repeated equilibrium distribution of -1

-2the component between the stationary and the mobile phase provides a method of determining the vapor-liquid equilibrium of binary solutions consisting of the pure component, hereafter referred to as the solute, and the immobile solvent phase. Ao Objective of Thesis The purpose of this work is primarily two-fold. Initially it is desired to determine the thermodynamic properties of binary solutions by means of gas-liquid chromatography (GLC)o These binary solutions, in contrast to those normally studied by this technique, are two component volatile systems. By:investigating such volatile binary systems, the range and versatility of GLC has been extended and also a comparison with other establi.shed equilibri-m techniques can be made~ Although other recent work has established GLC as a method for studying vapor-liquid equilibri'um at any desired solute concentration, this work is confined to solutions essentially at infinite dilution of the soiute, While such solutions are not of immediate practical value, their properties have much theoretical significance in enabling one to establish a so called "end point" value to which properties of more concentrated solutions can be extrapolatedo In actuality, it is in this extremely dilute region that the greatest discrepancies exist, and therefore data in this region is definitely needed, The second objective of this thesis is the investigation of the behavior of nonelectrolyte solutions, and the establishment of methods for predicting their behavior based on sound principles0

-3Rather than merely characterizing solution behavior on a macroscopic level phenomenologically, it is desired to describe the solute-solvent interactions on a molecular level and thus gain a clearer understanding of the predominant forces responsible for solution behavior, primarily deviations from ideality. To this end the binary systems will be chosen with care so as to adequately represent the various types of anticipated behavior. When studying solutions near infinite dilution the interactions and resulting behavior often deviate considerably from that displayed in more concentrated solutions due to different forces being predominant. This effect will be pointed up in the analysis and discussion of the results. B, Present Methods The principal techniques for experimentally determining vapor liquid equilibria presently consist of: 1. Dew Point-Bubble Point methods in which a gas mixture is introduced to a visual cell in a controlled temperature environment and the pressure is varied. The point at which condensation begins and ends is determined by visual observation. 2, Static methods where a gas mixture is placed within an equilibrium cell and subjected to suitable temperatures and pressures, After adequate mixing and contact is assured, it is assumed that equilibrium exists within the cell and samples of each phase are withdrawn and analyzed.

-43. Flow systems wherein a vapor phase is passed through an equilibrium vessel in which a portion of the vapor is condensed, forming two phases within the vessel, The two phases are continually removed for analysis. 4. Vapor-Recycle techniques which combine the best features of the static and flow systems. The vapor phase is drawn off from the vessel and recirculated through the liquid until equilibrium is reached. This assures a much better approach to equilibrium. Again vapor and liquid samples must be very carefully removed for analysis. 5. Optical methods in which a condensed mixture of known composition is charged to an optically transparent cell. After vaporizing a portion of the mixture and establishing equilibrium, light is passed through the cell and the decrease in incident intensity at a suitable frequency is determined. 6. Electrochemical techniques where the potential of a half cell reaction of a solution of known concentration is determined. As this reaction is generally reversible, equilibrium is established and the desired properties can be obtained. Of the above techniques, the first four represent the standard methods for determining equilibrium in such systems as hydrocarbons, organic liquids and other relatively low boiling liquids. The latter two methods are more applicable to high boiling binary mixtures and electrolytes. The technique of GLC, however, can be employed to study solutions in any of these classifications.

-5C. Advantages of GLC In the present research, the scope of GLC has been considerably curtailed, as this study is concerned solely with nonelectrolyte solutions at infinite dilution. However, in the following discussion, the full range of applicability will be considered. The bubble point-dew point method is dependent on the vision of the observer and is best suited for close boiling binary mixtures. Although GLC is normally utilized with large solute and solvent volatility differences, the present work studies close boiling binaries and the method is suited for the entire range of relative volatilities. In the static methods great care must be taken not to disturb equilibrium when removing the samples for analysis. In GLC no direction measurement of the liquid phase is needed and the mobile effluent phase is easily analyzed. The flow systems require large samples of the vapor phase and equilibrium is difficult to achieve, in contrast to GLC where minimal samples are needed and equilibrium is nearly instantaneous, The vapor-recycle technique, while quite flexible, requires fairly elaborate equipment. GLC is noted for the rather elementary apparatus required. In the optical method, suitable absorption frequencies must be available in the vapor state and the computational procedure for processing the data is rather complex. The computational requirements for GLC, as will be shown, are fairly elementary. The electrochemical techniques are only applicable to conductive solutions while GLC in principle can be used for either type of solutions.

The standard techniques also possess the disadvantage that vapor-liquid equilibria for a fixed composition in either phase can only be established by a trial and error approach to the desired composition, In GLC a fixed composition in the vapor phase can be determined directly. A primary advantage lies in the fact that a dynamic equilibrium exists between the solute in the mobile and stationary phases, Thus vapor liquid equilibrium can be established in a much shorter time using fairly simple equipment and uncomplicated procedure, by GLCo The technique also provides a very convenient method for measuring equilibrium in very dilute solutions without necessitating analysis of the liquid phase or extrapolation from finite concentrations to infinite dilution.

II. REVIEW OF LITERATURE A. Gas Liquid Chromatography Although the technique of chromatography had been known and utilized since the turn of the century, the first suggestion of using a liquid as a stationary phase and a gas as the mobile phase was made by Martin and Synge(70) in 1941, along with their now famous derivation of the plate theory. However, it was not until 1952 that James and Martin(47) heeded their own suggestion and utilized the technique of GLC to separate volatile fatty acids. Also in this paper the assumption of a constant pressure across a column, made in the plate theory, was theoretically removed. The importance of Martin's basic work was fully recognized when in 1952 he received the Nobel Prize. Following 1952 the number of published works in GLC has increased almost exponentially, indicating the high degree of interest and the utility of this simple inexpensive technique. The majority of work done utilizing GLC has been in purely analytical applications. However, again following suggestions made by Martin, other applications began to be investigated. In 1955, Littlewood and coworkers (65) published the first paper relating GLC to thermodynamics of solutions. Until this time much difficulty existed in attempting to reproduce a given set of results in another laboratory. Littlewood defined the specific retention volume which is the retention volume of the solute in the solvent divided by the amount of solvent in the column under consideration. This parameter when further corrected to a standard temperature, as also done by Littlewood et al., provided a -7

-8means for comparing work which was independent of many GLC operating variables. These workers also investigated the effect of many other experimentally variable factors such as size of the solid support, void volume in the column, percentage coating of solvent on the solid support and the effect of repacking a column with only a portion of the original contents. The specific retention volume was independent of all these parameters at a given temperature and pressure thus validating its utilization as a thermodynamic quantityo Littlewood, Phillips and Price also demonstrated the essentially linear relation between the specific retention volume and the reciprocal temperature of the column for a given solute in a given solvent. From this relation they were able to determine the heat of solution at infinite dilution. Subsequent to the initial paper of Littlewood 9 a number of papers appeared relating GLC and the thermodynamic properties of solutions, verifying that true vapor li.quid equilibrlium existed in the chromatographic column, and investigating the behavior of nonelectrolyte solutions by this rather novel technique~ Huoxwever-, essentially all of these works pertained directly to GLC systems. Now in GLC, as it is desired to have the solvent as a stationary phase 9 high boil.inrg nonvolatile liquids are normally utilized as solvents, In this manner the solvent remains intact on the solid support and the characteristics of the column. remain invariant with time. However, this led to studies of binary solutions such as butanol in carbowax and octane in transformer oil, Generally this type of binary mixture is not easily amenable to verification of solution theories, as the exact composition of the solvent is unkown. A few early works were done, however, utilizing fairly volatile solvents and thus yielding solutions of more general interest.

-9A basic desire of this thesis was to study water as the solvent or stationary phase. This was prompted by the early works of Purnell and Spencer(95) and Pollard and Hardy. (86) Purnell in 1955 conducted a rather preliminary investigation on the separation of chlrinated methanes utilizing water as the solvent. He concluded that essentially a boiling point separation resulted. Later, in 1956, Pollard and Hardy in a more thorough study determined that as the quantity of water involved increased, ioe., the solute concentration decreased, the elution order changed from that dependent on boiling points to that based on the solubilities of the chloromethanes in water, The present investigation confirms the results of Pollard and Hardy. Later work by Hardy included a further investigation of chlorinated methanes in water and also included the methanolwater system. These early workers were bothered by the nonstationary nature of the stationary phase and attempted to correct for this by calculating the rate of solvent depletion due to volatilization into the mobile gas phase. To partially reduce this problem of solvent depletion or "bleeding', Kwantes and Rijnders first utilized a forecolumn or presaturatoro In this presaturator the solid support is coated with the same solvent as that employed in the primary column. The mobile carrier gas passes through this column prior to introduction of the solute and is saturated with solvent at the presaturator temperature and pressure. While this reduces bleeding in the primary column to a large extent, the problem can never be fullr alleviated due to the expansion of the gas phase during its movement through the column. In addition to the works of Purnell and Pollard and Hardy previously mentioned, the study by

-10Kwantes and Rijnders represents the only other recorded usage of a volatile solvent in GLC. They studied normal paraffins, butane through heptane, in the next higher homolog, octane. The results concur very well with other theoretical and experimental studies by other techniques, thus verifying the feasibility of investigating two component volatile systems by GLCo Although this work is confined to infinitely dilute solutions, recently GLC has been applied to the study of solutions at finite concentrations by Kobayashi and his coworkers. (56,110,111) In this work, a rather different experimental technique is utilized. To study a mixture of fixed composition, special carrier gas blends are prepared containing the desired solute concentrations. Once equilibrium has been established within the column a radioactive isotope of the solute is injected and tracer techniques are used to detect its retention volume, This retention volume is actually that of the solute at the predetermined concentration in the solvent. A rather extensive theory has been developed concurrently justifying this technique and the equilibrium properties have been verified by separate solubility studies and existing data in the literature. The work had been entirely confined to n-paraffin systems but included an extremely wide range of temperatures and pressures. This same technique has been applied by Chueh(19) to the study of benzene in diethylene glycol and n-hexane in 1,2,4 trichlorobenzeneo The results again concur with literature values obtained by alternate methods. The validity of GLC data has been challenged by some investigators who question the role of the solid supporti ('7'79) Many of

-11the early supports used such as firebrick, Chromosorb P or R and similar materials undoubtedly exerted a considerable adsorption force on the solute. In fact in the above cited works the magnitude of the noted effect decreases most substantially when Chromosorb W is utilized as the support. Perhaps utilization of some of the more recently developed inert supports would alleviate the effect entirely. In any case one method of circumventing the solid support effects is to remove the solid support. To this end investigations of the thermodynamic properties of solutions utilizing capillary columns have been undertaken by Adlard, Kahn and Withham.(3) This type of column has the stationary phase deposited directly on the column surface and so is unsuited for use with volatile solvents. The results obtained for benzene in dinonyl phthalate using capillary columns show excellent agreement with the data taken previously on a packed column by these investigators. (2) Thus the role of the solid support in a properly packed column with sufficient solvent seems to be only that of an inert carrier for the solvent as deduced from the above results0 Indeed, however, for nonvolatile solvents the capillary column provides an even simpler method of measuring thermos dynamic properties of solutions0 B. Thermodynamics and Gas Liquid Chromatography As mentioned in the above discussion, the first work in which thermodynamics was related to GLC was the investigation of Littlewood, (65) Phillips and Price in 1955. However, during the same time the workers at Shell were actively pursuing a similar course0 Pierotti et al. initiated work on a structural correlation which was developed

-12using data obtained by means other than GLC. However, the relation to equilibrium properties obtained by GLC and to the partition coefficient was well established. More will be said concerning this correlation in (87) the analysis of the data, Porter and coworkers conducted an extensive investigation into the verification of GLC data as representing true vapor-liquid equilibrium, and also undertook to assess the effect of all the GLC operating variables on the partition coefficient, Even today this work constitutes one of the most thorough investigations in the field, They delve extensively into the manner of sample charging, the quantity charged and the effect on the shape of the elution curve. They conclude that the average chromatogram more closely resembles the case of complete mixing than the case of plug flow. However, the size of samples studied was quite large in comparison to todayts standard. More significant is the effect of operating variables. For a six-fold variation in column length and a ten-fold variation in carrier gas velocity the partition coefficient only exhibited a 5% deviation between the extremes. They also varied the amount of solvent per unit of solid support and the size of the support particles with no apparent effect. The work involves n-paraffins and substituted alcohols in diisodecyl phthalateo The verification of vapor liquid equilibrium was made by comparison with data for the same systems using both supported and bulk liquid solvent in static experiments. This not only verifies vapor liquid equilibrium but also the nonexistence of solid support effects for properly packed columns. From the thermal variation of the partition coefficient, the excess molar enthalpies were also calculated and found to be in suitable accord with data obtained by other workers using static techniques.

-13In addition to Porter's work in 1956, the First International Symposium on GLC held in London brought forth many other papers applying thermodynamics to GLC. The introductory paper by Herington(41) discussed the role of thermodynamics in GLC and pointed up its importance. The theoretical development, however, was based heavily on utilization of carbon number correlations and, as was pointed out in the discussion, these relations can only be expected to be rigidly valid for water as the solvent. Relations were also derived to handle multicomponent mixtures provided that sufficient resolution existed between the peaks. Bosanquet and Morgan(15) have calculated the heat of solution of propane and of propene in triisobutene from GLC data and compared these values with the heats of vaporization. As the difference is quite small, they conclude that the effect of temperature on the deviation from ideality is negligible. For most GLC systems this conclusion is valid as the deviation arises mainly in the excess molar entropy due to the large difference in molecular size between the solute and solvent. However, as a general statement, the conclusion is erroneous, and often led early investigators to believe they were determining the heat of vaporization irrespective of the solute-solvent pair studied. In a series of publications, Purnell and coworkers (4596) developed a theory relating the GLC variables to thermodynamic properties. These workers investigated paraffins, chlorinated paraffins and oxygenated hydrocarbons in "liquid paraffin" From the GLC data heats of solution were calculated. They also computed the ratio of the heat of solution to the heat of vaporization and deduced that for negative

-14deviations from Raoult's law the ratio was greater than one, while for positive deviations the ratio was less than unity. Both the ratio and the heat of solution are determined graphically from the data. Adlard(l) conducted an extensive study utilizing polyglycols for the stationary phase. For less than 100~C, polyethylene glycol 200 is recommended while for temperatures greater than 1000C polythylene glycol 400 must be used. For alkanes, aromatics, ketones, and esters, the solutions exhibit positive deviations from Raoult's law while alcohols have negative deviations, as would be anticipated. The determination of thermodynamic properties of halogenated hydrocarbons on a large variety of stationary phases has been investigated by Pollard and Hardy,(40'85'86) utilizing GLCo Both volatile and nonvolatile solvents were studied. No effect was noted on varying the sample introduction time from 3 to 20 seconds provided a column of sufficient length was used. With. volatile solvents the specific retention volumes were corrected for the loss of solvent to the carrier gas, assuming a linear rate of solvent depletion. For nonpolar solvents, i.e.o, "liquid paraffin" and silicone oil 702, a boiling point separation was achieved, while for polar solvents, i.eo, dinonyl phthalate, glycerol and water, the separation was determined by relative solubilities and hydrogen bonding. Static equilibrium experiments were also conducted using CH2C12, CHC1 and CC14 as solutes in silicone oil 702 and dinonyl phthalate and the partition coefficients thus obtained agreed quite well with the GLC data. Purnell's hypothesis concerning the ratio of the heat of solution to the heat of vaporization and the deviation from ideality was tested and verified for the chlorinated hydrocarbons in silicone oil 702, dinonyl phthalate and glycerol.

-15The work utilizing polyethylene glycol cresyl ether as the stationary phase is of interest as it offers not only a comparison between GLC and static data, but also a comparison between GLC data derived from two independent laboratories. Anderson and Napier(5'6) studied benzene and cyclohexane in the above named solvent and determined partition coefficients and heats and entropies of solution. The agreement between static measurements and GLC data was quite satisfactory. The validity of Henry's law in the dilute concentration region was also verified. Then Pyke and Swinbourne(98) independently remeasured the same systems, verifying the results, and extended the work to include cyclopentene and cyclohexene solutes. Benzene and cyclohexene systems behave essentially ideally while cyclohexane and cyclopentene systems exhibit positive deviations from Raoult's lawo In addition to binary organic solutions, the thermodynamics of (9) other types of systems have been studied by GLC. Barber et alo have studied systems in which transition metal stearates and oleates were used as solvents. The transition metal ions form complexes of varying stability with many compounds giving rise to specific interactions of a type other than hydrogen bonding. Organic solutes in these solvents all have activity coefficients considerably less than unity depending on the strength of the complex formed with the solvent, The solutions formed are endothermic in nature, Conversely metal salts may be utilized as solutes. Keller and Freiser studied tin, tantalum, titanium and niobium chlorides in squalane and octadecane. They determined the specific retention volumes and the heats of solution. Many other metals possessing volatile halides may be studied thermodynamically in this manner.

-16Interest has also existed in the thermodynamics of GLC as applied to the area of distillation. Warren and coworkers (118) have considered the analogy to extractive distillation. They obtained data by GLC and from a reflux still operated at equilibrium. As the solute concentration in the still was reduced toward infinite dilution the relative volatility obtained by the two methods converged. Thus GLC is a simple method of obtaining limiting relative volatilitieso Vapor liquid equilibrium constants may also be obtained from GLC data. The partition coefficient of GLC is actually an equilibrium constant but it is commonly expressed in other units. However, the two are very simply related. Preston(92) considered the relationship between GLC and hydrocarbon vapor liquid equilibrium and introduced the compressibility factor into the relations to account for the gas phase nonidealityo Kobayashi and coworkers in a continuing project have ex:tensively determined hydrocarbon vapor equilibrium constants. In their initial work(55) the system butane-dodecane was studied near atmospheric pressures the results showing excellent agreement with the NoGoAA. tabulations. The heats of solution of the C4 hydrocarbons in furfural were also determined in this study, again showing good agreement with static data of other investigations. Following this initial study more sophisticated investigations were made by Stalkup and Kobayashi. (110 111) The theoretical relations between vapor liquid equilibrium and GLC have been derived both from a plate concept and from a rate theory approach considering longitudinal mixing and radial diffusion effects. The mathematics have been formulated for considering a two component solute mixture at any desired concentration3 not solely infinite dil-utioc. Interestingly

-17enough, for conditions normally existent in a chromatographic column, the results of the more rigorous rate theory approach reduce to that obtained from the very elementary plate theory, thus justifying its usage under normal conditions. The solutes ethane, propane and butane were studied in the methane-decane system from 20 to 2000 psia and from 160 to -200F. Propane was also studied at finite concentrations in the methane-decane system at 40~F from 20-460 psia. The GLC data was also used to develop the phase diagram for the methane-decane system in the gas-solid region. Subsequently Koonce and Kobayashi(56) modified the previous theory to include an "n" component solute mixture. This study verified the earlier work and extended the technique to the methane-propane-heptane system, but only from -40 to -200F. Equally important, however, static equilibrium measurements were taken for the same systems and found to substantiate the GLC data completely thus further verifying GLC data as representing true vapor liquid equilibrium. Excellent agreement was also shown between this work and other data established in the literature. When determining accurate thermodynamic data from GLC, as was mentioned above, care must be taken to insure that the solid support does not contribute to the solute retention. Prior to the newer organic and inorganic supports now available this presented a formidable problem when studying polar solutes in nonpolar solvents. Following a sugges(109) tion made by Swedish workers, investigators replaced conventional firebrick with metal helices. Evered and Pollard(26) used this device when determining the activity coefficient of alkanes, alkyl nitrates, nitroalkanes and alcohols in squalane. However, when studying the same

solutes in dinonyl phthalate and diglycerol, standard supports were used. From the temperature dependence of the activity coefficients the heats of solution of the alkyl nitrates and the nitroalkanes in squalane and dinonyl phthalate are determined. The dinonyl phthalate systems have a much smaller excess molar enthalpy than do the squalane systems~ Kwantes and Rijnders,(58) in addition to studying a volatile solvent, also studied all possible combinations of solute and solvent based on polarity. They too used metal helices as a support for nonpolar solvents. For nonpolar solutes in nonpolar solvents, aliphatic and aromatic hydrocarbons were studied in hexadecane, tetracosane, pentatriacontane and squalaneo The results agreed with those calculated from theoretical methods. Water in diethylene glycol representing the polar solute in polar solvent and n-paraffins in 1,2,4 trichlorobenzene representing nonpolar solutes in a polar solvent also checked existing literature data. Alcohols, aldehydes, ketones and esters were studied in hexadecane for the final class of polar solutes in nonpolar solvents, again concurring with existing results~ In addition to the above studies butane, pentane, hexane and heptane were studied in octane using the presaturator technique described earlier, this being the only accurate work reported using a volatile solvent~ (24) Desty and Swanton in a study primarily designed to determine selective stationary phases for hydrocarbon separations utilized thermodynamics as a basis for evaluating solvent selectivity. In doing so, however, they compiled a vast quantity of thermodynamic data from GLC. The authors also show why it is preferable to use the temperature

-19variation of the activity coefficient rather than the retention volume or the partition coefficient to determine the excess molar enthalpy. In all the polar solvents studied the activity coefficients of aliphatic and aromatic hydrocarbons are greater than unity. The excess molar enthalpies and entropies of the various solutes in the solvents studied are also determined. Langer and Purnell, (61) in a solution study, measure the same systems as those of the above work. By carefully controlling all the parameters such as column temperature, carrier gas flow rate and column pressure drop they were able to reproduce the data of Desty and Swanton to better than + 1%, showing the value of data by independent workers. To further verify the validity of GLC data as representative of true vapor liquid equilibrium a few more checks between the two methods will be cited. Ashworth and Everett(8) studied benzene, cyclohexane, pentane, hexane, heptane, octane and 2,2 dimethylbutane in dinonyl phthalate and squalane by static equilibrium~ Spreading the solvent on the solid support did not affect the equilibrium state achieved in the bulk solvent but merely enhanced the rate of attainment of equilibrium. Only when the solvent constituted less than 10% of the stationary phase did the solid support affect the equilibrium. In dinonyl phthalate the aliphatic solutes exhibit positive deviations from ideality, while in squalane the converse is true. Then in a follow up study Everett and Stoddart(27) studied the same solutes in dinonyl phthalate by means of GLC. Again variation in sample charging time had no effect on the retention volume. The results obtained in this study

-20agreed very well with the earlier static measurements. The author's hypothesis concerning the use of the initial retention time, while satisfactorily representing data on overloaded columns, cannot be seen to have any actual basis in theory. In order to obtain sharp narrow peaks in the present study, very small samples were used along with low carrier gas flow rates. This prevented overloading and allowed equilibrium to be established in the column. Freeguard and Stock(32) also studied the two solvents dinonyl phthalate and squalane by static equilibrium measurements. The solutes examined were the chlorinated methaneso The dinonyl phthalate systems show very satisfactory agreement with the GLC data of Hardy. (T40) A few other applications of GLC to determine some of the less common thermodynamic properties'ill now be presentedo Takamiya and coyorkers,(115) utilizing the solution theory of Hildebrand and Scott,(42) derived the relation between the specific retention volume and the solubility parameter of the solute and the solvent~ The relation is used to calculate solubility parameters for many solventsof interest in GLC using alcohol solutes. Then the relation's validity is confirmed using n-paraffins by checking the measured retention volumes with the calculated values, Good agreement is obtained~ Following the technique pioneered by Kobayashi and coworkers, Chueh(l9) studied benzene in diethylene glycol and hexane in 1,2,4 trichlorobenzene for a wide range of solute concentrations and temperatures, The activity coefficients thus obtained agree well with data in the literature obtained by other means. Desty, Goldup, Luckhurst and Swanton(23) in an. extremely thorough investigation removed the gas phase nonideality contribution to the activity coefficient, They derive

-21the correct relation representing the true activity coefficient of the solute in the solution alone. Utilizing this relation along with very careful experimental measurements the authors are able to determine the interaction second virial coefficient from GLC data. This work represents a great stride forward in our ability to understand solution behavior from relatively simple experiments. Adlard, Khan and Whitham(2) in an earlier very careful work also were able to assess the effect of the gas phse nonideality on the activity coefficient. However some deficiencies existed in their theoretical development and so the absolute values of the results are slightly in error. The authors place the magnitude of the correction factor at 4c-5~% Again the results obtained for the GLC measurements agree quite well with the static values obtained by Ashworth and Everett, (8) In a later paper(3) the same authors also reproduce the data using a capillary column and thrus eliminate all possibility of solid support effects, In addition to all of the above cited w'i,-.orks relating GLC to thermodynamics and verifying the equilibrium nature of the process, the subject matter has been adequately treated in a number of very excellent textso (2154,66,97) It is thus felt that the technique has been very adequately verified and su.bstan.tiated in the litera.ture and sufficient justificatior e 5ists for extension of GLC into adjacent areas without further proof of its basic validityo C. Solution Studies Coincidently in. 1955, along with Littlewood s initial work (53) relating thermodynamics to GLC, Keulemans, Kwantes and Zaal conducted the pioneering investigation of solution behavior by GLCo The

-22authors considered deviations from ideal behavior in two parts, a geometric effect and an energetic effect. The geometric effect was due to unequal solute and solvent molecular dimensions while the energetic effect was attributed to Vander Waals forces. In the region of low solute concentrations encountered in GLC, Henry's law was considered a valid relationship. The Van der Waals forces in turn were broken up into Keesom, Debye and London forces. The Keesom or orientation forces represent the interaction between permanent dipoles of the solute and the solvent. The Debye or induction forces represent the interaction between the permanent dipole of the solute or solvent and the induced dipole of the other component. The London or dispersion forces represent the interaction between instantaneous dipoles in the solute and instantaneous dipoles in the solvent, neither possessing permanent dipoles. Generally speaking the induction forces are negligible when compared to the other two. However, in some instances, i.e., cyclohexane and benzene in dinonyl phthalate, the higher polarizability of benzene causes a larger induction force for the benzene and accounts for the separation of the two solutes, benzene being selectively retained. Keulemans et al. made extensive studies for separating polar and nonpolar solutes on many classes of solvents. They investigates systems in which orientation forces predominated and systems in which hydrogen bonding was a major factor. However, generally the dispersion forces represented the main contribution to the deviation from ideality. A second approach to analyzing the deviation from Raoult's law consists in considering the activity coefficient to be made up of two terms, an athermal term essentially temperature independent and a

-23thermal term varying with temperature. The former corresponds roughly to the excess molar entropy while the latter is related to the excess molar (8) enthalpy. Ashworth and Everett analyzed their static data by this technique. The athermal contribution arises from statistical effects due to molecular size differences between the solute and the solvent. To calculate this effect the technique developed by Guggenheim(37) is used which assumes a cell model of the liquid, each molecule having a given number of interacting neighbors. The thermal term is postulated to be proportional to the mole fraction of the solvent squared, which for most GLC systems is unity. The constant of proportionality is the interaction energy divided by the Boltzmann thermal term. Generally this interaction energy is temperature dependent. An alternate approach is that proposed by Hildebrand and Scott.(43) They define a regular solution as one in which the excess molar entropy is zero. Then to calculate the excess molar enthalpy, which is directly related to the activity coefficient, they assume that dispersion forces are the predominant solution interaction and express this in terms of Hildebrand's solubility parameters. This method while neglecting orientation and induction forces at least allows a quantitative estimate of the deviation from ideality to be made. The next step in the modification of Hildebrand's theory was developed by Van Arkel. (116) As the orientation forces can represent as large a contribution as the dispersion forces, Van Arkel added a term to Hildebrand's solubility parameters which expresses the permanent dipole-dipole interaction between solute and solvent.

-24In both of the above formulations the concept of a negative excess free energy was impossible to attain due to the nature of the restrictions imposed during the development. Martire,(73) in a very thorough work investigating the theoretical selection of a solvent for a given GLC separation, introduced an empirical constant which represented the specific interactions in a solution, such as hydrogen bonding. As Martire's technique is an extension of Hildebrand's work this empirical constant was expressed in terms of the solubility parameters of the solute and the solvent. In order to apply this development at least one experimental point was needed to establish this constant for each solvent, independent of the solute. Using this technique Martire predicted naphthylamine as the solvent for separating 2,4 dimethylpentane and 2,2,3 trimethylbutane, and the predicted values of the specific retention volumes agree closely with the experimentally determined values. In a later study Martire(74) utilized the development separating the activity coefficient into athermal and thermal contributions. Hildebrand's theory was used to estimate the thermal term -while the athermal term was determined from Guggenheim's development. The GLC values of the activity coefficients for hydrocarbons in aniline, isoquinoline, quinoline, 2 methyl quinoline and methyl naphthalene agree quite well with those predicted from the theoretical formulation. Hardy and Pollard(39) in a very comprehensive review have utilized the three types of Van der Waals forces along with specific interactions to classify solutes and solvents into five categories to be described in greater detail under the experimental program. They

-25have then utilized these categories to predict selective solvents for separating various solutes by GLC. Solutes are more strongly retained by solvents which are in a category adjacent to that of the solute. Bergeron in a rather exhaustive study investigated solutions of ketones, alcohols, and aromatic, aliphatic and cyclic hydrocarbons in tetradecane, hexadecane, eicosane and tetracosane from 30~ to 125~C by GLC. He attempted to correlate all the resulting binary mixtures using a single relationship but deduced that this task was impossible. Instead for each homologous series of solutes in each solvent he evolved a correlating equation which expressed the activity coefficient as a polynomial in the temperature. The constants for these correlating equations were determined from a regression analysis of the data. Littlewood in a pair of publications(67'68) investigated the factors affecting solution behavior by means of GLC. He attempts to relate the behavior of solutes in various solvents relative to two parameters, one being the specific retention volume ratio of an alkane in a nonpolar and polar solvent, the second being the specific retention volume ratio of a polar solute in a polar and nonpolar solvent, the solvents being the same in both instances. He notes the inability to describe the various solution behaviors in terms of a single parameter and chooses instead to correlate the behavior in terms of the above two parameters, the dipole moment and the polarizability. The GLC systems studied and correlated include paraffins, olefins, alcohols, esters, aldehydes, organic cyanides and halogenated hydrocarbons in monofunctional hexadecyl derivatives, i.e., chloro, bromo, cyano and hydroxy hexadecane. As can be seen this represents a very extensive study.

In addition to the above quoted studies of solution behavior utilizing GLC techniques, the generally available literature describes countless other studies by different methods as discussed in the introductiono Barker,(10) Guggenheim,(37) Hildebrand and Scott, (42,43) Hirschfelder et al., ) Ketelaar, (52) Prigogine and Defay, (93) Prigogine(94) and Rowlinson(l02) have all written excellent texts, of which the major portions are devoted to solution studies. The theoretical development and analysis of the results to follow owe much to all of these works. However, some of the above developments while theoretically sound are as yet in a highly unapplicable state. Also certain of these theories are amenable to verification if thermodynamic data are available over a range of concentrations, but for the present work with data at only one concentration, i.e., infinite dilution, no substantiation is possible.

IIIo THEORETICAL DEVELOPMENT Ao Derivation of Plate Equation The theoretical origin of GLC can be traced back to the initial work of Martin and Synge.(70) In addition to describing the basic process in which a liquid stationary phase and a mobile gas phase are used, they developed the basic mathematics describing the equilibrium process within the column. As the surface area is high with respect to the volume of the solvent, the attainment of equilibrium is very rapid and thus the assumption of equilibrium existing throughout the column was made. To aid in understanding this equilibrium process the authors invoked the theoretical plate analogous to other separation processes. Corresponding to this is the Height Equivalent to a Theoretical Plate, the thickness of the layer such that solute emerging from the layer is in equilibrium with the mean concentration of solute in the stationary phase throughout the layer. By developing the distribution of the solute in the column for infinitesimal volumes of the mobile phase, the resultant expression is a binomial expansion. Considering the relation for a large number of plates results in the plate equation of Martin and Synge The above assumes a small sample size so the solute is initially charged to a single plate, a constant partition coefficient k throughout the column, negligible mixing and diffusion effects, a linear distribution isotherm, i.e, validity of Henry's law, and no pressure drop across the column -27

-28This relation has been rederived countless times utilizing different approaches. Keulemans(54) develops the above relation from a consideration of statistical distributions of solutes in a theoretical plate. Although not the first to apply the concept, Stalkup(110) approaches the problem from a chemical engineering standpoint. A material balance is written for each plate in the column assuming equilibrium to be existent. The differential equations resulting are solved by Laplace transforms to yield the concentration on the "n-th" plate. The integrand of this expression is the Poisson distribution. To obtain the maximum in the solute concentration on plate "n" the derivative of the expression is equated to zero. After suitable mathematical manipulations Equation (1) is obtained. Rather than proceeding to reestablish this derivation in its formal entirety again, after having been treated exhaustively by previous workers, a slightly different approach will be developed. In this development the plate equation will be derived without recourse to the theoretical plate concept. While not completely rigorous in its development, relying on one's intuitive ability, it does provide a different insight into the problem. The general concept is due to Sternberg.(l3) Consider the definition of the partition coefficient, k o It is the ratio of the concentration of solute in the stationary phase to the concentration of solute in the mobile phase. Mathematically, - _ (2) - \)es19 @ @ _ R~~~V-

-29Now the total moles of solute is n_ — hz+L (3) The velocity of solute movement in the column is given by UP= UV ~ (4) As the fraction of the solute in the gas phase is n2/n2 (4) becomes 14__ UV u_ (5) but from (2) and (3) nor &~kV GG k\/ nz n Ge h&L Adz@+ h i k v \JE7+-k\JL (60) Also the velocity of an unretained component may be expressed as UJ (\ /L) (7) Therefore substituting (6) and (7) into (5) yields ('rI;_ _ _k L F (8) &I&IL) ~, kh. E(V&+-kVL /L] However, the velocity of solute movement may also be expressed as F V2- CV)L) (9) analogous to Equation (7). Now by equating (8) and (9), Equation (1) results \JR = \6 + k V, (1)

-30Thus with no recourse to theoretical plates, plate heights, or plate equilibrium the equation of Martin and Synge may be developed. Inherent in this development, however, is the concept of equilibrium involved by definition in the partition coefficient. While the plate concept is therefore no longer actually necessary, it still serves a useful purpose from an illustrative point of view. B. Thermodynamic Considerations In a chromatographic column the volatile solute molecules are for the greater part of the time dissolved in the stationary phase and are not transported during that time. For a small fraction of their total residence time in the column the solute molecules are in the mobile phase where they are transported by the moving carrier gas. As the rate of movement of the solute through the column is dependent on the distribution of the solute between the mobile and stationary phases, one must deal with the theory of vapor liquid equilibrium in binary mixtures. In the ideal case for a binary liquid the partial pressure of the vapor above the solution is given by the familiar expression 0 P'X sF9 ~~o ~~~(10) or for both components ply = ( -x~ pi" 28' xt pp X = A(11) A binary liquid mixture will form an ideal solution only if the solute molecules interact in the same way with the solvent molecules as they would with the surrounding solute molecules in the pure state. However,

due to differences in molecular dimensions, polarities, or interactions the assumption of an ideal solution is generally unjustified. The deviation from Raoult's law may be either positive or negative and will be discussed in greater detail in the analysis of the results. Fortunately, however, as the solute molecules commonly occur in very low concentrations and are not close enough to exert a mutual interaction, the environment of a solute molecule can be considered as a medium consisting of solvent molecules only. Thus these solutions may be referred to as "infinitely dilute". In such solutions the escaping tendency is mainly determined by the intermolecular forces between solute and solvent molecules alone. Therefore Henry's law will apply P = SX > (12) and a linear distribution isotherm will result. This relation will fail for higher solute concentrations so care must be exercised to use small solute charges. For low concentrations Henry's law approximates true solution behavior for either positive or negative deviations from Raoult's law. In this region the elution curves should be symmetric and this represents a valid test of the data. In order to evaluate K, Henry's law constant, one needs to compare Equations (11) and (12). For an ideal solution K is equivalent to the solute vapor pressure. To complete the evaluation it will be necessary to introduce a factor to correct for the nonideality of the solution behavior. Therefore Ptlr _. x, 8( ^(13)

-32For ideal solutions Y2, the activity coefficient, is unity. Throughout this work the activity coefficient will be defined with reference to the pure solute standard state at the temperature and pressure of the solution under consideration, The activity coefficient, which is a measure of the deviation of the solution from ideality, is a function of the nature of the solute and the environment in which the solute exists. Although not limiting the scope of 72 to the nonideality of the liquid phase, it will be assumed that the gas phase behaves ideally. Later this limiting assumption will be removed. By definition P2 may also be expressed as Pr _ 2a P (14) which leads to 8 2 ~P -= ~ >L X PA~~ ~(15) For dilute solutions, the partition coefficient k may be related to the mole fractions in the two phases. ~k - _-NIL (16) From (15) and (16) k AlL (17) Using Boyle's law for the gas phase 9/K~r = RT (18)

one obtains from (17) and (18) k N L. R p (19) The retention volume, defined as the volume of carrier gas required to elute the solute component from the column, may be related to the partition coefficient by Equation (1). The specific retention volume may also be expressed in terms of the parameters already established. JR/ = VR —..... -(20) In addition the expression for VR is usually corrected for the finite pressure gradient across the column by multiplying Equation (20) by j (21) This is the correction factor theoretically derived by James and Martin ) to account for the inequality of the inlet and outlet pressures of the column. In the present study the magnitude of j was always quite close to unity due to the low pressure drop across the column. By comparing Equations (1) and (20) one may express VR in terms of k 9k (22) o e Now realizing that P\L= e/M (23)

Equations (19), (22) and (23) may be combined to give = RT (24) a RM Pa This expression is the actual relation which links the normally obtained thermodynamic property, the activity coefficient, with the chromatographically determined variable, the specific retention volume. From the above formulae k has been expressed as a function dependent on the characteristics of the solvent, NL, of the solute, p, and of a factor which depends on both, y2 Also k and y2 have been related to the measureable parameters of a GLC experiment. Since k has been assumed constant throughout the column in the plate theory, this also places a restriction on y2. Neither of these conditions is entirely fulfilled in GLC, but the solute concentrations are generally so low that they can be considered to approach infinite dilution. In this case the activity coefficient will be referred to as Z2, the activity coefficient at infinite dilution, which is a constant. It should be realized, however, that in a band of solute in the actual chromatographic column a concentration gradient exists, and that particularly near the column inlet the assumption of constant y2 or k is not rigorously valid. Nevertheless for a column of sufficient length the value of k is deter00 o mined by 72 and P2 and is a true equilibrium value. This means that the experimentally determined values of y2 are independent of all the GLC operating variables as elaborated in the literature review.

-35The analogy between GLC and distillation referred to earlier can be pointed up clearly by a consideration of the above derived relations. Considering a pair of solutes in a given solvent, the partition coefficient can be obtained for each solute as kM -. R r and k.N. an (25) I, _'- _ k = — E Now the relative volatility is defined as CAB - 8| r= Me (26) Thus it can be seen that although NL affects k, it does not affect the relative volatility. Also, so long as the heats of vaporization of the two solutes do not differ greatly, the vapor pressure ratio will not vary rapidly. It is only when large temperature changes are involved that the ratio varies appreciably. Thus the concept of relative volatility has the same meaning essentially in GLC as in distillation, namely a factor which defines the ease of separation. Having established the relationships between the activity coefficient at infinite dilution and the GLC parameters, by further consideration of these relationships the partial molar properties of the solution will be determined. Consider the basic equation for the partial molar excess free energy A A H. - Ta E (27)

-36E The activity coefficient is related to aG2 by G / PA VI~ 2 (28) and E Eal A5 h GREtr = AHZ/T~ A (29) Now assuming AS2 and LA2 constant for a small change in temperature, the derivatives with respect to temperature of (28) and (29) are _ _ (30),, - _~ _' T" Therefore A.d 8 _ _ A —Wn (31) aT. T RT or alternately - 7 (32) Also, combining (28) and (29) =Ih~ nr A E 55 (33) I 2.~ - -

-37Now from (32) it can be seen that a plot of lny2 as a function of reciprocal temperature for a small range should yield a straight line, the slope of which is related to the partial molar excess enthalpy. All of the above equations involve relationships between thermodynamic properties. These properties will now be related to the appropriate GLC parameters. Taking the logarithm of (24) 1,.~ MDX= ) ~ir~ _ ~ /n VR - a~n P (34) and differentiating with respect to T yields (35) For most studies of interest the 1/T term is negligible and it will be considered so here. Now the Clapeyron equation is (36) Substituting (31) and (36) into (35) and rearranging gives __ f~t,, h~vqp(37) or (38)

-38Therefore the slope of a plot of In VR as a function of reciprocal temperature, for a small range, will determine the partial molar excess enthalpy. In many of the works cited in the literature review this method is the one actually used. An alternate procedure to the one delineated above consists in substituting (23) into (19) k- -----— o f(39) Taking the logarithm of (39) Irh k - 1^? e + n RT I I' P (40) and differentiating with respect to T yields ____ - ____aLhe - ___ (41) AT d~ T dt TA Now again substituting (31) and (36) into (41) and neglecting the 1/T term e- - - +- HV(42) A T' RT. ra'or A(LIT) R (43)

-39A plot of in k as a function of 1/T will generate a curve due to the added term RT 2d in p/dT. This is the relation postulated by Littlewood (65) et al. in their original work. From the above equations, utilizing E E ~E parameters obtained from GLC data, values of y2 G2 Nt and LES2 can be obtained. As mentioned earlier, the activity coefficient in the above relations is actually a hybird value representing the nonideality of the vapor and the liquid phases. This is due to the inclusion of the ideal gas law in the above derivations. This implies that no change occurs in the volume of an element of gas as it passes through the column. This condition does not hold rigorously as the gas density fluctuates throughout the column. A partial means of correcting this discrepancy lies in replacing the solute vapor pressure by its fugacity. In this manner Equation (24) is modified to (44) VRN'\ +a The activity coefficient calculated from (44) has a smaller temperature dependence than that determined from (24). However, the improvement is only slight and the problem of ascertaining fugacities for many compounds hardly justifies the added accuracy in the activity coefficient. An alternate approach to removing the gas phase nonideality, which has been more fruitful, involves the utilization of the virial equation of state, in particular the second virial coefficient. Although some early attempts to evaluate this gas phase nonideality in GLC were Adlard et al. (2) (27) attempted by Adlard et al.(2) and Everett and Stoddart, the mathematical representation of the problem was only recently correctly formulated

-40by Desty, Goldup, Luckhurst and Swanton. (235) The following development is due in large measure to their work. The activity coefficient of a solute in a solution is given by Equation (13). More correctly, the solute partial pressure as well as the solute vapor pressure should be replaced by the corresponding fugacities (45) Now Guggenheim relates the fugacities to the corresponding pressures by means of the second virial coefficients as follows lln $2 =,O _____ t BitAt(46) and v~- l~Ri~~=B-+ (47) where Pf O 9~/j (48) The second virial coefficient B12 characterizes the interactions between unlike molecules and is an important parameter in studying solution behavior. Now Equation (16) may be expressed as -k-. —- - -- -- L+. (49) YzR Ale YX \I, L G-ti r2

In the gas phase the solvent is the carrier gas, while in the liquid phase the solvent is the stationary liquid. Solving (45) for Y2 and taking the logarithm of the resulting expression gives ( I~7 ~e = Ir C- - I x e - \ C- o Equation (49) may then be solved for x2 and the logarithm taken of this relation k \/L IG7 + _ ln? X L k,L n1. \t Ji +:t:j,. (51) Now (46), (47) and (51) may be substituted into (50) to yield l n 8 R =. \ t pp t 9T(l - Bil B la + E2Za R VL' GTf n,'R T LnL+~ \2] -\ 2n (52) Now utilizing the logarithm of (14) in (52) I\' )= In' LN - + I - RT +ow evR Dber,, (er l ( B811? + Bws (3) Howe ver hG R snpa+ 2~ j( I-) AB + (1- Y f3 81 (54)

therefore Ba P o (55) RFT( Since in GLC the solute is essentially at infinite dilution, Y2 and L n2 approach zero and 2 2. Thus ____ R 2B -1 ^ p(56) Now as a first approximation so substituting (57) in (56) and cancelling terms yields oRRT RT tvo + a _t (58) BnhV = V(59) The fugacity varies with pressure according to the relation

Integrating (59) Ih (P)= R + + 4 (6) (60) Applying (60) for the pure solute vapor 4~ -s (F ] - = ~ (~) +- _"I (61) while for the solute at pressure P 1(~h 0)n ~ T= \ + P(62) Since the solutions are very dilute v2 = v2 Correcting the fugacities in (46) and (47) to a standard reference state would alter (58) as follows =~ - o W~+.B,2- P) —~ - B~-,,,) (63) Now as n/VL = NL, the first term in (63) is seen to be the logarithm of the hybrid activity coefficient as given by Equation (19). Utilizing (22) and (23) in (63) results in VX=n w t T (- P)-v) B-2- V~) (64) A comparison of (24) and (64) will show that the second and third terms of (64), involving the second virial coefficients, account for the gas phase nonideality and thus y2 as determined from (64) is a true activity

-44 - coefficient representing the deviation from ideality of the solute in the liquid phase. If instead of utilizing (54) for the gas phase molar volume, one neglects the second virial coefficient of the gas mixture then.._ 7 AT (65) and (64) becomes -N./ h Rm +P (ZF B,i- uij(B -V (66) which is the equation derived by Everett and Stoddarto (27) Further if one utilizes the Lewis-Randall postulate e~~~~~~~~~ Add W<2 8 18 (67) then (66) becomes __VR rVP B a _(68) (2) which is the equation derived by Adlard, Kahn and Whitham. Desty and coworkers studied helium, hydrogen, nitrogen, carbon monoxide, argon, oxygen and carbon dioxide to illustrate the effect of carrier gas on the true activity coefficient. They conclude that the magnitude of the correction factor is a minimum when using helium as a carrier gas, When exceptionally accurate values of VR are obtained the above relationships can be used to determine B12 from GLC data. Rearranging Equation (64) yields

RTe(B~-v;)-\n~ V } PA ( IB a-Va)- )1M a (69) By plotting the left hand side of Equation (69) as a function of P, the slope is (2B12 - v2) and the intercept, is - in Y2 By assuming B.ij, v, P2 and 72 independent of pressure for small changes in pressure, the variation in VR with P is determined experimentally by GLC and a plot of Equation (69) is used to evaluate B12 and 2. C. Nonelectrolyte Solution Theory As can be surmized from the literature review, three basic approaches to the theory of nonelectrolyte solutions will be attempted. In actuality one general procedure will be outlined with two variants to one part to follow later. From an inspection of Equation (33) i~ w RT R- (33) it can be seen that for small ranges of temperature the activity coefficient is composed of two terms, one thermally dependent and one essentially independent of temperature. This may be expressed as I1t~ >2~, = I\h'~'~ +;~ \(70) A direct relation, however, may not be drawn from (33) and (70) as yth is not related solely to LkH2 but also to SE 2 The 2ath term arises from statistical effects due to molecular size differences between the solute and the solvent. On the other hand th is associated with

-46the interaction energies between the solute and the solvent and therefore is temperature dependent. The dependence of yth on AS also, arises 2 2 from the nonconfigurational terms in the partition function to be described in the statistical mechanics of solutions. The two terms in Equation (70) may be treated separately as they are independent. Since yath is dependent on molecular configurations and geometry, the best approach for a theoretical formulation can be based on the cell theory of liquids and mixtures. A basic work in this area (37) is the fine text of Guggenheim. In the cell theory each molecule is considered imposed in a semi-rigid cell surrounded by neighboring molecules. Of these surrounding molecules a certain number immediately adjacent to the molecule under consideration are deemed nearest neighbors and only these are considered to have primary interactions with the molecule of interest. Other interactions are of a second order and considered negligible The mathematical treatment of these interactions need be considered in two cases depending on the molar volumes or sizes of the solute and the solvent. Consider the case where V1 > V ie, the solvent is 1 2 larger than the solute. According to Guggenheim the resultant relation is pz _ _ _l - Ql. (71) where s is a parameter defined by (_ - tZ - _ s (72)

For an infinitely dilute solution, 01( 51 and x2 approaches zero. Then p -,~ r~~~~pa~x,~ sF'8i(13) and 4A), _Ci Air <<-'a, Y 1 ~(73) so I-_ + n, =4 I-r (74) and utilizing (72) (r- -.- - -- zr (75) Substitution (13), (74) and (75) into (71) yields [- a — t a.1-~a2w (76) and taking the logarithm of (76) gives No accura_ t ~e tKh i ai o sn(t at or H(77) No accurate method is available of estimating z correctly. However, z will be chosen as 12 in view of the fact that most common lattices

-48have coordination numbers near this value. In actuality Guggenheim has shown that for z greater than ten, the difference in results between choosing z = 10 and z = co is very small. Therefore setting z = 12 in Equation (77) results in k.8 Bath 1u1 +t ) h +(78) On the other hand when the solute is larger than the solvent, ioe., v0 > vO the resultant relation is 2 1 with only the definition of "r" inverted. Again considering an infinitely dilute solution, 02 and x2 approach zero and 4X., _-:Y_ 2,, - - (80) also I- ~-~ —- q ~92 4 d i (81) Substituting (72), (13), (80) and (81) into (79) yields =8|0i+>8 r>^ _HasJ (82) -rem.:_._.u_:._-s~

-49 - Taking the logarithm of (82) gives Zt = (+ ) + tz -t r ) (l #(83) or with z = 12 *+hAt= Ih t+(f5rY ) \h5+ (84) ath Therefore for either of the above cases it can be seen that y2h is a function only of r, the molar volume ratio which is always greater than unity. For the case where r = 1 both Equations (78) and (84) give ath ath a2 = 1. It should also be noted that in 2th is always negative, this result being in agreement with the fact that the size contribution to the excess entropy term will always be positive. From either Equation (78) or (84) then, the athermal contribution to the activity coefficient may be calculated. While the above treatment appears to be the only theoretical development for determining ya2th which has been refined to a point of practical application, the same situation does not hold for th A number of methods have been proposed for computing the thermal contribution to the activity coefficient. In addition to the above determined relations, Guggenheim also formulated an expression for yth Inh) e+rh e/7W (85) where a 1\1= J, \N —- W' L (86)

-50and wij represents the energy associated with each interaction of an "i" molecule with a neighboring "j" molecule. However, the above relation is difficult to apply as the determination of the W i terms is not readily accomplished. The most generally applicable relation for determining yth is that derived from the solution theory of Hildebrand and Scott. (42) These authors consider regular solutions for which by definition ZSE is zero. The basic relation of Hildebrand s theory is E L HE_ C}; 6,) - (87) which is formulated by analogy to the early work of Van Laaro Utilizing the definition of volume fractions, (87) may be written as H =F(AL,~ ),- <jL~ ~, (88) Taking the derivative of (87) with respect to n2 yields _H E_ t~Eea (>/- s,)" X )_ (ho VlB SiL ((89) or h_ =,i(90) Now from (33), (70) and (90) one obtains t (s,- S (91) n. ~a. 7 T

-51Equation (91) is the most useful equation for calculating the thermal contribution to the deviation from ideality. However, Hildebrand's solubility parameter is based solely on dispersion forces and therefore cannot possibly describe the behavior of polar solutes and solvents or solutions in which there are specific interactions. It does represent a large number of nonelectrolyte solutions, however, in which the solute and solvent are electrically neutral or only slightly polar. This field encompasses the bulk of the petroleum industry as well as many other solutions of interest. Many variants of Hildebrand's theory have since appeared which attempt to remove the limitation of only being able to correctly explain dispersion forces. As can be judged from the above discussion, it would be highly desireable to treat solutions in which one or both components were polar in nature. Van Arkel(116) seems to have been the first to propose such a relation. Proceeding heavily on the basis formulated by Hildebrand, he added a second term to Equation (91) of the same form as the solubility parameters which was to account for dipole-dipole interactions, namely Jr Ti a i) (- i9)JI b (92) The "a" term was dependent on the dipole moment of the component being considered, but its exact form remained unspecified. The above relation still does not allow a negative deviation from Raoult's law, due to the assumption of a statistical distribution of molecules. However, when the pole of a dipole is near the surface of the molecule the distribution is

-52no longer random and the theory fails to account for the resultant behavior. Therefore in all future considerations of this relation it is tacitly assumed that dipoles are imbedded at the center of the molecule. To obtain an exact relation for the dipole interaction parameter one must turn to the theory of intermolecular forces. Before proceeding to such a discussion one further modification of Hildebrand's theory deserves comment. In an attempt to account for weak specific interactions such as only slight solute-solvent hydrogen bonding, Martire(73) has developed a modification of Equation (92) by again adding an additional term to those of the solubility parameters and the dipole interaction parameters. This term allows for negative deviations from ideality but is empirical in nature. The expression is t_[R I, it) + OWL- +] ~ (93) and J is defined by d - CI ( /1 ) ( (94) where C1 is a solvent dependent parameter given as C C,i\ sO =CF w,)(95) Therefore J may be expressed as J= C (96) Now C2 must also be a solvent dependent parameter, so in order to determine its value at least one experimental value of yth must be known for

-53each solvent under consideration, independent of the solute utilized. For systems of interest in GLC where no strong hydrogen bonding normally exists, Equation (93) predicts the specific retention volume very well, An alternate method of determining the thermal component of the activity coefficient lies in the theory of intermolecular forces. Three types of physical forces exist between molecules: orientation forces, induction forces, and dispersion forces. The first two of these can be understood from the classical theory of electrostatics but the third type can only be properly understood through a quantum mechanical interpretation. London(69) was the first to consider these interactions in detail. The dispersion forces are due to the fluctuation or displacement of the electrons from their normal positions, These oscillations tend to induce dipoles in the surrounding molecules and cause interactions. Using the quantum mechanical treatment for the kinetic energy of the electrons, London evolved the following expression for the interaction energy due to oscillating electrons between the solute and the solvent E -- 3.;,4e, Ail hv, ^~~;sp~~erson ZL~~~~~~ Crab~ h(97) while if it were an interaction between two molecules of the same component the expression would be EcA;spestsfot = h9 (98) The name dispersion forces arises from the similarity of the expressions with those evolved in optical dispersion studies. As it is often impossible

-54to determine the characteristic vibration frequency associated with the electron motion a simplifying assumption has often been made that Is- hot (99) The ionization potential here referred to is that associated with the removal of the first electron from the molecule. This assumption, however, is not always a valid one and the disconcerting fact is that determining its validity is rather an extensive task. Pitzer,(84) investigating the quantum mechanics underlying this assumption, mathematically analyzed the determinantal wave function for the electrons. London's treatment was actually a second order perturbation treatment of the wavefunction. Now the utilization of Equation (99) can be shown to be valid only when the off-diagonal terms of the wavefunction are zero. However, generally certain of these terms are nonzero and thus the value of hvi may be two to three times the ionization potential. Nevertheless this relation is constantly used because of its simplicity, An excellent discussion of Van der Waals forces is given by Hirschfelder et al. ( and Dal Nogare and Juveto Considering two molecules at a distance aij apart with their dipoles orientated in various manners, the mathematical relations for expressing the other two physical forces can be determined. By averaging over all possible orientations of the two dipoles, holding the intermolecular distance constant, and using the Boltzmann weighting factor, Hirschfelder derives the following relation for the orientation forces Eorieht+ ion= " 3 WET 3 (loo)

-55while for interactions between two molecules of the same component (oo100) becomes Eoviehit+ion 3iT (ici) To assess the induction forces consider two molecules a distance a.. 10 apart with one molecule being charged, i.e., possessing a permanent dipole. From Coulomb's law one can deduce that E l j; - (. e (.+ - i - ~ A/) (102) while again for like component interactions this becomes i_.,_ 6:: = (103) As was pointed out in the literature review the magnitude of the induction forces is generally considerably less than that of the orientation or dispersion forces, the dispersion forces usually predominating. However, in some instances they can explain the differences in behavior between two components of similar nature but differing in electronic structure. The success of Hildebrand's basic theory is actually due to the predominance of the dispersion forces in most nonelectrolyte solutions. Having formulated the expressions representing the molecular interactions due to physical forces, certain relations may now be drawn between the theory of intermolecular forces and Hildebrand's nonelectrolyte solution theory. First of all a relation may be derived for the dipole

-56interaction parameter, w Considering Equations (92) and (101) it can be deduced that c;g -- St T vL~ cr, o, (o104) This is the form of the relation postulated by Martire based on Van Arkel's work and the theory of intermolecular forces. As will be seen below, this is also the result arrived at by Hildebrand and Scott, (42) Now in order to be able to combine the Van der Waals forces together into a workable expression for th an analogy will be drawn with a more generalized from of Hildebrand's equation. One of the basic limitations of Hildebrand's method is the assumption of the geometric mean rule for expressing all the interaction properties between the solute and solvent molecules, namely A\X 2L (X 1 X 22(105) The most general form of Hildebrand's relation is (z-4T. 7Z'a" -ZZI3) a. Z.(106) In this expression the assumption of the geometric mean has been avoided and thus negative deviations from ideality are possible. Comparing Equations (92) and (106), and invoking (105) it can be seen that in Hildebrand's normal expression, neglecting induction effects Z = Zi. r Z W = +i (107)

-57At this point the analogy already suggested by Equation (o104) will be completed. Consider two solutes molecules interacting to form a 2-2 pair and likewise two solvent molecules interacting to form a 1-1 pair. Now for every solute-solvent interaction taking place when the binary solution is formed two 1-2 pairs are formed for each 1-1 and 2-2 pair interactions. Thus the bracketed group in Equation (106) could quite naturally represent the molecular interactions occurring in solution formation as postulated by the theory of intermolecular forces. Utilizing Equations (97) through (103) the following relations result 3__,, _ _ __ __._, __ = 3, A 2 7~Ir+ L~I (I.S, 44 6 V ia - - (108)'22R + 6e92' 2t6tZ. 3kTi av. V Thus Equation (106) can be used in conjunction with (108) to determine 2th using the theory of intermolecular forces. Conversely this analogy may be used to determine the relationship between Hildebrands parameters andthe intermolecular force theory. Recalling that Hildebrand neglects induction effects, a comparison of (107) and (108) yields 23 = 3 dt X(109)

-58and ) -. (0io4) assuming that Equation (105) holds for all the interaction properties, and is approximately equivalent to the harmonic mean. As has been mentioned a number of times, although the induction forces are usually negligible there are certain instances in which their effect is actually the determining factor in explaining solution behavior. For this reason a further refinement of Hildebrand's treatment is proposed here to account for this effect. As the solubility parameters term in Equation (92) represents the dispersion forces and likewise the dipole interaction parameters represents the orientation forces, a third term will be added to account for the induction forces. However, as can be seen from Equation (108) the approximation of (105) is in no way justifiable as a summation is involved for the Z12 term. Therefore the following relation by analogy is proposed " Yt V i ( - IXt (wT-Wu)vT 1 (110) where a::_ To.~t _q - &(o'~ o2,C"V) ~I.T.- ---- I z...\/.a (1ZV) In this relation, provided the induction forces are the deciding factor in solution behavior, even negative deviations from ideality are possible.

-59It is thus felt that Equation (110) represents the most generalized variant of Hildebrand's basic theory and should prove most valuable in attempting to compute the thermal contribution to the activity coefficiento Do Statistical Mechanics of Solutions The application of statistical mechanics to the behavior of liquid mixtures on a molecular level has been widespread. In fact four excellent texts by Barker,(10) Guggenheim, ) Prigogine and Rowlinson (102) exist in the field. There appears to be two general approaches taken when treating liquids. Either one views a liquid as a disordered solid and applies a lattice theory to describe its behavior, or the liquid may be viewed as a dense gas and distribution function theory used to describe its properties. The lattice theory approach is championed by Barker and Guggenheim in the above cited works. Most lattice theories are still based on the works of Lennard-Jones and Devonshire. The theory of distribution functions is utilized by Hildebrand and Scott(43) through the radial distribution function. By proper modification of this theory the final relations can be expressed by the equations evolved in the previous sectiono The chief problem connected with these statistical mechanical theories is the intractability of the final results. The derived relations have been used to confirm very simple liquids such as argon, but as yet have not been applied successfully to more complex liquids or to liquid mixtures. Even the more advanced lattice theories utilizing the concept of free volumes or "holes" still predict thermodynamic properties more in accord with the solid than the liquid state- Some of the more advanced theories of Prigogine, while applied successfully to

liquid mixtures of simple liquids, are sufficiently dependent on parameters which must be determined from other experimental data that they are of little value in a study such as this in which only one concentration is studied, iLe., infinite dilution. Since the lattice theories of liquids based on statistical mechanics are in a higher state of development at the present time, an attempt will be made to apply this theory to the present work in order to gain a more fundamental insight into the molecular behavior of solutions. Much of the rigor, however, will be sacrificed in order to produce relations amenable to practical applications. In this respect certain rather plausible assumptions as proposed by Moelwyn-Hughes(76) and modified by Adlard, Kahn and Whitham(3) will be incorporated into the development. Consider a binary solution of molecules, the solute and solvent having unequal molecular dimensionso In statistical mechanics the main goal is to express the thermodynamic properties of the system under study in terms of the partition function, As a general relation the total partition function for the binary solution may be expressed as; = /(9'nt)>6 (~i ) I;Lj L a T(112) Now the basic postulate of statistical mechanics is LA - - kT In V V= (113) By defining 2 —( t $t~ t E17 > ( B k 1h ). (114)

-61Equation (113) may be expressed as Ak, T It 7. k T QI (115) and MAl= - k, kTlng-7 T-K~ kng+-kTln QM (116) Now upon mixing the change in free energy is M- (Ap,+ — kI QM (117) Q, Q, and the configurational partition functions are defined as Q1 =~! f C (u~l ( d) r 2k 7a and QM U0 f -(UM/g-T)(z )t~lrD722 Q MI[ i~~~,'~~~'""/ A)(d7;jR'~du,)~+ (119) At this point the difficulty mentioned in the above discussion arises. No mathematically rigorous method exists for evaluating the configurational partition functions. The commonly accepted technique is to attempt an evaluation of Q by a cluster expansion. Expressing the exponential term within the integral as ~s [-V~/ 1 P?- FT = t. (i, I- d ) (120)

-62where 5d~j ~= C4FH~ u~(rm~/v] - 1,~ ~(121) and U( t =Xur Z (Tcj ) (122) Q is then represented as a sum of products of cluster integrals, each cluster representing a small subgroup of molecules comprising the whole of Q. In actuality the final state of affairs is only slightly improved mathematically as the cluster integrals cannot be rigorously evaluated either, Therefore it is at this point that the plausible assumptions discussed earlier will be drafted, As the problem lies with the evaluation of the integrals in Equations (118) and (119) it will be assumed that U is independent of coordinates, Then the relations can be integrated to Q o- ) / LW /k (123) and _ ("t7L v )p (_ UM/VT) (124) Now in order to formulate a practical solution for the thermodynamic properties of the binary solution in question some form must be assumed for Ui and UM'. According to Moelwyn-Hughes, these configurational potential energy terms may be related to the interaction energy of Guggenheim by

UL = ~4LR\N~J L=ILO (125) and LUM.w 7=.. +Th7L....v.. W (126) Therefore with these relations, the expression for Qi and QM are Q = (- %vL) - Y(- tU1'T (127) and rM (7,vL+2 y)T' e)I,w, + m'1wP A~T~'v loo' 7R LT Ihv, WIZ (128 Assuming that the volume change on mixing is small, v. will be replaced by v9o Also based on this assumption AGM is approximately equal to LAM With these changes in mind, substitution of (127) and (128) into (117) yields - G=on "" -T IT,v,OLT 1h71+%ic +hva! (129):a+ I VI k-ATh Wvo av'L,~ 11 7'Z a \1 For an ideal solution, by definition v1 = v2 and Aw = 0 so nAs e"=,S;T 1n a+ rr k T I h (130)

-64Now a GE = A (iJ -G i\( Geqt (131) therefore W T kT,. Lo INm -i-'v7L \X V,~ - Y (132) _ _.-.a W Next dividing (132) by kT and differentiating with respect to 2 yields vR, T[ (-/cl V1-(, _v (oIy, Vo z /V= ) ]V,+ — V l2, v''-' v?Fv,~+-P=,),l- (\ It- z~u,ov',2+VI _1 F T, 7 (lc, v,(~ + (- ~2L ) (,OI At infinite dilution 71241l approaches zero. With this relation in the above derivative one obtains ( a 4S,, ) W R~it j-~) ('1 o/ l; TJ, m —- =- (134

-65Expressing this relation in molar rather than molecular terms and substituting Equation (28) into (134) gives st L,+ (R),~) (135) This relationship expresses the activity coefficient of the solute in terms of the solute and solvent molar volumes and the interaction energy. Differentiating Equation (135) with respect to the temperature yields I ( w~ 1 ( O dl~aVa _NP~V oc3V - L L0 ] AhW (Io dT N/a (136) Now the cubical coefficient of expansion is defined as 3_ ( ad (137) Multiplying Equation (136) by -RT and substituting (31) and (137) yields u H(- (V( )(@.- r,)(18 -RT(1- 092)(@ l (1/ \Ja. 6 \NI H J40Ir

Also as A~m 5= -ft -R I's (33) one may utilize (135) and (138) to obtain _ (\)I/{L (- 2 w 1 4-B] (139) Thus the proposed model based on the lattice theory of liquids does provide relationships for determirning the thermodynamic properties of a solute at infinite dilution in a binary solution. However) in order to test the assumptions made concerning the coordinate dependence and the form of the configurational potential energy, independent data for the activity coefficient and the partial molar excess enthalpy sb.ould be utilized, Although, as was anticipated, a certain degree of rigor was sacrificed) at least tractable relations result for the desired properties from the above treatment

IV. EXPERIMENTAL PROGRAM A, Description of Equipment Experimentally the thesis was conducted on a highly modified F and M Model 609 Gas Chromatographo This model is equipped with a flame ionization detector and a linear column temperature programmer, However, all runs made in this investigation were performed under isothermal conditions. The unit as received could maintain the column temperature control to + 2~C at best. The heating circuit for the thermostated column chamber consisted of an on-off relay which alternately pulsed 110 volts to a 32 ohm resistance heater. This circuit was modified to give essentially a semi-proportional control by modifying the relay to a high-low operation and controlling the amount of voltage delivered to the heater. This voltage differed in the high and low modes of operation so that the high voltage circuit was only used occasionally to offset accumulated heat losses, In this manner the column temperature in the thermostated chamber could be maintained at + 0010C of the desired temperature over prolonged periods of time, In addition to the temperature control of the chamber, separate variable controls existed for setting the temperature of the sample injection port and the flame ionization detector block independently~ The flow system on the original unit consisted of a Moore constant volume flow controller set with a precision needle valve, a Brooks floating ball flowmeter, the sample injection port with -67

-68stream splitter, the actual chromatographic column, and the flame ionization detec+e-r, Brooks flowmeters were also provided for the hydrogen and air streams supplied to the flame ionization detector, As the solvents studied in this investigation were all quite volatile, having vapor pressures of the same order as the solutes studied9 the flow system was modified to accomodate a presaturatoro So as to prevent fogging in the flowmeter, the presaturator was installed following the flowmeter but prior to the sample injection port. This presaturator column was installed in the thermostated column chamber so that the helium carrier gas could equilibrate with the solvent in the presaturator prior to entry in the chromatographic column. As the inlet and outlet column pressures must also be known9 a 0-10 psig Matheson pressure gage was installed following the presaturatoro As the column outlet was located immediately adjacent to the flame ionization detector, the outlet pressure was taken as the prevailing atmospheric pressure as registered on a Pri.nco Fortmi.n-type mercuriali barometer mounted near the apparatus~ Following the flame i.onization detector, provision was made to instal:l a 25 cc soap bubble flowmeter. This flowmeter could be added to the flow system or not as desired. All Brooks flowmeters were calibrated with the soap bubble flo-rneter, and the pressure gage was calibrated using a ten foot mercury colurmn in the standards laboratory. The Brooks flowmeters were only used to approximately determine the flow rates, the actual determinations being made on the soap bubble flowmetero

Due to the high volatility of the solvents studied the rate of solvent depletion was reasonably high. In the normal mode of operation of the flame ionization detector the unit is designed to detect of the order of 10-12 gram atoms of carbon per second, The mode of operation as described by Sternberg et al, (l) is one of chemi-ionization, Now with the constant solvent depletion the rate of carbon atoms flowing through the detector is considerably higher than the above mentioned value and the effect is to saturate the output current to the preamplifier. Therefore the detector geometry had to be modified, The platinum loop electrode was placed in much closer proximity to the electrically grounded combustion jet, In this manner much of the actual ion production occurred in the upper region of the flame envelope and was never collected by the upper electrode, as this operation took place above the electrode, Although the electrode became hotter in this region than in normal operation, it was assumed that the work function of platinum was sufficiently high so as not to contribute any secondary emission, Also to minimize the noise due to random fluctuations in the hydrogen flow rate, a precision needle valve was installed in the hydrogen flow stream prior to the Brooks flowmeter, Two stage diaphragm pressure regulators and. appropriate check valves were installed on all compressed gas cylinders prior to connection with the gas chromatograph. A Minneapolis-Honeywell recorder with a one millivolt full scale range output was utilized to record the detector output signal. This unit was equipped with a Disc Instruments recording integrator.

In addition to displaying the detector output, independent thermocouple readings could be displayed indicating the temperatures of the sample injection port) the thermostated column chamber' the flame ionization detector block and the actual combustion flame. All these thermocouples, with the exception of the latter one, were calibrated using standardized Princo thermometers. The calibrated thermocouples were of the iron-constantan typeo A brief description of the apparatus flow system will now be given following the schematic diagram as shown in Figure 1o The helium carrier gas is controlled by a two stage regulator and a check valve. Following this the helium passes through the Moore constant volume flow controller, through the Brooks flowmeter and into the thermostated column chamber. The column chamber is heated by a resistance element which warms the air circulated by a small blower located outside of and below the actual chamber. The helium then is presaturated with solvent in a forecolumn, its pressure being registered on the Matheson gage, and passes into the sample injection port sweeping out the volatilized sample~ The samples were injected utilizing a Hamilton microsyrlinge with a Chaney adaptor or a WahlHenius syringe with volumetric spacers. Immediately adjacent to'the sample injection port is the chromatographic column0 The columns used in this study are 1/4 inch outside diameter aluminum tubing0 All interconnecting fittings were Swagelok to reduce the possibility of leakage0 Following the column the carrier gas i.s premixed with hydrogen and elutes through the combustion jet where it is.ignited

2 Stage Regulator Moore Flow Controller U ~~~~~~~~~~~~~~~~~~~Carrier Gas fCheck c I III IL lwee Helium ValveFlwer CarrierA Gas ~~~~~~Needle Valve Flame Ionization Detector ~~ ~I~~ I r I V ~Thermostated Chamber Hydrogen Fl ~owmetere 2 St~~~~age ~Main Column Needle ValvE Regulatorpo Check ValvE Check Air Peauao Valve Flowmeter Air ~~~~~~~~~~~~~~~~~~~~~2 Stage 0 Sample InjectionReuao Port Inlet Pressure Gage (0-10 Psig) Vibrating Reed 1 Millivolt Hdoe Amp lifier I 1 Recorder Figure 1. Schematic Diagram of Equipment.

-72and burned, The chemi-ionized radicals produce a current which is collected by the platinum electrode, amplified and displayed on the recorder. The remaining gases flow out of the detector chamber through the outlet port. Two additional gas streams are supplied to the flame ionization detector chamber, Hydrogen, premixed with the carrier gas stream, provides the combustion media. It flows through a two stage regulator and check valve to the Brooks flow, meter for the hydrogen. Prior to the flowmeter the flow rate is accurately controlled by a precision needle valve, The hydrogen then flows through the jet and is combusted, An air stream is also utilized in the flame ionization detector to support the combustion. The air flows through a two stage regulator and check valve, is metered through a Brooks flowmeter and then fed into the detector chamber through a diffuser to avoid turbulence near the flame envelope. B, Choice of Systems The systems chosen for investigation in this work represent the results of a very comprehensive study into the anticipated behavior of solutions and possible solute-solvent interactions, Rather than studying solutions normally of interest in GLC, it was decided to investigate binary systems of the normal type in which both components are volatile, As the intended purpose of the study was to provide a correlational technique valid for a large range of solutions, the.-s.olutes and solvents had to be such that all types of behavior were included, In order to cover all possible types of

-73interactions some method or scheme of liquid classification was sought which would accomodate most conceivable nonelectrolyte liquids. The earliest work uncovered in this study, and the one on which almost all subsequent work has been based, is that of Ewell, Harrison and Berg(28) in 1944. These workers in an attempt to classify liquids for predicting possible azeotrope formation, evolved a scheme based on hydrogen bonding and dispersion forces, They ascertained that these two solution interactions were responsible for the bulk of the deviations from ideality, the former being the more important effect, In hydrogen bonding a hydrogen atom can coordinate between two oxygen, nitrogen or fluorine atoms or between one of these donor atoms and a carbon atom provided that enough negative constituents are attached to the carbon atom. With these bond types the following classification of bond strengths can be made Strong Bond Weak Bond O ---- HO N - HN N -. HO (HCC12 O-*E-MNN N1 - > HCNO2 0HN N HCCN Based on this bond classification liquids may be categorized, into five groups Class I - Liquids capable of forming three dimensional networks of strong hydrogen bonds. -- e.g. water, glycols, glycerols, amino alchols.-.- hydroxyl amines, hydroxy acids, polyphenols, amides. Class II Go Liquids with molecules containing active hydrogen atoms and donor atoms, -- eg,. alchols, acids, phenols, primary

-74and secondary amines, oximes, nitro compounds with hydrogen atoms adjacent to the terminal carbon atom. Class III - Liquids containing only donor atoms. -- e.g. ethers, ketones, aldehydes, esters, tertiary amines, pyridines, nitro compounds and nitriles with no hydrogen atoms adjacent to the terminal carbon atom. Class IV - Liquids containing only active hydrogen atoms or pseudo active hydrogen atoms, i.e.g mobile electrons. -- e.g. halogenated hydrocarbons with hydrogen atoms on the terminal carbon atom, aromatic compounds, olefins. Class V - Liquids with no active hydrogen or donor atoms. -- e.g. hydrocarbons, CS2, CC14, sulfides, mercaptans. The first two classes are associated liquids in the sense that they hydrogen bond with themselves. Classes III and IV will form hydrogen bonds with the first two classes but not by themselves. The last class shows no tendency to hydrogen bond and thus the solution interactions are due mainly to dispersion forces. Considering the possible interactions between classes of liquids, again leads to five general categories. The first class comprised of I-V and II-V interactions shows limited solubility and always positive deviations from ideality with hydrogen bonds being broken, The second class having only III-IV interactions always shows negative deviations from Raoult's law as hydrogen bonds are formed, The I-IV and II-IV interactions compose the'third class,

-75This class again always shows positive deviations, but hydrogen bonds are broken and formed, However, the dissociation of the I or II component predominates. A fourth very extensive class is composed of I-IB I-II, I-III, II-II and II-III interactions and usually has activity coefficients greater than unity, However, the binary systems formed are quite complex and so negative deviations may occur. This is due to the simultaneous breaking and forming of hydrogen bonds, The fifth class comprising III-III, III-V, IV-IV, IV-V and V-V interactions behaves in a quasi-ideal manner as no hydrogen bonds are involved. The above classification scheme, as mentioned earlier, seems to have gained wide acceptance. The work of Keulemans, Kwantes (53) and Zaal,(53) described in the literature review, actually is patterned after the above classification. These authors studied C3 and C4 paraffins and olefins in transformer oil, dinonyl phthalate and dimethyl formamide, These three solvents fall respectively into Classes V, III and I, Dal Nogare and Juvet (21) in their excellent text, utilize this scheme to relate solution behavior and the resulting thermodynamic properties. Pimentel and McClellan(83) propose a liquid classification system which is almost the same as that of Ewell et al, with the exception that they combine Classes I and II into a single group, as both these types exhibit self-association. This work also predicts the effect of hydrogen bonding on the partial molar excess enthalpy based on their liquid classification, Generally speaking, with the exception of the IIT-IV interaction, the

-76thermal effect is endothermic. When compared with actual experimental results as done by Rowlinson,(101) it becomes clear that not only are the predictions of Pimentel concerning the thermal effects generally corrects but that quite often even III-IV binary solutions are endothermic, This would also tacitly imply that for certain of these solutions slightly positive deviations from ideality might exist as the strengths of the hydrogen bonds formed would be very weak, Rowlinson(103) in another study of hydrogen bonding investigated many groups of solutes in water, a Class I solvent, He found that ketones, nitriles, alcohols ethers and amines all exhibited activity coefficients greater than unity as expected for Class II and III solutes, While in general all the solutions formed were endothermic, certain I-I systems at dilute solute concentrations were exothermic, This effect is a function of the number of bonds formed and the solution temperature, having an inflection point. Based on the above discussion and classification scheme the systems for this work may now be chosen so as to encompass all possible types of solution behavior, The actual solutes and solvents chosen will also allow a comparison between the results of this work and existing literature values for certain selected systems. From a close appraisal of the possible classes of interactions it- can be seen that by utilizing solvents from Classes I, III and V all anticipated types of behavior will be included with only the magnitude of the effect varying,. As all solvents must be volatile and a desire

-77existed to investigate water systems, the solvent choices are: Class I - water, Class III - 2 pentanone, and Class V - 2,3,4 trimethylpentaneo All of these solvents have comparable vapor pressures and boil near 10OO0~C Thus unless all systems studied exhibit the same behavior, the hypothesis that similar boiling substances should exhibit similar behavior will be repudiated. Having determined the three solvents, the choice of solutes is largely a personal matter, so long as all classes of liquids are included. Therefore the solutes to be studied are: Class II - methanol, ethanol, propanol; ethylamine, propylamine, butylamine; Class III - methyl formate, ethyl formate, propyl formate; acetaldehyde, propionaldehyde, butyraldehyde; Class IV - dichloromethane, trichloromethane, tetrachloromethane; and Class V - pentane, hexane, heptane, These solutes should include all possible types of binary interactions as previously discussed. Although all solutes are chosen to be more volatile than the solvents, the technique is not restricted to such conditions and actually any solute could feasibly be studied in any solvent providing the solvent was normally in the liquid state at the conditions of operation. C. Experimental Techniques The following discussion will present the major operations in preparing for and conducting an actual experimental run. The effect of the GLC operating variables on the resultant thermodynamic properties as investigated in this work will be presented and a short accompanying analysis will be given. Other details of lesser

-78significance for an understanding of the work but highly important for a continuing study will be found in the appendix. 1. Procedure As water, 2 pentanone and 2,3,4 trimethylpentane are not standard partitioning liquids used in GLC, a few words will be said concerning the preparation of the chromatographic columns utilizing these solvents. Initially the solid support is weighed in a container of known mass. The solid support is then completely flooded with solvent and mixed thoroughly to insure complete coating of all particles. All solid supports used in this study were 40/60 mesh cuts, utilized as received. Following this thorough mixing the saturated support is carefully heated in a constant temperature oven, vaporizing the solvent. This process is continued with intermittent weighings until the desired amount of solvent, expressed percentagewise as grams of solvent per gram of solid support, is obtained. The container is then closed and the stationary phase is completed. To pack a column, the empty column and full packing container are weighed, some packing quickly transferred to the column, and then the full column and slightly depleted packing container are reweighed. In this manner the initial weight of the solvent in the column is determined and checked. At the conclusion of a run the column is reweighed and the lossage of solvent during the run is determined by difference. The presaturator columns utilized in this work were five and six feet in length while the main chromatographic columns were six and nine inches long, The rather short columns were necessitated by

-79the long retention volumes of most of the solutes, However, due to this short length and the high volatility of the solvents, the columns had to be repacked for each run. As the temperature of the sample injection port, the flame ionization detector and the thermostated column chamber could be controlled independently, each was set at an optimum value. In the case of the thermostated chamber, runs were made at 200~C 300C and 40~Co The sample injection port must be sufficiently hot to insure vaporization of the liquid sample. As all the solutes boiled below 1000~C, the injection port temperature was sustained at 1000~C Similarly to prevent condensation of bleeding solvents and other material, the detector block temperature was held at 110~C. These latter two temperatureswere maintained throughout the experimental work. Prior to making an actual run the column chamber was heated up and equilibrated' at the desired temperature. Due to the high depletion rate of solvent from the column, the normal operating mode of the flame ionization detector was unsuitable. In order to lessen the problem of current saturation, the carrier gas flow rate was maintained in the region of 15 to 20 cc per minute. Even with this low flow rate the operation was difficult. In actually carrying out a run, once all temperatures were equilibrated at the desired value, the presaturator and chromatographic column were quickly installed and the flame ionization detector ignited, Then the collector electrode to jet distance was varied

-80until the amplifier background signal could be electrically balanced out, In this mode of operation the detector output may be nonlinear but as no quantitative analysis is being made, it makes no difference, Once equilibrium is reestablished and flow rates ascertained using the soap bubble flowmeter a sample is injected. Now in all runs in which the final data was obtained, 0,.04 microliters of solute was injected. In this manner infinite dilution could actually be approached, i.e., liquid solute mole fractions of the order of 10-5 and symmetric peaks resulted indicating linear absorption isotherms. The peaks obtained with such small sample sizes were quite sharp, exhibiting very little broadening, After each peak eluted another sample was injected and this process was continued until changing elution times indicated that the column was nearly depleted of solvent0 The run was then terminated and the columns withdrawn from the thermostated chamber and reweighed. Although the runs were continued until the column was nearly exhausted of solvent, no data was accepted for which the quantity of solvent in the column was less than 15% w/w. As the initial quantity of solvent in the column was approximately 40 to 50% w/w, this meant that a run would last about 60 to 90 minutes depending on the temperature of operation. These statements apply when water or 2 pentanone was used as the solvent. The limits differ for 2,3,4 trimethylpentane as will be explained shortly. To point up the effect of the presaturator, attempts were made to conduct a run

-8lwithout presaturation, After installation of the columns, approximately 20 to 25 minutes is required for thermal equilibrium to be reestablished. Without the presaturator, by the time equilibrium was reached the chromatographic column was depleted of solvent. In order to compute the desired properties from the GLC data, the weight of solvent must be known, Due to the constant temperature and carrier gas flow it is assumed that the depletion rate is constant and a linear change in amount of solvent present results, This assumption is verified by the fact that upon observing the recorder signal, although sporadic deviations occur above the background noise, no continual drift or trend in deviation can be observed, If a constantly drifting signal occurred this would indicate a varying amount of solvent bleed being ionized in the flame. As this does not happen the assumption is justified. Concerning the remark about the double standard for solvent depletion depending on the solvent, this may be explained on the basis of solid, support. With each solvent the most inert support was used, limited by the wetability of the support by the solvent. For water, the support chosen was Chromosorb W; for 2 pentanone, HMDS treated Chromosorb W was used; Fluoropak 80 was used to support the 2,3,4 trimethylpentaneo Now the Fluoropak 80, a teflon polymer, has a much lower specific surface area than the other supports. Therefore less liquid can be coated on the support, but also less liquid is needed to insure coverage of the support. Thus for 2,3,4 trimethylpentane only 15 to 20% w/w of solvent existed initially and the data was taken

until the quantity of solvent became less than 5% w/w. More will be said concerning the solid support in the following discussion, 2. Effect of Variables Although the independence of the resulting thermodynamic properties from the GLC variables has been rather thoroughly investigated by other workers, some investigations were also conducted in the present study, Due to the relative ease of obtaining the water systems data, the studies were performed with water as the solvent, Chromosorb R, Firebrick, and Chromosorb W were all tried as solid supports, and provided that sufficient coating, i.e., 10% w/w or more, was maintained on the support no effect was noticed. Support adsorption effects only occur at low solvent concentrations and subambient operating temperatures. In the present work somewhat idealized calculations indicate that for a 20% w/w coating of water on Chromosorb W the liquid layer would be approximately 700 molecules thick, indicating a sufficient coverage of the solid support. Funk and Houghton(34) have derived a theoretical relation for the depth of penetration of the solute into the solvent and. have used this model on the isobutylenedinonyl phthalate system, They find that the fractional penetration varies from 0,60 to 0.84 of the total thickness as the coating varies from 10 to 24% w/w dinonyl phthalate. This indicates that for lower solvent concentrations the effect of solvent adsorption is much more feasible, Chueh(l9) points out that if the solute remains near the surface of the solvent a high "effective" concentration of solute would

-83result, which for a system exhibiting positive deviations from ideality causes activity coefficient values below the true results, As will be seen in the discussion of the results, if anything the contrary condition exists in the present study. Thus it is felt that both solid support and solvent adsorption effects are absent from the results obtained in this study and true equilibrium properties are obtained. In addition to the solid support studies the other parameters involved were also varied. The helium flow rate was varied from 15 to 50 cc per minute with no noticeable change in the activity coefficient, The percentage coating of the solvent on the solid support was varied from 10 to 50% w/w and the total amount of solvent in the column was varied from 0.1 to 4,0 grams, all of which produced a constant value of the activity coefficient, within the experimental error, The values obtained for the thermodynamic properties remained the same whether or not a presaturator was used, Therefore the only effect of the presaturator is to retard the rate of solvent depletion and allow a longer run to be conducted, This is due to the fact that essentially laminar flow existed through the main column and thus no bulk flow of solvent occurred, In this mode of operation the solid support remained covered by solvent at all times, The effect of varying the columi length from six inches to six feet was negligible as well as the effect of varying the inlet and outlet pressure over a narrow range, It should be recalled that varying the mean column pressure over a moderate range will result in a variation in the activity

coefficient due to the gas phase nonideality correction. However, in this respect, helium was used throughout as the carrier gas and in the light of the theoretical development this choice tends to minimize the gas phase nonideality. Sample size variation has a very definite effect on the activity coefficient, as it is a function of concentration, However, in the runs made to obtain the present data, 0.04 microliter samples were used which was near the limit of detection with the noise level existent during the experiment. The sample injection time was instantaneous and so should have no effect. In contrast to the results of Stalkup,(110111) the values of the gas phase volume in the column determined by the retention time of an unretained component and by geometrical calculations were essentially coincident, More will be said concerning this in the appendix. Thus it is felt from the above studies that the results obtained in this investigation are completely independent of the GLC variables and are true equilibrium properties,

V0o RESULTS AND DISCUSSION A. Presentation of Thermodynamic Properties The actual process of determining thermodynamic properties from GLC consists of measuring the chromatographic parameters experimentally and then utilizing the relations derived in the theoretical development. The results obtained in this fashion from Equations (20) and (24), knowing the retention volume, are given in Table I for the three solvents at 20, 300 and 40~C. The data shown in Table I represents average values for a number of runs on each binary system. The general internal consistency of the data was quite good, the overall average error being + 5%,, with the 2,3,4 trimethylpentane systems being somewhat better while the 2 pentanone systems were slightly worse than this value. Due to the lengthy retention times of the alcohols and amines, as compared to the other solutes, more difficulty was experienced in obtaining the data for binary solutions with these solutes~ As no carbon atoms are present in waters the flame ionization detector is oblivious to this solvent and thus although initially anticipated to provide the most trouble, the water binary systems were the easiest to study experimentally. Utilizing the data in Table I and Equation (28), the results in Table II are computed. From the thermal variation of the activity coefficient, the partial molar excess enthalpy can be determined using Equatlon (32). In actuality the value of AU2E is determined from the slope 285

-86TABLE I INFINITELY DILUTE ACTIVITY COEFFICIENTS FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP AT 200, 300 AND 40~C Water 2 Pentanone 2,3,4 TMP Solute 20 ~C 30 ~C 40 ~C 200 C 300C 40 ~C 200C 300C 40 ~C C5H12 945 796 517 5.27 3.99 5.36 0.99 0.97 0.97 C6H14 2940 2225 1465 6.53 4.65 6.16 1.10 1.13 1.09 C7H16 8050 6160 3925 8.51 5.36 7.36 1..07 0.98 0.98 CH2C12 209 201 153 1.18 0.95 1.21 2.26 1.97 2.23 CHC13 571 568 425 1.19 1.13 0.93 1.59 1.35 1.56 CC14 2870 2150 1490 3.61 2.73 2.41 5.51 6.48 8.63 MeFo 16.6 17.4 14.2 2.58 1.95 2.18 5.57 5.11 4.92 EtFo 46 51 41 2.66 1.96 2.25 3.52 3.40 3.78 PrFo 150 168 131 3.66 3.24 3.65 3.11 2.70 3.13 CH3CHO 3.59 4.36 3.71 2.06 1.73 1.65 5.17 5.00 5.24 C2H5CHO 14.7 17.6 15.4 2.25 2.01 1.77 4.14 3.77 4.18 C3H7CHO 63 73 61 3.97 2.59 2.66 4.04 3.62 3.72 EtAm 0.37 0.69 0.44 0.50 0.41 0.50 2.18 1.80 1.85 PrAm 2.33 2.85 2.44 3.00 2.14 2.50 2.23 2.15 2.48 BuAm 4.00 4.70 3.70 4.40 4.31 4.58 1.76 1.45 1.84 MeOH 2.69 2.53 2.30 5.60 3.93 5.12 39.9 39.4 33.9 EtOH 6.51 6,15 5.50 6.52 4.24 6.01 28.1 22.6 22.4 PrOH 24 26 22 7.21 4.60 6.27 23.0 12.8 18.3

-87TABLE II PARTIAL MOLAR EXCESS FREE ENERGY (CAL/MOLE) FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP AT 200, 30~ AND 400~C Water 2 Pentanone 2,3,4 TMP Solute 20 ~C 30 ~C 40 ~C 200 ~C 300C 40 ~C 200C 300C 40 ~C C5H12 3990 4020 3880 970 830 1040 -10 -10 -20 C6H14 4650 4640 4530 1090 920 1130 60 70 50 C7H16 5230 5250 5140 1250 1010 1240 40 -10 -10 CH2C12 3110 3190 3130 100 -30 120 470 410 500 CHC13 3690 3820 3760 110 80 -50 270 180 280 CC14 4630 4620 4540 750 600 550 990 1120 1340 MeFo L630 1720 1650 550 400 480 1000 980 990 EtFo 2230 2370 2310 570 410 500 730 740 830 PrFo 2920 3080 3030 750 710 800 660 600 710 CH3CHO 740 890 810 420 330 310 960 970 1030 C2H5CHO 1560 1730 1700 470 420 350 830 800 890 C3H7CHO 2410 2580 2560 800 570 610 810 770 820 EtAm -580 -220 -510 -400 -540 -430 450 350 380 PrAm 490 630 520 640 460 570 470 460 560 BuAm 810 960 850 860 880 950 330 220 380 MeOH 580 560 520 1000 820 1020 2150 2210 2190 EtOH 1090 1090 1060 1090 870 1110 1940 1880 1930 PrOH 1850 1960 1920 1150 920 1140 1820 1530 1810

of a plot of the logarithm of y2 as a function of reciprocal temperature. Now as tle overall temperature range of this investigation was 200C, and HI2E is being determined by graphical differentiation of the data, no attempt is made to analyze the temperature dependence of LH2E A Rather a best straight line fit of the three data points is utilized and AH2E is assumed constant over the 200C range. As the anticipated change in LH2E with temperature is of the order of 5 cal/mole - ~K for most organic binary solutions according to Littlewood, (68) the average error in Y2 does not justify a more detailed interpretation on a 200C Y2 range, The results of this procedure are presented in Table III. Knowing the values of AG2E and ZAH2E from Tables II and III and utilizing Equation (27), the partial molar excess entropies may be evaluated. These are tabulated in Table IVo From an inspection of the activity coefficients in Table I it can be seen that the alkanes and chlorinated methanes are only slightly soluble in water) thus forming very non-d.eal solutions, Also, as the number of methylenic groups increase in the hydrocarbon radical) any solubility tendencies created by the functional group in water are masked out and lost, As 2 pentanone has solution properties generally near the mean of the solutes studied) none of its binary solutions show a very large deviation from ideality. On the opposite end of the scale the alkanes form essentially ideal solutions with 2,3,4 trimethylpentane as both components are nonpolar and so little solute-solvent interaction exists, It should be noted that

-89TABLE III PARTIAL MOLAR EXCESS ENTHALPY (CAL/MOLE) FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP FROM 200 TO 400~C Water 2 Pentanone 2,3,4 TMP Solute 200 - 40~C 200 - 400C 200 - 40~C C5H12 6340 -90 180 C6H14 6550 540 80 C7H16 6480 1350 580 CH2C12 2760 880 210 CHC13 2650 2480 180 CC14 5950 3580 -3990 MeFo 1120 2240 860 EtFo 770 1920 -250 PrFo 960 1650 0 CH3CHO -110 2010 -90 C2H5CHO -720 2170 -110 C3H7CHO -130 5140 720 EtAm -2490 -410 1390 PrAm -1090 1390 -600 BuAm 106 -410 -550 MeOH 1450 310 1430 EtOH 1480 360 2270 PrOH 1060 320 1550

-90TABLE IV PARTIAL MOLAR EXCESS ENTROPY (CAL/MOLE O ~K) FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP AT 200, 300 AND 400C Water 2 Pentanone 2,3,4 TMP Solute 20 ~C 300C 400 ~C 200C 300 ~C 400~C 200C 300C 40 ~C C5H12 8.0 7.7 7.9 -3.6 -3.1 -3.6 0.7 0.7 0.7 C6H14 6.5 6.3 6.5 -1.9 -1.3 -1.9 0.1 0.0 0.1 C7H16 4.2 4.o 4.3 0.4 1.1 0.4 1.8 1.9 1.9 CH2C12 -1.2 -1.4 -1.2 2.7 3.0 2.4 -0.9 -0.7 -0.9 CHC13 -3.6 -3.9 -3.6 8.1 7.9 8.1 -0.3 0.0 -0.3 CC14 4.5 4.4 4.5 9.7 9.8 9.7 -17 -17 -17 MeFo -1.7 -2.0 -1.7 5.8 6.1 5.6 -0.5 -0.4 -0.4 EtFo -5.0 -5.3 -4.7 4.6 5.0 4.5 -3.4 -3.3 -3.5 PrFo -6.7 -7.0 -6.6 3.0 3.1 2.7 -2.3 -2.0 -2.3 CH3CHO -2.9 -3.3 -3.0 5.4 5.6 5.5 -3.6 -3.5 -3.6 C2H5CHO -7.8 -8.1 -7.7 5.8 5.8 5.8 -3.2 -3.0 -3.2 C3H7CHO -8.7 -9.0 -8.6 14.8 15.1 14.5 -0.3 -0.2 -0.3 EtAm -6.5 -7.5 -6.3 0.0 0.4 -0.1 3.2 3.4 3.2 PrAm -5. 4 -5.7 -5.1 2.6 3.1 2.6 -3.6 -3.5 -3.7 BuAm -2.4 -2.8 -2.4 -4.3 -4.2 -4.3 -3.0 -2.5 -3.0 MeOH 3.0 2.9 3.0 -2.4 -1.7 -2.3 -2.5 -2.6 -2.4 EtOH 1.3 1.3 1.4 -2.5 -1.7 -2.4 1.1 1.3 1.1 PrOH -2.7 -3.0 -2.7 -2.8 -2.0 -2.6 -. 0.1 -0.8

-91within any homologous series of solutes at a given temperature the acitivity coefficient increases with increasing size of the hydrocarbon chain. This result will be the basis of a very interesting correlation. As the partial molar excess free energy is related exponentially to the activity coefficient, the trends observable in Table I also exist in Table II but in a somewhat normalized fashion, Although Equation (32) would indicate that at least for a narrow range of temperature'H2E should be a constant, this is not rigorously valid, as can be seen from an inspection of Table I as a function of temperature for any given binary system. In fact the accuracy of determining thermal effects of solutions from vapor liquid equilibrium has been questioned repeatedly in the past. The results obtained by this procedure never do fully concur with independent calorimetric data. Granted then that this procedure is suspect, and bearing in mind that the overall average error of the E data is + 5%, it is best to view the values of AH2 as semi-, quantitative in nature. They are very useful in discerning trends and general patterns but no great significance should be placed on the absolute values. Only with exceedingly accurate vapor liquid equilibrium data can a reasonably accurate analysis of the thermal effect be made. Anderson et al.(7) attribute AH2E to two sources, the physical forces always present which cause a positive thermal effect, and specific interactions or chemical forces which yield negati;ve

contributions to,2 This latter contribution decreases with E increasing temperature, Thus a small AhH2 does not necessarily i.nd:i.cate an i.deal soluti.on but may merely be a balancing of the two effects~ The verification of this last conclusion can be seen in Table III for the amines and alchols in 2 Pentanoneo A positive excess enthalpy also indicates the loss of cohesive energy of the solvent. Upon viewing Table D'T it can be seen that AS2 is less than zero for most of the solutes in water. This may be at;tributed to the fact that the solute motion is more restricted due to specific interactions with the solvent than it was in the pure solute environment~ The negative values of AS 2E for all the solutes but the alkanes in 2,3,4 trimethylpentane are caused by geometric hinderances due to the much larger molecular size of the solvent wit h respect; to the solutes. Other trends due to hydrogen bonding wi-i be presented. in the following discussiono B. Comparison wi.th? L:iterature Data As mentioned in the experimental program, certain of the systems studied were chosen to provide a compari.son between the re-; sults of this work, and data obtained by other vapor liquid equ:ii.L. briurm techniques, The majority of the systems to be compared involve water) as this is a commonly studied liquid~ Copp and Everett(20) in a study correlating activity coefficients of various so:lutes in water have studied the amlnes in water at 250C, They quote the excess free

-93energies of solution as follows: ethylamine, -500 cal/mole; propylamine, 300 cal/mole; and butylamine, 800 cal/mole. As can be seen from Table II, these values agree quite well with the data. Davison, Hood and Harris(22) also studied amines in water. The only data at infinite dilution quoted by these authors is the partial molar excess enthalpy of ethylamine which is given as -6300 cal/moleo While this value differs considerably from that listed in Table IV, only semi-quantitative agreement can be anticipated, as was mentioned, Suffice to say that both values are exothermic and in the region of -5 kcal/mole. Pierotti et al.(81) have studied alkanes in water by static techniques at 25~C, They obtain activity coefficients at infinite dilution for pentane and hexaneo The values are 1,250 and 3,150 respectively as compared to 945 and 2,940 at 20C obtained in this study, This verifies the present work and the conclusion drawn concerning limited solubility in these systems, The system methanolwater has been studied by Brown and Martin(17) and in the International Critical Tables (119) Brown gives Y2 = 2,3 at O"C, while the IoCoTr value at 40~C is y2: 2.6, These results agree quite favorably with the data in Table I, but the thermal dependence appears to be in the opposite direction, More will be said concerning this discrepancy later in this section. Very little data for comparison exists other than the water binary systems. Studies made involving 2 pentanone have all been conducted at constant pressure and are thus unsuited for this purpose,

-94Likewise, no work apparently exists involving 2,3,4 trimethylpentane, However, Kretschmer, Nowakowska and Wiebe(57) have studied ethanol in 2,2,4 trimethylpentane, which is a more common solvent. The results, therefore, while not directly comparable could be useful in at least a qualitative sense, These authors quote an activity coefficient of 31 at 250C, as compared to 28 for ethanol in 2,3,4 trimethylpentane at 20~C, This comparison for similar solvents is quite favorable. Likewise, the data obtained by Kwantes and Rijnders(58) for polar solutes in paraffin solvents can confirm the general validity of the results for 2,3,4 trimethylpentaneo They study oxygenated hydrocarbons in hexadecane at 25^C and 40~C at infinite dilution by GLCo Their results are as shown below. 0 at Solute 250C 40~C Methanol 71.5 45o0 Ethanol 470 30. 5 Propano 310 5 19 5 Acetald ehyde 7 3 6 1 Propionald ehyde 400 3 4 Ethyl Formate 3.7 3o2 Realizing that hexadecane has a longer hydrocarbon chain length but similar polarity properties, the analogy between the above data and that listed in Table I is exceptionally good, As 2,3,4 trimethylpentane has fewer methylenic groups, the corresponding values in Table I should be lower than those given by Kwantes. It should be noted that the trends in the activity coefficient as the chain length increases within a homologous series as well as the thermal effects

-95correspond very well between the two works. In fact for the solutes which do not exhibit association with themselves, the values of the activity coefficient almost completely agree} indicating that the addition of methylenic groups to the solvent has little effect in this case, The remaining system for which a comparison with the existing literature can be made is ethanol-water, As this system is of definite commercial interest much work has been spent studying the vapor liquid equilibrium properties. However, as will be pointed out in the following discussion, a rather large discrepancy exists among the various investigators as to the value of the activity coefficient of ethanol at infinite dilution. The International Critical Tables(1l9) quotes extensive data on this system. From a plot of the data given there, the activity coefficients at various temperatures are as follows: at 20~C, y2 = 4~5; at 40~C, 72 = 6.1; at 55~C, Z2 = 6.8; and at 75~C Y72 = 7.6. They also report the only calorimetric data from which AH2E can be obtained independently. Comparing this data with that in Table I shows reasonable agreement but again the temperature dependence of the two sets are reversed. In 1943, Jones, Schoenborn and Colburn(49) in a careful study also examined this system, The activity coefficients reported by these workers are~ at 50~C, 2= 4.4, while at 60~C, y2 = 5.2. This data, while not agreeing with either the present work or the I.CT. values, does agree with the calorimetric data also presented in the ICoT, However

the interpretation and emphasis given to certain data points in the dilute region is questionable and it is believed that a better representation of the data would yield higher values than those given here, Rao, Acharya and Rao(99) studied ethanol-water by static techniques in the dilute region and obtained the following activity coefficients: at 650C, 72 = 4.8; at 70~C, 72 = 4.3; and at 80C, y2~ = 3,2 The temperature dependence of this work can be seen to correspond to the data of this study. However, the data of Rao et al, exhibit a maximum in the region of three mole percent ethanol, Altsheler, Unger and Kolachov(4) using an equilibrium still have obtained data for this system at extremely dilute concentrations, Unfortunately the data is at constant pressure rather than constant temperature, as is most data available in the literature, However, at 760 mm pressure and an ethanol mole fraction of 0o00043 they report 72" = 3o8. Interestingly enough they too report a maximum in the data occurring at about 0.2 mole percent ethanol, The analysis technique utilized to determine phase concentrations by these workers is rather suspect of possible errors, One final study by Hansen and Miller(38) of this system yielded an activity coefficient value at 25~C of 40,O concurring fairly well with the work of Jones et al, As the above studies would indicate a range of values for 7Y2~ from 4.0 to 6,1 in the temperature region of interest and the present data falls within the upper portion of this range, one might be content to let the situation pass. However, in an attempt

-97to resolve this discrepancy a more extensive study was made of this binary system in which the variation of y2 with mole fraction of ethanol was investigated. This was accomplished with GLC by allowing the water in the column to become partly depleted, while still insuring coverage of the solid support, and by increasing the sample injection size in increments from 0,04 microliters to 1,0 microliters. In this manner the ethanol mole fraction was varied from 7.6 x 10-5 to 0~022. The results of this work are shown in Figure 2. As can be seen, the data can be fitted rather nicely by a smooth continuous curve in the entire region. Thus the value of y2 for any concentration may be obtained by interpolation. Now the above quoted literature values of Y2 are all determined by extrapolating data obtained by static methods to infinite dilution, Generally the most dilute data point is obtained at a mole fraction of 0,02 to 0.03, such as in the study of Hansen and Miller or Jones et al. Now a comparison of their values at x2 = 0.02 and Figure 2 indicate complete agreement, ioe.o, 2 = 3.8 at x2 = 0.02 as compared to 2 = 4o,1 at x2 = 0002 in this study, Being as x2 - 0,02 represented a maximum value for this work and a minimum for the literature studies, it is felt that there is more justification for a smooth interpolation through the data of this study to infinite dilution than a very nonlinear extrapolation of the literature work to zero mole fraction. A word will now be said concerning the reverse trends between this study and the literature data on the thermal effects,

L0 i I I I I I I I I0 9 8 0 4- -- I -_ C.OOO~sO 0 I I I I I I I II 0.00000 0.00400 0.00800 0.01200 0.01600 0.0200 0.02200 ETOH Figure 2. Activity Coefficient of Ethanol in Water as a Function of Concentration in the Dilute Solution Region at 30~C.

-99Again the fact must be brought out that most literature data is for solute mole fractions of the order of 0.02 to 0.05 and higher. From this point excess property plots are extrapolated to a zero value at zero concentration and the tangent-intercept method is used to determine the respective partial excess properties. Careful studies may often indicate devious behavior in these regions, however. Prigogine(94) while investigating the ethanol-water system in the very dilute water region observed inversions in the excess properties curves which would indicate an inverted thermal dependence of the partial excess properties. Also Lewis(64) has indicated that such behavior in very dilute solutions is not uncommon in liquid-liquid chromatography and ion exchange chromatography. Thus it may be that due to the existing data being at essentially high concentrations with respect to infinite dilution, such behavior has not been commonly observed, Further investigations into this area based on molecular concepts could provide fruitful if impractical research, C. Discussion of Thermodynamic Results As most of the discussion concerning the results of this work will accompany the correlation and analysis of the data, this section will be devoted to comparing the resultant thermodynamic properties with those anticipated in the experimental program. Trends and behavior of solutions will be discussed, Also the magnitude of the gas phase nonideality and its effect on the activity coefficient in the present study will be considered. Methods for determining the virial coefficients from other sources will be described,

-1001o Analysis Based on Hydrogen Bonding Theory In the experimental program the classification scheme of Ewell(28) was presented and liquids were categorized into five types. The classification scheme of Pimentel(83) was then shown to be equivalent to that of Ewell if the self associating liquids were grouped into a single class. Thus Ewell's scheme, although postulated on azeotrope formation, is in reality based on hydrogen bonding, as was apparent by this point. Based on this scheme then certain interactions were postulated and anticipated deviations from ideality given. How well this anticipated behavior was substantiated by the present data will now be determined, According to the classification of interactions proposed, the interaction of Class I liquids with Class IV and Class V components should always result in positive deviations from idealityo The data on the alkanes and chlorinated methanes in water adequately bear this out, as shown in Table I. The I-II and I-III interactions are more complex but again should usually show positive deviations, as hydrogen bonds are both broken and formed but the breaking process is predominant. Again, upon viewing the water systems this hypothesis is fulfilled with the exception of the ethylamine-water mixture, In this case association between ethylamine and water must be the important effect. Turning to the Class III solvent, 2 pentanone, its solutions with Class II and Class III solutes should in general have activity coefficients greater than unity due to hydrogen bond breakage. Again this effect is seen to be true with the exception of

-101ethylamine-2 pentanone interactions which deviate negatively from ideality. Similarly Class V solutes form solutions with positive deviations, but this effect is due to physical forces such as dispersion, orientation and induction, rather than hydrogen bonding which does not occur in these solutions. The only interaction predicted to show negative deviations from ideality is the Class III-Class IV solution. However, Table I indicates this to be only partially true for the chlorinated methanes in 2 pentanone. This is most probably due to the formation of weak hydrogen bonds only, the effect of which is overridden by the magnitude of the physical forces. As no hydrogen bonds can be formed with a Class V solvent, all deviations from ideality must be positive or quasi-ideal. The Class II solutes show the largest deviations as hydrogen bonds are broken as the solutes become surrounded by solvent. This can be seen to be the case for alcohols in 2,3,4 trimethylpentaneo For Class III and Class IV solutes no hydrogen bonding exists and the positive deviations are due to physical forces interacting between the solutes and the 2,3,4 trimethylpentaneo The alkanes represent the only true quasi-ideal solutions studied here and the activity coefficients are nearly unity as only very weak dispersion forces exist between solute and solvent, Thus the data very nicely confirms the behavior anticipated according to Ewell's classification. Pimentel's hypotheses concerning the partial molar excess enthalpy will now be tested, bearing in mind that slight contradictions

-102do not invalidate the conclusions due to the uncertainty in the values of nZH2 determined in this study. For water binary systems, Class IV and Class V solutes should form endothermic solutions. Also Class II and Class III solutes should usually form endothermic solutions. From an inspection of Table III these predictions can be seen to hold quite well with the exception of the amines in water. Here again the hydrogen bond formed between the amine and water must be of a particularly strong nature although the trend decreases as the hydrocarbon radical in the amine increases, indicating a decreasing bond strength. The value of AlH2 for all the solute classes in 2 pentanone should be positive, ioe., endothermic solutions, with the exception of Class IV, with chlorinated methanes. Once again the data in Table III for III-IV interactions imply weak hydrogen bond formation between solute and solvent and so the physical forces dictate the solution behavior, As no hydrogen bonding is possible with 2,3,4 trimethylpentane all solutions formed should be endothermic regardless of the solute involved, The data in Table III confirm this postulate very well with the exception of CC14. The reason for this deviation is not understood, From the above discussion the conclusion may easily be drawn that the majority of binary nonelectrolyte solutions are endothermic and exhibit positive deviations from ideality, thus concurring with hydrogen bonding theory.

-1032. Effect of Gas Phase Nonideality The activity coefficient discussed in the above analysis, as has already been mentioned, is actually a hybrid coefficient representing the deviations from ideality in both the liquid and the gas phases. In order to remove the gas phase nonideality, the relations derived in the theoretical development will be used to replace the ideal gas law assumption with the more accurate virial equation of state. However, the resulting expressions for y2 involve the second virial coefficient, Bij, which is not readily available for most pure substances, let alone the interaction virial coefficient B12 o Therefore some means of estimating this property must be utilized. The most general technique available is that of Guggenheim and McGlashan(36) and its extension by Fox and Lamberto(31) The method is based on the theory of corresponding states and expresses the results in terms of reduced properties~ Therefore knowing the critical temperature and volume of a particular component, the virial coefficient may be evaluated at any given temperature, For interaction virial coefficients, pseudo-critical properties are obtained by using the geometric mean temperature and the arithmetic mean of the cube roots of the critical volumes. While this technique works well for nonpolar and slightly polar vapors, it does not adequately represent the virial coefficients of highly polar vapors as are considered in this study. For these vapors the method proposed by Rowlinson(lOO) must be used. This system is also based on reduced properties, but not in the usual sense~ The reduced virial coefficient

-o104is tabulated for two reduced parameters, one a function of the dipole moment, the intermolecular distance, and the minimum potential energy, the other dependent on the minimum potential energy and the temperature, Again for interaction virial coefficients the pseudo-reduced properties based on geometric and arithmetic mean laws are used. At any rate utilizing one of the above two techniques, values of Bij may be determined. Knowing Bij and utilizing Equation (64) the true value of Y2~ may be computed from GLC data. The two correction terms in Equation (64), involving the second virial coefficients, remove the gas phase nonideality. In the present study as both solute and solvent are volatile, in actuality a ternary system exists in the vapor phase. However, in order to determine the magnitude of the two correction terms to the value of y2 as listed in Table I, a worst possible binary system will be chosen typifying nonideal vapor behavior, and this will be used as representative, Although in the present work the carrier gas and the solvent are the two major components in the vapor phase, helium exhibits very little deviation from ideal behavior as has been verified by Desty et al(25) Therefore a solute-solvent binary mixture will be chosen which would be anticipated to be highly nonidealo Such a binary system is ethanol and water~ In this case as both components are highly polar the method of Rowlinson was used to compute B12 and B22 at 40~Co Utilizing these values in Equation (64), the two correction terms amount to - 0~024 or a 2o4% effect on the value of y2 in Table I

-105due to the vapor phase nonidealityo Now as the overall average error in the value of y20 was + 5%, and the present example is a worst possible case, the correction to y2 due to the ideal gas law assumption was neglected in this work. However, it must be remembered that in instances where an alternate carrier gas which is less ideal is used or with long GLC columns for which the mean pressure is a larger value, the effect may become important and the data should be corrected. Also, when data of a higher order of accuracy is obtainable, Equation (69) may be used to obtain the value of B12 and thus study solute-solvent interactions directly by GLCo

VIo CORRELATION AND ANALYSIS OF DATA Ao Empirical Homologous Series Approach In the discussion of the results, it was noted from an inspection of Table I than within any homologous series of solutes at a given temperature the activity coefficient increases with increasing size of the hydrocarbon chain. This fact was also noticeable in Table II, but here the increases were of a more uniform nature. Needless to say, this was not the first time that the relation was noted. Butler, Ramchandi and Thomson(18) while studying alcohols in water observed that a linear increase in the partial molar excess free energy occurred as each additional methylenic group was added to the -OH functional group. Bronsted and Koefoed (16) in their principle of congruence expressed the fact that in paraffinparaffin systems the activity coefficient could be related to the difference in the number of carbon atoms between the solute and the solvent. The constant of proportionality was a function of temperature only, independent of hydrocarbon chain length of either species for the solutions they studied. Copp and Everett(20) extended the work of Butler et alo to include alcohols, amines, alkanes, aliphatic acids and alkyl acetates in water. Much of the data originated from sources already mentioned. The relation noted by Butler was verified for all these solutes in water. In addition Copp and Everett derived other parallelisms for the various solutes in water for more concentrated solutions -106

-107Discussions of the work of Herington(41) have indicated that the above observed linear relation in water binary solutions should not be expected to hold for nonaqueous solvents. The reasons behind this fact will be the subject of discussion in the next section. At any rate as water and 2,3,4 trimethylpentane are two of the solvents studied in this work, an attempt to correlate the data by this technique should prove interesting. In Figures 3 through 11 this correlation for all the solutesin each of the three solvents is presented at 200, 30' and 40~Co An inspection of the graphs showsthat the correlation represents the water binary systems very well and the 2,3,4 trimethylpentane binary systems quite satisfactorily0 However, the 2 pentanone systems, with the exception of the alkanes and the alcohols, deviate considerably from the anticipated behavior0 It is also interesting to note that the chlorinated methanes in water exhibit the same linear relation for the partial molar excess free energy when the number of chlorine atoms is used as the parameter in the homologous series in place of the number of carbon atoms0 This effect is not observable with the other two solvents. B. Homologous Series Approach Based on Group Interactions It has been noted that the 2 pentanone binary systems do not follow the anticipated linear relation described above, and also that such a relation should only be expected to be valid for water as a solvent. The reasons for this behavior can be better understood

CARBON NUMBER 4 5 6 7 5000- ~ Alkane s O Alkyl formates A Aldehydes El Amines 0 4500 V Alcohols 0 Chloromethanes 4000 - 3500 - 0 3000 - 2 3 4 CHLORINE NUMBER D I! I I / I~~~~ G) 3000 o 2500 2000 1500 1000 500 0 -500 - I 2 3 4 CARBON NUMBER Figure 3. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in Water at 20~C.

-109CARBON NUMBER 4 5 6 7 8 5000- * Alkanes O Alkyl formates A Aldehydes 4500 Amines 4500 V Alcohols O Chloromethanes 4000 3500 0-I 3000 I / 8 2 3 4 CHLORINE NUMBER 3000 3 ~~~~~~~20000 / V // q~~~~~~0 2500 2000 - 1500 1000 0 500 0 -500 - I I I I 0 I 2 3 4 CARBON NUMBER Figure 4. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in Water at 30~C.

-110CARBON NUMBER 4 5 6 7 8 I I' I, 5000 - Alkanes G Alkyl formates A Aldehydes 4500 0 Amines q Alcohols O Chloromethanes 4000 3500 - -I 3000 8 I 2 3 4 CHLORINE NUMBER G) 3000 - C 0 25002000 j 15001000 500 -500 0l 0 I 2 3 4 CARBON NUMBER Figure 5. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in Water at 40~C.

-1114 5 6 7 8 I I I I i I I I I I I I I I I I I 1600 - 0 Alkanes O Alkyl formates A Aldehydes 14000 - Amines Z Alcohols 1200 1000 - -I 800 El1 2 3 m 600 0 0 3 400 - o 200 0-200 - -400 - -600 - 0 2 3 4 CARBON NUMBER Figure 6. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2 Pentanone at 200C.

-1124 5 6 7 8 1600 Alkane s O Alkyl formates A Aldehydes 1400 0E Amine s V Alcohols 1200 1000 V 800 0 -4600 118 I> m ~~~~~~~~200~~ ~ ~ 3 0 -200 -400 -600 0 2 3 4 CARBON NUMBER Figure 7. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2 Pentanone at 30~C.

-1134 5 6 7 8 1600 Alkanes O Alkyl formates A Aldehydes 1400 El Amines V Alcohols 1200 1000 -600 E l 800::-200 l 400 A -600 0 1 2 3 4 CARBON NUMBER Figure 8. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2 Pentanone at 40~C.

I 2 3 4 2200 2200 Alkanes O Alkyl formates \ Aldehydes ~~~~~~2000-~~ ~ 13 Amines 2000 V Alcohols 1800 V 1600 1400 1200 - - Ii 8 1000 1 800 - 600 0 400 - 200 - O -0 4 5 6 7 8 CARBON NUMBER Figure 9. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2,3,4 TMP at 20~C.

-115I 2 3 4 2200 * Alkanes O Alkyl formates A Aldehydes 2000 0 Amines V Alcohols 1800 1600 1400 1200.-I 1000 D 800 a o0 600 400 4 5 6 7 8 CARBON NUMBER Figure lO. Incremental Relation Between Excess Free Energy and Molecular Structure for Solutes in 2,3,4 TMP at 30~C.

-1162200 0 Alkanes O Alkyl formates A Aldehydes 2000~ 0G\E Amines |2000~~~~~~~ \ ~~v Alcohols 1800 1600t 1400 1200- 1400 0 4OOG 200 4 5 6 7 8 $ 06 CARBON NUMBER Figure 11 Incremental Relation Between Excess Free Enery and Molecular Structure for Solutes in 2,3,4 TMP at 40~C.

-117by considering the problem on a molecular level and examining the possible interactions which can occur. For a solute molecule D2Y2 and a solvent molecule D1Y1 the possible interactions are as shown. C5 I 1 lI \ / I IC I, / In this case Di represents the nonfunctional hydrocarbon radical and Yi represents the functional terminal group. The possible molecular interactions are represented by C3 through C8. The following treatment is due to Pierotti, Deal and Derr.(82) They assume that the contribution of each interaction to the logarithm of the activity coefficient is additive and dependent only on the number of methylenic groups in the solute and in the solvent. The postulated relation is In >2 = C 3 + C + + (140) The above quoted works of Butler et al.(18) and Bronsted and Koefoed(16) were used to determine the exact form of some of these terms. From

an inspection of Equation (140) and the proposed interaction scheme, certain conclusions may be drawn. For a given solvent C8/Q 1 and C4/O 1 are constants while for a given solute C5/,2 is a constant, Therefore when studying a homologous series of solutes in a particular solvent, many terms are fixed. The various constants in Equation (140) are functions of temperature only, being independent of the number of methylenic groups under consideration. The experimental results of Pierotti have also indicated that slight branching of the Di radical not immediately adjacent to Yi has a negligible effect on 72 o The exact form of Equation (140) applicable to the particular binary systems of interest in this work will now be considered. For the alkanes in water, as no D1 or Y2 groups exist, C5, C6, C7 and C8 are zero and In = CO +Ct9 (141) This is the equation of a straight line and therefore the behavior exhibited in the empirical correlations shown in Figures 3, 4 and 5 can actually be substantiated by the present development based on group interactionso For other solutes in water the C5 term is nonzero and In W = C3 Ca #t C / I (142) However, judging from the linear relations obtained for all the solutes in water the effect of the third term must be of a second

-119 - order. Proceeding in this fashion for alkanes in 2 pentanone, Equation (140) becomes Int \/ a. C Q+C (Pz-' (143) while for all other solutes in 2 pentanone all possible interactions exist and the full form of Equation (140) is needed. The alkanes in 2,3,4 trimethylpentane show the least interactions. They can be represented by I C ( -~, (144) The remaining solutes in 2,3,4 trimethylpentane follow the relation It /z= +-Cs/22+C bo Q^QI)+C 1 8 (145) At this point the reason why the 2 pentanone systems do not follow the empirical correlation should be quite clear. Equation (140) is not a linear relation in'2. The values of C6 used by Pierotti are those given by Bronsted. As the term C6(J 2 - 1)2 is always considerably smaller than the other group interactions, it can be seen that Equations (143) and (145) reduce to a pseudolinear relation in 2 2 This fact is the underlying reason why the alkanes in 2 pentanone and all the solutes in 2,3,4 trimethylpentane show nearly linear relations in the previous correlation, That a linear relation also results for alcohols in 2 pentanone is purely fortuitous,

-120Using the above relations, Pierotti calculated the values of the constants from data obtained by static techniques for many systems. However, two discrepancies exist in his application of the above theory which cannot be resolved satisfactorily. First, he assumes that the interaction represented by C7 is negligible or can be included in the C8 interaction and second, the conclusions drawn concerning the constancy of C8/k 1 and C4/t1 for a given solvent and C5/g,2 for a given solute are disregarded. Now in an infinitely dilute solution the solute molecule is completely surrounded by a matrix of solvent molecules, and therefore no reason can be seen at all for neglecting the C7 interactions, Likewise the second discrepancy is an unnecessary inconsistency. For these two reasons, the constants in Equations (140) through (145) were determined independently utilizing the data of this study, and are given in Table V. These constants are devoid of the discrepancies described above, Since in a given solvent certain terms are constant, most systems of homologous series are over defined, in a mathematical sense, and thus a best fit of the constants is used, Because of this fact, Equation (140) with the constants of Table V actually represents the experimental data only to within + 15%. C, Infinitely Dilute Solution Theory This section will parallel the theoretical development for nonelectrolyte solutions and therefore will consist of two parts, the athermal and the thermal contributions to the activity coefficient,

-121TABLE V CORRELATION CONSTANTS FOR INFINITELY DILUTE ACTIVITY COEFFICIENTS e2 C5 /2 2 In 2 = C + C4 + + C6(2-1) + C7 + C8/1 Solute Solvent Temp. C3 C4 C5 C6 C7 C8 Series Series ~C Alkanes Water 20 1.15 1.14 30 1.58 1.02 40 1.05 1.04 Alkyl Water 20 1.43 1.14 0.24 Formates 30 1.94 1.02 -0.10 40 1.65 1.04 -0.04 Aldehydes Water 20 0.68 1.14 -0.54 30 1.21 1.02 -0.76 40 1.03 1.04 -0.76 Amines Water 20 -3.07 1.14 0.85 30 -2.57 1.02 1.23 40 -2.70 1.04 0.69 Alcohols Water 20 -0.29 1.14 0.14 30 o.35 1.02 -0.44 40 0.06 1.04 -0.27 Alkanes Ketones 20 0.00 0.17 -. 00110 0.42 30 0.00 0.12 -.00115 0.44 40 0.00 0.11 -.00120 0.74 Alkyl Ketones 20 0.03 0.17 0.24 -. 00110 -0.03 0.42 Formates 30 0.21 0.12 -0.10 -.00115 -0.08 o. 44 40 -0.25 o.11 -0.04 -.00120 -0.04 0.74 Aldehydes Ketones 20 0.16 0.17 -0.54 -.00110 0.06 0.42 30 -0.15 0.12 -0.76 -.00115 0.18 0.44 40 -0.46. 11 -0.76 -.00120 0.13 0.74 Amines Ketones 20 2.40 0.17 0.85 -.00110 -2.26 0.42 30 2.47 0.12 1.23 -.00115 -2.45 0.44 40 2.18 0.11 0.69 -.00120 -2.24 0.74 Alcohols Ketones 20 0.72 0.17. 14 -.00110 0.02 0.42 30 0.44 0.12 -0.44 -.00115 0.16 0.44 40 0.49 0.11 -0.27 -.00120 0.07 0.74 Alkanes Alkanes 20 -. 00110 30 -.00115 40 -. 00120 Alkyl Alkanes 20. 85 0.24 -.00110. 08 Formates 30 0.75 -0.10 -.00115 0.13 40 1.04 -0.04 -.00120 o. 06 Aldehydes Alkanes 20 1.25 -o. 54 -.00110 0.12 30 1.09 -0.76 -.00115 0.17 40 1.19 -0.76 -.00120 0.16 Amines Alkanes 20 0.39 0.85 -.00110 0.02 30 0.37 1.23 -.00115 -0.04 40. 65 0.69 -.00120 -0.04 Alcohols Alkanes 20 2.88 0.14 -.00110 0.10 30 2.01 -0.44 -.00115 0.27 40 2.62 -0.27 -.00120 0.16

-122The athermal contribution, as derived earlier, is rather straightforward, However, many variants exist for the thermal contribution, primarily based on the work of Hildebrand, The advantages and disadvantages of each of these variants will be presented, as well as a comparison between the activity coefficient as predicted by the particular techniques and those measured experimentally. 1o Athermal Contribution to Nonideality Since the athermal contribution to the activity coefficient is dependent on the geometry and the spatial orientation and distribution of the solute with respect to the solvent, Guggenheim's treatment based on the cell theory of liquids has been shown to provide the best approach to evaluating this effect. The method is a very plausible one to evaluate geometric dependency, as the cell theory provides a rigid structure for liquids for which definite dimensions and orientations can be visualized. Also this development appears to be the only one for evaluating this effect which has been reduced to a form where practical calculations can be made, Work done in the theory of high polymers considers this type of contribution, but the final results are essentially coincident with the treatment of Guggeheim for a large number of nearest neighbors, The two relations derived from this theory are _~,. or

-123when the solute molecule is smaller than the solvent molecule, and Itm>& - Ir V-i( 5Yi-I)n s. (84) when the solute molecule is larger than the solvent molecule. The results of this prediction for the various solutes in the three solvents are presented in Table VI. As can be seen in the table, the values of ln72ath are always negative indicating that the size contribution to AS2E is always positive. It can also be noted that with the exception of the water binary systems the solute and the solvent have approximately the same molecular dimensions. Therefore a really thorough evaluation of the theory for the athermal effect is not possible. Nevertheless, as it represents the only available method for predicting this contribution to nonideality, the values in Table VI will be used in conjunction with the results of the next section to attempt to predict the infinitely dilute activity coefficients determined experimentally by GLCo 2. Thermal Contribution to Nonideality Two alternatives exist for evaluating the thermal contribution to the activity coefficient. One may either use the work of Hildebrand or one of the later modifications of his work, or the theory of intermolecular forces may be employed. However, even when using the latter technique, analogies to Hildebrand's work must be used to formulate the complete relationship. Conceptually the two

-124TABLE VI ATHERMAL CONTRIBUTION TO THE ACTIVITY COEFFICIENT AT INFINITE DILUTION FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP Water 2 Pentanone 2,3,4 TMP Solute r ln 2th 7227th r in 2th 72 C5H12 6.45 -3.19 0.04 1.09 -.01 0.99 1.42 -.06 0.94 C6H14 7.25 -3.81 0.02 1.23 -.02 o.98 1.27 -.02 0.98 C7H16 8.14 -4.48 0.01 1.38 -.05 0.95 1.13 -.01 0.99 CH2C12 3.53 -1.10 0.33 1.67 -.11 0.90 2.59 -.33 0.72 CHC13 4.43 -1.71 0.18 1.33 -.05 0.95 2.07 -.21 0.81 CC14 5.36 -2.38 0.09 1.10 -.01 0.99 1.71 -.13 0.88 MeFo 3.40 -1.04 0.35 1.73 -.14 0.87 2.70 -.34 0.71 EtFo 4.46 -1.71 0.18 1.32 -.o4 o.96 2.06 -.21 0.81 PrFo 5.43 -2.43 0.09 1.08 -.01 0.99 1.69 -.13 0.88 CH3CHO 3.12 -0.85 0.43 1.89 -.17 o.84 2.94 -.40 o.67 C2H5CHO 4.00 -1.42 0.24 1.47 -.07 0.93 2.29 -.26 0.77 C3H7CHO 4.90 -2.05 0.13 1.20 -.01 o.99 1.87 -.16 0.85 EtAm 3.55 -1.13 0.32 1.66 -.10 0.90 2.58 -.32 0.73 PrAm 4.57 -1.80 0.17 1.29 -.03 0.97 2.01 -.18 0.85 BuAm 5.49 -2.46 0.10 1.07 -.01 0.99 1.67 -. 11 0.90 MeOH 2.24 -0.38 0.68 2.62 -.33 0.72 4.09 -.62 0.54 EtOH 3.24 -0.95 0.39 1.82 -.14 0.87 2.83 -.36 0.70 PrOH 4.15 -1.53 0.22 1.42 -.06 o.94 2.21 -.22 0.80

-125methods are also closely linked, In Hildebrand's original relation, it was assumed that the only solute-solvent interactions occurring in solution were dispersion forces. Although the primary solution interactions are of this type, many other solutions exhibit other interactions due to the polarity of the components. This is especially true of the solutions examined in this work. In the following discussion in order to show the effect of the various modifications, each of the variants will briefly be presented followed by a tabulation which will illustrate the effectiveness of the method in predicting the thermal contribution to nonidealityo The basic relation first postulated by Hildebrand(42) is St), = S, (91) It was postulated assuming a regular solution. Although some theoretical basis can be attributed to its formulation, it is largely empirical being quite closely related to Van der Waals' equation, Nevertheless, it provided a practical method for determining the activity coefficient and worked quite well provided that the solution components were not very polar and no specific interactions occurred, The results utilizing Equation (91) are presented in Table VIIo As the temperature dependence of many of the physical properties are unknown and the values available are at 250C, all subsequent calculations will be made at this temperature.

TABLE VII THERMAL CONTRIBUTION TO NONIDEALITY USING HILDEBRAFND' S FORMULATION FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP Water 2 Pentanone 2,3,4 TMP Solute (1_-2 )2 In yth 7th (62)2 in yth 7th (61-2)2 in yth th C5H12 243 47.7 6x1020 1.96 0.39 1.48 0.09 0.02 1.02 C6H14 243 53.7 2x1023 1.96 0. 43 1.54 0.09 0.02 1.02 C7H16 243 60.2 2x1026 1.96 0.49 1.65 0.09 0.02 1.02 CH2C12 164 17.6 5x107 1.96 0.21 1.23 9.61 1.03 2.80 CHC13 185 24.9 7x1010 0.36 0.05 1.05 5.29 0.71 2.04 CC14 205 33.3 3x1O14 0.01 0.00 1.00 2.56 0.41 1.51 MeFo 156 16.2 1x107 2.89 0.30 1.35 11.6 1.20 3.33 EtFo 180 24.3 4x101~ o.64 0.09 1.09 6.25 0.85 2.34 PrFo 196 32.4 lx1014 0.4 0.01 1.01 3.61 0.59 1.81 CH3CHO 161 15.3 4x106 2.25 0.21 1.23 10.2 0.97 2.64 C2H6CHO 174 21.2 2x109 1.00 0.12 1.13 7.29 0.89 2.44 C3H7CHO 188 28.0 lx1012 0.25 0.04 1.04 4.84 0.72 2.06 EtAm 166 18.0 6x107 1.69 0.18 1.20 9.00 0.97 2.64 PrAm 185 25.7 lx1011 0.36 0.05 1.05 5.29 0.73 2.08 BuAm 199 33.2 3x1014 0.01 0.00 1.00 3.24 0.54 1.72 MeOH 74 5.1 2x102 31.4 2.14 8.50 53.3 3.63 37.7 EtOH 104 10.3 3x104 16.0 1.58 4.86 32.5 3.21 24.8 PrOH 130 16.4 1x107 7.8 0.99 2.70 20.3 2.56 13.0

-127From an inspection of the data in Table VI and Table VII it can be seen that by and large the athermal contribution to nonideality is negligible compared to the thermal contribution. This is true because in most instances the solute and solvent are of the same order of molecular dimensions, However, in solutions usually studied by GLC the solvent is much larger than the solutes and the athermal effect is the predominant one. Such is not the case here, Also by comparing the values in Table I and Table VII, already reasonable agreement is obtained for the 2 pentanone and 2,3,4 trimethylpentane binary systems. This does indicate that dispersion forces are a predominant effect, However, for the water binary systems the predicted values deviate widely from the experimental data. This is due primarily to hydrogen bonding, about which more will be said later. At an early point workers began to realize that in solutions in which the solute or solvent possessed a sizeable dipole moment the Hildebrand formulation was inadequate, In addition to dispersion forces, orientation forces also existed. Van Arkel(ll6) appears to be the first to propose a modification of Equation (91) to account for this interaction, Based on the form of this relation he proposed = RT[(i 92 (92)

-l28The additional term was to account for the dipole-dipole interactions, The improvement gained by utilization of this relation may be seen in Table VIIIo Here the first column for each solvent is the magnitude of the added term while the second and third column represents the entire equation for lny2th including all the terms. By comparison of Table VII and Table VIII the effect of dispersion forces and orientation forces as empirically formulated by Hildebrand's techniques may be ascertained, Generally for water binary systems the orientation forces are about 60% of the dispersion forces, while for 2 pentanone binary systems the orientation effect is usually twice as large as the dispersion forces, The results for the 2,3,4 trimethylpentane binary systems are quite variable but the orientation forces always make a sizeable contribution to the activity coefficient, Utilizing Van Arkel's modification greatly improves the predicted deviation from ideality when compared with the experimental results for 2 pentanone and 2,3,4 trimethylpentane systems with the exception of the alcohol solutes, The values for the water systems, however, become even larger, This further exemplifies the importance of hydrogen bonding and the inability of this technique to account for specific interactions, Also it should be noted that in the present modification it is still impossible to predict a negative deviation from ideality, This will be the topic of the following discussion. Martire(73) in an attempt to account for weak specific interactions proposed a modification of Hildebrand's work which

TABLE VIII THERMAL CONTRIBUTION TO NONIDEALITY USING VAN ARKEL'S FORMULATION FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP Water 2 Pentanone 2,3,4 TMP 2 th th 2 th th 2 th th Solute (w(-Oy) in 12 72 (wl-2) ln 72 72 2) lin 72 72 C5H12 45.6 56.8 5x1024 5.97 1.58 4.86 0.00 0.02 1.02 C6H14 34.3 61.2 4x1026 4.82 1.49 4.44 0.00 0.02 1.02 C7H16 26.0 66.2 1x1029 4.36 1.56 4.76 0.00 0.02 1.02 CH2C12 90.3 27.3 7xl101 4.85 0.70 2.02 2.53 1.30 3.67 CHC13 48.2 31.3 4x1013 5.56 0.82 2.27 1.22 0.88 2.41 CC14 45.6 40.7 5x1017 6.32 1.03 2.80 0.00 0.41 1.51 MeFo 51.8 21.6 3x109 4.63 0.78 2.18 3.34 1.54 4.67 EtFo 29. 9 28.4 2x1O12 3.06 0.52 1.69 3.15 1.27 3.56 PrFo 25.2 36.6 8x1015 3.12 0.79 2.21 2.21 0.96 2.61 CH3CHO 8.58 16.1 lx107 3.87 0.57 1.77 8.12 1.74 5.70 C2H5CHO 3.57 21.7 3x109 0.52 0.18 1.20 5.69 1.58 4.86 C3H7CHO 5.78 28.9 4x1012 0.08 0.05 1.05 4.31 1.37 3.94 EtAm 64.2 24.9 6x110' 6.72 0.90 2.46 1.70 1.14 3.16 PrAm 49.o 32.5 1x1014 5.69 o.84 2.32 1.18 0.90 2.98 BuAm 37.4 39.4 lx1017 5.03 o.84 2.32 0.89 o.69 2.00 MeOH 66.3 9.7 2x104 11.0 2.89 18.0 5.14 3.99 54.1 EtOH 52.2 15.4 5x1o6 9.04 2.48 11.9 3.31 3.53 34.1 PrOH 44.3 21.9 3x109 9.19 2.16 8.7 2.36 2.85 17.3

-130allowed for negative deviations from ideality. The formulation, however, involves an empirical constant which must be determined from independent experimental data, It is only dependent on the solvent and therefore once determined for a given solvent, say 2 pentanone, it is applicable for any solute. In actuality although only one experimental data point was needed to evaluate the constant, as it is still empirical in nature a mean constant was determined by averaging the best constants for each solute in a given solvent, The results of this technique are tabulated in Table IX, Again the first column for each solvent represents the value of J, the empirical constant as defined by Equations (94) through (96), while th the second and third columns represent the entire value of lny2 as obtained from -1e+ - [( a (wX_ J o (93) From the values listed in Table IX for J three definite conclusions can be reached. For the water systems no single correlational constant will suffice to represent the data. This is due to the strong hydrogen bonding role dominating the solution behavior, As the J value is negative for the 2 pentanone systems this indicates that in actuality the systems deviate more positively from ideality than the dispersion and orientation forces alone would predict, Finally, for the 2,3,4 trimethylpentane systems since no

-131TABLE IX THERMAL CONTRIBUTION TO NONIDEALITY USING MARTIRE'S FORMULATION FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2,3,4 TMP Water 2 Pentanone 2,3,4 TMP th t~h th th th th Solute J in y2 72 J in 72 yth J i n y2 72 C5H12 326 - 7.3 7x10-4 -.84 1.72 5.59 0 0.02 1.02 C6H14 367 -19.6 3x10-9 -.45 1.70 5.47 0 0.02 1.02 C7H16 411 -35.1 6x10-16 -.99 1.79 6.00 0 0.02 1.02 CH2C12 128 13.5 8x105 -.33 0.77 2.16 0 1.30 3.67 CHC13 175 7.9 3x103 -.45 0.86 2.36 0 0.88 2.41 CC14 229 3.5 3x101 -.59 1.13 3.10 0 0.41 1.51 MeFo 118 9.3 1x104 -.31 0.81 2.25 0 1.54 4.67 EtFo 171 5.3 2x102 -.44 0.56 1.76 0 1.27 3.56 PrFo 223 - 0.31 7x10-1 -.58 0.62 1.86 0 o.96 2.61 CH3CHO 111 5.6 3x102 -.29 0.60 1.83 0 1.74 5.70 C2H5CHO 149 3.5 3x101 -.39 0.23 1.26 0 1.58 4.86 C3H7CHO 194 - 0.08 9x10-1 -.50 0.12 1.13 0 1.37 3.94 EtAm 130 10.9 5x104 -.34 0.94 2.56 0 1.15 3.16 PrAm 179 7.7 2x103 -.46 0.90 2.46 0 0.90 2.98 BuAm 229 1.2 3x100 -.59 0.94 2.56 0 0.69 2.00 MeOH 56 5.7 3x102 -.15 2.90 18.2 0 3.99 54.1 EtOH 91 6.4 6x102 -.24 2.49 18.2 0 3.53 34.1 PrOH 130 5.6 3x102 -.34 2.19 8.9 0 2.85 17.3

-132specific interactions between solute and solvent are anticipated, J is set at zero. The effect of J for the water systems has been to normalize the data about an activity coefficient of unity, but the spread in the values remains equally as great as in the previous tabulations. The 2,3,4 trimethylpentane systems remain unchanged from Van Arkel's treatment as J is zero. On the other hand, the 2 pentanone systems are predicted more closely to the actual experimental results than in the other modifications of Hildebrand. Nevertheless, this technique is limited by the fact that an empirical constant has been introduced which must be evaluated with at least one independent data point. In an attempt to remove the empiricism of the above correlation and yet maintain the possibility of predicting negative deviations from ideality, recourse will now be made to the theory of intermolecular forces. In the theoretical development, expressions were derived relating dispersion, orientation, and induction forces to the polarizabilities, dipole moments, ionization potentials and intermolecular separation of the solute and solvent, These expressions were then combined by analogy to the generalized form of Hildebrand's equation to yield In >3 = - RT (Z,,t Zz2- Z~t ~1 (106) where Z11, Z22 and Z12 are as defined in Equation (108). As Z12 is not the geometric mean of Zll and Z22, the activity coefficient determined from Equation (106) may be less than unity~ The

-133values predicted by this technique based on intermolecular forces are given in Table X. Arithmetic mean values are used to compute 12 and l2 o From a comparison between Table I, Table IX and Table X it can be seen that the values for the activity coefficients predicted from the theory of intermolecular forces are in poor agreement with the experimentally determined values and therefore do not compare well with Martire's formulation either. As the relation between the activity coefficient and the intermolecular forces was formulated by analogy to Hildebrand's expression and both methods are considering dispersion, orientation, and induction forces, this lack of agreement at first seems strange. This anomaly, however, disappears after further considerations illustrate the two methods not to be so congruent. From a comparison of Equations (104) through (109) it can be shown that not only does Hildebrand use the geometric mean values for Z12 but also for a12 and v12 o As the more common arithemetic mean was used in compiling Table X, the only way to remove the differences between Table IX and Table X would be to equate the two averaging techniques. This implies that 1 = C22 and vll = v22. However, these conditions are not even closely met in the binary systems studied in this work, Therefore the two techniques, Hildebrand's modification and the theory of intermolecular forces, should not be anticipated to produce essentially similar results.

TABLE X THERMAL CONTRIBUTION TO NONIDEALITY USING THE THEORY OF INTERMOLECULAR FORCES FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 293,4 TMP Water 2 Pentanone 2 3 4 TMP zll = 605 Zll = 9.44 Zll - 3.96 Solute Z22 Z12 nyth 72th Z12 n2th h th Z12 Y2 C5H12 6o13 16.74 113 2x1049 5.59 0.86 2.36 4.82 0.09 1.09 C6H14 5.22 13.59 129 ix1055 5.48 0.82 2.27 4.54 0.02 1o02 C7H16 4.58 10.74 146 3x1064 4.77 1.11 3004 4.27 0.00 1,00 CH2C12 14.96 54,60 54.9 8xlo23 10.25 0.42 1.53 6.38 0.66 1.94 CHC13 11,37 34.49 73,8 1x1032 9.02 0.37 1.45 6.14 0o41 1,51 CC14 9~89 19 56 9359 6xlO40 7.41 0.74 2,10 6~05 0,29 1.34 MeFo 16.16 68.76 50 1 6x1021 12.45 0.07 1.07 5.96 0.85 2.34 EtFo 12.47 55~09 68~8 lxlO30 10,49 0.13 1o14 5.73 0.67 1.96 PrFo 9.02 31.95 91o0 4x1039 8.84 0.13 1.14 5.532 0,39 1.48 CH CHO 35592 121.8 57,8 5x1016 16.51 1.17 3023 5.36 2.77 16,0 C2H5CHO 17.85 47 57 64.2 1x1028 12.60 0.25 1.29 5.23 1.38 3598 C3H7CHO 12.16 31.76 82~6 9x1035 10.68 0.04 1o04 5.02 0o91 2,49 EtAm 13587 45.34 57.1 8x1024 10,15 0.01 1o01 6531 0,56 1,76 PrAm 10o11 52.55 76,4 2x103355 864 0.32 1o38 5.80 0O34 1,41 BuAm 6o 06 24 00 94.1 1x1041 7~85 0,00 1,00 5o 57.o 19 o 8 MeOH 23592 94,58 30~0 ixlO13 13.46 0.44 1 56 5,71 1. 12 307 EtOH 15.97 68.66 47.8 6x1020 11,62 0.21 1,24 5.94 0.79 2o21 PrOH 11o52 435 18 67.0 2x1029 9,61 0,22 1,o 25 4.68 0,77 2 16

-135In addition, in determining the dispersion forces which are generally the dominant solute-solvent interaction, the use of Equation (99) was made. As was pointed out in the theoretical development this relation may be in error by a factor of two or three, holding only for molecules with closed sp shells. In an attempt to cope with this problem Finch and Van Winkle(30) have introduced a structural constant into Equation (109) to gain equivalence. An analysis of the present systems under study also indicatesthe need for such a constant. However, as the determination of this parameter is purely empirical and the effect of this empiricism would only reduce the method to an equivalent position with that of the previous technique, no such constant will be introduced. It is doubtful even with the introduction of this constant if the values in Table X could be made to approach the experimental data as well as the results presented in Table IX due to the other factors brought out in the above discussion. At this point three general results have become clear, Due to hydrogen bonding the predictive techniques based on physical forces alone seem to fail when applied to the water binary systems. The modification proposed by Van Arkel seems to fit the data for the 2,3,4 trimethylpentane systems as well as any other correlational technique. From an inspection of Martire's method for the 2 pentanone systems it is clear that as J is a negative value the dispersion and orientation forces alone are insufficient to accurately represent the experimental facts, With these results in mind a final modification

will be proposed which conbines the advantageous features of the previous techniques. As induction forces, although generally negligible, can sometimes be important, Van Arkel's relation will be modified to include this effect. As a geometric mean representation is clearly insufficient for these forces, the form derived in the theory of intermolecular forces will be used, employing geometric mean values for v12 and a12 to insure overall consistency. The resulting expression is = R2 (110) where IoTo is defined by Equation (111). In Equation (110) no empirical constants are employed and providing the induction forces are the deciding factor in solution behavior, even negative deviations from ideality are possible. This formulation represents a very generalized variation of Hildebrand's technique incorporating molecular interactions. As this method should provide the optimum correlational technique the full results are presented for all three solvents in Table XI, Comparing the values of y2th in Table IX and Table XI it can be seen that the results obtained from Equation (110) are in each case at least as good and in most instances much better than those predicted by Martire's method. Therefore the former method is to be preferred as the predictive technique is based solely on theoretical development and necessitates no empirical parameters0 Again, however,

TABLE XI THEORETICAL DETERMINATION OF INFINITELY DILUTE ACTIVITY COEFFICIENTS FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE AND 2, 3 4 TMP Water Solute (61-n2) (x-2) ITo in 2h t2 72 2(xptl. ) 2 2 2 C5H12 243 45.6 18.4 58.1 2x1026 -3.19 7x1024 871 C6H14 243 34.3 1903 65. 7 4x1028 -3.81 7x1026 2582 C7H16 243 26~0 19.8 71.3 ix1031 -4.48 1x1029 7105 CH2C12 164 90~ 3 15 0 28.8 3x1012 -1.10 lxlO12 205 CHC13 185 48.2 16.1 33.6 4x1014 -1.17 7x1013 570 CC14 205 45.6 17.0 43.4 8x1018 -2.38 7x1017 2510 MeFo 156 51.8 14.4 23.0 lx1010 -1.04 4x1O9 17.0 EtFo 180 29.9 17.3 30.6 2x1013 -1.71 4x1012 49 PrFo 196 25.2 17.3 39.1 lx1017 -2.43 1x1016 159 CH3CHO 161 8.58 13.8 17.7 5x107 -0.85 2x107 4.0 C2H5CHO 174 3.57 15 6 23.7 2x1010 -1.42 4x109 16.1 C3H7CHO 188 5.78 16.7 31 3 4xiO13 -2.05 5x1012 68 EtAm 166 64.2 14.4 26.5 3xlOl -1.13 lx11o O0 5 PrAm 185 49.0 15.8 34.5 lxlO15 -1.80 2x1014 2.6 BuAm 199 37.4 16.7 42.1 2x1018 -2.46 2x1017 4 4 MeOH 74 66.3 13.5 10.6 4x10o4 -0.38 3x104 2.6 EtOH 104 52.2 14.7 16.8 2x107 -0.95 8x106 6.3 PrOH 130 44.3 16.1 24.2 3x1010 -1.53 6x109 25

TABLE XI ( CONT 0 D) 2 Pentanone Solute 2 (&812-6~T2). (t n ItT o in 72 Z2 in 72 72 2(xptl) 1 2 72 72 Y2 Y02(xPtlo) C5H12 1.96 5097 o0.o6 1.54 4.66 -0.01 4.6 4.6 C6H14 1.96 4.82 0.00 1.49 4.44 -0.02 4 4 5.6 C7H16 1.96 4.36 0.03 1.56 4.76 -0.05 4.6 6.9 CH2C12 1.96 4.85 =0. 17 0 71 2.04 -0.11 1.8 1 1 CHC13 0.36 5.56 -0.17 0.77 2016 -0.05 2.1 1.2 CC14 0.01 6.32 -0,20 1.00 2.72 -0.01 2.7 32 MeFo 2.89 4.63 -0.12 0o.77 2.16 -0.14 1 9 2,3 EtFo o.64 3.06 0.12 0.52 1.69 -o.o4 1.6 2,3 PrFo 0.04 3.12 0,06 0.53 1.70 -0.01 1.7 3 5 CH3CHO 2.25 3.87 0.20 0.60 1.83 -0.17 1.5 1.9 C2H5CHO 1.00 0.52 0.03 0.19 1.21 -0.07 1.1 2.1 C3H7CHO 0.25 0.08 0.06. 06 1.06 -0.01 1.1 3.3 EtAm 1.69 6.72 -0.14 o.89 2.44 -0.10 2.2 0,5 PrAm 0.36 5.69 -0.20 0.81 2.25 =0,03 2.2 2.6 Bu.m 0.01 5.03 -o,09 o.83 2o30 o0.01 2.3 4,3 MeOH 31.4 11.0 0o09 2.90 18.2 -0o33 13.1 4.8 EtOH 16.0 9 04 =0.09 2.46 11o8 -0o 14 10.2 5 4 PrOH 7.8 9.19 0o06 2. 16 8. 7 -0.06 80 2 5.9

TABLE XI (CONT'D) 2,3, 4 Trimethylpentane 2 2 th th ath o Solute ( 162 2 ()la2) Io T. in 72 72 in y2'2 2 (xpt.) C5H12 0.09 0.00 0.00 0.02 1.02 -0.06 1.0 1.0 C6H14 0.09 0.00 0.00 0.02 1 02 -0.02 1.0 1.1 C7H16 0.09 0.00 0.00 0.02 1.02 -0.01 1.0 1.0 CH2C12 9.61 2 53 0.17 1.32 3.75 -0.33 2.7 2.1 CHC13 5.29 1.20 0.09 o.89 2.44 -0.21 2.0 1. 5 CC14 2.56 0.00 0.00 0.42 1.52 -0.13 1.3 6.0 MeFo 11.6 3.34 0.20 1.56 4.76 -0.34 3.4 5.3 EtFo 6~25 3.15 0.37 1.32 3.75 -0.21 3.0 3.5 PrFo 3061 2.21 0.23 1.00 2.72 -0.13 2.4 2.9 CH3CHO 10.2 8.12 0.55 1.80 6.05 -0o40 4.1 5.1 C2H5CHO 7.29 5.69 0.26 1.61 5.01 -0 26 3.9 4.0 C3H7CHO 4.84 4.31 0 20 1.39 4.02 -0.16 3.4 3.8 EtAxn 9.00 1.70 0.29 1.19 3.29 -0.32 2.4 2.0 PrAm 5.29 1.18 0.12 0.92 2,51 -0.18 2.1 2.2 BuAm 3o24 o.89 0.14 0.71 2.04 -0.11 1.8 1.6 MeOH 53.3 514 0.52 4.02 55.8 -0.62 30.0 39.6 Et OH 32.5 3.31 0.26 3.56 35.2 -. 36 24.6 25.3 PrOH 20. 3 2. 36 0. 20 2.88 17. 9 -0.22 14.3 17. 9

-140the predicted values for the activity coefficients in the water systems are grossly in error due to the hydrogen bonding effect. Thus one conclusion to be drawn from this development is the inability of the technique to properly account for strong specific interactions. For the 2 pentanone and 2,534 trimethylpentane systems the agreement between predicted and experimental activity coefficients is quite good, considering that the only parameters used in predicting the deviations from ideality are the physical properties of the pure componentso Utilizing Equation (70) the optimum thermal and athermal contributions are combined and also tabulated in Table XI, The predicted values for the 2,3,4 trimethylpentane systems concur with the experimental results within an average deviation of 18% while the discrepancy between predicted and experimental values for the 2 pentanone systems is 39%o This discrepancy is larger than that in the 2,3,4 trimethylpentane systems due to the hydrogen bonding effect between many of the solutes and 2 pentanoneo D. Specific Interactions In the above development it became rather obvious that in systems which exhibited hydrogen bonding interactions the theory based only on physical forces was unable to properly predict the deviations from idealityo This is clearly pointed up for the water systems in Table XI and to a lesser extent for the amines and alcohols in 2 pentanoneo The present state of understanding concerning hydrogen bonding allows a very adequate qualitative description of the problem but unfortunately no quantitative analysis has been

-141successful as yet. The problem existing is two-fold, one half of which has been solved. In order to be able to quantitatively evaluate hydrogen bonding effects one must know the strength of the bond involved and the number of bonds formed or broken. The strength of a hydrogen bond, in actuality the energy of formation or dissociation, has been determined by various techniques. Lambert (59) studied association in pure components and binary mixtures by determining the virial coefficients in the vapor state. Assuming an equilibrium between the associated and dissociated states, he computed enthalpies and entropies of bond formations in various polar substances. Becker(11) has used spectroscopic techniques to study polar solutes in nonpolar solvents and determined enthalpies of bond formation from shifts in known spectroscopic lines due to changes in vibrational and rotational frequencies between the associated and unassociated species. Problems, however, exist with both of these techniques. One is not sure if the actual species of interest is the species measured in the vapor state. Also, the effect of the nonpolar solvent in spectroscopic studies is unclear. Suffice to say that the energies of bond formation for both pure component self association and solute-solvent association can be determined. Pimentel and McClellan(83) provide a large compilation of these bond energies. The second part of the quantitative problem is as yet unsolved. The prediction of the number of bonds formed or broken

-142represents a sizeable task, When two self associating components are mixed there are two types of hydrogen bonds being broken and at least a third type being formed, The extent to which bonds are broken and formed depends on the new environment the solution creates for both components as well as the degree of association existing in the pure liquids prior to mixing. Paraskevopoulos and Missen(78) while studying alcohols in CC14, benzene and hexane noted that the partial molar excess enthalpies and entropies of the alcohols were independent of the hydrocarbon chain length in the alcohols and only dependent on the choice of solvent, They studied methanol through octanol, They attributed the positive excess properties to the breaking of hydrogen bonds of the alcohol as the solution was formed, This effect should be predominant as any solute-solvent bonds formed utilizing these particular solvents would be of a weaker nature, Benjamin and Benson(13) in an investigation of the methanol-water system obtained negative values for nAH2E and AS2E This was due to the formation of hydrogen bonds between the methanol and water which were of a stronger nature than those existing in either pure liquid, Although the formal number of hydrogen bonds present must necessarily be reduced when mixing water and molecules with inert hydrocarbon groups, these workers postulated that the mean number of bonds may actually increase due to stabilization of aggregates around the hydrocarbon group, This work was done at higher solute mole fractions and is thus not directly applicable to the present study, The point to be made here is that for a

-143given binary solution in which hydrogen bonding is anticipated to be a major interaction, it is not always clear whether bonds are formed or broken let alone the number of bonds involved which are being formed or broken. Even though the above dilemma exists quantitatively, much can be said concerning hydrogen bonding in a qualitative sense. Prausnitz and Blanks(91) have summed up the above development in the following general rules. For solutes exhibiting self association, as a non-self associating solvent is added hydrogen bonds are broken and a positive partial excess enthalpy results. If the solute is not self associating then as the solvent is added hydrogen bonds are formed and the partial excess enthalpy is less than zero, indicating evolution of energy. Consequently from the net value of AH2_ one may determine whether hydrogen bond breaking or formation is predominant, as was done in the discussion of the results. As mentioned previously, solution behavior due to hydrogen bonding cannot be predicted solely on the basis of bond strengths. Moelwyn-Hughes and Thorpe(77) in a study of hydrogen bonding found that although N-H 4.v 0 bonds are weaker than N-H... N bonds in association, both types formed endothermic solutions, Also, although oxygen is more electronegative than nitrogen, tetrahydropyran mixed endothermally with piperidine. Therefore the nature of hydrogen bonding is not simply predictable and is dependent on other factors besides bond strengths and electronegativity. The local polarizability

of lone pair orbitals appears to be an important factor. Also, hydrogen bonding requires a more precise orientation of the molecules involved than that needed for dipole-dipole interactions. The reasoning put forward in the above discussion can only qualitatively explain the behavior of the water binary systems. In order to bring the predicted deviations as shown in Table XI into closer agreement with the experimental results it would be necessary to postulate the breaking of a number of hydrogen bonds in most cases. For very dilute solutions, the solute is essentially surrounded only by solvent molecules and so any self association would undoubtedly be reduced freeing the solute and solvent molecules within the solution environment, As in the majority of the binaries formed only water is self associating, the effect would not be so pronounced as there are few solute molecules0 However, qualitatively it would appear that consideration of hydrogen bonding should reduce the predicted values into a closer accord with the experimental facts0 Unfortunately, except for this qualitative reasoning no further analysis of the water systems can be made0 Thus it appears that the initial correlation utilizing the empirical homologous series approach is the best method of representing the experimental water systems data of this work0 Although empirical in nature it is felt that the technique, based on the group interaction theory of Pierotti, is justified and in fact very adequately correlates the water systems data0 For systems in which specific interactions are not expected to play a major role, the theory based on physical forces is to be preferred~

E. Statistical Mechanical Analysis Utilizing the principles of statistical mechanics as applied to a binary solution in which the components are of different molecular sizes, the following relations were derived in the theoretical development for the solute at infinite dilution IM~~+t(, RT (135) Ra- RT- 2(-.) (.@- &2) (138) - (,) I(I-,)w + (159) However, as was also pointed out at that time, in order to test the validity of the underlying assumptions made to simplify the mathematical treatment, independent vapor-liquid equilibrium data and calorimetric data should be used. As no independent calorimetric data is available for most of the systems studied in this work,

-146instead an evaluation of the contributions of the various factors to the thermodynamic properties, as indicated in the above relations, will be made, From this result qualitative conclusions regarding solution behavior can be drawn, 1o Geometric Effects The procedure to be followed in this analysis is to use both the activity coefficient and the partial molar excess enthalpy from the experimental results in conjunction with the above three relations to determine three unknowns. The three unknowns in this case are the interaction energy Aw, its temperature dependence, and the partial molar excess entropy, AS2. Let us define three terms as follows CqERI[ - vt+l l~ —) (146) C, 0 RT(.)(-,')(I- v-' ) (147) and C 1 ( \~ 8. 2b (~ @1) tW t 1ad (148) From a comparison of Equations (146), (147), (148) and Equation (139) it can be seen that AS2E may be expressed as 6(Ci+ c, C,- i (149) =-( ( E )H( * (A~E). 2a t,,t C \ 1tr )

-147where C9 and C10 are functions of molar volumes and cubical coefficients of expansion only and C11 is dependent on the interaction energy as wello Thus a clear distinction may be made of the contributions to the partial molar excess entropy by geometric effects and energetric effects, From Equation (135) and the values of the activity coefficient given in Table I, the interaction energy is computed, Then utilizing the data of Table III together with Equation (138) the temperature dependence of the interaction energy is determined. Finally Cg, C10 and C11 can be calculated. As this section is concerned only with the geometric effect, ioe., Cg and C10, the magnitude of these terms as well as the partial molar excess entropy, assuming the interaction energy to be zero, are given in Table XII. Again due to a limited knowledge of the physical properties, all values are for 25~Co An inspection of Table XII reveals a number of interesting facts. The C9T term is negative for all binary systems, As this term is a function of the molar volumes of the solute and solvent alone, it is analogous to the athermal contribution to the deviation from ideality discussed in the earlier correlations, The two terms are both always negative yielding a positive contribution to the partial molar excess entropy. This result is in accord with the theoretical development of the two methods, The magnitude of both the C9T and C10T terms for the water systems is quite large, This is due to the small molar volume and cubical coefficient of expansion of water, Thus the geometric effect for the water systems

TABLE XII GEOMETRIC CONTRIBUTION TO THE PARTIAL MOLAR EXCESS ENTROPY FOR VARIOUS SOLUTES IN WATER9 2 PENTANONE AND 293.4 TMP Water 2 Pentanone 2 93,94 TMP Solute C9T C10T (TAS2E) G C9T C10T (TAS2E)G C9T C10T (TS2E) G C5H12 -2125 -1393 3518 -2 -7 9 -34 21 13 C6H14 -2527 -1389 3916 -14 -11 25 -15 7 8 C7H16 -2980 -1472 4452 -34 -12 46 -4 2 2 CH2C12 -752 -530 1282 -66 14 52 -196 14 182 CHC13 -1148 -642 1790 -23 3 20 -126 0 126 CC14 -1587 -775 2362 -3 0 3 -74 -4 78 MeFo -699 -572 1271 -74 27 47 -215 32 183 EtFo -1160 -736 1896 -20 9 11 -120 11 109 PrFo -1622 -828 2450 -2 1 1 -70 0 70 CH3CHO -580 -572 1152 -98 45 53 -248 55 193 C2H5CHO -953 -650 1603 -39 14 25 -154 17 137 C3H7CHO -1368 -763 2131 -10 4 6 -98 4 94 EtAm -758 -727 1485 -66 45 21 -196 60 136 PrAm -1214 -793 2007 -19 11 8 -114 18 96 BuAm 1652 -918 2570 -2 2 0 -66 8 58 MeOH -255 -229 48.- -206 7 1Q9 -395 -1 396 EtOH -628 -343 971 -88 -10 98 -237 -22 259 PrO[: -1024 o417 1441 -34 -13 47 -147 -30 177

-149will play a major role in the overall excess entropy of the solute. On the other hand, the molar volumes and expansion coefficients of the other solvents are quite similar to the majority of the solutes studied and therefore the C9T and C1OT terms are quite small, often partially canceling each other. Thus it is anticipated that the geometric effect in these binary systems on Ss2E will be of much smaller magnitude. 2. Energetic Effects From the above development the energetic term has been defined as Cll. In actuality this term represents a conglomeration of all the effects, as it is a function of the molar volume ratio and the difference in expansion coefficients as well as the interaction energy and its temperature derivative. Nevertheless, as no method exists to completely isolate the energetic term, Cll will be taken as representative of this effect, In Table XIII, results are presented for the interaction energy and its temperature dependence as well as for C11T, the energetic contribution to the partial molar excess entropy. Also included are values for TAS2, which is the algebraic sum of the two effects. As anticipated from the results of Table XII, the energetic contribution to the excess entropy represents a major portion of the total. Even in the water binary systems the energetic contribution is larger than the geometric contribution. However, the two effects for these systems are approximately the same magnitude. In

TABLE XIII ENERGETIC CONTRIBUTION TO THE PARTIAL MOLAR EXCESS ENTROPY FOR VARIOUS SOLUTES IN WATER, 2 PENTANONE ANT 2,3,4 TMP Water 2 Pentanone 2,5,4 TMP Solute Aw (TdE2 )E AS2E rZn- (TAS,2 E T-AS2E Aw (TAS2E) TEs2E dT dT dT C5 H12 2415 -0,2 -1189 2529 871 5.0 -1004 -995 40 -0.7 170 185 C6iH14 2657 0.8 -2020 1896 951 1.4 -501 -476 80 -0.1 16 24 C7 H16 2888 2,0 -5117 1335 1006 -0.6 161 207 4 -2.1 57577 CH~c12 2076 1.7 -1669 -587 158 -3.4 774 825 1017 2,1 -411 -229 CHC1 2525 3,4 -2965 -1175 150 -9.1 2548 5367 532 0.9 -185 -58 CC14 2692 0,2 -1061 1501 724 -10.2 2891 2894 1493 22.7 -5126 -5048 MeFo 1291 2,5 -1836 -565 746 -7,7 1702 1785 1972 1.4 -510 -127 EtFo 1659 4.5 -5427 -1531 590 -5.5 1419 1450 1231 5.2 -1106 -996 PrFo 1984 5.4 -4506 -2056 775 -5.2 goo go9 909 5.1 -700 -651 CH5CHO 792 5.4 -2085 -951 654 -7,5 1582 1635 2075 6.6 -1245 -1049 C2H5CHO 1501 5.9 -5965 -2560 580 -7.0 1699 1724 1478 5.3 -1075 -955 C35Hf7CHO 1749 6.3 -4762 -2631 779 -16.2 4578 4584 1216 0.7 -161-68 EtAm 209 6.5 -5609 -2124 -445 0.2 -21 0 971 -4.8 846 982 PrAm 833 5.2 -3651 -1644 664 -5.2 819 827 819 5.4 115605 BuAm 1082 4,2 -3341 -771 896 4.4 -1272 -1272 444 5.8 -882 -824 MeOH 552 -1.2 587 871 1856 4.4 -817 -617 5251 7.9 -1144 -748 EtOH 955 0,7 -578 393 1467 5.4 -733 -656 3643 -0.2 98 PrOH 1456 5,2 -2280 -859 1291 3.3 -769 -722 2769 2.1 -554 -157

-151the 2 pentanone systems the geometric effect is completely negligible. As the cubical expansion coefficient of 2 pentanone is nearly equal to that of the majority of the solutes, and the interaction energy for these systems is quite small by comparison to the other binary systems, the energetic contribution is in actuality composed primarily of the temperature derivative of the interaction energy. Thus for 2 pentanone systems the partial molar excess entropy is due mainly to the temperature dependence of the interaction energy, From Table XIII one may also deduce that the energetic effect is predominant in the 2,3,4 trimethylpentane systems. However, in these systems the interaction energy is generally quite large and so the energetic effect is evenly distributed among its components. It is interesting to note that for the alkanes in 2,3,4 trimethylpentane the interaction energy is extremely small implying quasi-ideal solutions, Many other deductions may be reached from an analysis of the results in Table XII and Table XIII and this will be the topic of the following discussion. 3. Solution Behavior Implications The analysis of the binary systems studied by statistical mechanics can shed a good deal of light on the behavior of nonelectrolyte solutions. Wood(l21) has shown on statistical mechanical grounds that the partial molar excess entropy may originate from three sources: (1) difference in molecular volumes of the components of the solution, (2) relative spatial distribution of the molecules about a given reference molecule, and (3) relative orientational

-152distribution of the molecules about some reference molecule. The spatial distribution effect is the smallest of the three and is usually negligible0 On the other hand the partial molar excess enthalpy is strongly dependent on this effect, receives some contribution from the orientational distribution of the molecules, and is completely independent of the first effect. The physical interpretation of the first effect is quite straightforward~ The arrangement of molecules of different sizes is less uniform or more disorderly and so gives rise to a larger number of distinguishable configurational arrangements than would result with molecules of equal size. Thus it should always produce a positive partial molar excess entropy. Although this effect is discernible, it is still usually quite small as can be seen for the majority of the systems in Table XIIo In many instances the thermal expansion effect actually tends toward compensation of the volume differences, nullifying the disorder resulting from a mixed population of molecules, The orientational distribution of the molecules is the largest effect and accounts for 60 to 90% of the total excess entropy according to the results in Table XIII. The orientational effect may be postulated to be due to the degree of mobility which the solute gains or looses in going from the pure liquid to the solutiono If the randomness of orientation becomes greater in the solution than in the pure liquid a positive excess entropy will result, and conversely a negative excess entropy indicates a loss

-153in randomness of orientation in forming the solution, As in Table XIII for the water systems the energetic contribution to the excess entropy is negative, a gain in orientational order in the formation of the solution is indicated. This implies that pure solute and solvent hydrogen bonds are broken and new solute-solvent interactions are formed. Nonbonding solutes are also restrained in the three dimensional lattice formed by the self associated water, This restricts their mobility and increases the orientational order. In the other solvents the results of Table XIII indicate that generally a gain in randomness of orientation occurs from solution formation, implying breakage of any pure solute hydrogen bonding and also the lack of strong solute-solvent specific interactions. Thus the results obtained from a statistical mechanical analysis of the data can be seen to be very useful in explaining the behavior of the binary solutions studied in this work.

VIIo SUMMARY AND CONCLUSIONS The two-fold objective of this work was to determine the thermodynamic properties of infinitely dilute binary solutions, in which both components were appreciably volatile by means of gasliquid chromatography, and to study the behavior of nonelectrolyte solutions with the desired goal of using the data obtained by the above method to formulate a predictive or correlative technique, applicable to a wide range of solutes and solvents, which was based on molecular interactions. In order to achieve the first goal, GLC was first substantiated as a valid method for studying vapor-liquid equilibrium. This fact was established repeatedly in the literature review by a presentation of other studies utilizing GLC for the same general purpose and the resulting comparison with data obtained by static techniqueso That the data obtained represents true equilibrium was further confirmed by a comparison between the results of this work and literature values obtained by conventional methods. For the binary systems for which this comparison could be made the results were very favorable. Finally in the appendix a discussion is provided which explains the concept of the dynamic equilibrium in a chromatographic column and how this type of equilibrium differs from the time invariant static equilibrium~ It is thus felt that GLC has been more than adequately verified as a method for obtaining equilibrium thermodynamic properties of solutions~ To insure that the desired correlations would be valid for a wide range of solutes and solvents, a systematic classification

-155scheme was used to aid in determining the systems to be studied in this work. The classification scheme, which is based on the theory of hydrogen bonding and intermolecular forces, groups liquids into five categories depending on their ability to contribute donor or acceptor atoms or both to a potential hydrogen bond. Utilizing this scheme and considering possible solute-solvent interactions, the solvents chosen for study were water, 2 pentanone, and 2,3,4 trimethylpentane. Homologous series of alkanes, chlorinated methanes, alkyl formates, aldehydes, amines, and alcohols were then studied in each of the three solvents, In order to determine other thermodynamic properties, the studies were conducted at 200, 30~ and 40~Co The upper temperature limit was set by the high volatility of the solvents and the added experimental difficulties which this caused, When studying two component volatile systems by GLC the upper temperature will be one of the limiting factors of the technique. The experimental program consisted of modifying an existing chromatograph to meet the present needs, and then investigating the GLC operating parameters for a range of variables to insure that the results were independent of any effects except for temperature, pressure and concentration, Once it had been verified that the results were independent of these GLC parameters, the experimental data for all possible binary systems was obtained, Each run was repeated both on the same column and in a second independent column to guarantee the precision of the data. The overall accuracy of the data was + 5% based on the mean values of these repetitive determinations,

-156Compilations are presented for the activity coefficient at infinite dilution, the excess partial molar free energy, the excess partial molar enthalpy and the excess partial molar entropy for all the solutions studied, Tha analysis of the data based on the earlier mentioned hydrogen bonding theory shows an excellent agreement between the experimental and the anticipated thermodynamic properties. The GLC variables are related to the thermodynamic solution properties by the following relations RT V m PA (24) Y1sa = ST~ S;s (28), N(,T) (32) and E f pHmt- if z E T\ 6e_ = (27) An attempt was made to correct the activity coefficients for the gas phase nonideality by utilizing the expression c-1 4L_ r. anB, _.7,J a

-157However, as helium was used in this study as the carrier gas the correction for a worst possible binary system amounted to 2.4%o Since this correction was less than the overall accuracy of the data, no attempt was made to incorporate this factor in the results of the experimental work, as the effect is insignificant. When using other carrier gases or higher mean column pressures the effect does become significant and must be taken into account, Utilizing the solution theory for nonelectrolytes, various correlational techniques were attempted to predict the experimental results. As early workers had noticed a linear relation within a homologous series between the partial molar excess free energy and the number of carbon atoms in a solute, this technique was tried with the present data, The results were quite satisfactory for the water and 2,3,4 trimethylpentane binary systems but the correlation failed for the 2 pentanone solutions, The reasons for the success or failure of this homologous series approach can be clearly understood by considering the possible group interactions on a molecular level as done by Pierotti, Applying his general technique but eliminating the inconsistencies, the data was used to obtain the constants in the following relation j C C511-tao -% 0C In = 3 + X7 + C7 + (140) for all the various solutes in the three solventso This technique reproduces the data to + 15%.

-158Alternately the activity coefficients at infinite dilution may be predicted from the theory of Hildebrand and its modifications. The activity coefficient may be expressed as n & - + h e (70) From Guggenheim's cell theory the athermal contribution is given by In b\ = ItY A to in r l(78) o o when v2 > v1 and by o o ath when v1 > v2 In any instance y2 is always negative causing a positive excess entropy. Hildebrand's basic theory as well as early modifications, both theoretical and empirical, are considered for y2th H0 owever, each of these omit some phase of solute-solvent interaction and thus do not represent the experimental data wello The theory of intermolecular forces is employed, which avoids some of the earlier limitations, but does not coincide with the data established in this work. This is partially due to the lack of accurate characterization of the dispersion forces which are a dominant solute-solvent interaction, Therefore a modification of the above treatments is proposed which accounts for all the major physical interactions as follows

-159=At s~-wT( -i ( W-W (110) where I-T _ ib - I_ A, _ tdCA) () and LUm (104) Equation (110) when used in conjunction with either Equation (78) or (84) predicts infinitely dilute activity coefficients which are within 18% of the experimental results for the 2,3,4 trimethylpentane systems and 39% for the 2 pentanone binary systems. This result is quite satisfactory considering that the technique utilizes only the physical properties of the pure components to predict binary solution properties. The above technique predicts results which are in gross error for the water solutions. This is because of the failure of the theory to account for specific interactions such as hydrogen bonding which is so very prevalent in water systems. As the present state of hydrogen bonding theory is yet unable to provide a quantitative

interpretation of the effect, the initial empirical homologous series correlation most adequately represents the experimental results for water solutions. This approach is justifiable based on molecular group interactions, and correlates the data quite wello Thus in synopsis, when strong specific interactions such as hydrogen bonding are absent the above method based primarily on intermolecular forces is to be preferred for predicting activity coefficients, It is better than empirical approaches as the entire relation is theoretically derived and depends only on pure component properties. No such generalized relations exist for solutions which exhibit strong interactions, but for the water binary systems the empirical homologous series correlation very adequately represents the data. A statistical mechanical. analysis of the data based on the lattice theory of liquids leads to the conclusion that the partial molar excess entropy is composed of two effects, the energetic contribution depending on the interaction energy between solute and solvent molecules, and the geometric contribution which depends on the mo].Lecular vol'umes and expansion coefficients of the solute and the solvent. Depending on the sign of the partial molar excess entropy, many conclusions may be drawn about the orientational dish tribution and mobility of the solute in the solution based on the above analysis. The contribution to AS2E from both of these effects, utilizing the data of this work to determine the interacti.on energy, is tabulated for the various systems, Generally the energetic effect is predominant as the molar volnumes of the components studied in this work are quite similar, with the exception of watero

In conclusion then, based on the above findings, the technique of GLC has been justified as providing true vapor-liquid equilibrium. The predictive methods outlined herein may be used in GLC to determine the best solvent to separate a given solute mixture. The activity coefficients may be calculated for each solute-solvent pair and the relative volatility determined by a 0 PB (26) The solvent providing the largest tAB value for a given pair of solutes will yield the best resolution. Usually the best solvent for a given separation is one in which the solute solubilities increase with decreasing vapor pressures. Fortunately in GLC systems of common interest hydrogen bonding does not play the major role so this technique should be very useful in these instances. The GLC technique of establishing vapor-liquid equilibrium is also quite valuable for studying very dilute solutions and in this respect may supplement normal static equilibrium methods. In fact the ability to study very dilute solutions, coupled with the short equilibration time and the lack of need for liquid phase analysis are the primary advantages of the GLC technique. Based on the above considerations it is thus felt that this work has achieved both of its initial objectives.

APPEND ICE S -162

APPENDIX A EXPERIMENTAL DATA TABLE XIV CHROMATOGRAPHIC COLUMN PROPERTIES Run Solvent Run Time T Pi Po F ms mf V No. (WPT) (min) (~cC) (psig) (mmHg) (cc/min) (gms.) (gms.) (cc) 29 W 200 29.5 8.5 730.1 57.72 2.682 2.392 26.15 30 w 164 29.7 8.5 746.0 57.72 2.392 2.259 26.44 31 w 152 30.2 1.3 747.5 48.24 0.177 0.032 4.85 32 w 140 29.5 0.6 745.4 45.90 0.173 0.077 4.87 33 w 156 29.7 o.6 745.9 47.76 0.170 0.034 4.87 34 W 132 30.2 0.7 742.3 46.02 0.175 0.074 4.87 35 w 212 20.8 7.2 737.4 47.94 2.257 2.182 26.31 36 w 208 21.9 7.2 739.0 49.32 2.182 2.111 26.65 37 W 184 21.1 0.5 728.0 49.20 0.151 0.052 4.92 38 w 196 21.0 o.6 727.6 47.64 0.174 0.067 4.87 40 w 188 41.3 7.0 738.5 43.98 2.111 1.969 26.72 41 w 180 40.1 6.9 727.1 44.64 1.969 1.857 26.86 42 w 152 4 0.0 o.g 739.8 38.94 0.188 0.056 4.83 43 w 140 39.8 0.7 739.3 39.36 0.182 0.055 4.85 48 P 180 29.2 0.3 731.5 18.42 0.497 o.186 5.52 49 P 204 30.7 0.3 740.2 18.30 0.500 0.232 5.51 50 P 124 29.4 0.3 743.4 17.88 0.258 0.030 4.64 51 P 120 29.7 0.3 746.1 18.30 0.270 o. o48 4.61 52 P 120 29.7 0.3 747.0 16.92 0.280 0.042 4.59 53 P 120 30.2 0.3 735.9 17.16 0.274 0.043 4.60 54 P 124 31.3 0.3 742.7 18.78 0.288 o.o46 4.57 55 P 128 29.6 0.3 745.1 18.30 0.295 0.069 4.55 56 P 144 29.6 0.3 733.9 6.66 0.294 0.167 4.56 57 P 128 29.2 0.3 737.8 18.06 0.294 o.o68 4.56 58 P 116 29.0 0.3 743.3 15.60 0.291 o.io6 4.56

TABLE XIV (CONT'D) Run Solvent Run Time T Pi F ms mf VG (W,P,T) (min) (0C) (psig) (mmHg) (cc/min) (gms.) (gms.) (cc) 59 P 136 29.5 0.3 736.8 16.38 0.268 0.122 4.61 60 P 152 29.7 0.3 742.5 17.34 0.276 0.148 4.60 61 P 184 29.7 0.3 736.3 18.30 0.296 0.195 4.55 62 P 160 20.6 0.3 734.5 17.34 0.280 0.071 4.59 63 P 184 20.1 0.3 742.4 15.48 0.277 0.091 4.59 64 P 140 19.4 0.3 733.9 18.06 0.277 0.078 4.59 65 p 144 18.9 0.3 740.8 17.64 0.281 0.092 4.58 66 P 148 22.6 0.3 736.1 17.34 0.274 0.102 4.60 67 P 176 20.8 0.3 738.5 17.52 0.281 0.128 4.58 68 P 108 39.8 0.3 739.4 17.76 0.275 0.091 4.60 69 P 104 39.6 0.4 745.2 17.88 0.280 0.114 4.58 70 P 136 19.8 0.3 745.9 17.16 0.271 0.152 4.62 71 P 100 41.0 0.4 732.3 17.16 0.279 0.111 4.59 72 P 92 39.2 0.5 743.4 18.oo 0.276 0.125 4. & 73 P 100 40.8 0.3 738.1 17.10 0.268 0.134 4.62 74 P 104 20.8 0.3 745.8 17.94 0.072 0.047 4.91 75 P 248 20.8 0.3 735.4 25.44 0.4:' 0.036 4.54 76 P 160 41.4 0.3 733.0 24.84 0.429 0.015 4.56 77 P 168 41.0 0.3 744.3 22.50 0.473 0.007 4.51 78 P 116 40.1 0.3 745.0 26.04 0.509 0.001 4.67 79 P 144 40.8 0.3 745.4 23.10 o.486 0.045 4,64 80 T 156 20.5 2.3 740.6 17.70 0.213 0.028 3.99 81 T 152 20.8 0.4 745.1 22.74 0.170 0.007 4.16 82 T 104 30.2 0.3 740.0 19.86 0.158 0.001 4.30 83 T 112 30.7 0.3 735.4 18.30 0.174 0.007 4.21 84 T 112 30.9 0.5 742.4 17.10 0.342 0.192 4.80 85 T 260 41.1 1.1 746.5 17.22 0.352 0.079 4.70 86 T 92 20.4 0.5 745.9 22.74 0.232 0.144 5. ~~~~~~~~~~~~~~~~~~~~~~.16.

TABLE XV SOLUTE RETENTION VALUES Run Solute tR m Solute tm Solute t m Solute t m No. (min) (gms) (mln) (gms) (min) (gms) n) (gms) 29 C3H7CHO 6.80 2.415 C3H7CHO 6.72 2.403 MeFo 5.08 2.539 MeFo 5.08 2.530 C2H5CHO 9.38 2.446 C2H5CHO 9.23 2.428 EtFo 4.33 2.555 EtFo 4.30 2.547 CH3CHO 12.43 2.487 CH3CH0O 12.43 2.467 PrFo 3.91 2.580 PrFo 3.77 2.571 PrFo 3.77 2.564 CH2C12 1.04 2.600 CHC13 0.89 2.596 CC14 0.65 2.590 C5H12 0.58 2.622 C6H14 o.60 2.615 C7H16 0.61 2.606 30 C3H7CHO 6.77 2.266 C2H5CHO 9.28 2.272 MeFo 4.91 2.292 MeFo 4.88 2.297 CH3CHO 12.12 2.281 EtFo 4.13 2.307 EtFo 4.13 2.311 PrFo 3.67 2.315 PrFo 3.63 2.318 CH2C12 1.01 2.330 CHC13 0.87 2.326 00CC14 0.65 2.323 C H12 0.57 2.343 C6H14 o.60 2.337 C7H16 0.62 2.334 31 PrOH 4.88 0.158 EtOH 6.73 0.150 MeOH 7.47 0.139 32 BuAm 4.80 0.146 BuAm 5.17 0.138 BuAm 5.08 0.131 PrAm 2.76 0.126 PrAm 2.63 0.120 PrAm 2.45 0.115 EtAm 2.70 0.111 EtAm 2.93 0.107 33 EtAm 3.75 0.141 EtAm 3.87 0.131 EtAm 3.33 0.122 EtAm 3.00 0.113 EtAm 2.93 0.109 EtAm 2.70 0.104 PrAm 1.92 0.090 PrAm 1.87 0.085 BuAm 2.83 0.071 34 PrOH 4.42 0.153 PrOH 4.38 0.149 EtOH 6.12 0.143 MeOH 7.12 0.135 BuAm 4.75 0.129 BuAm 4.60 0.120 BuAm 6.46 0.112 BuAm 6.25 0.103 BuAm 3.92 0.094 BuAm 3.25 0.089 BuAm 2.83 0.083 35 CH3CHO 20.75 2.185 C2H5CHO 16.58 2.194 MeFo 7.35 2.214 MeFo 7.37 2.211 C3H7CHO 12.45 2.206 C3H7CHO 12.33 2.201 EtFo 6.63 2.220 EtFo 6.58 2.217 PrFo 6.oo 2.225 -PrFo 6.oo 2.223 CC14 0.78 2.228 CHC13 1.16 2.230 CH2C12 1.35 2.234 C7H16 0.74 2.235 C6H14 0.70 2.238 C5H12 0.68 2.241 36 CH3CH0O 21.42 2.115 C2H5CHO 17.17 2.124 MeFo 7.42 2.141 MeFo 7.42 2.143 C3H7CHO 12.83 2.130 C3H7CHO 12.92 2.135 EtFo 6.62 2.146 EtFo 6.60 2.149 PrFo 6.17 2.151 PrFo 6.22 2.154 CC14 0.78 2.157 CHC13 1.18 2.158 CH2C12 1.36 2.160 C7H16 0.74 2.161 C6H14 0.71 2.163 C5H12 0.70 2.167 37 EtAm 7.62 0.117 EtAm 6.75 0.111 EtAm 7.25 0.105 PrAm 4.13 0.100 PrAm 3.72 0.096 PrAm 3.22 0.093 BuAm 6.50 0.087 BuAm 7.08 0.080 BuAm 5.05 0.076

TABLE XV (CONTID) Run Solute m Solute tR m Solute tR m Solute tR m (min) (gms) n) (gms) (min) (gms) min ( gms) 38 r~MeOH 12o25 0.151 MeOH 11o 50 0o130 EtOH lo 47 0o144 EtOH 9~67 0o123 PrOH 8~00 0o137 PrOH 7 ~60 0o117 EtAm 7~83 0o111 PrAm 3o73 0.099 PrAm 4~25 0.095 PrAm 3~37 0o091 BuAm 6~55 0~086 BuAm 5~05 0.081 BuAm 5 75 0~076 40 C 3H7CHO 5~27 1 976 C3H'7CHO 5~ 38 1o 981 PrFo 3~27 2o 016 PrFo 3~27 2. 020 CHBg""O 7.12 1.987 @c 2CHO 7o08 1 993 PrFo 3~25 2.023 EtFo 3~68 2 027 CH3CHO 9~65 1.999 CH3CHO 9o87 2o009 EtFo 3 70 2 030 MeFo 4,43 2.034 MeFo 4~42 2.037 CC14 0o80 2~047 CC14 0.79 2o051 CHC13 0o98 2~057 CH2C12 1.l 2.063 C7H16 0~76 2C068 C6H14 0.75 22074 C5H12 0074 2~082 C 5H12 0.74 2.o088 41 C3H7C'HO 5~72 1.865 C3H7C HO 5.83 70 Pr Fo 343 1.900 PrFo 3~24 1.904 C3HC HO 7 62 7875 C23HCHO 7 67 1.880 PrFo 3 40 1.906 EtFo 3.83 1 910 CH3CHO 10-17 1.885 CH3CHO 10 10 1.893 EtFo 3.83 1 913 MeFo 4 50 1 916 MeFo 4o50 1.920 CH2C12 1.12 1.936 CHC13 1.O0 1.931 CC14 O.80 1.927 C5H12 0.74 1,950 C6H14 0.75 1.944 C7H16 0o77 1o940 42 MeOH 7~67.o165 MeOH 7~50 0o157 EtOH 5.58 0o150 EtOH 5,45 0.143 PrOH 3~73 0o139 Pr OH 3.75 0o135 EtrAm 487 0o117 Et6Am 3o87 o110 EtAm 4~50 o0104 EtAm 3~57 0.100 PrAm 1o92 O.087 PrAm 1o60 o083 PrAm 1o53.0o82 BuAm 2.67 0o070 BuAm 2~67 Oo 064 43 MeOT 7.75 o.155 EtOH 5072 0o147 PrOH 3~78 0o142 EtAm 3o17 o111 EtAm 3~38 0.105 EtAm 3~00 0o101 PrAm 1o93 0o091 PrAm 1o98 0~084 PrAm 2o20 o0.83 BuAm 3~33 0o076 BuAm 3~o8 08072 BuAm 3,12 O,067 48 MeFo 4o08 o.418 MeFo 3o67 O o406 MeFo 3~77 0o395 EtFo 8o 36 Oo380 EtFo 8o17 ~.367 C5H12 1o42 0o271 C5H12 1o38 0,265 C6H14 3~40 0o257 C6H14 3~37 0.246 C7H16 8~08 0~229 C7H16 7~67 0~208 49 C5H12 260 o.473 C 5H 2 2, 58 Oo470 C6H14 6o33 O.458 C6H14 6.08 O,445 CHCi3 10 30 0.396 CH20!2 9o00 0O375 MeFo 2070 o 329 MeFo 2o68 O~320 CH2C12 8.83 0.361 EtFo 5~60 0o311 EtFo 5~53 0o291 EtFo 5~50 0~280 50 C5H!2L~ 1o 32 0.212 1.5H1 o 32 0~,206 C 5H!f2 l 130 0,203 C6H14 3,17 O 193 C6H!4~ 3~05 o.184 07H16 6~62 0o149 C7H!6 4. 00 0o107

TABLE XV (CONT'D) Run Solute tR m Solute tR m Solute tR m Solute tR m No (min) (gms) (min) (gms) (min) (gms) (min) (gms) 51 CH2C12 3.35 0.157 CH2C012 3.38 0.152 C7H16 6.67 0.185 C7H16 6,17 0.168 CH2C12 3.08 0. 140 CEC13 6.62 0.127 C:!;l3 5.42 0.113 52 MeFo 2.08 0.196 MeFo 1.83 0.183 EtFo 3.88 0,171 EtFo 3,66 0.161 C7H16 9'31 0,210 53 CH2C12 7.00 0,222 CH2012 6.17 0.207 54 CH3CHO 1.50 0.243 CH3CHO 1o55 0.237 PrFo 4.20 0.133 PrFo 3.75 0.122 CH3CHO 1.52 0.231 CH3CHO 1.48 0.227 C2H5CHO 3.70 0.217 C2H5CHO 3.30 0.206 C2H5CHO 3.08 0.196 C3H7CHO 7o30 0.178 C H7CHO 5.30 0.159 C3H7CHO 4~75 0.145 55 CH3CHO 1.58 0~265 CH30HO 1.48 0.245 PrFo 6.07 0.180 CHC13 6,38 0o149 CH3CHO 1.45 0,242 C2H5CHO 3,42 0.233 C2H5CHO 3.52 0.226 C3H7CHO 7.25 0.209 C3H7CHO 6.65 0.194 56 CHC13 27.56 0.244 CH:C13 24.38 0.234 CC0014 1717 0213 CC14 16.87 0.205 CC14 14.96 o 195 14 16.38 o 186 0C04 16 09 0.177 57 CC14 9.17 0.227 CC14 7.68 0.202 C014 650 0o.184 CHC13 7 17 0.135 CHC13 4.67 0.120 58 CH3CHO 2 12 0.258 PrAm 3.83 0.187 rAm 3.80 0.179 PrAm 2.60 0o171 PrAm 3.38 o.165 PrAT 3.63 0.155 EtOH 4.75 0.127 59 PrAm 2,92 0.199 PrAm 2.92 0o194 MeOa 3.75 0o182 MeOH 3.67 0.169 MeOH 3.37 0.162 EtOH 6.25 0.153 EtOl 5,81 0o144 PrOH i.67 0.128 60 PrAm 4.50 0o241 Pr Am 4.67 0.235 BuAm 5.33 0.229 BuAm 4 95 0o219 MeOH 4.67 0.200 MeOH 4. 58 0.192 EtOH 7.67 0.181 EtOH 7,25 0o173 61 BuAm 6.83 0.257 BuJAm 6.42 0.241 BuAm 50 o8 0~236 PrOH 22,72 0 221 PrOH 19.40 0,212 EtAm 4.67 0.205 EtAm 4.25 0o201 EtAm 4.67 0.198 62 C-I3CH0 2.30 0.242 CH3CHO0 2.18 0.236 MeFo 2.42 0.208 MeFo 2,33 0.203 C2H5CHO 6.00 0.226 C2H5CHO 5.50 0.213 EtFo 5.00 0.193 EtFo 4~75 0.183 PrFo 7.83 o. 148 PrFo 6.92 0o131 PrFo 6.o8 0.119

TABLE XV (CONT1 D) Run Solute tR m Solute tR m Solute tR m Solute tR m No. (min) (gms) (min) (gms) (min) (gms) (min) (gms) 63 CH3CHO 2.42 0,249 CH3CHO 2.33 0.245 MeFo 2.75 0.224 MeFo 2.75 0.220 C2H5CHO 6.33 0.237 C2H5CHO 6.o8 0.228 EtFo 6.17 0.212 EtFo 5.72 0.202 CH2C12 6.74 0.193 CH2C12 6.72 0.187 PrFo 12.75 0.168 PrFo 10.17 0.153 C3H7CHO 6.67 0.138 64 C5H12 1.42 0.212 C5Hl2 1.40 0.208 C6H14 3.40 0.201 C6H14 3.33 0.193 CI2C12 5.88 0.184 CH2C12 5.50 0.172 C7H16 6.53 0.158 C7H16 5.75 0.148 C3H7CHO 6.42 0.137 C3H7CHO 5.42 0.122 65 C5H12 1.60 0.234 C5H12 1.58 0.230 C6H14 4.15 0.224 C6H14 3.95 0.216 MeGH 5.83 0.205 MeOH 5.08 0.196 C7H16 8.47 0.182 C7H16 7.50 0.166 CHC13 11.50 0.144 CHC13 9.75 0.136 CHC13 8.69 0.131 CC14 6.67 0.117 CC14 4.50 0.103 66 MeOH 6.17 0.227 MeOH 3.50 0.164 CHC13 7.72 0.130 EtOH 8.50 0.184 EtOH 7.75 0.169 CC14 5.53 0.155 CC14 4.83 0o.145 PrOH 13,40 0.113 67 MeOH 5.51 0.236 EtOH 5.84 0.185 EtOH 5.58 0.174 PrAm 2.88 0.167 PrAm 2.46 00163 68 CH3CHO 1.45 0.233 CH3CHO 1.37 0.228 MeFo 1.42 0.202 MeFo 1.38 0.197 C2H5CHO 3.42 0.221 C2H5CHO 3.12 0.210 EtFo 2.83 0.190 EtFo 2.67 0.183 CH2C12 2.92 0.176 CH2C12 2.75 0.169 PrFo 3.67 0.141 PrFo 2.83 0.130 C3H7CHO 4.20 0.158 C3H7CHO 3.70 0.148 PrFo 2.33 0.123 69 CH3CHO 1.23 0.240 CH3CHO 1.20 0.236 MeFo 1.32 0.217 MeFo 1.25 0.214 C2H5CHO 2.97 0.230 C2H5CHO 2.75 0.223 EtFo 2.62 0.207 EtFo 2.48 0o201 CH2C12 2.68 0.194 CH2C12 2.48 0o.184 70 MeOH 6.33 0.238 Me 0W 5.83 0.229 EtOH 12.17 0.216 EtOH 11.00 0 203 71 C5H12 0.87 0.227 C5H12 0o85 0,224 C6H14 1.97 0.219 C6H14 1.83 0,214 C7H16 4.18 0.202 C7H16 3.67 0.194 72 C5H12 0.83 0.228 C5H12 0.82 0.227 C6H14 1.83 0.222 C6H14 1.73 0.219 C3H7CHO 4.0o8 0.193 C7H16 3.88 0.211 C7H16 3.63 0.202 73 MeOH 2.22 0.231 MeOH 1.75 0.225 74 PrOH 5.50 o060 PrOH 5.25 oo058 PrOH 4.88 0 o056

TABLE XV (C ONT' D) Run Solute tR m Solute tR m Solute tR m Solute tR m No. (min) (gms) (min) (gms) (min) (gms) (min) (gms) 75 C5H12 1.70 0.414 C5H12 1.80 0,409 C5H12 1.17 0.259 C5H12 0.80 0.162 C5H12 0. 40 0.058 C5H12 0.29 0.029 C5H12 0.32 0,037 MeOH 5.17 0.365 CH3CHO 2.52 0.399 CH3CHO 2.30 0.389 MeOH 5. o6 0.343 MeOH 5. 01 0.313 CH3CHO 2.28 0.382 MeOH 4.63 0,289 MeOH 4,41 0.269 MeOH 3.78 0.238 MeOH 3.94 o0220 MeOH 4.17 0,199 EtOH 3.02 o0,089 EtOH 2,91 0,074 PrAm O.83 o0.056 PrAm 0.82 0.054 PrAm 0.82 0.053 EtAm 1.10 0,052 EtAm 1.02 0.050 EtAm 1.26 0.046 EtAm 1.10 0.043 BuAm 0.90 0.036 BuAm 1.00 0.035 BuAm 1.10 0.033 BuAm 1.15 0,031 BuAm O,97 00035 BuAm 1.40 0.036 PrOH 2.99 0.030 PrOH 3.17 0.032 PrOH 3013 0,034 76 C5H12 0.58 0.231 C5H12 0.57 0.224 C5H12 0.33 o.o85 C5H12 0.28 0.056 CH3CHO 1.47 0.402 CH3CHO 1.35 O 393 C5H12 0.23 0.026 MeOH 2,08 0.371 CH3CHO 1.35 0.384 CH3CHO 0.23 0.015 MeOH 2.57 0.348 MeOH 2.53 O 335 o EtAm 2.17 0.213 EtAm 1.67 0.198 EtAm 1.75 0.186 BuAm o.96 0.115 BuAm 1.07 0.100 BuAm 1.10 0.0o93 77 C5H12 1.08 0.441 C5H12 1.00 0.401 C5H12 0.90 0.350 C5H12 0,75 0,275 CH3CHO 1.78 O.469 CH3CHO 1.80 O.467 C5H12 O.53 0.164 C5H12 O.35, 073 CH3CHO 0.23 0.008 PrAm 3.33 0.462 PrAm 3.33 0o.459 PrAm 3.20 0.453 PrAm 0.35 0.023 CHC13 10.39 0.340 CHC13 7.60 0.230 CHC13 5,08 0.179 CC14 2.60 0.140 CC14 2.33 0.110o CC14 2.05 o.o86 78 CH2C12 4.28 o.462 CH2Ci12 3.78 o.430 CHC13 8.25 O.331 CHC13 7 O0 0.265 CH2C12 3.88 0.397 CH2C12 1.67 0.159 CHC13 5,75 0.212 CHC13 4.27 0.173 CH2C12 1.58 00150 CH2C12 0.90 0.077 CC14 2.22 0.121 CC14 1083 0.106 C3H7CHO 1.05 057 C3H7CHO 0. 92 O. 043 CC14 1.58 O. 084 MeOH O.33 o, 023 C3H7CHO 0.93 O. 037 MeOH 0.18 o. 001 EtOH 0. 32 0.015 EtOH O 30 ~ 013 EtOH 0 32 0. 011 79 CH3CHO 1.50 o.438 CH3CHO 1,66 o 422 MeOH 2.75 0.o 366 MeOH 2, 48 O.343 CH CHO 1.70 o0,414 MeOH 2,53 0.327 MeOH 1.17 0.136 MeOH 0.90 0,098 Me30H O.87 o.og4 MeOH 0.61 0,070 MeOH O. 67 o0o66 MeOH O,57 0.052 MeOH 0,53 0,046 MeOH 0.52 0o0o45 PrOH 8.23 0.283 PrOH 7,57 0,239 PrOH 6~50 o0,196 PrOH 4.25 o0,160 PrOH 2085 0o0o86 PrOH 2,72 0.078

TABLE XV (coNTID) Run Solute tR i Solute tR i Solute tR i Solute tR i No. (min) (gis) (minn) (gins) (min) (gs) (in)s) 80 CH3CHO o.6o 0,172 CH3CHO 0.58 0.167 Pr OH 2.80 0.113 PrOH 2.75 0.109 CH3CHO 0.58 o.i66 C2M5 C HO 1.58 0.161 PrOH 2,70 0.101 EtFo 1,32 0.089 C25ICHO 1.57 0.158 C2I5CHO 1.55 0.155 EtFo 0.087 EtFo 0.085 C3H7CHO 1.25 0C1H77 c3CH0 1.00 0o.140 PrFo 3,33 0,080 PrFo 3.17 0,071 C3H7CiO 3.83 0.131 PrFo 3.17 0o069 C5H12 1.50 oo64 C5H12 12 o,6 C 5 -T-1 2 1.38 0.058 C6HI1 3.75 0.052 C6H14 3,32 o0o16 C7Hi6 7,92 0.035 81 c5Hl2 2.55 0.135 051112 2,112 0.131 c5Hl2 2.35 0.126 EtAm o.6, 01211 EtAm 0.63 0.120 EtAi 0,63 0.117 PriAm 1.65 0.109 PrAm 1,6o oio6 PrAm 1.58 0.102 Bu.Am 5.28 0.095 BulAm 5.00 0.088 BuAm 4175 0.081 CH2C12 0,90 0,076 CH2C12 0,88 0.074 CHC13 2,22 o.o69 CHC13 2.00 o.o65 CH12C12 0.88 0.072 CHC13 2.02 o.o6i ce14 1,20 0.058 CC14 0,97 0.055 ca14 0,97 o.054 c6Hi1 2,67 0.0117 c6H14 2.42 00113 c6H14 2,25 o.o11 C7H16 5.25 0.031 C7H~16 11,67 0.022 C7H16 3.18 0.017 C7Hi6 2,50 0.012 v' 82 C2H5CHO 0.78 0.100 C2H5CHO 0,78 o.o98 C5H12 1.75 0.121 C512 1.68 0.115 C2H5CHO 0.80 0.095 37CHO.68 0,092 C5H12 i.68 0.110 PrOH 1.37 o.o6o C3H7CIC0 1.75 o.o86 C3H7CHO 1.75 0.082 PrOH 1,13 0,057 PrOH 1.30 0,052 MeFo 0.32 0.019 EtFo 0.50 0.031 EtFo 0.50 0,032 EtFo o.48 0.031 PrFo 0.85 0,028 PrFo 0.87 0,023 Pr-Fo 0.82 0.021 PrFo 0,78 0.018 C6Hl~14 00.75 0,015 06Hl4 0. 0.012 C 6H1 4 0. 7 0.011 C7Hl6 1,08 0.008 83 C5 12 2.12 0.138 112 223 06134 H12 02 0.013 C Cl3 3,12 0,118 5ii2 5 ~~~~223 0131 C5H1 1 CH2Cl2 1.28 0.131 CHi2C12 1.28 0,128 CHC13 3.05 0.110 CHC13 2.95 0i11 CH2C12 1.27 0.121 CC14 1.13 0.101 CC14 1.13 0.098 CC14 1.17 0.096 PrAm 0.97 0.072 Pi-Ai 0.93 o.o69 BuAm 3,00 0.063 BuAn 3.05 0.057 BuATn 2.75 0,051 c6H11 2.05 0.0112 C6H141 1.92 0,038 C`116 4,152 0.030 C7IH16 3.67 0.023 Y- 71H16 3,17 0o016 81 Cin3CH-0 0.73 0,290 CHCHO 0.72 0.286 C5H12 7 0,02 11112 0,291 84 3H,7 020 3 05 5 C'3OHO o.6 0,281184 C3CO o.65 0.282 512 2,77 0,199 C5H12 2.75 0.191 CH3CHO o.65 0.281 CH 3 C0 o.65 0,277 MeOR 0.58 0,263 MeOH o.58 0.262 G2HSudO 1.77 0.273 c2 117H0 1.77 0.270 MeOH1 0.58 0.260 EtOH 1.30 0.258 CH5CHO 17 0.266 Et0 1 0.7 255 EtO 1.25 0.252 MeFo 0.80 0.250 MeFo 0.80 0,217 MeoF 0.80 0,244 EtFo 1,95 0.,240 Et-Yo 1.87 0,237 EtFo 1.83 0.233 DL 1.02 0.231 EtAn 0 o0,8 0,92 EtAm 0.95 0.221 Et-An 0.95 0,222 Pt?-Crrn 2,32 0,213 PrAm 2.20 0.209 PrAm 2.22 0,205

TABLE XV (C ONT' D) Run Solute tR m Solute tR m Solute tR m Solute tR m No, (min) (gms) (min) (gms) (min) (gms) (min) (gms) 85 C H12 3058 0. 319 C H12 3~ 57 0.312 C H12 1.33 0. 093 C H12 1 o18 0,086 C~3CHO o.60 0.309 Cf3CHO O.60 0.307 C5H12 1.13 o.o83 MeOH 0o57 0,305 CH3CHO o.60 0o.306 MeOH 0.58 O.304 MeOH O.57 O.303 MeFo o.83 O 300 MeFo 0.78 0 ~299 MeFo 0 77 0.298 MeFo 0 77 0,296 EtAm O o 93 0,294 EtAm 1.03 0.2 92 EtAm 1o 02 0 o 290 EtAm O 0 97 0.o 288 PrAm 2~ 10 0 2 84 PrAm 2.07 0.282 PrArn 2000 0,278 EtOH 1008 0.275 EtOH 1005 0,274 C2H5CHO 1.33 0,270 C2H 5CHO 1.37 0.268 EtOH 1.00 0.273 EtFo 1.70 0.263 C2H5CHO 1.35 0.266 EtFo 1.58 0.261 EtFo 1.65 0.258 CC14 1,55 0,255 CH2C12 1062 0.248 CH2C12 1.62 0.245 CC14 1,53 0.253 CC14 1.50 05 CH2C12 1.55 0,243 PrOH 2.57 0.235 PrOH 2e33 0.232 PrOH 2043 0 C3H7CHO 3.18 0.224 C3H7CHO 3. 07 0.219 PrFo 4 00 0.209 PrFo 3.75 0 204 C3H7CHO 2.95 0.214 PrFo 3.65 0.199 CHC13 3.37 0.194 CHC13 3.28 0.189 BuAm 4.72 0.178 BuAm 4o 52 O.165 CHC13 3030 2o e18 5 C6H14 5.o8 0.158 C6H14 4.75 0.151 C6H14 4.53 0.145 C7H16 12.18 0,130 C7H16 11.67 o.116 C7H16 10.75 0.101 86 C5H12 3.75 0.204 C5H12 3.75 0.199 C5H12 2.78 0.153 C5H12 2.85 0,150 MeOH 0.60 0e195 MeOH 0060 00193 Me OH 0 62 0.192 MeOH o0,60 o 191 MeFo.7o o189 MeFo 0o 75 0188 MeFo 0 73 0o187 MeFo O 0 73 0.185 EtOH 1032 o.183 EtOH 130 0.181 EtOH 1o 30 00179 EtOH lo 30 0,177 PrOH 3.58 0.174 PrOH 4.o03 0.168 PrOH 3.75 0o162 PrOH 3070 0,157

APPENDIX B EXPERIMENTAL DETAILS From the discussion in the experimental program, the main experimental difficulties seem to center around the possible adsorption of the solute, and the determination of the gas phase volume. In addition, working with solvents of appreciable volatility caused a number of problems both in detection, as has already been discussed, and in the actual column operation. Therefore these effects will be discussed here in detail and the methods of alleviating these problems outlined. The adsorption of the solute can occur in three ways, all of them undesirable. The solute may be adsorbed on the column walls, by the active sites on the uncovered support, or by the solvent itself rather than being absorbed, The possible effect of adsorption by the column metal itself has been investigated by Beckman and Bevenue.(12) These authors studied columns made of copper, stainless steel, aluminum and quartz, The percentage recovery of halogenated hydrocarbons was determined in each of these columns. Although quartz had the lowest solute retentivity, aluminum was the best metal investigated. The experience of the present writer in adsorption of trace hydrocarbon constituents also indicates aluminum to be the most preferrable choice for column material, Therefore in the present study all columns were constructed of aluminum. The possibility of solute adsorption by the solvent surface has been discussed in the main portion of this works Based on Funk -172

-173and Houghton's penetration factor,(34) the possibility of solvent adsorption was seen to be highest for very low solvent coatings on the solid support. As in the present study only coatings greater than 15% w/w were used to obtain experimental data, the possibility of solvent adsorption should be minimized. Also static equilibrium studies conducted with the solvent in bulk phase or coated on a solid support gave the same result, as described earlier. If solvent adsorption had occurred this result could not have been reached. Finally the works performed which indicate the possibility of this effect (71,72,79) also indicate that upon utilization of a more inert support the effect very noticeably decreases or becomes negligible, From the above reasoning it can be concluded that the possibility of solvent adsorption effects occurring in this work is quite minute, On the contrary to the preceeding conclusion, the effect of solid support adsorption is a very real and probable event. Thus care must be taken to insure that this effect does not interfere with the experimental results, In this respect one must utilize the most inert support possible and be sure that the entire surface is covered with solvent. Scholz and Brandt(l05) have investigated solid support effects and concluded that at least 10% w/w minimum coating must be used to nullify solid support interactions, This is due to the hydrogen bonding sites which exist on most diatomaceous earth supports in the form of silanol and siloxane groups. They concluded that the flux calcined diatomaceous earth support is to be preferred for oxygenated or polar solutes in nonpolar solvents, Perrett and Purnell(8r) have

-174investigated the possibility of reacting the hydrogen bonding sites with hexamethyl disilazane (HMDS) to deactivate them according to the following reaction (C H3gSi NHSi(C a+ (. oH) —-2, aH o3]+ N Hz The resultant support shows much less adsorptive tendencies and the pores of the support remain unaffected, In order to insure total surface coverage of the support, investigations have been conducted of the surface and pores of the support particles by Janak and Staszewski(48) and Smith.(l07) These investigators used electron microscopy to study the surface coverage for various percentage liquid coatings. They conclude that the interstices are essentially filled with solvent for a 20% w/w coating and that the solvent is uniformly distributed over the surface in multilayer coatings providing complete coverage. Thus the possibility of uncoated support with a 20% w/w solvent loading seems very unlikely, Sawyer and Barr (104) in a very exhaustive investigation of solid supports studied Chromosorb R, Chromosorb W, Glass Beads, Carborundum, Stainless Steel, Nichrome, and Fluoropak 80. They measured retention volumes for all types of solutes both in an empty column and a column packed with the uncoated supports. Their conclusion was that the most inert possible support was Fluoropak 80. Based on the above studies and considering the solvent polarity and wetability of the various solid supports, the following supports were chosen for this study: water - Chromosorb W, a flux calcined diatomaceous

-175earth was used; 2 pentanone - HMDS treated Chromosorb W, as described above, was employed; and 2,3,4 trimethylpentane - Fluoropak 80, a teflon polymer, was chosen as the most inert support. With these supports and the studies conducted concerning the effect of GLC variables, it is felt that the results of this work are devoid of support adsorption effects and are true equilibrium values. The determination of the gas phase volume, although a minor consideration, has attracted attention due to the general inaccuracies connected with its determination. Stalkup,(110'111) attempts to determine VG by the retention time of an unretained component and by calculation based on column geometry and system dead volume measurements, and gets poor agreement. When using a katharometer detector the normal unretained component studied is air, However, as air is not chemi-ionized in the flame ionization detector some other component must be chosen. Smith(l06) has pointed out that the substance generally employed, methane, is actually retained, in some instances quite well, and thus should not be used for this purpose, For the solvents under consideration in this study methane is partially retained and so can not be used. To circumvent this problem a somewhat different technique was utilized in this work, As the solubility of helium in pure hydrocarbons is quite low, pure methane was employed as the carrier gas and a small sample of helium was injected. The helium essentially preferentially displaced a momentary slug of methane which was registered by the flame ionization detector, As the helium is unretained by the

-176solvents of interest this method should provide a true determination of the gas phase volume. A second method of determining VG consisted of using an empty column of known dimensions and measuring the retention volume of methane. From this value the system dead volume may be determined. Then for a given column knowing the dimensions, the density of the solid support, and the density of the solvent, the value of the gas phase volume may be computed. Utilizing the above two procedures carefully, the values of VG obtained in each case were coincident with each other. Therefore in the experimental program, as utilizing pure methane carrier gas presents a safety hazard, the geometric method of determining the gas phase volume was employedo The distinction of this work from that of previous investigators was the thorough investigation of two component volatile systems by GLCo Concomitant with this distinction are the added experimental problems incurred with the utilization of a volatile solvent, Three general methods exist to cope with such a situation~ The first and simplest technique consists of reducing the operating temperature to some subambient value where the solvent volatility is also reduced and obtaining the data at this temperature, This approach was attempted by Porter and Johnsono(90) The partial molar excess enthalpy data is then assumed constant and the results may be extrapolated back to the temperature region of normal interest. Two problems existing here are the long retention times at subambient temperatures and the constancy of AlH2E The first is avoided by

-177utilizing a low percentage coating on the support but then solid support effects arise again. Thus the technique has basic limitations which are not, however, insurmountable. An alternate approach also put forward by Porter and Johnson88 is designated as circular GLCo In this method the inlet and outlet of the column are joined by a peristaltic pump and the carrier gas is constantly recirculated. In this manner the carrier gas becomes saturated with solvent and the remaining solvent remains in place on the support. In fact the support may be coated in situ by this technique but the uniformity of coating is questionable. The main disadvantage of this method is that the solute never elutes from the column but is constantly recirculated until it becomes an integral part of the carrier gas. Thus if it is desired to remain near infinite dilution, every few solute injections the system must be emptied out and replaced with a new solvent charge. The method actually employed in this study is that of Kwantes and Rijnders,(58) In this approach a forecolumn is inserted into the flow system prior to the sample injection point. The purpose of this forecolumn is to presaturate the carrier gas with the solvent of interest and reduce "bleeding" in the main column. The presaturator packing is support material coated essentially at saturation with the solvent, The presaturator column is then thermostated at the same temperature as the main column so as to avoid solvent build up in the main column. The method is quite effective

-178but not perfect, as the associated pressure drop across the main column changes the carrier gas saturation conditions and some solvent still is depleted. Thus as this latter technique seemed to have fewer limitations, it was chosen as the preferred method,

APPENDIX C PHYSICAL PROPERTIES OF MATERIALS A short discussion of the various physical properties of the solutes and solvents employed in this study seemed in order as often these are derived properties rather than those directly measurable and tabulated in the common sources. The complete tabulation of all the properties discussed below is given in Table XVIo A word will now be said about the origin of each of these properties. Essentially all the values in Table XVI are at 25~C or very near this value. The dipole moments tabulated there have been taken from the compilations of Wesson(120) primarily and (63) LeFevre The values of the ionization potentials for removal of the first electron from the molecule are from the work of Field (29) and Franklin. 9) In order to compute the cubical coefficient of expansion the variation in density of the component with temperature over a small region was needed. This data was obtained from Dreisbach (25) Friend and Hargreaves, (33) and Hodgman (46) Hildebrand's solubility parameter is defined as the energy of vaporization per unit volume. To compute this quantity heats of vaporization and molar volumes were determined from Hodgman,(46) Dreisbach(25) and Washburn~(119) The polarizabilities proved to be the most difficult property to ascertain. Some values were available from investigations by Smith(108) and Stuart (114) These values are determined by secondary methods from experimental data. An attempt was made to -179

TABLE XVI PHYSICAL PROPERTIES OF MATERIALS PxlO3 T E Z/Hval I v O 1 a x02 Material (OC —) 9Yi (Debye) (cal/m) (ev) (cc/mole) (AO) (cal/cc)2 (cc/mole) Water 0.21 100.0 1.85 78.5 539.6 12.67 18.0 2.6 22.5 1.5 2 Pentanone 1.20 10303 2.71 15.5 90.0 9.59 106.1 5.6 8.3 9.9 2,3,4 TMP 1.27 113.6 0.00 2.0 68.4 9.90 165.1 6.4 6.6 16.2 MeOH 1o26 6407 1o66 32.6 262.8 10.88 40.4 4.0 13.9 3.2 EtOH 1.08 78.4 1.74 24.3 204.3 10.60 58.4 4.5 12.3 5.3 PrOH 0o96 97.8 1.65 20.1 164.4 10.42 74.7 4.9 11.1 7.3 EtAm 1.83 16.6 1.28 6.9 146.0 9.32 63.9 4.6 9.6 6.8 PrAm 1.47 48.5 1.26 5,5 120.2 9.17 82.2 5.0 8.9 8.7 BuAm 1.38 77,8 1,20 5.3 104.9 9.19 98.8 5.3 8.4 10.7 CH CHO 1.74 20.2 2.70 21.1 136.2 10.28 56.2 4.5 9.8 4.4 C2H5CHO 1.44 48.8 2.54 18.5 118.8 10.06 72.0 4.9 9.3 6.3 C3H7CHO 1.32 75-7 2.57 13.4 104.4 10.01 88.2 5.3 8.8 8.3 MeFo 1.56 32.0 1.77 8.5 112.4 (10) 61.2 4.5 10.0 5.6 EtFo 1.42 54,3 1.94 7.2 97.2 (10) 80.2 4.9 9.1 7.5 PrFo 1,27 81,3 1,89 7.7 88.1 (10) 97,8 5.3 8.5 9.5 CH2C12 1,40 40o7 1o55 9.1 78.6 11.40 63.6 4.7 9.7 6.5 CHC13 1.27 61.3 1o27 4.8 59,0 11,35 7907 5.0 8~9 8.2 CC14 1.22 76.7 0.00 2.2 46,4 11.10 96.5 5.3 8o2 10.5 C5H12 1o66 36 1 O00 1.9 85.4 10055 116.1 5o5 6.9 10.4 C6Hl4 1o147 68~7 0.00 1.9 80.5 10,43 130.5 5.8 6.9 12,0 C7H16 1.38 98,4 0.00 1. 9 7605 10.35 146.5 6.1 6.9 13.9

-181determine the remaining values employing the commonly accepted Clausius-Mosotti relation, which is dependent on the dielectric constant, The values of the dielectric constant were obtained from the tabulation of Maryott and Smith(75) and the polarizabilities calculated. Due to the highly polar nature of the majority of the materials involved, the relation failed miserably when compared with the available experimental values. Therefore the method of computing polarizabilities by summing the contributions of the individual bond polarizabilities as outlined by Hirschfelder, Curtiss and Bird(44) was used. The calculated results agreed very well with the above experimentally determined properties, The intermolecular distance between molecules i and j was determined as suggested by Hirschfelder et al.(44) using critical volumes as tabulated by Hodgman(46) and Langeo(60) This method may be questioned as the constant of proportionality varies from author to author. However, at least the method used here is consistento All other commonly determined physical properties were obtained from Dreisbach, (25) Hodgman,(46) Lange (6) and Washburn (119) In addition to those properties listed in Table XVI a knowledge of the variation of vapor pressure with temperature was needed, Graphs with this information were very excellently compiled by Jordan(50) and so are not reproduced here.

APPENDIX D DATA PROCESSING AND EVALUATION METHODS The actual process for determining m Y VG i VR, j E E E VR G2 A RZH2E and aZS2 will be outlined in detail both in principle and with a sample calculation. The method for determining the thermal contribution, including dispersion, orientation and induction forces, will also be presented and substantiated with numerical results. Finally the technique for obtaining the interaction energy based on statistical mechanics and its temperature derivative will be delineated, The constants for Pierotti's homologous series correlation will also be determined. As the ethanol-water system has been used as an example system previously at 40~C, it will again serve the same purpose. From Table XIV, consider Run 42. Knowing ms and mf and the time of the run and assuming a linear rate of solvent depletion the value for m at any given time in the run may be calculated. Specifically the rate is 0, /I - o, o0 - 0008-79 s/,h =ate -0O7/ i Now from the actual chromatogram for EtOH, the time of emergence of the peak maximum was 52 minutes after the run had begun so m = O, 5.- (5'a) (.o 0-7 )= 0,/+ 39 5 -182

-183which is the value tabulated in Table XV along with the retention time. This is how m values were computed. To determine VG - the sum of the void volume within the column and the system dead volume, as ascertained according to the method outlined in Appendix B, is calculated. C = \ Ci A \o lu me+ 5sr, Lead o0lume The system dead volume of the F and M Model 609 Gas Chromatograph as modified was 2.36 cc. The internal volume of the six inch aluminum column was 2.89 cc. As the density of the Chromosorb W was 2.30 gms/cc and the water was 1.0 gms/cc, the void volume was determined by subtracting the volume of the support and the solvent from the column internal volume. In this case as a 36% w/w coating was used, 0.188 gis of water and 0.527 gms of Chromosorb W were contained in the column. Therefore and m-c, 3-.-, D 2 7, CC and X/e-A +-a, 3b = -,83 c., This is the result given in Table XIV and the above procedure represents the process of determining this quantity. Now to determine the retention volume, the retention time in Table XV is multiplied by F from Table XIVo

-184Next the factor j is determined using Equation (21) I PLIp.- -l,, lb Now VR is calculated using Equation (20) multiplied by j V (( \/R- = 0,9( )74= ) 42, cj and from Equation (24) knowing M = 18 and R = 82.06 and obtaining p2~ from Jordan(50) as 0.184 atm oo RT_ (t2.o0)(313) _ 5-+e \-_ J-. VR M pz IlljZ, )(16) From this point on the remaining properties to be calculated are thermodynamic in nature and no longer need be related to the GLC variables. From Equation (28), Gk'- = T r Iht' = ( teq/)(313)(1"7~'47)= - o t, $ 8 mole According to Equation (32) ~~dt'~~~lrt R~ ~(32)

-185and a plot of ln72 as a function of (1/T) using the data in Table I should yield a straight line such that For example at 40~C, y2 = 5.50 and at 200C, Z2 = 6o51 so E *A E ( \L\ (o';.. \ q;f -) J,L() In actuality the slopes are determined graphically by a best fit of the three available data points. From Equation (27) A:-, o I.'5'~ c t Having determined all the thermodynamic solution properties at infinite dilution, the methods used in attempting to predict and correlate these properties will be presented, To determine the athermal contribution to nonideality either Equation (78) or Equation (84) will be used depending on the relative sizes of the solute and solvent~ For EtOH-water, as v2~ > v j then Y) g t _ 1t(84) and EtX ]5 - (3#(":"Ff") a O4 _ c~~h_ -a -I4 ( — 4

ath or 2ath = 039 ~ To determine the thermal contribution many variants were presented in the correlation and analysis of data~ However, in this discussion only the final proposed correlation, as presented in Table XI, will be considered as it represents the best predictive technique and also embodies all the other calculational methods. The relations are l h EA-: i( I - m: I /Cl 1 (110) I;T_ 2iA it (111) and t2 _ it 3- 66 (104) As the solutions studied are essentially at infinite dilution, (1, 1 and v2 v2 0 Also geometric mean values are used to calculate a12 and v12 0 Proceeding in a stepwise approach the proper conversion units must be incorporated to produce homogeneous results. Molecular units must be transformed to molar quantities throughout. Recalling that R = 74ok, 1 Debye = 10 18 esuocm, and 1 cal = 4.186 x 107 ergs results in

-1873 RT 1b(e 186X Jo7) LS 6 where vii. is in cc/mole and a12 is in cm. Grouping all constant terms together one obtains a(( ((6'6a:oa3)(-,Lo)')' r,, _ 3(1 99)(a98)(+,1bxo7)a6 \1 L62 or (_____a__ 2__2X 5 _ 0t 0 where r12 is in A, vii in cc/mole, and 4i in Debye. Utilizing the same procedure for the induction term yields t'T?(+ )s6 x 1or% z Lm,611 o.. vc1 or JZ 18 1CI /t4. _ _________ _T oe Cr e where aij is in A vij in cc/mole, Ki in Debye and ai in cc/mole x 1024

-188The above terms will now be calculated for the EtOH-water system - (,~ iL~~i~)~ ~,~'~' 1 -7~~.~'~ (w,-w-=- 5,~ ca1 ice (WI- - = We-1 _.. LT, S) (l8) (45 5B -74) (15) (1H44e5 ) ()"NYb5 or TIT, = I+.1 cal/ and (No f a2) = (E -3) =Ca Substituting these terms into Equation (110) and Now from Equation (70),Bow i s+W t ~>h

-189and?- 8e3xlob To calculate the separate terms for the various other correlative techniques, the individual contributions computed above are used separately or in partial summation in the corresponding relation, The statistical mechanical development allows the interaction energy and its temperature dependence to be evaluated, as well as the geometric and energetic contributions to the partial molar excess entropy. From Equation (135) the interaction energy is given by AW =a. a\ -C -o or A = (W cm- ((1-),+ qSS'c e Now from Equation (138) dht - T L - R- ('an of s T + RT I-<) (- C or AAsw ~ 9 W (1-,08- 0.2.1(55) -(3 ) X ) Ila [L - +(c1 4(a)(I-3,a)()o3)(/. S- 0.21)

-190and ad W = 0 Scal/le. OK To calculate the geometric contribution to LS2E one must know C9, C10 and Cll defined by Equations (146), (147) and (148). From Equation (146) Cq9= [i- h +9- 2 - ( 1~H )176 (I =3' or C_= - 2 1 1 Cal//o9e OK and From Equation (147) C = - T(,-,) - I ) Nie=- (.,qq q(KO-'( — +) or Finally from Equation (148) o,KC cIT ([Iio~e2)10)( ~ or _II= 1. _. Ci~lm~le. It

-191Now from Equation (149) = E = - Cq — C_,- C,,.'-.'~1 1- 4 = 1.3ac.l/rnole. K where C9 + ClO is the geometric contribution, 3.26 cal/mole ~K, and Cll is the energetic contribution. To compute the constants for Pierotti's homologous series correlation the correct equation for the system studied must be employed. For alcohols in water, Equation (142) should be used. 1&:= C3, C Ia —C5/Q; (142) B.~il +C At 40~C from the alkanes in water data, the value of C4 has been determined as 1.04, i.e., see Table V. Thus two data points are needed to determine C3 and C5. From Table I for MeOH-water, Y2 = 2.30 while for PrOH-water, 72 = 22. Therefore y) a.30 = C3 +.o* + cs5l Int - C +3a-,H + Cs and solving the two relations simultaneously yields C3 = 0o06 and C5 = -0.27. In certain instances the system of equations is overdefined in that more data points exist than equations. In that case a "best" set of constants is determined to fit all the data.

APPENDIX E VAPOR -LIQUID EQUILIBRIUM IN GAS LIQUID CEROMATOGRAPHY At first the concept of vapor liquid equilibrium in the normal static sense seems a bit foreign when applied to GLCo The transient nature of the process, which on a macroscopic scale is in unsteady state, immediately causes one to think of the process as a nonequilibrium occurrence. The burden of proof that in fact vapor-liquid equilibrium does exist within the column may take one or both of two paths. By a logical consistent set of arguments, one's intuitive insight and feeling may be appealed to concerning the actual transfer of solute between the vapor and liquid phase and the equilibration which takes place. Alternately one may show supporting work which substantiates the hypothesis and concurs completely with equilibrium data obtained by other wsell accepted techniques. In order to confirm that equilibrium truly exists within the GLC column, both of these approaches will be used in the present discussion. Thie latter technique has already widely been used throughout this text to -validate the method. In the normal static sense vapor liquid equilibrium does not exist in a chromatographic column. In essence this i.s t;he crux of the entire problem. As the carrier gas is constantly flowing through the column sweeping the solute toward +he exit during a short fraction of the total residence time, one must realize that a dynamic equilibrium exists here and not a static time invariant phenomena. In viewing a flow system one may adopt one of two points of view~ The Eu.l.e-rian approach may be used and one may sit;uate his Maxwell's demon at one point along -192 -

-193 - the column waiting for reports concerning the solute from time to time. One report would note the presence of the solute while the remaining reports would note nothingo Alternately one may adopt the LaGrangian view, correctly so, and order his demon to jump on a solute molecule and report back his findings irrespective of time interval. This is the approach to be pursued if the nature of the dynamic equilibrium in GLC is to be understood. Consider a chromatographic column divided along its length into a number of very small yet distinct zones which shall be referred to as plates, as shown in Figure 12. Let us adopt this plate model of the column and imagine that initially a particular solute is all contained in the first plate, i.e., Figure 12(a). On passing an incremental volume of carrier gas, 6V, some of the solute in the gas phase is swept onto the second plate where it equilibrates with the solvent, That equilibration occurs is logical during the short time period because the solvent is spread quite thinly having a high surface to volume ratio. Thus the solute does not have to penetrate far into the liquid phase to insure adequate contact with the solvent. Also very little solute is present initially so the process occurs on a microscopic or molecular level and the equilibration is very rapid, i.e., dynamic. Meanwhile the solute remaining in the liquid phase on the first plate equilibrates with the solute-free carrier gas entering the column as shown in Figure 12(b). On passing further increments of carrier gas this process repeats itself, see Figure 12(c), and slowly the vanguard of the solute moves along the column while the concentration on the first plate decreases until essentially no solute remains and the whole zone of solute

-194o 1 2 3 4 5 6 N-1 "Vapor Phase Start L Liquid Phase (a) 8v (b) (c) n$V ntV I I 1 1, 1 1 X J I (d) Figure 12. Elution Progress in a Column Composed of Plates.

-195has effectively moved along the column as in Figure 12(d), The way in which the solute is distributed among the plates after passage of a given number of increments of carrier gas depends on the relative crossections occupied by each phase and upon k, the equilibrium partition coefficient. Using the above type of intuitive argument led Martin and Synge(70) to derive the plate equation which relates the equilibrium GLC properties to the volume of carrier gas needed to elute the solute from the column. As mentioned initially each plate or zone, although very small, remained distinct. More recent theoretical developments have reduced or eliminated the plate height, Lapidus and Amundson(62) and Van Deemter, Zuiderweg and Klinkenberg while considering the effects of mass transfer resistance and longitudinal diffusion adopted a rate approach to deriving Equation (1). In these theories, the concept of local or point equilibrium is utilized. This concept is validated by the relatively fast mass transfer rates achieved and the low linear velocities through the chromatographic column. The fast mass transfer rates are due to the small support particle size providing the large surface area for the solvent. These authors show that for most normal conditions existing in a chromatographic column the theoretically more appealing rate approach reduces to a form equivalent to that obtainable from the less elegant plate theory. Thus regardless of approach the same result is obtained and therefore the concept of vapor-liquid equilibrium in a chromatographic columnn be it on an infinitesimally small plate or at a local point, has been substantiated.

1l96At the risk of repetition the alternate approach of substantiating GLC results by comparision with static equilibrium data will now be discussed in a bit more detail. In the literature review countless instances were cited quoting agreement between GLC data and static results, Also in the discussion of the results many cases were given showing excel lent agreement between the data of this study and results in the literature determined by other methods. A short recapitulation of the more significant works will now be given wkhich have been deemed highly pertinent, Porter, Deal and Stross (87) studied the effect of the GLC variables on the resulting thermodynamic solution properties and conclusively showed that they were dependent solely on temperatire, pressure and concentration. These workers also show that effects such as longitudinal diffusion should have no effect on Equation (1)o They also studied the same systems by bulk equilibriu-m techniques.hlich tthey had inrestigated by GLC and obtained very good agreement betweenz the davta determined by the tw.^To different methods. Kobayashi and Mellado(55) studed hydocarbon vapor-liquid equllibri.um by GLC and rel.ated the equilibriumL consta.nt to the part ition coefficient used in GLCo. ThLe two are related by tlhe ratio of NL/NG, being inversely proportional. The data obtained by Kobayashi showed good agreement with the standard No.G.A.A tabulations, Everett and Stoddart(27) studied normal. and branched hydrocarbon solutes in dinonyl phthalate'by GLC The results they obtained compared exceptionally well with the static studies on the same systems conducted (8) by Ashworth and Everett. These latter authors examined the hydrocarbons in dinonyl phthalate both in the bulk phase and with the solvent spread on a solid support. The vaalues of the partiti.on coefficient derived from tlhe

-197two methods of studying static equilibrium were identical. The only effect of the solid support was to enhance the rate of attainment of equilibrium over that achieved in the bulk state. This, as was mentioned above, is due to the higher solvent contact area with the solute reducing the resistance to mass transfer. Stalkup and Kobayashi,(lll) in a continuation of Kobayashi's earlier study, investigated binary and ternary hydrocarbon vapor liquid equilibrium at pressure up to 2000 psia. Again comparison between the GLC derived equilibrium constants and those determined from static equi(56) librium stills was quite favorable. Koonce in a further study in this area extended the work of Stalkup and conducted independent solubility studies on the same systems. The agreement obtained between the GLC data, the solubility studies, and the N.G.A.A. values is remarkably good. This work substantiates GLC as a vapor-liquid equilibrium technique valid for high pressures, finite concentrations, and multicomponent systems. Finally Adlard, Khan and Whitham(2) have studied cyclohexane, benzene and CC14 in dinonyl phthalate by GLC used normal packed chromatographic columns. The resultant activity coefficients agree very well with the data the same authors(3) obtained at a later date using capillary columns. Also, both these results concur with the study of Freeguard and Stock(32) on the same systems using static measurements. These results again show the validity of GLC as a technique for obtaining equilibrium data, and that the solid support, present in normal packed columns, has no effect on the resultant properties. From the above discussion and substantiation it is felt that GLC has definitely been proven

-198to be an equilibrium process, in a dynamic sense, capable of providing the same data obtainable by the more common static techniques in a quicker more straightforward manner.

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