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PHASE EQUILIBRIUM IN SYSTEMS CONTAINING FLUOROCARBONS By BENJAMIN G. KYLE A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA FEBRUARY, 1958 ACXXOVL19DGNKII The author wishes to thank Dr. T. N. Reed for his advice and guidance throughout this investigation. Appreciation is expressed to the supervisory comiLttee members, Dr. Iack Tyner, Dr. W. S. Brey, Dr. E. X. mschlitz, and Dr. R. B. Bennett for their aid and cooperation. TABLE OF CONTENTS LIST OF TABL . . iv LIST OF ILLUSTRATIONS . vi CHAPTER I PURPOSE . . 1 II NOMENCLATURE . .. 2 III INTRODUCTION . 5 IV BINARY SYSTEMS FORMING TWO LIQUID PHASES 9 V TOTAL VAPOR PRESSURE OF BINARY MIXTURES 18 VI VOLUME CHANGES IN MIXING FLUOROCARBONS AND HyROCABOS . 30 VII ESTIMATION OF THERMODYNAMIC PROPERTIES 45 VIII TERNARY LIQUIDLIQUID SOLUBILITY STUDIES 55 IX EXTRACTIVE DISTILLATION STUDIES 67 X EVALUATION OF METHODS OF SEPARATING FLUORO CARBON MIXTURES . 79 XI CONCLUSIONS . . 82 APPENDIX . . 85 TABLES . . 91 FIGURES . . 129 REFERENCES . . 183 BIOGRAPHICAL ITEMS . 186 iii LIST OF TABLES TABLE Page I TEST OF THE CONSOLUTE TEMPERATURE CRITERION II CHECK RUN IN TWO LIQUID PHASE STILL . III ISOTHERMAL COMPRESSIBILITIES FOR USE IN EQUATION 34 . . IV O8LVENT SELECTIVITIES . V COMPARISON OF DIFFERENCE . VI CALCULATION OF d3 FROM EQUATION 64 . VII PHYSICAL PROPERTIES OF HYDROCARBONS USED IN THIS WORK . . VIII PHYSICAL PROPERTIES OF FLUOROCARBONS USED IN THIS WORK . . IX THERMOCOUPLE AND THERMOMETER CALIBRATIONS X PYCNOMETER CALIBRATIONS . . XI VAPOR PRESSURES OF PURE FLUOROCARBONS . XII SOLUBILITY DATA . 1 XIII COMPARISON OF CALCULATED AND OBSERVED CONSOLUTE TEMPERATURES AND COMPOSITIONS 1 XIV TOTAL VAPOR PRESSURETEMPERATURE DATA XV COMPARISON OF VAN LAAR ACTIVITIES WITH ACTIVITY RANGE CALCULATED FROM EQUATION 15a . . XVI VOLUME OF MIXTURES OF PERFLUOROHEPTANE AND CARBON TETRACHLORIDE; PERFLUORO CYCLIC OXIDE AND CARBON TETRACHLORIDE; PERFLUOROCYCLIC OXIDE AND nHEPTANE; AND PERFLUOROHEPTANE AND nEPANE . iv 1 1 1 16 19 41 59 63 75 91 92 93 95 96 .01 .07 .08 09 11 TABLE Page XVII TOTAL VOLUME CHANGE AND PARTIAL MOLAL VOLUME CHANGE ON MIXING . 114 XVI11 CALIBRATION DATA FOR ANALYSIS OF SYSTEMS: C7716C.1s60FCC14; Cr716'CgF16oC7H 16s AND C6Hs5C.C6H11CH3C7F15COOCCa 118 XIX TIE LINE DATA . 120 XX ACTIVITIES CALCULATED FROM EQUATION 59 122 XXI ACTIVITIES CALCULATED FROM EQUATION 61 123 XXII CHARACTERISTICS OF CHROMATOGRAPHY COLUMNS USED IN EXTRACTIVE DISTILLATION STUDIES 124 XXIII APPEARANCE TIME OF C7F16, C8F160, C7H16 AND C6HlCH3 IN THE VARIOUS PARTITIONING LIQUIDS . 124 XXIV RELATIVE VOLATILITY OF THE C7F16C8F160 SOLVET AND nC7H16C6H11CH3 SOLVENT STSTSs .. . s25 XXV ACTIVITY COEFFICIENT RATIOS BASED ON AVERAGE RELATIVE VOLATILITY FOR ALL SOLVNTS................ 125 XXVI PROPERTIES OF PURE COMPOUNDS FOR USE IN EQUATION 684 . 126 XXVII DATA FOR USE IN EQUATIONS 37, 40, AND 46 127 XXVIII DATA USED IN ESTABLISHING EMPIRICAL COR RELATION FOR EXCESS FREE ENERGY 128 LIST OF FIGURES Figure Page 1. Vapor Pressure Data for Fluorocarbons 129 2. Solubility Cell .. .. 130 3. Binary Solubility Curves Systems Containing CyF16 . . 131 4. Binary Solubility Curves Systems Containing C8F160 . 132 5. Binary Solubility Curves Systems Containing (C4F9)3N . . 133 6. Binary Solubility Curves Systems Containing C7F15C000C3 . 134 7. Binary Solubility Curves Systems Containing C7F5l H . 135 8. Activity Isotherms . 136 9. Two Liquid Phase Still . 137 10. Van Laar Constants Versus Temperature 138 11. Total Vapor Pressure Plot System: Per fluorocyclic OKidenBeptane 139 12. Total Vapor Pressure Plot System: Per fluorocyclic OxideToluene 140 13. Total Vapor Pressure Plot System: Per fluorocyclic OxideMethylcyclohexane 141 14. Total Vapor Pressure Plot System: Per fluorocyclic OxideCarbon Tetrachloride 142 15. Total Vapor Pressure Plot System: Per fluoroheptaneCarbon Tetrachloride 143 Figure Page 16. Total Vapor Pressure Plot System: Per fluorobeptanenHeptane . 144 17. Activity Coefficients System: C5H12C5F12 T = 262.40 K. . 145 18. Excess Free Energy of Mixing System: CS3FI2C.12H .. 146 19. Excess Free Energy of Mixing System: C4F10C4HlO a & 147 20. Excess Free Znergy of Mixing System: C7F16._C8H18 at 300 C. . 148 21. Van Laar Activity Coefficients 149 22. Van Laar Activity Coefficients Temperature Dependence . . 150 23. Pycnometer Filling Arrangement 151 24. Volume Change on Mixing System: C8F160CCI4 at 50 C. . .. 152 25. Volume Change on Mixing System: C7Fl6C7H16 at 50 C. . 153 26. Volume Change on Mixing System: C7FI6CC14 at 60 C. . 154 27. Volume Change on Mixing System: C8F160aC71H6 at 50 C. . 155 28. Partial Molal Volume Change System: CF 160n e at 500 C. . i6 29. Partial Nolal Volumg Change System: C8F160CC14 at 50 C. . .. 157 30. Partial Molal Volume Change System: C7Fl6CC14 at 60 C. . 158 31. Partial Molal Volume Change System: C7F16nC7H16 at 50 C. .. 159 vii Figure Page 32. Partial Molal Volume Change . 160 33. Thermal Coefficient of Expansion System: C7F16CC14 . . 161 34. Thermal Coefficient of Expansion System: C7F16nC716 . 161 35. Thermal Coefficient of Expansion System: C8F160CC14 . 162 36. Thermal Coefficient of Expansion System: C8F160nC7H16 ... . 162 37. Volume of Mixing System: C7F16CC14 163 38. Volume of Mixing System: C7F16C7H16 164 39. Volume of Mixing System: C7F16.CH 18 165 40. Calibration of System C8F160C 716 166 41. Calibration for System CC14C8F160 167 42. Calibration for System C8F160nCH16 168 43. Calibration for System C6H~E3C6H5CH3 169 44. Calibration for System C6H 11C3CF C150OCH3 170 45. Phase Diagram System C7F16C8F160CC14 at 30 C. . . 171 46. Phase Diagram System: C7F16CsF160nC7H16 at 30 C. . . 172 47. Phase Diagram System: C6H5CH3C6H11CH3 C7F1]COOC% at 25 C. . 173 48. Phase Diagram System: C6H5C%C6H11CH3 C7Fl5COOCH3 at 10 C. . 1. 74 viii Figure Page 49. Heat of Mixing System: C7F16anC7H16 at 500 C. . . 175 50. Heat of Mixing System: C7F16CC14 at 600 C. 176 51. Heat of Mixing System: C F iC H 7 16 8 18 at 300 C. . . 177 52. Heat of Mixing System: CF 10C H10 178 53. Heat of Mixing System: C5F12C5H12 179 54. Excess Free Energy of Mixing system;, C7F16CC14 . . 180 55. Free Energy Correlation for Fluorocarbons and Paraffin Hydrocarbons . 181 56. Excess Entropy of Mixing System: C F 6C8 H18 at 300 C. 182 CHAPTER I PURPOSE The purpose of this work is twofold: 1. The determination of the necessary phase equili brium data for the evaluation of various methods of separat ing fluorocarbon mixtures and hydrocarbon mixtures, partic ular emphasis being given to the methods of liquid extrac tion, extractive distillation, and aseotropic distillation. 2. The calculation of the thermodynamic properties of some flurocarbonhydrocarbon mixtures and the comparison of these calculated properties with properties predicted from various theories of solutions. CHAPTER II NOMENCLATURE a Activity, standard state taken as pure substance A Van Laar constant B Van Laar constant d Distance between centers of nearestneighbor mole cules H Partition coefficient, defined as the ratio of solute per unit volume of solvent to solute per unit volume of gas phase I Ionization potential N Number of theoretical plates pi Inlet pressure in chromatography column po Outlet pressure in chromatography column P0 Vapor pressure of pure compound R Gas constant T Absolute temperature, oK. V Nolal volume, cc Vg Volume occupied by vapor phase in chromatography column Vr Retention volume, defined as the volume of carrier gas passed through chromatography column when solute peak appears 3 Vs Volume occupied by stationary solvent phase in chromatography column Vs Molar volume of stationary solvent phase, cc v Weight fraction x Mole traction y Mole fraction of a component in vapor phase z Correction factor AA Change in Helmholtz Free Energy As Change in Internal Energy A F Change in Gibbs Free Energy A H Change in Enthalpy AS Change in Entropy Xo Coefficient of thermal expansion 0( Relative volatility Isothermal compressibility 3 Solvent selectivity Y Activity coefficient, standard state taken as pure substance 0C Solubility parameter, ( V/y)1/2 (calories/cc)1/2 TT Total vapor pressure Volume fraction 6 Retention time, defined as time for appearance of solute peak Subscripts 1 2 Refer to components 3 C Refers to consolute properties D Refers to distillate composition 9 Refers to mixture properties 0 Refers to ideal solution properties P Refers to constant pressure process V Refers to constant volume process W Refers to composition of material in distillation pot Superscripts * Refers to excess properties M Refers to mixing process V Refers to vaporization process I Refers to hydrocarbonrich phase CHAPTER III INTRODUCTION Before any e equipment affecting physical separation of two or more components can be designed, phase equilibrium data must be available. Since the majority of the unit operations involve the contacting of two phases under condi tions approaching equilibrium, the determination, correla tion, and prediction of phase equilibrium data play an im portant role in the field of chemical engineering. A most desirable method of obtaining necessary phase equilibrium data would involve the calculation of the pro perties of the mixture from those of the pure components; however, to be used with confidence, any such method should have some sound theoretical basis. At present there are several approaches to the theory of solutions, most of which have a statistical mechanical basis and require many assump tions and approximations and yield equations which are com plex and cumbersome. A simple theory that has achieved considerable suc cess in the treatment of solutions of nonelectrolytes is one developed independently by Scatchard and by Hildebrand (11). By making four simple assumptions, Scatchard and Bildebrand 6 arrived at the following expression for the energy of mix ing in a binary system:* X : (x *1 xV2) ( Q :2 2 2 (1) The four assumptions were: 1. The energy of a system can be expressed by sum mation of the interaction energies of all possible pairs of molecules. This interaction energy was assumed to depend only on the distance between the two molecules. 2. The distribution of molecules is random with respect to position and orientation. 3. There is no volume change on mixing at constant pressure. 4. The interaction energy between 12 pairs of mole cules is the geometric mean of the interaction energy between 11 and 22 pairs. Strictly speaking this theory applies only to systems containing nonpolar molecules between which only dispersion forces are operating. By further assuming that the entropy of mixing has the same value as that of an ideal solution (a solution obey ing Raoult's law) it is possible to write for the free energy of mixing *A tabulation of the nomenclature used in this work is given in Chapter II. AP x (11 x2V2)( 2l ) { 1 2 + RT(xln x1 X2 inx2) (2) and for the activity coefficients RT InY = VI(C1 i 2) 2 + ) 2 RT laY2 V2 ) 2 ) >i, 2 (3) From its inception in 1932 until about 1950 the success of the ScatchardHildebrand theory had been measured by its prediction of the properties of hydrocarbon systems. Since 1950 much work has appeared concerning fluorocarbon hydrocarbon systems which were not adequately accounted for by the theory. These systems have such larger positive de viations from aoult's law than are predicted. For some systems these positive deviations are large enough so that at room temperature two liquid phases exist. Because of their nonconformity to the existing theory, fluorocarbonhydrocarbon systems have stimulated the interest of many investigators. The first comprehensive study of fluorocarbonhydrocarbon systems was made by Simons and Dunlap (39) followed later by Simons and Mausteller (40); these investigators determined the thermodynamic properties of CSF2IC5H12 and C4110C4H10 systems respectively. Simons and Dunlap found the ScatchardHildebrand theory to be inadequate in predicting the thermodynamic 8 properties of their system, and improved the agreement by rederiving equation 1 omitting the assumption of no volume change on mixing. Later Reed (32) showed that for fluoro carbonhydrocarbon mixtures the interaction energy between unlike pairs of molecules is not the geometric mean of like pairs as was also assumed in the derivation of equation 1. Reed also rederived equation 1 omitting the assumptions of the geometric mean and no volume change. Be was alle to calculate values of the heat of mixing which agreed very well with the experimental data of Simons and Dunlap, and Simons and Mausteller. Since most fluorocarbonhydrocarbon mixtures do not conform to the present theory, their study should prove use* ful toward further development and evolution of the theory and the understanding of solution processes. CHAPTER IV BINARY SYSTEMS FORMING TWO LIQUID PHASES The study of binary systems forming two liquid phases was undertaken for two reasons: 1. To determine solubility relationships which might be useful in selecting a solvent for separating fluorocarbonfluorocarbon mixtures and hydrocarbonhydro carbon mixtures. 2. To obtain a measure of the positive deviations from Raoult's law exhibited by binary mixtures of two par tially miscible liquids. Experimental.The properties of the pure compounds used in this study are tabulated in the appendix under Tables VII and VIII. The unmixing temperature of a known binary mixture was determined by heating the mixture until the two liquids were completely miscible, then cooling the solution slowly and observing the temperature at which the second liquid phase appeared. The appearance of the second phase on cool ing is marked by cloudiness; this cloudiness is sometimes masked by an opalescence which occurs about 2 or 3 degrees above the consolute temperature. Due to this opalescence, the determination of the unmixing temperature depends to some 10 extent on the judgment of the observer. The solubility apparatus shown in Figure 2 consisted of a heavywalled glass test tube clamped between two staen less steel flanges by means of four brwas bolts. A Teflon gasket placed between the open end of the tube and the top flange was used to seal the tube. A thermaocouple, which passed through the top flange, was used to measure the tem perature of the mixture. The whole tube assembly was ia mersed in an oil or water bath, which provided the necessary temperature control. The solubility data are tabulated in Table XII and the solubility curves, which were obtained by plotting the unmixing temperaturecomposition data, are shown on Figures 37. Published data are available for the two perfluorohep tane systems (17); these points are plotted on Figure 3 along with the present data. The agreement between the two sets of data is satisfactory. Due to the presence of air in the solubility tube, the values of the unaixing temperatures so determined per tain to the mixture saturated with air and at a pressure in excess of the equilibrium vapor pressure of the mixture. The difference between these values and those of the mixture under its own equilibrium vapor pressure is generally assumed to be negligible, but in order to justify this assumption the un sixing temperature was determined for a degassed ixture of toluee and perfluorocyclic oxide* in a sealed glass tube under its own equilibrium vapor pressure. This value of the unmixing temperature is plotted on Figure 4 along with those obtained in the presence of air and it can be seen that there is no significant difference. Theoretical Calculation of Consolute Temperature and Composition.The thermodynamic conditions necessary to de fine the consolute temperature are da1 ag "Ia 0 da io W or \(4) dls 421a i 1  0 00" This requirement can be seen from examination of Figure 8, where three isothermal curves of activity are plotted versus composition. For illustrative purposes the activity is cal. culated from the following equation n a1 = In X BK2 (5) At T1, a temperature below Tc (conaslute temperature), there exist two liquid phases having the same activity. These *A description of this material is given in the appendix. 12 phases correspond to points A and B. The dashed portion of the curve has no physical significance and corresponds to the Van der Waals isotherm in the two phase region on a pressurevolume diagram of a pure substance. As the tem perature is increased, the length of the line AD decreases until the consolute temperature Tc is reached and a point of inflection, C, is observed in the activity curve. At this point the first and second derivatives of the activity are equal to zero. At a temperature T2, above Tc, the deviations from Raoult's law become smaller and the activity is a single valued function of composition. The value of the activity as predicted by the Scatch. ard Hildebrand theory is In a1 = In x1 4 (C1 d 2 422 (6) Using equation 6 for the activity and applying the condi tions of equation 4, the following expressions result for the consolute temperature and composition. RTc xSaa2V22 (fl )2 (7) R TC ....(.. + ... XI a (Vi 2 2 2 '2 V ), 1/2. V V2 m 1 By using the entropy of nixing for molecules of different I 13 sisMe as calculated from a lattice model along with the energy of aixing as given by equation 1, Hildebrand (18) derived expressions for the consolute temperature and com position somewhat different from equations 7 and 8 OTN 2jlV2 2>2/ /2 1 V/22 (9) 2 1/2/2 1/2 V1/2 9i : 2V1Y2(dj 4) / (VS  ) (9) 1/2 The consolute temperatures and compositions have been calculated from equations 7 aud 8, and 9 and 10 for the Systems rcreted in this work and are tabulated in Table XIII. The values of the consolute composition in Table XIII are given only to two figures because of the uncertainty in locat iag the composition corresponding to the maxima temperature. From Table XIII it is obvious that equations 8 and 10 predict the consolute composition quite well while equations 7 and 9 provide poor estimates of the consolute temperature. Only for the system perfluorocyclic oxidetoluene was the consolute temperature correctly predicted by equation 7. The fact that equations 8 and 10 predict the consolute composition would indicate that the volume fraction is a use ful variable in correlating solution behavior. This is borne out by the successful correlation of experimental activity coefficients by the Van LUar equation, which 18 similar in form to equation 3, but contains two adjustable parameters instead of constants which are fixed by the physical proper ties of the pure components. The failure of equations 7 and 9 to predict the consolute temperature is probably due partly to the failure of fluoroearbonhydrocarbon mixtures to eofomer to the geometric easn aseeaption which is implicit in these equa. tions. Equation 9 predicts lower temperatures than equau tion 7 because the exeoss entropy of nixing due to different volumes is always positive and therefore the deviatonas from aoult's law due to this correction are always negative. Sioe f luorocarbonahydrocarbon mixtures show auch larger positive deviations than predicted, the entropy correction Iapairs the agreement between the observed and predicted temperatures. It can not be stated, however, that the use of the entropy term for unequal volumes is incorrect since the small effect it contributes is ovoershadoed by the larger effect probably duo to the geometric mesa assumption. It should be mentioned that, although often used in the literature, couparlson of the calculated and observed conaolate temperature is not a good criterion for testing the applicability of the ScatchardHldebrand theory. It 15 equations 7 and 8 predict the correct temperature and com position, this means that the first and second derivatives of the true activity coefficient with respect to composition are equal to the corresponding derivatives of the activity coefficient as given by equation 3. This is a necessary, but not a sufficient condition which must be fulfilled by equation 3, for it is conceivable that two different func tions could have equal first and second derivatives at a given composition. This reasoning can be substantiated by comparing activity coefficients calculated by equation 3 with experimental values for some systems which conform to the consolute temperature criterion. This is done below. In a two liquid phase system the activity of a comm ponent is equal in both phases and we can write xi 1 a Y a(1) In many fluorocarbonhydrocarbon systems which form two liquid phases the mole fraction of hydrocarbon in the hydro. carbonrich phase approaches unity at low temperatures and the activity coefficient also approaches unity. Thus by set ting Y1' equal to unity, the activity coefficient of the hydrocarbon in the fluorocarbonrich phase ( TY) is equal to the ratio xl'/xl. Values of In Y 1 so calculated are com pared in Table I with values predicted by equation 3 for 16 three systems in which the observed and calculated conso lute temperatures are in good agreement. TABLE I TEST OF THE CONSOLUTE TEMPERATURE CRITERION Tc0 InY SYSTEM obe. eq.7 C) x x'1 eq. eq. 2J2. (C) 11 3 I 323.5 325 26.3 0.306 0.960 1.14 0.913 19 II 358.5 360 61.1 0.320 0.956 1.09 0.900 19 III 386 377 69.0 0.256 0.981 1.34 0.977 this work I. perfluoromethylcyclohexane and chloroform II. perfluoromethylcyclohexane and benzene III. perfluorocyclicoxide and toluene One would expect the same percentage difference be tween the logarithm of the activity coefficients as between the two temperatures in Table I since both Tc and In V are directly proportional to the (1 6 )2 term. Inspection of Table I reveals that the percentage difference between the logarithms of the activity coefficients is much greater than between the consolute temperatures. Since the values of InYl 17 and To in Table I are compared at different toperaturea., the possibility arises that the activity coefficients pre dicted by equation 3 are equal to the true activity coof ficients at the consolute temperature only, and not at other temperatures. From consideration of the consolute tempera ture alone one would erroneously aassme that the three systems in Table I closely conformed to the theory. CHAPTER V TOTAL VAPOR PRESSURE OF BINARY MIXTURES ExperWiental.Total vapor pressure versus temperam ture data were obtained for six binary fluorocarbon.hydro carbon fixtures. The physical properties of these compounds are listed in Tables VII and VIII. The measurements were made in the two liquid phase region since liquid compositions could be determined from the temperature and the experimentally established soli. bility curve. A dynamic boiling still was used for these measure* eants, the design details of which should be obvious from examination of Figure 9. The still was designed so that vigorous boiling and low liquid level would prevent super heating while the insulating vapor space would prevent any heat lose by the vapor in the inside tube. Daurinag operation of the still undor equilibrium conditions no condensation was observed inside the ianer tube. A calibrated thermocouple was used to measure the vapor temperature; the calibration data for this thermocouple is reported in Table IX. The still was connected to a vacuum system contain a mercury mnaome ter which could be read to the nearest tenth of a millimeter by use of a cathetometer. As a check on the performance of the still the total pressure of the system 2 butanonewater was determined at two temperatures. These values compare favorably with the reported literature values (29) as shown in Table II. TABLU II CHUCK RUN IN TWO LIQUID PHASE STILL System: 2 butanonewvater reference 29 Literature This Work Pressure Temperature Pressure Temperature M oC m OC 760 73.3 768 73.6 500 62.0 503 62.0 The experimental total vapor pressure versus temperature data are reported in Table XIV. Calculation of Activity Coefficients from Liquid. Liquid Solubility Data.The following method for calculat ing activity coefficients has been described by Carlson and Colburn (6). In a two liquid phase system the activity of a component is equal in both liquid phases and we can write xI 1 x' 1' (11) z21 : z2' 2' 20 The mole fractions are known from the solubility data and we have two equations containing four unknown quantities. The number of unknowns can be reduced to two if it is an sumed that a twomcoustant equation can be found vhich correct ly expresses the activity coefficients as a function of composition. One such equation which has proved useful in correlating experimental activity coefficients is the Van Lear equation. Y "2 113) la Y 8 (14) Ift equations 13 and 14 are substituted into equations 11 and 12 written in logarithamic form, values of the constants A and B can be found. This procedure can be repeated at several temperatures so that the temperature dependence of A and B can be determined. The Van Lear A and B have been calculated for several of the fluorocarbonhydrocarbon systems for which the solubility curves were determined and it was found that the constants were always linear functions of temperature. Figure 10 shows several of these linear plots. In order to have confidence in values of the activity 21 coefficient as calculated from equations 13 and 14, some method should be available for determining whether the Van Laar equation accurately predicts the activity coefficients. One method of accomplishing this is to compare experimentally determined total vapor pressures with thost calculated from equation 15 using the vapor pressures of the pure compounds, solubility data, and the Van Laar equation to determine the activity coefficients. TT : x1 TIPl + x2 2po (15) A graphical comparison of calculated and experimental total vapor pressures is given in Figures 1116, where it is re vealed that the agreement is quite good at lower tempera tures, but becomes poorer as the temperature increases. The fact that calculated and experimental values of the total vapor pressure agree should not be taken as conclusive proof that the activity coefficients predicted by equations 13 and 14 are correct, however, since there is an infinite number of combinations of Y1 and T2 which will satisfy equation 15. By rearranging equation 15 we see that the activity of component two is a linear function of the activity of component one. a2 T/P2o alPlo/p20 (15a) 22 By using equation 15a we can establish limits for the ac tivity of the fluorocarbon (component 2) from the limits of the hydrocarbon activity. The upper limit for the ac tivity of the hydrocarbon will be set at unity and since these mixtures all exhibit positive deviations from Raoult's law, the lower limit will be set at the mole fraction of hydrocarbon in the hydrocarbonrich phase. Table XV shows the activity limits of the fluorocarbon as determined from equation 15a along with the values calculated from the Van Laar equation for all six systems for which the total vapor pressure was determined. Table XV reveals that for most systems the calculated activities fall within the range cal culated by equation 15a at the low temperatures, but deviate at higher temperatures following a pattern similar to the observed and calculated total vapor pressures. The Van Laar activity coefficients determined from the solubility data of Simons and Dunlap (39) are plotted on Figure 17 along with their activity coefficients determined from partial pressure data for the system perfluoropentane npentane. The value of the total vapor pressure in the two liquid phase region for this system at 262.4K., calculated from the Van Laar equation, is 214 ma. as compared to the reported value of 216 am., and the Van Laar activity of 0.766 falls within the 0.718 to 0.855 range calculated from equation 15a. It can be seen from Fig. 17 that the Van Laar 23 equation with constants determined from solubility data predicts values of the activity coefficients which agree very well with the experimental ones. The Van Laar equa tion with constants determined from solubility data has successfully predicted excess free energies of mixing in other fluorocarbonhydrocarbon systems for which the ther modynamic properties have been determined. Figures 1820 show that the calculated and experimental excess free energies of mixing for the systems nperfluoropentane and npentane (39), nperfluorobutane and nbutane (40) and perfluoroheptane and isooctane (26) are in good agreement. These experimental values of the excess free energy of mixing were determined from partial pressure data. The solubility data for the system perfluorohep tane and isooctane were taken from reference (17); calcu lated values of A Fe for this system were made from the solubility data and the Van Laar equation at 170 a while the reported data are at 30 C. The excess free energy data of Simons and Dunlap and Simons and Mausteller are the averages of several temperatures in the ranges 262 to 293 K. and 233 to 260 K., respectively, while those cal culated from solubility data are at 262.4 and 220 K. re spectively. The small difference in temperature between calculated and observed free energies is negligible since 24 the temperature derivative of the excess free energy of mixing is the excess entropy of mixing at constant pressure. Values of excess entropy of mixing are tabulated below for several systems. System at x 2 0.5, cal./mole OK Reference C4'1O C410 1.00 40 CS12 CSH12 0.43 39 C716 iCS.18 0.24 26 This entropy term does not usually exceed one entropy unit and a change of ten degrees would result in less than a 10 calories per mole change in the free energy term. The partial molal heat of mixing can also be cal culated from the Van Laar equation and the temperature deriva tives of its constants ANL L A (16) T T Ax1l 12 Lk.B2 25 Beats of mixing calculated from the Van Laar equation are approximately twice as large as those determined experi mentally in the three fluorocarbonhydrocarbon systems cited above. Wood (48) has calculated the thermodynamic properties for the system cyclohexanemethanol from solu bility data alone, but using a twoconstant Scatchard equa tion instead of the Van Lear equation to represent activity coefficients. He found that his calculated excess free energies of mixing were in line with those reported for the methanolbenzene and methanolcarbon tetrachloride systems, but his calculated heat of mixing values were about twice as large as those for the two reported methanol systems. Besides the Van Laar equation, twoconstant Margules and Scatchard equations were used in this work for substi tution into equations 11 and 12, but these equations pre dicted total vapor pressures that did not agree with the ob. served vapor pressures as well as did those predicted from the Van Laar equation. These two types of equation also predicted heats of mixing which were in poorer agreement with the experimental values than those predicted by the Van Lear equation. Since the temperature derivative of the free energy is needed for calculation of the heat of mixing, mall errors in the free energy will produce larger errors in the heat of mixing. The disagreement between experimental heats of mixing and those calculated from the Van Laar equation could be attributed to small errors in the free energy as predicted by the Van Laar equation. However, these errors are not of a random nature since the calculated value is always about two times as large as the experimental values. In order to determine why the Van Laar equation fails we should consider in detail the process by which the Van Laar constants are determined. Figure 21 illustrates graphically the conditions required to obtain the Van Laar constants. Equations 11 and 12 can be rearranged to In YI In Tl' : In x1'/x1 (lla) In Y2 In Y2' lan x2'/x2 (12a) The differences In1 In YT' and In 2 In Y2' are rep resented on Figure 21 by ab and cd respectively. Using equa tions 11, 12, 13, and 14 is equivalent to finding the con stants A and B such that at x1 and xl* the differences In Y 1 In Y I' and In 2 In 2' given by the Van Laar equation are equal to the corresponding differences between the true activity coefficients. This does not mean that the actual values of the Van Laar activity coefficients are cor rect or that the Van Laar curve is identical with the true 27 activity coefficient versus composition curve. At lower temperatures the composition of the con jugate phases approaches that of the pure compounds and the true activity coefficient and Van Laar activity coefficient both approach unity. This means that at lower temperatures the activity coefficients Y1' and Y2 corresponding to points a and c on Figure 21 can be predicted by the Van Lar equation. Since the Van Lear activity coefficients and true activity coefficients approach each other at a and c, and since ab and cd as given by the Van Laar equation are equal to ab and cd corresponding to the true values of In Y^ In Y 1' and In Y 2 In Y2', the Van Lar and true ac tivity coefficients also approach each other at b and d. This is manifested by the very good agreement between ob served and calculated total vapor pressures at lover tempera tures. As the temperature increases the concentration of the major component in each phase decreases causing the ac. tivity coefficients to differ from unity and it is possible that differences occur between the Van Laar and true ac tivity coefficients at a and c. This would result in dif ferences at b and d and would cause the values of the observed and calculated total vapor pressures to diverge, One reason why the Van Laar equation does not correct ly predict heats of mixing can be seen from examination of 28 Figure S22. Curves 1 and 2 on Figure 22 represent the Van Lear equation at two temperatures, curve 1 being at the lower temperature. Curves 3 and 4 represent the true ac tivity coefficient curves, where curves 3 and 1, and 2 and 4 are at the same temperatures. Only the curves for one component are shown for the sake of simplicity. The shape of the two types of curves is greatly exaggerated for illustrative purposes. At the temperature T1, the Van Lear equation (1) predicts correct values of the activity coef ficient at a and b even though its form is different from the true activity coefficient curve (3) at that temperature. Increasing the temperature to T2 causes only a slight change in the true activity coefficient curve (4), but due to the difference in form the Van Lear curve (2) must change by a greater amount in order that it may predict the activity coefficients at c and d. Since the heat of mixing is de termined from the temperature derivative of the logarithm of the activity coefficient at constant composition, it can be seen that larger heats of mixing would be obtained by the Van Lear equation. We see that the inability of the Van Lear equation to predict heats of mixing could be due to a dif ference in form between the calculated and true activity coef ficient curve. This difference is undoubtedly small since the 29 excess free energy of mixing curves calculated from the solubility data using the Van Lear equation agree in aag nitude and in shape with experimentally determined excess free energy.curves. Based on the preceding considerations it is con cluded that the Van Lear equation can be used to estimate free energies in systems which form two liquid phases if the constants are determined at temperatures where the com positions of the two coexisting phases approach the pure compounds. Of course more confidence can be placed in the Van iLar equation if total pressure data are available. Since the temperature derivative of the free energy is small, these estimated free energies can be used without appreciable error at other temperatures within 20 or 30 C. of the tem perature at which the estimate was made. It is further con cluded that the heats of mixing predicted by the Van Laar equation are unreliable. CHAPTER VI VOLUME CHANGES IN MIXING FLUOROCARBONS AND HYDROCARBONS Experimental.The molal volumes as a function of composition were determined for four fluorocarbonhydro carbon systems. The physical properties of the pure com pounds are given in Tables VII and VIII. Pycnometers de scribed by Lipkin (22) and having a nominal capacity of 5 milliliters were used to measure the volumes of mix. tures of known composition. These pycnometers were cali brated with distilled mercury at 40, 450, 50, and 600 C.; the calibration data are given in Table X. The molal volumes of the fluorocarbonhydrocarbon solutions were measured over the entire composition range at a temperature slightly above the consolute temperature of each system. The molal volumes were also measured over the limited composition range at two other temperatures 5 and 10 C. below the complete isotherm. For the systems perfluorocyclic oxidenheptane, perfluorocyclic oxide carbon tetrachloride, and perfluoroheptanenheptane the isothermal volume measurements were made at 400, 450, and 50o C. while for the system perfluoroheptanecarbon tetra 31 chloride they were made at 50, 55, and 600 C. The thermal coefficient of expansion of the materials limited the teon perature range to ten degrees for one filling of the pyonom eter. Since some of the mixtures were two liquid phases at room temperature it was necessary to fill the pycnonoeter at a temperature above the consolute temperature. Figure 23 shows the arrangement for filling the pycnometer. The de sired mixture was weighed out into the transfer tube, which was then closed off by means of a ground glass stopper and placed in the water bath at a temperature above the consolute temperature of the system. After remaining in the water bath several minutes the tube was shaken until mixing was complete and the ground glass stopper was replaced by the syphon tube, which had been heated to the bath tem perature. The pycnometer was connected to the transfer tube by a small section of Tygon tubing and was filled by applying auction to the other arm. The pycnometer was al ways filled at the highest temperature of each series. The pycnometer reading was taken after approximately fifteen min utes at the bath temperature, then the bath temperature was lowered five degrees to the next temperature. The water bath temperature was controlled manually 32 by meaas of an electrical heating element connected through a Variac. The mercuryinglass thermometer measuring the bath temperature could be read to + 0.02 C. and was checked against a thermocouple calibrated by the National Bureau of Standards. The temperature of the bath never varied more than 0.05 C. from the desired temperature while the pyc nometer was approaching thermal equilibrium. After the pyc nometer reading was made at the three temperatures the pyc noaeter was removed from the bath and allowed to cool to room temperature. The pycnometer was then weighed, emptied, and weighed empty; all weights were corrected to weights in vacuo, Knowing the weight of material in the pycnometer, the composition of the material, and the pycnometer read* ingas it is a simple matter to find the molal volumes of the mixture at the three temperatures. The molal volumecomposition data is tabulated in Table XVI. The volume change on mixing was calculated by equation 17 AV*= V IM x" LV 22 T (17) The partial molal volume change on mixing was determined by plotting the total volume change versus mole fraction of hydrocarbon, graphically taking the tangent to the curve at the desired composition, and determining the value of the 33 intercepts of the tangent line at x, : 0 and x, : 1. These values of the intercepts are the partial molal volume changes of mixing of components 2 and 1 respectively. Plots of the total volume change on mixing ( AVM) versus mole fraction of hydrocarbon are shown on Figures 2427, Values of the partial molal volume changes on mixing are tabulated in Table XVII and plotted versus composition on Figures 2831. Figure 32 shows the plots of partial molal volume changes versus composition for the systems perfluorocyclie oxidenheptane and perfluoroheptanenheptane superimposed, One can see from Figure 32 that the partial molal volume changes are practically identical for each type of compound in both solutions and since the systems are almost symme trical the partial molal volume changes are nearly equal for all three components. Since the two systems involving carbontetrachloride were not determined at the same tem perature one would not expect the two partial molal volume change curves to be superimposed. It was found for these four systems that the total volume change on mixing increased with increasing tempera ture; this type of behavior was also found in the C5F12.CsEH C4F10C4H10 and C6F14C6H14 systems (2). 34 The coefficient of thermal expansion (ot) as de fined by equation 18 was determined from the temperature volume data of the pure compounds and the binary mixtures. o( : 1 fy (18) v V T/P Figures 3336 show that plots of d0 versus composition for some of the systems exhibit maxim a. The thermal coeffi eient of expansion for an ideal mixture (a(o) is a linear function of the volume fraction as shown below. 0 1V1 l* a2V \1V14 x*V2/ p 0o = XLVl & xi2 l1f S XV1 x2V2 Equation 19 is also plotted on Figures 3336 for comparative purposes. In order for the total volume change to increase with temperature it is necessary that the thermal coefficient of expansion for the mixture be greater than the coefficient for an ideal solution. This can be shown by dif ferentiating equation 17 with respect to temperature d AM sdV dVo 2 Vo< V VO < dT _W y 0 0 Since V t Vo d AVN . In order for dAY to be positive Qo( must be greater than 3a? (oo; this is in accord with the experimental values of AVN and ( Since the values of o( plotted on Figures 3336 were determined in the region of the consolute temperature the large values of o( might be due to the breaking up of clusters in the liquid as the temperature increases. The formation of clusters in systems exhibiting partial misci bility has been generally recognized (50). The opalescence observed Just above the consolute temperature is believed due to the scattering of light by clusters of molecules. A molecule in a cluster would have more likemole cules as nearest neighbors than it would have if the mixture were homogeneous; as the temperature is raised thermal mo tion combats the tendency to cluster and the mixture approach es homogeneity. If we consider the case where one 11 and one 2.2 pair rearrange to form two 12 pairs we find that the interaction energy of the system containing 1.2 pairs is 2 E12 while the interaction energy of the system containing 11 and 22 pairs is E C22 or twice the arithmetic aean of E11 and E Since E12 Is approximately the geometric mean of 6 il and 22 where only dispersion forces are acting, and since the geometric mean is always less than the arithmetic mean, the interaction energy of the system is less when 12 pairs are present. These weaker attractive forces result in a volume expansion and an in crease in the enthalpy of the system. The dispersion of clusters due to thermal agitation would explain the fact that the volume change on mixing in creases with temperature and thus one would also expect the heat of mixing to increase with temperature. The heats of mixing in the system perfluoroheptaneisooctane (26) were found to increase with temperature as shown by the follow ing values; at a mole fraction of onehalf, the heats of fixing were 402, 468, and 616 calories per mole at 300, 50, and 709 C. respectively. The volume change on nixing for this system was reported only at 300 C. However, the data of Taylor and Beed (42) show that the volume change on aix ing for this system also increases with temperature. The volume change on mixing is an important property in the study of solutions and for this reason it would be desirable to have a theoretical expression which would pre dict this property. Scatchard (38) and Hildebrand (13) have 37 shown that the Gibbs free energy at constant pressure ( AFp) is related to the Helaholtz free energy at constant volume ( A A) by the following equation AFp AA I ( AY")2 (20) 2/pV The correction term involving AV amounts to less than 10 calories per mole as compared to about 350 calories per mole for AFp, and for this reason it is usually neglected. Hildebrand used this approximation in deriving an expression for the volume change on nixing. He started with the ther modynamic relation AV : \ ) T and by substituting A A for AFp he obtained Ay Z T Av ) T 4 'w ( T By further assuming that the pressure derivative of the entropy was zero he arrived at S p /T "T Z(Vo T Ti T (21) (22) (23) His final assumption was that 1 1/z n TV VDT )T as V (24) and that n = 1. 38 This assumption is based on the fact that for several non polar liquids the internal pressure )T as calculated from the thermodynamic relation (1 ), TA ( )z P (25) can be represented by equation 24 where the coefficient n varies from 0.9 to 1.1. After making this assumption, Hildebrand arrived at the following equation for ATV AVN /a o aW (26) Using equation 1 for ABl yields go22 =(c1 )j 2 41 2 (27) An alternate theoretical expression for AVM can be obtained using Reed's (32) correction instead of the geometric mean assumption, but retaining the condition of constant volume. Under these conditions NEVN is given by : (xl1 4 12S2) .l () 2 d'61 S2(lff)12 (28) 311 & 12 : 2(do22/doll)1/2 (34 1 d 2/doll The ratio d22/d011 can be evaluated from the cube root of 0) 39 the solar volume ratio. Substituting equation 28 into equation 26 results in AV /3o(iLVl 4 xa2V2) [(I 2)2 + 2 61S 62(1 fID] +1 2 (31) Still another expression can be obtained for DVM if it is assumed that the entropy of mixing at constant volume is the ideal value, then 4A B in equation 26 can be replaced by AFIp according to the following: AFp sAAy AtyV1 TS y and Ap ,es A&M TASe If A y is assumed to have the ideal value then and thus / Av" : A re (32) In order to calculate AYV from equations 27, 31, and 32, it is necessary to know /o, the compressibility of a solution showing no volume change on mixing. The com pressibility is defined by equation 33 /3 : 1 a V) (33) SV i Pi T and it can be shown that 3O is a linear function of the volume fraction as van oo. 1o3 4A + 2 2 (34) Isothermal compressibility data needed for equations 34, 27, 31, and 32 are available in the literature for per. fluoroheptane, and carbon tetrachlorlde (20) and nheptane (46). Pressurevolumetemperature data for liquid lso octane are also available in the literature (3) from which the isothermal compressibility was determined by graphical differentiation. eostwater, Frantz, and Hildebrand (46) have shown that for a pure liquid the quantity a as defined by equation 35 tois independent of temperature a = V2T0/3 (35) Equation 35 can be used to extrapolate compressibility data from one temperature to another if volume and coef ficient of thermal expansion data are also available. The values of /3 used in equation 34 are tabulated below in Table III. 41 TABLE III ISOTHREMAL COMPRESSIBILITIES FOR USE IN EQUATION 34 Compound Temperature OC. /3 Atam1 Cyr7l 30 2.65(104) Cy7Fi 50 3.03(104) C716 60 3.42 (104) nC7yI6 50 1.82 (10"4) CCl4 60 1.55(10"4) 1CsS18 30 1.21(104) Values of 11~v as calculated from equations 27, 31, and 32 are plotted on Figures 3739 along with the ex perimental values for the systems perfluoroheptanecarbon tetrachloride, perfluoroheptanenheptane, and perfluoro. heptaneisooctane. Figure 37 reveals that for the C7F16CC14 system the agreement between experimental values of AV* and those calculated from the experimental AFpe is quite good; the theoretical equation 31 also gives a fair ly good estimate of AVY. For the systems C7F16uC7H16 and C7F16iC8H18, however, all these relations prove to be 42 poor estimates of AVM. It should also be noted that the theoretical equations 27 and 31 predict values of VIE which are symmetrical with respect to volume fraction and therefore should have their maximum values at a volume frac tion of 0.5 (about 0.3 0.4 mole fraction of fluorocarbon). Figures 2427 reveal that the volume changes for the four systems of this work and the C7F161CgH18 system are mor nearly symmetrical with respect to mole fraction, having their maxima at a sole fraction of approximately 0.5. Since equations 27, 31, and 32 failed to predict reasonable values for &V it might be instructive to ex. amine critically some of the assumptions and approximations involved In obtaining equation 26. The first approximation involved the neglect of the pressure derivative of the correction term (a V)2 when sub stituting for AFpe in equation 21. Although this term is small and can be neglected in equation 20 its pressure deriv ative may not be small enough to be neglected in equation 22. Another source of error in equation 2# might result from the assumption that the pressure derivative of the entropy term in equation 22 is zero. It should be mentioned, how ever, that unless these two assumptions are made the ex pression for AV* becomes extremely complicated. 43 Another assumption, the effects of which can be clearly seen, is the assumption that the internal pressure can be represented by equation 24, where a is equal to unity. The data are available with which to calculate the internal pressure of perfluorobeptane (20) from equation 25. This calculation was made and it was found that a value of n equal to 1.40 was necessary to satisfy equation 24. If the coefficient n is not assumed equal to unity, equation 26 would be written AV a noaIyN (36) Since n for a fluorocarbonhydrocarbon mixture would pro. bably lie between 1.0 and 1.4, equation 36 would predict values of &VU larger than those predicted by equations 27, 31, and 32, which implicitly assume a value of n equal to unity. A value of n between 1.0 and 1.4, however, would still predict low values of aVT for the C7F16nC7y16 and C7F16iC8H8 systems since a value of n between 2.0 and 3.0 would be required for these systems. Since equa tions 31 and 32 closely predict &yV for the C7F16CC14 system the inclusion of n in equation 36 would impair the agreement in this case. 44 It is possible that equation 26 is reasonably correct and that the expressions for AE are in error. This possibility will be discussed in more detail in Chapter VII. It is concluded that there are many assumptions and approximations involved in the derivation of equation 26 which prevent the accurate prediction of volume changes. CHAPZU VII NBTINATICK OF THUF ODYAMIC PROPEBTI B Heat of Mixing.It was previously mentioned that Reed rederived the equations of Scatchard and Hildebrand omitting the assumptions of no volume change and the geooe trio mean, and obtained an expression which predicted heats of mixing in agreement with experimental values. Reed's expression for the heat of mixing in a binary mixture is given below: AM: = (z 1V xgaV) ( + 22) 2 <1 (1 A I D) 2 1(1 I ) + X2(1 ) (37) *j VlV2 Where (1/) 2 (38) The terms fI and tD were defined previously by equations 29 and 30. Although equation 37 predicts values of AZp it can be shown that the difference between ApRp and AHp is neg. eligible. In order to use equation 37 it is necessary to know the ionization potentials and partial molal volumes of coa ponents 1 and 2. Reed (34) has presented a method of pre dicting the ionization potential of a compound from its po larisability and structure which yields good results and can be used in the absence of experimental data. Hildebrand (14) has shown that by considering the vol 45 46 ume change on mixing that the heat of mixing can be calcu lated from the following expression. AHP: &ay (1. OLT) (39) If the entropy change at constant volume is assumed ideal, then &I*N can be replaced by AFpe and &Hp = A p(1. O c T) (40) Equation 40 can be used to calculate heats of mixing in fluorocarbonhydrocarbon systems for which the thermal coef ficient of expansion (o ) is known and where AFpe can be calculated from the binary solubility data as outlined in Chapter V. Still another method of estimating the heat of mix ing involves the use of the following thermodynamics relation AHp = arp TASp (41) In terms of the excess properties, equation 41 can be written AdRp p A fe TSA S (42) Since a method of estimating A Fp is available it is only nec essary to estimate 6 Sp. The entropy change due to the vol ume change on mixing can be determined from the following Maxwell relation 1681 = (43) For a volume change at constant pressure A 8 is given by /Vo AM AS : ( ) dV (44) 47 By assuming that ( .P ) is constant over the small volume \(T/ V change, equation 44 results in A~sf =Y The 68 in equation 45 represents the change in entropy be. tween a constant pressure and a constant volume process. Equation 45 can then be used in equation 42 giving AHp 1 AFpe 4 TZP ) AV)v T ASYe (46) If A e is again assumed equal to zero, equation 46 can be used to calculate heats of mixing where binary solubility data, volume change on mixing data, and the value of/ Pl for the pure compounds are available. Westwater, Frants, and Hildebrand have measured the quantity (4P) for several pure compounds and equiaolar bins. ry mixtures and have found that the( Z P term for mixtures \VT )T V can be calculated from those of the pure compounds through the following relation 1/2 1/2 2 amix : (xlal x2a2 ) (47) where a is defined by equation 35. The heats of mixing have been calculated from equa tions 37, 40, and 46 for the systems C7F16nC7118 6 C7F16 CC14, 1F6~IClHi8, CS12*C5O1I and C4710C41R0, and are plotted versus composition on Figures 4953. The data neces sary for these calculations is tabulated in Table XXVII. The necessary (~P data are not available for the The nece sary V 48 C512C5H12 and C4F10C4H10 systems and therefore equation 46 cannot be used. Figures 5153 reveal that equations 37 and 40 predict values of the heat of mixing in good agreement with the reported literature values. The agreement between equations 37, 40, and 46 is very good in the case of the C7F16CC14 system although no experimental values of ABp are available for comparison. Agreement between equations 37, 40, and 46 is not too good, however, in the C7yF6nC7HI6 system where again no experimental values of AH are available for comparison. Free Energy of Mixing..As was mentioned in Chapter V the excess free energy of mixing can be estimated quite well from binary solubility data. Equation 28 can also be used to estimate excess free energy of mixing if it is as sumed that the entropy of mixing at constant volume has the same value as for an ideal system. Figures 1820 show a com parison of AFpe calculated from equation 28 and from binary solubility data. Reported literature values of AFp are available for comparison in the CsF12C5H12, C4F10C4H10L and C7F16C8H18 systems. In the case of C7716CCI4 no literature values are available, but agreement between AFp9 calculated from equation 28 and A Fpe calculated from solubil ity dr :a is good. In the remaining systems equation 28 always predicts values of AFdy which are too low. The excess free energy of nixing can be estimated in an empirical manner. If it is assumed that equation 28 is 49 the correct expression for A( y* and that the excess entropy of mixing at constant volume can be represented by equation 48, then it is possible to write equation 49 for ApF . OSe xiV i 1 1 x2V) *1 ZO 2) 2 t 2 4S 62(1 DI 1 42 (48) AFpL (1 + zT) (xzl1 V xgV2) (( 1 12)2 2d1JC2(1 f ID) 2 (49) The term z in equation 49 is merely a correction factor and can be determined from an empirical correlation of z versus 2)1 e) 2 6l (l fifD)] shown on Figure 58. Values of z used in establishing this correlation were obtained from free energy and consolute temperature data reported in the literature for fifteen fluorocarbonhydro carbon systems. For all these systems the equations of Scatchard and Hildebrand predict values of the free energy or consolute temperature which are too low. The ScatchardHildebrand equations for the excess free energy and consolute temperature can be written AFe (xIVI x2V2)K 1 2 (50) RC (i X2V2)3 (51) where K = (1 + zT) [(d1 d)2 .2& d4(f fD1f (52) The parameter K represents the effective value of (1 & 2 )2 d d"2d ( I. f o)] necessary to fit the ScatchardHildebrand equations to the 50 experimental data. The value of z was determined from the reported free energy and consolute temperature data by using equations 50, 51, and 52. Values of K and z for the fifteen systems are tabulated in Table XXVIII along with the literature reference and the method of obtaining K. This correlation is only applicable to mixtures of fluorocarbons and paraffin hydrocarbons. Systems con taining benzene, carbon tetrachloride and chloroform could not be so correlated. A glance at Figure 55 reveals that the points are widely scattered about the correlation line and suggests that values of AFpe calculated from z and equation 49 would be subject to quite a bit of error. This is not the case because z is a correction factor and large differences in s result in smaller differences in the factor 1 + sT. This correlation fits the excess free energy data with an average deviation of 7 per cent and a maximum deviation of 20 per cent. Entropy of Mixing.The entropy of mixing at con stant pressure can be given by equation 45 ASoP an to) o+ the (45) or in terms of the excess properties Ap AB (le + Va (45) 51 For the CyF1i"CaH18 system values of ASp' and AVf have been reported (26) and the necessary ( p P data are available in the literature (20) (3). Values of TA5Be and TeZl A4 are plotted versus composition on Figure 56 where it can be seen that the T z Aym teom is much larger than T ASpW indicating negative values for A Sye. Negative values of A8e would also explain the fact that lFe as calculated from equation 28 Are lower than experimental values, since in using equa tion 28g ASye was assumed equal to zero, These negative values of A Sye would also explain the large difference between experimental values of AH and those calculated by by equation 46 as shown on Figure 51. The same conclusion concerning A 8 in the Cjl6en. CH16 system could also be drawn from Figure 49, The C7F16CC14 system however, appears to have a value of d SyW equal to zero since from Figure 54 it can be seen that F4 7 calculated from equation 28 is in agree sent with AF determined from solubility data. Also values of AH calculated from equations 37, 40, and 46 are in good agreement as shown on Figure 50. Another argument in favor of negative values of A~ is the fact that the empirical correlation involving 52 z and equation 49 predicts free energies of nixing. This correlation is based on the assumption that A Sy can be predicted by equation 483 Since a is a positive number then ASy* as given by equation 48 will be negative. If negative values of A8Sy are common to most fluorocarbonhydrocarbon solutions, it is surprising that equation 40 predicts values of AH in agreement with experi mental values in the C7116iC8H18, C51Cg512, and C4o10C410 systems. In order to understand why equation 40 is successful in this respect it would be well to ex amine its derivation. This is done in the following parao, graphs6 In order to determine the effect of small volume changes on A By as given by equation I, Hildebrand ex panded A Ey about Vo using a Taylor series and obtained IT " (53) By negle,'ting second order and higher terms in AV and using the thermodynamic relation he obtained 4Z a & BYv q T7;)V A'V1 T P 'AT1 (54) 53 The relation between AEpO and 4Hp is aHp s 4XI PaVM (55) Substituting equation 55 into equation 54 gives A Up 4 ay We have already seen from equation 26 that the volume change on mixing is related to the energy of mixing at constant volume (26) By substituting equation 26 into equation 56 Hildebrand obtained AHS: a E T /3, AyM (57) If /3 and 30 are assmed equal then equation 39 results A Hp = A (1 oT) (39) A possible reason why equation 40 predicts reason able values of A H in spite of negative values of ASe is apparent from equation 56. The substitution of A F for ARv in equation 56 would result in values of AH which were too high. This effect is compensated by expressing AT by equation 26, which we have seen generally predicts values of AYV which are too low. Thus equation 40 provides a good estimate of AH, probably due to a fortuitous cancel lation of errors. The fact that it is possible for equation 40 to pre dict reasonable values for A H even though A W is not zero 54 and the fact that AFe as calculated by equation 28 is less than the observed values leads to the conclusion that &8Ve could also be negative in the C5F12CH12 and C4F10C4Hlo systems. Negative values of ASVe for fluorocarbonhydrocarbon systems are not unreasonable and are consistent with the con cept of clustering. In a mixture containing clusters, the distribution of molecules would not be random and one would expect the entropy of mixing to be less than the ideal value. The effect of raising the temperature would be to increase the random thermal motion of the molecules and decrease the clustering tendency. Thus the value of A tye should be come less negative as the temperature is increased, causing the value of LSpe to increase with temperature. This effect was found in the C7H16iC8H18 system where the following values of A8pe were reported for an equimolar mixture. t AlSpe (cal./mole OK) 30 oC. 0.24 50 OC. 0.46 70 oC. 0.89 CNAP!'U VIII TERNARY LIQUIDLIQUID O8LUBILITY STUDIES The ternary liquidliquid solubility studies were undertaken to determine whether fluorocarbon mixtures could be separated by solvent extraction, and whether fluorocarbons would be good solvents for mixtures of other types of coa pounds. Various types of organic compounds were tested as possible solvents for separating a mixture of perfluoro heptane (C7Fi6) and perfluorocyclic oxide (CsFL60). Mperimental,.These preliminary studies were per formed by vigorously shaking an approximately equiaolar mixture of the two fluorocarbons with the prospective sol vent in a small screvcap vial and using a PerkinKlaer "Vapor Practometer" to analyse the two coexisting liquid phases. The criterion of a good prospective solvent was tak en to be the difference in the C71F6 and C8130O peak height fractions in the two liquid phases. Of all the organic sol vents tested, carbon tetrachloride (CC14) and aheptane (nC7uH16) were found to be the most promising. The ternary liquidliquid phase diagrams were determined for the systems C7Fl6CSF60nyHi16 and C7F11C8Q160CCl4 at 300 C. 55 56 The methyl ester of perfluorooctanoic acid (C7F15COOCH) was tested as a possible solvent for mixtures of toluene (CgHNCH3) and methyl cyclohexane (COH1ICH3)oince the consolute temperatures for these two binary systems containing the eater were quite different. Toluene and the eater are completely miscible at room temperature where as the consolute temperature of the methyloyalohexaneester system ts 45 C. The ternary liquid phase diagram was deo termined for this system at 253 and 100 C. The isothermal ternary liquid phase diagrams were determined from chromatographic analysis of the two coex isting liquid phases. The liquid mixture was contained in a screwcap vial and was vigorously shaken while immersed in a water bath. After being shaken for some time, samples of each phase consisting of approximately 0.04 ml. were with drawn for analysis by a hypodermic syringe and the mixture was again shaken. Two or three successive samples were taken with shaking in between sampling. The hypodermic syringe was warmed to approximately 100 C. above the temperature of the mixture prior to sampling in order to prevent any con centration changes due to cooling the saturated phases. The sample was injected into the chromatograph immediately after sampling so as to prevent formation of a second phase in the syringe upon cooling. The water bath used in these determinations was deo scribed in Chapter VI. The vial was shaken by hand during the determination et the toluenemethylcyclohexaneester system, but it was found that considerable shaking was neces sary to effect equilibrium between phases in the two perfluo robeptaneperfluorocyclic oxide systems. Therefore, the vial was shaken by an airdriven mechanism for approximately thirty minutes before and between sampling. The agreement between the analyses for successive samples was taken as the criterion of equilibrium. Since analyses were performed chromatographically, it was first necessary to find a suitable partitioning liquid that would resolve the ternary mixture into three separate peaks on the chromatograph with no overlapping. After the proper partitioning liquid had been found, it was then neces sary to prepare calibration curves of peak height fraction against weight fraction for two of the three possible binary mixtures, since it was found that a ternary mixture could be analysed from calibration data for only two of the three possible binary mixtures. This is due to the fact that the solutes are in very low concentration in the partitioning liquid and therefore act independently of each other. The calibration data and curves used for analyses are given in Tables XVIII and Figures 4044. 58 The peak height traction for aucoessive samples of one phase were usually in good agreement and the compoel tion was determined from the average peak height fractions. Where significant differences occurred between peak height fractions of Successive samples, the compositions of each sample wer also calculated and are tabulated. The tie l11e data necessary for construction of the phase diagcrms is taba lAted in Table XIX sad the phase diagrams are ahown on Figures 45.45' Conjugate curves are drawn on the phase diagrams for the purpose of interpolating tie lines; the plait points for two of the systems were outlasted by extrapolating the conjugate curve to its intersection with the binodal eurve. ohese conjugate curves were constructed from points located by drawing lines through each end of the tie line parallel to the side of the diagram in such a manner that these two lines iater eoted inside the diagrams. Varteressian and renake (44) found that ternary sol m ability data could be represented by the following relationship /3 Wl j , VI 2 3' X2 The tern /1 is known as the selectivity of the solvent aad gives a measure of the ease with which a binary mixture can be separated with a give solvent by solvent extraetion 59 methods. A /3 value of unity would indicate no selectivity while solvents having higher values of /3 we mare selective. The seleetivity is amnlogous to the relative volatility vhi h is need as a measure of the ease with whibh a binary mixture can be separated by distillation. Values of the selectivity have been calculated tfro the tie lie data sad equation 88 tor the four system studied in this work. inse these values of the selectivity vary only slightly with composition, their average values are tabulated below in Table IV. TABL IV SOLVUTT LaCTIVITTI8 Mixture to be solvent t c. Average C1eIoC77r1 ccI4 so3 1.20 Ce5ruce3ls ,C7Ne i300 1.09 C6e5Ca3PC1c4xC3 C71PcscOc3 3sI0 .a16 eaeaCs.Nclncsa ir77cooc3 1o 1.s23 Table IT tetrashloride is ahows that neither aeptaae nor carbon a good solvent for the fluorocarbon miature 60 but that carbon tetrachloride is the better of the two. It is also obvious that the ester is not a good solvent for the hydrocarbon mixture. From consideration of the ScatchardHildebrand the ory one would not expect a nonpolar solvent to be very se lective for either C7F16 or C87160 since their solubility parameters (C) are almost equal, being 5.93 and 6.05 re spectively. The difference is a measure of the deviation of a binary system from Raoultt* law as shown by equation 3. One can see that for a given solvent the S difference be tween C7F16 and solvent is practically the same as the Cr difference between C8F160 and solvent. The high solvent selectivity found in some reported systems can be attributed to specific effects such as association, solvation, or hy drogen bonding, which are not present in nonpolar systems. Since the solubility parameters of the fluorocarbons are almost equal, and since they are nonpolar they cannot exhibit specific interaction effects with the solvent, It is con sidered unlikely that a separation can be effected by sol vent extraction. Theoretical Calculation of Activities in Ternary Systems.Hildebrand (15) has extended the treatment of solu tions of nonelectrolytes to ternary systems and has arrived 61 at equations 59 for the activity coefficients in terms of the properties of the pure compounds. Rt In Y< 1 3 Vi 2 d 2) ( 1 63) 3] 2 (59) T ]A Vg 2 Z 2 RTlnY3 V3 (3 1S)s f (3 2) ] 2 Using equations59 the activities in the two conu. gate liquid phases can be calculated from the tie line data. If equations 59 correctly predict activity coeffi cients, the calculated activities must satisfy the condition that the activity of each component be equal in both phases. Z1 YL x YI x2) 2 x2'Y2' (60) 3 3 s3 3 Squations 59 were used along with the tie line data to calculate activities in the coexisting phases for the systems CF71.C816OCCL4 and C716C810.OaCC716. The solubility parameters were evaluated froa the properties of the pure components. These calculated activity values are tabulated in Table XX. From Table XX it is obvious that the results of equations 59 do not satisfy the conditions of equations 60. If, however, equations 59 are used with the solubility parameters evaluated from the binary solubility data, the activities are found to satisfy equations 60, s can be sees trom Table XX. The "etteetive" solubility parameters eaa be found from the binary solubility data by substituting equations 3 into equations 11 and 12. Two empirical values of each difference are obtained trom this procedure sinoe there are two equations (11 and 12) sad only one uaknown (the X ditf tmenoae) It was found that there was only a slight dif ferenee between the two f difference terms sad therefore aa average value vwa used for substitution into equation 59o Since the following relation holds &1 needed to evaluate all possible c difterenaes required by equations g9. Valuea of the O dffttreace evaluated ftro the binary solubility data are compared with these evaluated from properties of the pure compounds n Table V. TAME V COUPARIS0N OF S DMFFRENCE S e Difference System . Pure Compounds Solubility C716.nCAH16 1.43 2.87 CgF60inC7H16 1.31 2.78 C7r16cc14 2.52 3.10 C1r6O0CC14 2.40 2.94 8ince the Van Laar equation has proved useful in treating binary systems it would be interesting to see if ternary systems are also amenable to this treatment. White (47) has applied the Van Laar equation to calculate equilibrium vaporliquid compositions in ternary systems from data obtained from the binary systems. He compared the calculated results with experimental data for three ternary systems and found the agreement to be good enough for engineering purposes. Robinson and Gilliland (36) have shown that the Van Laar treatment can be extended to ternary systems where the Van Laar constants for only two binary systems are needed to calculate activity coefficients in the ternary system. The ternary Van Laar relations are 'A2 x3A32 vAW/%s in Y_2 x2A12 All *_ xA_32_ 32 21/12 *, 2 + zx3A32B32] in Y3 1  12 rA31/B12 1' 32 [ /lA Bl: 4+ 2 + Ax3A32/SS In evaluating the constants in equations 61 the relations are used 2 (61) 2 following A12 B21 812 A21 and A21 B12 Since the square roots of the binary Van Laar con stants are needed for equations 61 the question arises as to whether the positive or negative root should be used. In This case the binary Van Laar equation is considered similar in form to equations 3, where the constants can be written A12 V1 (1 d2) 2 1,f 2 3 ( &2 2)2 22 T and A12 V1 The square root of A12 is taken to be positive if 6 is In Y1 = greater than C2 and negative if the reverse is true. The relation existing between the constants which allows the evaluation of all constants from the constants of two bi nary systems is \A \/ ra3X 0 The necessary constants for use in equations 81 were determined from the binary Van Lar constants by the pro cedure described above. The activities for each component in the two coexisting phases were calculated for the systems CyF16C8gF10CC14 and C7F6CgsF1r60WC718.6 These activities are tabulated in Table ZXX and it can be seen that equations 61 satisfy the conditions of equations 60. Thus we see that equations 59 or 61 can be used to predict activities in ternary systems when the constants are evaluated experimen tally from two binary systems. It is also possible to use equations 59 or 61 to construct the ternary phase diagram from the binary solu bility data. This can be done graphically by using equation 59 or 61 to plot contours of constant activity for each com ponent on a triangular diagram. The composition of the two phases in equilibrium can be found by locating two points at which the activity of each component is equal. An at tempt was made to use this method to calculate the phase 66 diagram for the C7716CF160CC14 system, but location of the phase compositions proved very difficult since it was necessary to interpolate between three sets of activity contours. CHAPTER IX ETRACTIVE DISTILLATION STUDIES The term extractive distillation refers to the process of adding a solvent to a Mixture to be separated by distillation in order to improve the relative volatility. The solvent is able to improve the relative volatility by altering the activity coefficients of the various compo nents. The relative volatility (0() is defined for a bi nary mixture by equation 62 ( = y (62) i Y2 (In equation 62 the subscript 1 refers to the more volaw tile compound.) For systems obeying Dalton's law of par tial pressures and where deviations from ideal gas behavior can be neglected the ratio yl/x1 is given by yl/xI a Substituting into equation 62 gives o1 A1f (63) From equation 63 it can be seen that by selecting a solvent 63 which increases the ratio of activity coefficients the rela tive volatility is increased. In practice the solvent used is essentially non volatile or of a low volatility compared to the original components and the quantity used is such that the original components are in low concentrations in the liquid phase and dc not interact with each other appreciably. This being the case, the ternary mixture can be treated approximately as two binary mixtures involving each original component with the solvent. Since the solvent is essentially nonvolatile the vapor phase is assumed to consist only of the original components. The ScatchardHildebrand theory can be used to pre dict some properties of a good solvent for extractive distillation. Assuming two independent binary systems, the expression for the logarithm of the activity coefficient ratio as given by equation 3 is RT lan Y1/ Y2 00 V1 4 3 V2 4 <) 32 (64) (In equation 64 the subscript 3 refers to the solvent.) If the molal volumes of components 1 and 2 are ap proximately equal then equation 64 becomes S in [Y/ 2) (, (65) 69 From equation 65 we see that the logarithm of the activity coefficient ratio depends upon the square of the volume fraction of solvent and upon the solubility parameter of the solvent. From the standpoint of separating power the properties of a good solvent will be those which increase the right hand side of equation 64 or 65. This indicates that the molal volume and the solubility parameter are im portant factors in selecting a solvent. It is difficult to predict the effect of temperature upon the activity coeffi cient ratio as given by equation 65 since the molal volume changes in the same direction as the temperature, and the difference term is more or less independent of temperature. One would therefore not expect the activity coefficient ratio to be a strong function of temperature. In this work several compounds will be evaluated as extractive distillation solvents for mixtures of perfluoro. heptane (CyFl6) and porfluorocyclic oxide (C8F160); also nheptane (nC7H16) and methylcyclohexane (C6gl11C%). A convenient method of evaluating prospective ex tractive distillation solvents is by means of gasliquid par tition chroaatography. Porter, Dual, and Stross (30) have shown that the activity coefficient of a solute in an in finitely dilute solution in the partitioning liquid can be obtained from the appearance time of the solute peak. The activity coefficient ratio in equation 63 can be found from the appearance times of components 1 and 2 when the prospec tive solvent is used as the partitioning liquid. The follow ing relations were given by Porter et al for determining the activity coefficient in the infinitely dilute solution. V R 0 VO+ B av (66) S : aT/YOpVs (67) V 0 V (p/ ) ) (68) R L,3(Pi/ Po)2 The volume occupied by the vapor phase in the column (V0) is usually mall compared to V0 and can be neglected. Neglecting V0 and combining equations 66 and 67 we get o VgRT VR O (69) P Vg If the appearance times, for components 1 and 2 are de termined under the same conditions of constant flow rate and constant pressure drop through the partitioning column then we can write S02 R2 02 (70) . . (0 From equitiun 69 the ratio VR2/ v1i can be written vT = 91 (71) YR 2 oP 71 Equating equations 70 and 71 gives (72) Y20 GlPlO Substituting equation 72 into equation 63 yields the follow ing expression for the relative volatility of components 1 and 2 at infinite dilution in the partitioning liquid. o0 : e0/ 0e (73) Since the value of the relative volatility as given by equa tion 73 is for an infinitely dilute solution, the ratio of the appearance times gives the maximum separation that can be obtained when using the partitioning liquid as an extractive distillation solvent. Experimental. The chromatography columns used in this work were made from one meter lengths of onefourth inch copper tubing; these columns were used in a PerkinBlmer "Vapor Fractometer,' model 154. The stationary phase was Celite C44857 (Johns Manville), a diatomaceous earth having rather uniform parti cle sime. Before this celite was used the very small parti cles were removed by allowing the material to settle in water and decanting the water containing the suspended fines. After this the celite was washed several times with concentrated hydrochloric acid, then washed with distilled water and dried in an oven. The prospective solvents were perfluorokerosene, and three KelF oils having the general structure Cl(CF2CFCl1)Cl. These oils are products of the N. W. Kellogg Company and were designated KelF oils 1, 3, and 10. The N. W. Kellogg Company reports the following vapor pressures for these oils at 1000 C. KelF Oil 1...17 mm KelF Oil 2... 1 Ma KelF Oil 10..0.1 ma These four liquids were chosen as partitioning liquids since their vapor pressures were low enough to prevent their removal from the packing during operation of the column at adequate gas flow rates and temperatures. The ratio of partitioning liquid to Celite used in the preparation of the partitioning columns was 0.5 to 0.7 ml of liquid per gram of Celite. The weight of packing required to fill the column was measured so that the void volume and the volume of the stationary phase could be computed. The properties of these columns are tabulated in Table XXII. The four above mentioned par' zoningg liquids were evaluated as possible extractive distillation solvents for the binary systems C7F16 with C8F160, and C7H16 with C6HICE3*. 73 Table XXIII gives the appearance times of C71F8, C8160, CyH16 and COH11C3 in the partitioning liquids and Table XXIV gives the values of the relative volatility as cal culated from equation 73. From Table XXIV it can be seen that all four sol. vents can be rated equally as extractive distillation sol. vents frr both binary systems. The pronounced effect of team perature upon the relative volatility is also noted from Table XXIV. The C7F16CsF160 system was investigated by Yen (49) and was found to obey Raoult's law. Since this system is ideal the relative volatility is merely the ratio of vapor pressures. Using the vapor pressures listed in the appendix for C7716 and C8g160, the calculated relative volatilities for this system at 350 and 80 C. are 2.34 and 1.96 rela tively. Using an average value of the relative volatility for these compounds in the four solvents it can be seen that the addition of the solvent changed the relative volatility from 2.34 to 2.62 at 350 C. and from 1.96 to 2.16 at 800 C. This change corresponds to a change in Y*/ Y2 from 1.00 to 1.11 at 35 C. and from 1.00 to 1.10 at 800 C. The effect of temperature upon the activity coefficient ratio is very slight as was previously suggested. 74 The nheptaneaethylcyclohexane system was investi gated by Bromiley and Quiggle (4), who found the average value of the relative volatility to be 1.074 in the temperature range 900 to 101 C. The system obeys Raoult's law and the relative volatility can be expressed as the ratio of vapor pressures. Using the vapor pressures calculated from the Antoine equation given by reference 1 the calculated relative volatilities for this system are 1.003 and 1.057 at 35 and 800 C. respectively. Again using the average value of the relative vola tility for all solvents it is seen that the relative vola tility for these hydrocarbons changed from 1.003 to 1.11 at 350 and from 1.057 to 1.21 at 800 C. The addition of the sol vent caused the activity coefficient ratio to change from 1.00 to 1.11 at 35 C. and from 1.00 to 1.14 at 800 C. Again the effect of temperature on the activity coefficient ratio is seen to be slight. Since the physical properties necessary for evalua tion of the solubility parameters of the solvents (Cf3) are not available it is not possible to predict the expected value of the activity coefficient ratio as given by equation 64 or 65. Equation 64 can be used, however, to evaluate the solvent solubility parameter ( 63) by using the experimentally determined activity coefficient ratio and the necessary phys 75 leal properties of the solutes given in Table XXVI. Values of S3 were calculated from data for the C7F16C68018  solvent, and C7I16C6H11CR3 solvent systems at the tem peratures of 3U C. sad 80 C. These values of f3 are tabulated below and it can be seen that 63 ea oentially the me value when evaluated from experimental data f ra two different systems. TABLE VI CALCULATION OF d0 3 GM EQUATION 64 t (C.) C716CSgF1OSolvent C7HlgCgNlCC1solvent 35 7.88 8.05 so8 7.80 7.52 The results in Table VI indicate that the equations of Seatahard and Nildebrand are applicable to prediction of solvent properties. From the results of Table VI the average solvent solubility parameters are 7.98 at 380 C. and 7.51 at 80 C. These values of the solubility parameter nay seem somewhat high for chlorofluerocarbon compounds since chloro. flueorocarbons for which data are available have solubility parameters between these of fluorocarbons and hydrocarbons 76 kaviag the Sme boiling points. It should be acted, how.. ever, that the solubility parameter iaereasem with lacreso Lag molecular weight within a homologous series a is ob vious from the following table of solubility parameters for the paraffin series as reported by Hildebrand (16). compound a at 2s c. ! A%" 7.05 WC. 14 7.30 _n yCa 7.,. 0% 4 8.0 It right be argued that the large olubility parsme ter of the solvets would le4d to imiastellity in the case of the fluoremarbons, but since the molal volumes of these solvents are undoubtedly large the entropy effect due to vol ame disparity should be considered. The effect of differences in moIal volumes to to decrease the positive deviatloas from Raoult'a law and it is possible that the volume disparity is large *ough to permit miscibility in spite of the large difference. In the light of the volume disparity it would be 77 interesting to determine the effect of this factor upon the activity ooeffieieat ratio of solutes in an extractive distillation solvent Instead of using equation 3, the folloviag equatioea as give by Hildebrand (12) will be used far the activity oeeefieiont since a corretion term for volume disparity is ieclu4ded Ia Y11 (c 6) xa 4 i/2 (I ) (74) T2 If ve again ask the assumption that the volume fraction of solvent is large enough that component 1 and 2 act ainde pendeatly of seah other v oea write for the activity 0oef. ftlient ratio In I/ Cs )2 +:2 '12 S2 CF3&2 02s xL';: Vl/ "" (7$) V2 When the nolal volumes of the solutes are apprxiaately equal the last two teras in equation 76 awe eligible and equation 7T reduces to equation 64. Thus while the volume eorreetion does affect the ladividmal activity sooefileents, the relative volatility of the solutes is unaffected. The success of the Scatehard4ild ebrmad Theory is predicting rel ative volatilitte for extractive distillation As then due to the eamoellation of errors in the individual activity coeffl eient expressions when the ratio of activity ooefflieeata are 78 used. hies tact wM rwcogaiad by meed (3s) sad vwa ued by bin to explala the uneosm of the Scateard "bild raad the ory in prediCting asetropes (33) sad relative velatil.tis in hydrocarbon system. CHAPTER X EVALUATION OF METHODS OF SEPARATING FLUOROCARBON MIXTURES This discussion will deal mainly with possible pro cedures for separation of fluorocarbon mixtures since separation procedures for hydrocarbon mixtures have been covered quite thoroughly by Rossini et &1a (37). Distillation.Several binary systems containing fluorocarbons have been investigated (5) (24) (49) with ideal solution behavior reported in all cases. Since fluoro carbonfluorocarbon mixtures can be expected to follow ideal behavior, the relative volatility or the ease of separation depends upon the ratio of vapor pressures of the compounds to be separated. Yen has shown that when fluorocarbon mixtures are distilled, laboratory distillation columms are approximately onehalf as efficient as when hydrocarbon mixtures are dis tilled. A laboratory distillation column having 100 theoret ical plates in a hydrocarbon separation would have approxi mately 50 theoretical plates in a fluorocarbon separation. Aseotropic Distillation.As would be expected from the large positive deviations exhibited by fluorocarbon hydrocarbon mixtures, aseotropes are formed between fluoro 79 carbons and hydrocarbons even when differences in normal boiling points are large. This azeotropic tendency has been exploited by Mair (23), who used fluorocarbons as azeotrop ing agents in separating paraffin and cycloparaffin hydro carbons. The C7F16 and CSF160 used in this work were each purified by azeotropic distillation with nC7H16. Since the addition of a hydrocarbon azeotroping agent to a fluorocarbon mixture would also increase the efficiency of the distilla tion column, it is possible that azeotropic distillation holds some promise as a means of separating fluorocarbon mix tures. Extractive Distillation.*It was shown earlier that some enhancement of the relative volatility of a fluorocarbon mixture could be obtained by employing a chlorofluorocarbon solvent for extractive distillation. Yen found chlorofluoro. carbons to have column efficiencies slightly less than hydro carbons, but approximately twice as large as fluorocarbons, In this case the added solvent would enhance the separation by increasing the relative volatility and by increasing the column efficiency. The effect of the relative volatility and column effi ciency upon the separation obtainable by distillation can be seen from an equation derived by Fenske (8). X2) D /w (76) Equation 76 applies for conditions of total reflux and con stant o0. The left hand side is a measure of the separation attainable in a column of N plates; a large value of the ratio on the lefthand side indicates good separation. The effect of increasing the coluxa efficiency is to increase the number of theoretical plates (N); thus if both the relative volatility and the column efficiency are increased the re sulting change in separation can be large. Liquid Jatraction.We have seen earlier that separam tion of fluorocarbons by liquid extraction is not feasible where specific interactions between one component and the sol vent are absent. Where a functional group is present in a fluorocarbon, there is the possibility that a solvent can be found which will be selective for this compound. An example of this type could be found in the system C81F60C1F35H C2H5OH where C8gl60 and C2HsOH are practically immiscible while C7F15H and C2H50H are miscible even at temperatures as low as 50 C. In this case there is undoubtedly a hydrogen bonding effect which would permit the separation of C7F15H from C81F60 by extraction with C2Hs5O. CHAPTER XI COWCLUSIONS The experimental work and discussion included in the previous sections of this dissertation provide the basis for the following conclusions. 1. The simple ScatchardRildebrand theory is in adequate for predicting excess free energies of mixing, heats of mixing, and volume changes in fluorocarbonhydro carbon mixtures. 2. The ScatchardBildebrand theory with the modi fications introduced by Reed provides good estimates of the heat of mixing in fluorocarbonhydrocarbon systems. 3. Good estimates of the excess free energy of mix ing can be calculated from the Van Laar equation and bi nary solubility data. 4. Beats of mixing calculated from the Van Laar equation and solubility data are unreliable. 5. The excess free energy of mixing fluorocarbons with paraffin hydrocarbons can be estimated from an empiri cal correlation if values of the solubility parameters, ionization potentials, and molal volumes are available. 6. Comparison of the calculated and observed con solute temperature is not a good criterion for testing the applicability of the ScatchardHildebrand theory. 7. Mixtures of fluorocarbons with hydrocarbons exhibit large volume changes on mixing (in the order of 3 per cent of the total volume at 50 mole per cent). This volume change on mixing was found to increase with increas ing temperature. 8. A negative excess entropy of mixing at constant volume can be used to explain the disagreement in some fluorocarbonhydrocarbon systems between observed thermody namic properties and those calculated from the Scatchard Hildebrand theory. 9. The concept of clustering can be used to explain the negative values of the excess entropy of mixing at con stant volume. 10. ScatchardHildebrand or Van Laar equations may be used to predict activities in ternary systems if the con stants are determined empirically from the solubility data for two of the binary systems. 11. The ScatchardHildebrand equations can be used to predict relative volatilities in systems containing an extractive distillation solvent. 84 12. The possibility of separating a mixture of two fluorocarbons by liquid extraction is slight unless one fluorocarbon contains a functional group which will permit some sort of interaction with the solvent. 13. Future work should be directed toward the measurement and theoretical calculation of the excess entropy of mixing at constant volume. 14. The problem of theoretically calculating the volume change attending mixing remains unsolved. Some light may be shed upon this problem when a theory is developed which will predict the entropy term. APPENDIX I. Purity of Compounds Used Hydrocarbons.Most of the hydrocarbons used in this work were obtainable commercially in a reasonable degree of purity and were not further purified. The physical proper ties of these compounds are listed in Table VII along with the reported literature values. Fluorocarbons.Five fluorocarbon compounds were used in this work. The physical properties of which are listed in Table VIII. The physical properties of some of these fluorocarbons have been reported in the literature; these values are also included in Table VIII. Since the supply of some of the fluorocarbon compounds was limited it was necessary to recover some fluorocarbons from mixtures with hydrocarbons and repurify then. Where this was done the physical properties of both batches are recorded in Table VIII. 1# Perfluorocyclic oxide, C8F160. This material was the major constituent in "Fluorochemical 075" manufactured by the Minnesota Mining and Manufacturing Company. It is believed that this fluorocarbon is a five or six membered, oxygencontaining ring with side chains. This material was first fractionated in a labo ratory distillation column having 60 theoretical plates 85 (when tested with hydrocarbons). The center cut from this fractionation was further purified by an aseotropic distillation with nheptane. The fluorocarbon was then separated from the hydrocarbon by cooling the azeotrope to dry ice temperature where liquid phases were found having very low mutual solubility. The perfluorocyclic oxide was then freed from the small amount of remaining nheptane by redistillation in a 30 theoretical plate column (when tested with hydrocarbons). A chromatograph of this purified material revealed only one peak. 2. Perfluoroheptane, C7F16. This material was a constituent of "Fluorochemical 101" marketed by the Minn esota Mining and Manufacturing Company and was purified by the same procedure as perfluorocyclic oxide. This purified material also exhibited only one peak when sub jected to chromatographic analysis. 3. Perfluorotributyl amine, (C4F9)3N. This material was the center cut obtained by fractionation of Minne sota Mining and Manufacturing Company's "Fluorochemical N43" in a 60 theoretical plate column (when tested with hydrocarbons). Chroastographic analysis indicated that this material was a mixture of several components, proba bly isomers. 4. 1Hydroperfluoroheptane, C77F15H. This material 87 was prepared in the Fluorine Research Laboratory by Dr. N. C. Brown by the decarboxylation of the sodium salt of perfluorooctanoic acid. This material was puri fied by simple distillation in a column having 60 theoret ical plates (when tested with hydrocarbons). 5. Methyl perfluorooctanoate, C7F15COOCH3. This material was also prepared by Dr. H. C. Brown from per fluorooctanoic acid and was purified by simple distilla tion in a 60 theoretical plate column (for hydrocarbons). II. Thermocouple and Thermometer Calibration All thermocouples used in this work were the copper constantan type. Thermocouple readings were made with a Leeds and Northrup potentiometer No. 8662 which could be read to 0.001 millivolt. 1. Thermocouple in two liquid phase still. The calibration temperatures for this thermocouple were the ice point and the boiling points of methylcyclohexane at 757.45 and 381.05 pressure. The boiling points of methylcyclohexane at these pressures were determined from the Antoine equation given in reference 1. The poten tiometer readings (in millivolts) at these temperatures were used to determine the constants in a threeconstant equation. The calibration data and equation are given in Table IX. 88 2. Thermocouple in Solubility Cell. This thermo couple was calibrated against a thermocouple previously calibrated by Dr. T. K. Reed of the Fluorine Research Laboratory having the following calibration equation. t 0.050 + 24.91e 0.3592.2 The two thermocouples were immersed in a wator bath and both readings were made at the same temperature. These millivolt readings are listed in Table IX along with the bath temperatures calculated from the above calibration equation. Since the two thermocouple readings were practically identical, the calibration equation for the thermocouple in the solubility cell was taken to be t Z 0.050 + 24.91e 0.3592e2 3. Thermometer in Temperature Bath. This mercury inglass thermometer was graduated in tenths cf degree centigrade and could be read to 0.02 C. This ther mometer was calibrated against a thermocouple calibrated by the National Bureau of Standards. The calibration data are given in Table IX. Pycnometer Calibration Data and Equations.The calibration data for five pycnoneters at several tempera tures are tabulated in Table X. The pycnometers were de signed by Lipkin (22) and w.wr: essentially U tubes with a 89 bulb in one arm. The arms were capillary tubes provided with etched graduations. At a constant temperature each pycnometer was cali brated by determining the volumes corresponding to three dif ferent liquid heights in the capillary arms. The volume was related to the total liquid height by the following equation V = Vo + ah The constants Vo and a were determined by the method of least squares. The volume of a pycnometer at a particular liquid height was determined from the weight of distilled mercury occupying the pycnometer and the density of mercury at that temperature. All weighing were corrected for air buoyancy. The pycaometers were kept in a constant temperature bath for approximately thirty minutes before the liquid heights were read. The constant temperature bath never varied more than 0.050 C. froa the calibration temperature. Vapor Pressure Measurements.*The vapor pressures of all of the pure fluorocarbons were determined over a range of temperatures by measuring the boiling temperature under various applied pressures. The still shown on Figure 9 and a boiling point still similar to that described by Quiggle, Tongberg, and Fenske (31) were used for these measurements. Calibrated thermocouples were used for temperature readings. The stills 90 were connected to a closed system containing a mercury manometer which could be read to 0.10 am by means of a cathetometer. The experimental data are reported in Table XI and log p is plotted versus 1/T in Figure 1. 11 A AF 4 A^ A* A #A U A fIQ 6r4Cf P4C4 r4 ri) u4< 94 %woe M 0 1 M6 "4 m . 1 eg a 0 0 . 0 14 *t tc o . j ^' *I ." 8 ft 2 4 ^*'B 8^ >^ti <(^ ~ i A 54 4 !M e g 8 +f t % a o S. *  4 11043 8 2 8 ^. H . 00 i 0 "1 0 0 cc0 &r go 5 0 0. 0 m M 0. 0 0. 8 ^ i 00 0 p4 r(0 0 f I '4"I i~it.. 0. C' 440 0 sd Owd i 0r 0 0 S m i~ 00 3*4 1 j~  ff i dca  d__' ____ a & nsa Aug 91 