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Vapor-Liquid Equilibria For The Benzene - N-Octane System Near The Regionof The Critical-Locus

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Vapor-Liquid Equilibria For The Benzene - N-Octane System Near The Regionof The Critical-Locus

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Content VAPOR-LIQUID EQUILIBRIA FOR THE BENZENE-n-OCTANE SYSTEM NEAR THE REGION OF THE CRITICAL LOCUS by Charles Robert Koppany A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Chemical Engineering) August 1972 INFORMATION TO USERS This dissertation was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pages you wish reproduced. University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 A Xerox Education Company I I 73-745 KOPPANY, Charles Robert, 1941- VAPOR-LIQUID EQUILIBRIA FOR THE BENZENE-n- OCTANE SYSTEM NEAR THE REGION OF THE CRITICAL LOCUS. University of Southern California, Ph.D., 1972 Engineering, chemical University Microfilms, A XEROX Company, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. U N IV E R S IT Y O F S O U T H E R N C A LIF O R N IA T H E G R A D U A T E S C H O O L U N IV E R S IT Y P A R K LO S A N G E L E S , C A L IF O R N IA 9 0 0 0 7 This dissertation, written by Charles Robert Koppany tinder the direction of h.is... Dissertation Com mittee, and approved by a ll its members, has been presented to and accepted by The Graduate School, in partial fulfillm ent of requirements of the degree of D O C TO R O F P H IL O S O P H Y Date August 1972 DISSERTATION COMMITTEE PLEASE NOTE: Some pages may have indistinct print. Filmed as received. University Microfilms, A Xerox Education Company ACKNOWLEDGMENTS I wish to gratefully acknowledge my adviser, Dr. C. J. Rebert, for his valuable assistance and encourage ment in this work. I also wish to acknowledge my committee members, Dr. J. M. Lenoir and Dr. P. R. Choudhury, for their help ful suggestions and advice. I would like to express my appreciation to Mr. J. M. Scott, the laboratory mechanic, and to Mr. G. W. Berkstresser (soon to be Dr. Berkstresser), for their assistance and suggestions on the mechanical aspects of the equipment. Finally, I wish to express my deep gratitude to Mrs. Ruth Toyama for her very valuable assistance in the administrative details and in the final preparation of this dissertation. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ........................................ ii LIST OF T A B L E S ........................................ v LIST OF FIGURES.......................................... vii INTRODUCTION .......................................... 1 AVAILABLE EQUILIBRIUM D A T A ............. 4 EXPERIMENTAL PROCEDURE ............................... 5 PRESENTATION OF EXPERIMENTAL DATA.................... 20 EQUILIBRIUM DATA FROM ENTHALPIES.................... 53 LIQUID PHASE ACTIVITY COEFFICIENTS FROM VAPOR- LIQUID EQUILIBRIUM D A T A .......................... 65 LIQUID PHASE ACTIVITY COEFFICIENTS FROM HEATS OF MIXING.............................................. 81 SUMMARY................................................... 103 REFERENCES...............................................106 APPENDICES...................... 108 Appendix A - Sample Preparation and Experimental Procedure.......................... • 109 Appendix B - Calibration of Equipment ............ 117 Appendix C - Calculation of Sample Composition from the Capillary Loading Technique 124 Appendix D - Determination of Sample Compositions by Gas Chromatography.................. 130 Appendix E - Determination of True Temperature and Pressure of Sample . ........... 137 Appendix F - Reduced Experimental Data ............ 144 iii Page Appendix G - Discussion of Errors................. 155 Appendix H - Purity of Fluids U s e d ...............157 Appendix I - Listing of Computer Programs and Printouts............................. 159 iv LIST OF TABLES Table No. Page I Summary of Corrected Benzene-n-Octane Compositions . . . 14 II Comparison of Critical Pressures and Temperatures for the Benzene-n-Octane System . 18 III Comparison of Critical Pressures and Temperatures for the Pure Components......... 19 IV Summary of Regression Constants for the Fit of Equation 2 to the Bubble and Dew Curves of the Benzene-n-Octane System .................. 26 V Definition of Popovics1 Statistical Parameters...................................... 27 VI Summary of Popovics1 Statistical Parameters for the Fit of Equation 2 to the Bubble and Dew Curves of the Benzene-n-Octane System . . 29 VII Pressure-Temperature Relations at the Phase Boundaries of the System Benzene-n-Octane at Equal Intervals of Temperature............. . 31 VIII Smoothed P-X-Y Data and Calculated Equilibrium Ratios................. 47 IX Enthalpy-Based Bubble and Dew Pressures at Equal Intervals of Temperature............... 56 X Coefficients to Equation 7 for Benzene and n-Octane............... ................... .. . 68 XI Calculated Heats of Mixing from Enthalpy Data for the Benzene-n-Octane System ............. 82 XII Smoothed Heats of Mixing for the Benzene-n- Octane S y s t e m ................................. 86 XIII Thermocouple Deviation Data .................. 119 v Table No. Page XIV Summary of Equations for Obtaining True Boiling Temperatures of Standard Calibration Fluids ........................... 120 XV Sample Calculation of Mixture Composition . 125 XVI GE Time-Sharing Program for Hyperbolic Fit . 134 XVII Output to Hyperbolic Fit Program......... 135 XVIII Sample Data Reduction Sheet ........ 138 XIX Reference Chart for Iron-Constantan Thermocouple ................................. 139 XX Interpolation Chart for Iron-Constantan Thermocouple ................................. 141 XXI Mercury Vapor Pressure Chart for Experimental Range.........-...................142 XXII Reduced Experimental D a t a ................ 145 XXIII Listing of GE Time-Sharing Program CRKl . . 160 XXIV Sample Printout for Program CRKl......... 161 XXV Listing of GE Time-Sharing Program CRK8 . . 162 XXVI Sample Printout for CRK8.................. 163 XXVII Listing of GE Time-Sharing Program CRK3 . . 164 XXVIII Printout for Program CRK3 .............. 165 XXIX Listing of GE Time-Sharing Program CRK4 and a Sample Printout for 260°C 166 XXX Listing of GE Time-Sharing Program CRK7 . . 167 XXXI Sample Printout for Program CRK7......... 168 vi LIST OF FIGURES Figure No. Page 1. Sample Recovery Assembly ..................... 9 2. Sample Composition Correction Curve for the Benzene-n-Octane System .................... 12 3. Critical Pressure Locus of the Benzene-n- Octane S y s t e m ............................... 15 4. Critical Temperature Locus of the Benzene- n-Octane S y s t e m ............................. 17 5. Comparison of Vapor Pressures for Benzene and n-Octane................................. 22 6. P-T Phase Boundaries for the Benzene-n- Octane S y s t e m ............................... 23 7. P-T Phase Boundaries for the Benzene-n- Octane S y s t e m ............................... 24 8. P-X Isotherms for the Benzene-n-Octane System........................................ 43 9. P-X Isotherms for the Benzene-n-Octane System........................................ 44 10. P-X Isotherms for the Benzene-n-Octane System........................................ 45 11. Equilibrium Ratios for the Benzene-n-Octane System........................................ 51 12. Equilibrium Ratios for the Benzene-n-Octane System at 2 9 0 ° C ............................. 52 13. P-T Bubble Curves Generated from Enthalpy Data.......................... 54 14. P-T Dew Curves Generated from Enthalpy Data 55 15. Comparison Between Equilibrium and Enthalpy Based Pres sure-Compos it ion D a t a ........... 58 vii ___ _ l Figure No. Page 16. Comparison Between Equilibrium and Enthalpy Based Pressure-Composition Data................59 17. Comparison Between Equilibrium and Enthalpy Based Pressure-Composition Data ....... 60 18. Comparison of Equilibrium Ratios at 250°C (482°F).......................................... 63 19. Saturated Molar Liquid Volumes for Benzene and n-Octane....................................71 20. Vapor Phase Mixture Fugacity Coefficients for Benzene Calculated by the Redlich-Kwong Equation of State............................... 75 21. Vapor Phase Mixture Fugacity Coefficients for n-Octane Calculated by the Redlich-Kwong Equation of State............................... 76 22. Liquid Phase Activity Coefficients Calculated from Measured Vapor-Liquid Equilibrium Data . 77 23. Heats of Mixing for the Benzene-n-Octane System as a Function of Temperature........... 84 24. Determination of the Minimum Value of the Objective Function for Selection of the Best Wilson Parameters ...................... 92 25. Calculated Heats of Mixing from the Wilson Model at 220 and 2 4 0 ° C .........................94 26. Calculated Heats of Mixing from the Wilson Model at 260 and 2 8 0 ° C .........................95 27. Liquid Phase Activity Coefficients Calculated from a Fit of the Wilson Model to Heats of Mixing Data......................................96 28. Redlich-Kister Consistency Test for the Activity Coefficients at 260°C from Figure 2 7 ...............................................98 29. Vapor Phase Mixture Fugacity Coefficients for Benzene as Derived from Heats of Mixing . . . 100 viii Figure No. Page 30. Vapor Phase Mixture Fugacity Coefficients for n-Octane as Derived from Heats of Mixing . . 101 31. Experimental T u b e ..............................110 32. Schematic of Loading Apparatus .............. Ill 33. Schematic of Assembled Apparatus ............ 114 34. Pressure Gauge Deviation Chart .............. 118 35. Thermocouple Deviation Chart ................ 122 36. Vapor Pressures of Benzene and n-Octane at Loading Temperatures 126 37. Density of Liquid Benzene and n-Octane at Loading Temperatures ........................ 127 38. Component Weight as a Function of Liquid Length in Measuring Capillary ............. 129 39. Typical Chromatogram for the Benzene-n- Octane S y s t e m ..................................131 40. Benzene-n-Octane Gas Chromatograph Calibration....................................133 INTRODUCTION Many investigators have experimentally studied the vapor-liquid equilibria of hydrocarbon mixtures. Most of the systems investigated have been of great practical im portance to the petroleum and natural gas industries. The vast majority of the experimental data reported have been for binary systems. There have been few systems for which vapor-liquid equilibrium data have been reported in the region of the critical locus. The close-boiling benzene-n-octane system is a particularly interesting system to study in the region of the critical. This pairing of an aromatic with a rather long-chained paraffin gives an interesting system to study from the point of view of high liquid and vapor phase non ideality. Not only does appreciable nonideality exist, but also the critical locus shows a minimum temperature. Another incentive for studying the vapor-liquid equilibria of the benzene-n-octane system is to confirm the enthalpy derived phase boundaries reported by Lenoir and co-workers (16) for six benzene-n-octane mixtures varying in concentration from 27.1 to 93.0 mole percent benzene. The phase boundaries of all six mixtures were reported at conditions fairly close to the critical temperature of each mixture. These boundaries are not the result of direct 2 measurements but are the loci of the points of discontinu ity of the measured enthalpy-temperature isobars. This study is primarily devoted to the experimental determination of the liquid and vapor P-T phase boundaries of sixteen benzene-n-octane samples within the temperature range of 190 to about 290°C (critical region). The samples vary in concentration from nearly pure n-octane to nearly pure benzene. Over this range of temperature and composi tion, the benzene-n-octane system exhibits total miscibil- ity in the liquid phase and forms no azeotropes. In the critical region of this system, equilibrium pressures can be as high as 700 psia. As a result, there is a definite deviation of the equilibrium vapor from that of an ideal gas. The activity coefficient is the characteristic thermodynamic parameter for representing solution non ideality. In this study two different approaches are il lustrated for calculating liquid phase activity coeffici ents for the system of interest. In the first approach activity coefficients are cal culated directly from the measured equilibrium data through use of the equation of equilibrium. The Redlich-Kwong equation of state is used to calculate the vapor phase mixture fugacity coefficient for each component. The second approach for calculating activity co- 3 efficients employs liquid phase heats of mixing which are derived from saturated liquid enthalpy data reported by Lenoir et al. (16). The resulting liquid phase activity coefficients from both methods are tested for thermodynamic consistency. These two analyses show that the equilibrium vapor phase of this system in the region of the critical is indeed highly nonideal and cannot be characterized by any of the available equations of state such as the Red lich-Kwong equation. AVAILABLE EQUILIBRIUM DATA Vapor-liquid equilibrium data for the binary system benzene-n-octane are available in the literature at pres sures of one atmosphere and lower. Elshayal and Lu (7) re port isothermal data at 55, 65, and 75°C. Their system pressures were all subatmospheric. Ellis (6) and Sieg (24) have independently reported experimental vapor-liquid equi librium data for this system at atmospheric pressure. Kay and Hissong (13) have measured the critical pressure and temperature of pure benzene, pure n-octane, and several benzene-n-octane mixtures varying in concentra tion between 10 and 90 mole percent benzene. The apparatus and procedures were essentially the same as employed in this research. These investigators did not degas their mixtures. However, they did compare the critical constants for air-saturated pure hydrocarbon samples with degassed samples. They found that the critical pressure and temper ature of the air-saturated samples were high by about 2 psi and 0.1 to 0.2°C, respectively. Kay and Hissong further showed that the critical locus of this system possesses a minimum temperature point. They feel that this is evidence of the possible formation of an azeotrope with a composition very high in benzene. 4 EXPERIMENTAL PROCEDURE Experimental Apparatus The experimental method used was essentially that of Young (27) and Kay (14), and used after modification by Rebert (21). The experimental procedure involves the use of two separate apparati. A description of each apparatus is given in Appendix A. The loading apparatus is basically a vacuum still in which it is possible to degas the experi mental fluids and successively transfer known amounts of each fluid by distillation. A known mass of sample of fixed composition is confined in a 2 mm. i.d. Pyrex tube with mercury. The tube is then mounted in a specially built well (compressor block) so that pressure may be ap plied to the sample through the mercury. The mounted sample tube is surrounded by a thermostat in which a li quid may be boiled. The condensing vapors transfer heat to the sample. The pressure within the thermostat can be varied so that the boiling point of the liquid is changed. By varying the pressure at a given temperature, the bubble point and the dew point can be established. Phase Boundary Measurements The phenomena observed were bubble points, dew points, and the critical point for each composition 5 6 studied. The thermostat surrounding the sample tube was only partially silvered, allowing the operator to observe the state of the sample. Equilibrium between the liquid and vapor phases of the sample was rapidly established by the movement of a small steel ball through the sample by means of a series of magnets. Because of the fixed working volume of the experi mental tube, there existed a minimum temperature and pres sure for each mixture at which the entire sample could be vaporized. Consequently, the determination of dew points was limited for all samples. Sample Composition The measurement of the quantity of each component to be loaded in a sample tube is done with a calibrated precision bore capillary tube. The calibration of this capillary is covered in Appendix B. The method of select ing the amount of each component is covered in Appendix C. The volume of the liquid portion of a component in the capillary is represented by the calibration equation V = 0.004675L - 0.000114 (1) V is the liquid volume in cc, and L is the liquid length in cm. The total volume of the measuring capillary, in cluding the volume up to the isolation valve, is 5.99 cc. As a result, the vapor portion of the component occupies a 7 volume of 5.99-V cc. Each component is measured in this manner and then transferred to the sample tube. The pro cedure shown in Appendix C is used to convert the volu metric measurements to composition in mole percent. For the binary system of interest in this investigation, the composition is expressed as mole percent benzene in a mix ture of benzene and n-octane. Composition Discrepancies For several samples of benzene-n-octane of prede termined composition, the P-T phase boundaries were traced. These data were subsequently crossplotted on a pressure- composition diagram for several temperatures. At composi tions ranging between about 10 and 30 mole percent benzene, it was very apparent that the bubble and dew points were not in line with points plotted at higher benzene concen trations (50 mole percent and higher). It was therefore impossible to draw smooth bubble and dew curves which passed through the high concentration points, the vapor pressure of n-octane, and the points between 10 and 30 mole percent benzene. In order to get the latter points to line up with the rest, they had to be shifted 5 to 7 mole per cent higher in benzene concentration. This observation immediately cast doubt on the reliability of the composi tions determined by the capillary measuring technique. This dilemma made it necessary to search for an alternate 8 technique of determining sample composition. Gas Chromatography Since some doubt arose as to the accuracy of the compositions as determined by the capillary measuring technique, a number of sample compositions were measured by gas chromatography after the P-T phase boundaries had been determined. Appendix D describes the complete chro matographic analytical procdure, including a description of operating conditions and calibration. The instrument employed was a Hewlett-Packard 7620A thermal conductivity gas chromatograph. First Sample Recovery Technique Before a sample composition could be determined by chromatography, the sample had to be recovered. In the course of this investigation, it was necessary to develop two recovery techniques. The first technique is illustrat ed in Figure 1. This assembly is actually part of the sample loading apparatus described in Appendix A. After the phase boundary measurements are made, sample tube 15 is removed from the compressor block and attached to member 12 by means of swivel 34. A special attachment 35, with a side neck is connected to member 11 by means of a ground glass joint. A small recovery tube 36 with a small stain less steel ball at the bottom is connected to the side Li - v f , < 3 ; i Cold Trap > , ; , Sample Tube V\ v\ . . . j j t . . . . Figure 1 Sample Recovery Assembly To Vacuum Pump And Mercury Diffusion Pump 10 neck. After this entire assembly is sealed and leak checked, valve 1 is opened and the system is pumped down for several hours. The stem of mercury in the sample tube isolates the sample itself from the evacuated space. After thorough pumping, valve 1 is closed. A dry ice-acetone bath 29 is placed around the tip of tube 36. The swivel and sample tube are rotated until the tube is on an in cline. This permits gravity flow of the mercury into the bottom of attachment 35. The sample is subsequently distilled over to recov ery tube 36. After the sample has transferred completely (frozen), tube 36 is removed and corked up. The sample is thawed, and a magnet is used to stir the small steel ball in order to insure that the sample is completely mixed. The length of tube 36 is specially designed so that a 10 Hamilton syringe can be used to extract the sample for injection into the chromatograph. Eight benzene-n-octane samples, ranging in composi tion from about 3 to 40 mole percent benzene, were pre pared very approximately with the loading apparatus. The comparison of the two independent methods for measuring composition in this range showed a consistent bias for a low benzene concentration as determined by capillary loading. 11 Second Sample Recovery Technique Because of the above composition bias, sixteen samples varying from about 20 to 90 mole percent benzene in n-octane were prepared by capillary loading, transferred directly to tube 36, and analyzed by gas chromatography. This procedure is referred to as the Second Recovery Tech nique. The results are plotted in Figure 2 as composition by capillary loading versus composition by chromatography. From Figure 2 it is quite apparent that there is a composi tion discrepancy at higher levels of benzene concentration. At 75 mole percent benzene and higher the capillary loading compositions are consistently high by 2 mole percent. At 52 mole percent the compositions are equal. At lower con centration levels, the capillary compositions are consis tently low, and the deviation is greatest at the lowest composition reported. In this region the deviations vary from about 5 to 7 mole percent benzene. This result is consistent with earlier observations. The composition correction curve exhibits a defi nite trend with composition level. The chromatographic analyses reveal a higher concentration of the minority component. This effect becomes stronger as the extremes of composition are approached. Corrected Compositions An enlarged version of Figure 2 was used as the tools Percent Benzene b y Capillary Loading 12 Figure 2 Sample Composition Correction Curve for the Benzone-n-Octane System Hole Percent Bonzone by Chromatography 13 basis for correcting the compositions of the high benzene mixtures. The results are listed in Table I under Second Recovery Technique. The table also lists: the compositions determined by the first recovery technique. The estimated accuracy of the corrected compositions is no better than +0.1 mole percent but no worse than _+ 0.5 mole percent. As a result, the corrected compositions are reported only to the nearest 0.1 mole percent. A more complete discussion on composition accuracy is presented in Appendix G. The presentation of the final pressure- composition plots is given in the next general section en titled Presentation of Experimental Data. Critical Locus Figure 3 shows a comparison of the critical pres- sure-composition locus as measured in this investigation and as reported by Kay and Hissong (13) for the benzene-n- octane system. Below 65 mole percent benzene, it appears that the critical pressures reported here should be shifted some 1 to 2 mole percent higher in benzene concentration in order to agree with Kay and Hissong. Above 65 mole per cent benzene, the reverse is true. The critical pressures from this investigation should be shifted 1 to 2 mole per cent lower in benzene concentration. As mentioned previ ously, Kay and Hissong's samples were not degassed, and the critical pressures were believed to be high by about 14 Summary of X. First Recovery Technique Benzene Capillary Loading 11. Q2 18.59 II. Second Recovery Technique Benzene Capillary Loading 54.64 59.42 70.17 79.15 90.17 91.54 TABLE I Benzene-n-Octane Compositions Compositions in Mole Percent Direct by Chromatography 2.71 6.59 14.1 20.2 17.9 24.4 86.8 34.8 41.9 Compositions in Mole Percent Correction by Fig. 2 54.2 59.0 69.4 77.2 88.2 89.6 These samples were prepared very crudely on the loading apparatus. Accurate capillary measurements were taken for only two of these samples. 15 Figure j :Critical Pressure Locus of the Bensene-in-Octane System ^80 = 500 This Work ■ Kay and iiissong Uj (13) O' "20 " ~hrr r ' : 7 > 7 " ' " 7 ; :: f W . j " --,50 SO TOO Concosition-l'ole Percent Benzene 16 2 psi. If their critical pressure curve were lowered by 2 psi, the comparison above 65 mole percent would be great ly improved. However, below 65 mole percent, the discrep ancies in pressure would be increased by 2 psi, and the two curves would deviate consistently from one another by about 2 mole percent. This comparison is simply a further check on the compositions determined in this investigation. The critical temperature-composition locus for this system is fairly insensitive to composition. Figure 4 shows the critical temperature-composition locus measured in this investigation. The corresponding locus reported by Kay and Hissong is not plotted here. The critical temperature locus passes through a minimum of 287.9°C at approximately 81-82 mole percent benzene. Table II shows a tabular comparison of the critical pressure and temperature loci reported here and by Kay and Hissong. In most instances the critical temperatures devi ate by no more than 0.1°C. Finally, Table III summarizes the critical pressure and temperature of pure benzene and n-octane as measured in this work and as reported by sev eral other investigators. Temperature- 17 Figure h - Critical Temperature Locus of the Benzcnc-n-Octane System 300 298 292 290 2-36 20 kC 60 80 Composition-Ncle Percent Benzene 100 18 TABLE II Comparison of Critical Pressures and Temperatures for the Benzene-n-Octane System Mol. % Critical Pressures psia Critical Temperatures Benzene Kay (.13) This Work Kay(13) This Wo: 0 363.3 362.8 295.7 296.2 10 388.6 390 294.6 294.8 20 414.5 418 293.4 293.5 30 441.4 445 292.2 292.2 40 469.5 474 291.0 291.1 50 500.3 504 289.9 290.0 60 534.3 536 288.9 289.0 70 572.0 570 288.2 288.3 80 613.4 610 287.8 287.9 90 660.2 654 287.9 288.0 100 712.1 712.7 288.9 289.4 19 TABLE III Comparison of Critical Pressures and Temperatures for the Pure Components Hayworth Rebert Kay Benzene Critical temp. °C Critical press., psia n-Octane Critical temp. °C Critical press., psia (11) (21) (13) 289.5 288.7 288.9 713 710 712.1 Young Kay This (28) (13) Work 296.2 295.7 296.2 362.3 363.3 362.8 This Work 289.4 712.7 PRESENTATION OF EXPERIMENTAL DATA Reduced Data The pressure of the liquid and vapor phase bound aries of pure benzene, pure n-octane, and sixteen benzene- n-octane mixtures were determined within the temperature range of 190 to about 290°C. A tabulation of the reduced experimental data is presented in Table XXII of Appendix F. These data are presented as they were originally observed and corrected for known deviations of the measuring instru ments. The critical point of each sample is also reported and noted by the letter C next to the observed temperature. Vapor Pressures The measurement of vapor pressure is a very severe test of the purity of a single component fluid. In this investigation the vapor pressures of the pure hydrocarbons were measured. As mentioned above, these results can be found in Table XXII of Appendix F. For either component the spread in bubble and dew pressures at any temperature varies from 2 psi at the higher temperatures to 5 psi at the lower temperatures. The actual vapor pressures are re ported as the mean values of the bubble and dew pressure at any temperature. Some very excellent vapor pressure data have been 20 21 reported in the literature. Bender et al. (2) and Young (28) report vapor pressures for benzene and n-octane, res pectively at temperatures varying from 190°C to the criti cal. Figure 5 shows a comparison of these literature vapor pressures with the vapor pressures reported in this work. In general, the literature values agree quite precisely with the measured dew points of this work. In their ex perimental procedure these investigators measured the pres sures of samples in the two-phase region. As a result, it is expected that their results should lie between the bubble and dew pressures measured here. In any case, the overall agreement between vapor pressures appears to be satisfactory and reflects the purity of the hydrocarbons used in this work. A further discussion on the purity of the fluids used is presented in Appendix H. Phase Boundaries Figures 6 and 7 show the pressure-temperature phase boundaries for the benzene-n-octane system. The smoothed curves were generated by fitting the basic bubble and dew point data to the Clausius-Clapeyron equation. LnP = A/T + B (2) T is the temperature in degrees Kelvin. P is the bubble or dew pressure in psia. Since the P-T envelopes are rather narrow and Figure 5 Comparison of Vapor Pressures for Benzene and n-Octane / i : -1 700 d“3 650 ° Measured Bubble Point A Measured Dew Point rt ;-55c Vapor Pressures from j - 0 - tiie Literature Benzene-Bender(2) ; ■ ■ / ■ ■ ■ n-Octane—Young (2o) r~rr~\— ... - r , n-Ootano •1200 Tmpmr.ture- C i - i • ; ( : 2C0 210 220 230 2l!0 2*50 260 270 2o0 290 KS . . i ' Kola > • > Bensona Santa a r— ,700 •N6?0 Benzana -:~550 -------- Critical locus Figure p ‘ 3 7 Phase Bottndarles for the Benz ana n-Octane Sy ijrr*50 ” -boo -2 eO p— 100 200 210 220” 230 2J :0 250 260 270 2^0 220 S'arrola I'olo £ :£:P“ -ZTTT -----------Critical Locus’ too Figure 7 P~F Phase Boundaries .for the Benzene— n-Cctane System I-!— >50 Octanei ..... :T -•*100 ; • . Temper attire— C" . ", , - 1 . ■ - i : • i - » : L ---> ■ ' 1 : • • ; ' ' 200 210 220 230 2-:-0 otQ pOO oyQ pflr- ooq 25 exhibit an insignificant retrograde region around the critical, the bubble and dew curves can be fitted to Equa tion 2 by least squares up to at least 1°C of the critical temperature. Table IV lists the best regression constants for the pure components and the sixteen mixtures. The overall goodness of fit for each envelope has been determined with the aid of the Popovics' statistical parameters (20). The Popovics method basically shows how well a set of observed and calculated points fit the line of equality. Definitions for the statistical parameters are given in Table V. Table VI gives the values for these parameters when the method is applied to evaluating the goodness of fit of Equation 2 for the bubble and dew curves of the sixteen mixtures and the vapor pressures of the pure components. For either the bubble or dew curves the standard error of fit, Sp/X, varies from about 1 to 3 psia. In all cases the fit coefficient, F, is very close to unity. A value of unity indicates a perfect fit. The deviation factor (DF) generally shows a small positive trend or one-sidedness. In general, it is well within the +1 psi uncertainty in the basic pressure measurements. The maximum DF noted is +3.9 psi. The computations for generating the values shown in Tables IV through VI were performed on a General Elec tric Time-Sharing terminal using the BASIC Language TABLE IV Summary of Regression Constants for the Fit of Equation 2 to the Bubble and Dew Curves of the Benzene-n-Octane System Mol. % Dew Curves Bubble Curves Benzene -A B -A B 0* 4224.37 13.3150 4224.37 13.3150 2.71 4486.7 13.8073 4011.3 12.9713 6.59 4502.93 13.8642 3847.29 12.7207 14.1 4391.53 13.7343 3734.5 12.5941 17.9 4744.76 14.3846 3767.05 12.6758 20.2 4862.72 14.6166 3752.19 12.6663 24.4 4952.31 14.7961 3734.17 12.6557 34.8 4581.93 14.2252 3551.54 12.4242 41.9 4516.48 14.1763 3642.1 12.6512 54.2 4504.81 14.2537 3579.98 12.6313 59.0 4476.07 14.2397 3595.03 12.6901 69.4 4349.46 14.0786 3511.46 12.6100 77.2 4150.21 13.7874 3600.88 12.8212 86.8 4126.42 13.8157 3594.75 12.8797 88.2 4056.23 13.7007 3608.02 12.9069 89.6 4015.57 13.6353 3553.26 12.8216 97.0 3741.11 13.1962 3560.88 12.8793 * 100 3709.910 13.1644 3709.910 13.1644 *Fit of the mean values of the bubble and dew pressures measured at each temperature. 27 TABLE V Definition of Popovics1 Statistical Parameters Basic Definitions: PQ ** Experimental value of bubble or dew pressure Pc = Calculated value of bubble or dew pressure N = Number of the (P0,PC) points or pairs P = Value of the bubble or dew pressure on the line of equality, the equation of which is Pc = P0. P1 = * Least squares estimated value of the pressure; that is the regression line where P1 «* a + bPD. PQ = Average value of PQ = y^P^/N Pc = Average value of Pc = y P n/N = Variance of the P1 points of the regression line about the line of equality 2 S„ = Variance of the P„ values about the mean y u o S^x = Variance of the calculated points about the line Pc = Po Sp^x = Standard error of fit, SEF F = > Fit coefficient DF = Deviation factor, which is a measure of the one sidedness of the deviations SEF/PC = Relative standard error of fit, RSEF Basic Equations: h . NZ popc - Z poIpc Pc - bP0 28 TABLE V (con't.) s2 - L 1 £ < p. - P)2 s2 = y il/'c - V q 2 a . = p/x F2 = 1 - Sp/x/(SL + DF » 2 >o - 2 *. TABLE VI Summary of Popovics1 Statistical Parameters for the Fit of Equation 2 to the Bubble and Dew Curves of the Benzene-n-Octane System Mol. % Benzene SEF, psia Dew RSEF Curves F DF, psia SEF, psia Bubble RSEF Curves F DF, psia 0* 0.774 0.00304 0.999959 0.245 0.774 0.00304 0.999959 0.245 2.71 1.420 0.00452 0.999628 0.203 1.465 0.00604 0.999884 1.637 6.59 1.4782 0.00465 0.999607 0.239 1.807 0.00699 0.999827 2.166 14.1 2.228 0.00722 0.999679 0.747 1.452 0.00515 0.999889 1.022 17.9 2.245 0.00618 0.998918 0.258 0.975 0.00359 0.999960 0.885 20.2 1.493 0.00410 0.999355 0.0556 1.416 0.00511 0.999909 1.213 24.4 1.290 0.00348 0.999607 0.0367 1.315 0.00481 0.999921 1.126 34.8 2.098 0.00567 0.999642 0.186 1.762 0.00546 0.999872 1.440 41.9 2.939 0.00777 0.99954 -0.00025 0.990 0.00306 0.999968 0.505 54.2 3.351 0.00767 0.999273 0.726 1.036 0.00306 0.999969 0.824 59.0 2.130 0.00507 0.999809 -0.505 0.804 0.00220 0.999979 0.378 69.4 1.763 0.00378 0.999854 0.199 1.716 0.00424 0.999928 1.089 77.2 1.827 0,00379 0.999864 0.288 0.968 0.00239 0.999978 0.356 86.8 3.095 0.00557 0.999412 0.4181 1.281 0.00293 0.999969 1.029 88.2 2.312 0.00420 0.999722 0.328 1.674 0.00369 0.999945 0.958 89.6 3.536 0.00655 0.999532 1.244 1.735 0.00363 0.999939 1.213 97.0 2.494 0.00521 0.999914 2.889 3.034 0.00631 0.999853 3.891 100* 0.983 0.00158 0.999953 -0.00758 0.983 0.00158 0.999953 -0.00758 Fit of the mean values of the bubble and dew pressures measured at each temperature. ro vo 30 (Beginner's All-Purpose Symbolic Instruction Code). A listing of this program (CRK1) and a sample output are given in Tables XXIII and XXIV of Appendix I. Pressure-Composition Diagrams With the aid of Equation 2 and the regression con stants in Table IV, smoothed P-T values were generated at 5°C intervals. These smoothed data are listed in Table VII. These points have been plotted as pressure versus composition at fixed temperature. Figures 8 through 10 are the results of such plots at 10°C intervals in temper ature from 220 to 280°C. Bubble points are denoted by open circles and dew points by open triangles. The solid triangles represent extrapolated dew pressures. Beside each solid triangle is shown the extent of extrapolation in degrees Centigrade. Essentially all of the dew points at 220°C have been extrapolated? in some cases by as much as 50°C. Consequently, the smooth curve through these points represents a region of great uncertainty. Visually smoothed curves have been drawn through all of the P-X-Y data of Figures 8 through 10. Each set of curves is ter minated at the ends by the vapor pressures measured and repotted in this work. On Figures 8 through 10 there are points plotted at approximately 97.0 mole percent benzene. This set of data corresponds to Sample BO-16 listed in Table XXII of 31 TABLE VII Pressure-Temperature Relations at the Phase Boundaries of the Systems Benzene-n-Octane at Equal Intervals of Temperature Temp. °C Mean Pressure, psia Data for Benzene 245 405.28 250 433.98 255 464.11 260 495.72 265 528.82 270 563.47 275 599.69 280 637.52 285 677.00 289.44 C 712.73 Data on n-Octane 225 125.85 230 136.91 235 148.70 240 161.25 245 174.58 250 188.73 255 203.72 260 219.59 265 236.36 270 254.08 275 272.76 280 292.43 285 313.14 290 334.90 295 357.76 296.21 C 362.77 32 TABLE VII (con’t.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-1 2.71 mol. % Benzene in n-Octane 190 - 74.48 195 - 81.70 200 - 89.44 205 - 97.74 210 - 106.60 215 - ■ 116.06 220 - 126.15 225 - 136.88 230 - 148.28 235 - 160.38 240 - 173.20 245 _ 186.77 250 - 201.11 255 202.82 216.25 260 219.64 232.22 265 237.51 249.03 270 256.45 266.72 275 276.52 285.30 280 297.75 304.81 285 320.19 325.27 290 343.88 346.70 295.58 C 372.61 372.61 Data for Sample BO-2 6.59 mol. 7. Benzene in n-Octane 190 - 82.61 195 - 90.27 200 - 98.46 205 - 107.20 210 - 116.51 215 - 126.41 220 - 136.92 225 - 148.07 230 - 159.88 235 - 172.38 240 - 185.57 245 - 199.50 250 191.91 214.17 33 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-2 (con’t.) 255 208.20 229.61 260 225.53 245.84 265 243.94 262.89 270 263.47 280.77 275 284.17 299.51 280 306.07 319.13 285 329.23 339.64 290 353.67 361.08 295.43 C 382.15 382.15 Data for Sample BO-3 14.1 mol. % Benzene In n-Octane 190 - 92.85 195 - 101.20 200 - 110.10 205 - 119.58 210 - 129.64 215 - 140.32 220 125.14 151.64 225 136.84 163.61 230 149.37 176.27 235 162.76 189.62 240 177.06 203.70 245 192.30 218.52 250 208.53 234.10 255 225.77 250.47 260 244.08 267.64 265 263.49 285.64 270 284.05 304.48 275 305.79 324.18 280 328.76 344.77 285 352.99 366.27 290 378.53 388.69 294.01 C 402.87 402.87 34 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-4 17.9 mol. % Benzene in n-Octane 190 - 93.92 195 - 102.44 200 - 111.53 205 - 121.22 210 - 131.51 215 - 142.45 220 - 154.04 225 - 166.31 230 - 179.29 235 - 193.00 240 - 207.46 245 - 222.68 250 - 238.71 255 - 255.55 260 241.12 273.22 265 261.90 291.76 270 284.04 311.18 275 307.60 331.50 280 332.64 352.75 285 359.20 374.93 290 387.36 398.09 293.76 C 411.59 411.59 Data for Sample B0-5 20,2 mol. % Benzene in n-Octane 190 - 96.06 195 - 104.75 200 - 114.00 205 - 123.86 210 - 134.34 215 - 145.46 220 - 157.25 225 - 169.73 230 - 182.92 235 - 196.85 240 - 211.53 245 - 227.00 250 - 243.26 35 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-5 (con’t.) 255 - 260.35 260 - 278.29 265 265.28 297.09 270 288.29 316.79 275 312.82 337.39 280 338.93 358.92 285 366.70 381.41 290 396.19 404.87 293.24 C 417.63 417.63 Data for Sample BO-6 24.4 mol. % Benzene in n-Octane 190 - 98.82 195 - 107.71 200 - 117.18 205 - 127.26 210 - 137.97 215 - 149.34 220 - 161.38 225 - 174.13 230 - 187.59 235 - 201.80 240 - 216.78 245 - 232.55 250 - 249.13 255 - 266.55 260 - 284.82 265 268.76 303.97 270 292.51 324.02 275 317.88 344.99 280 344.93 366.90 285 373.73 389.77 290 404.36 413.62 293.24 C 425.55 425.55 36 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-7 34.8 mol. % Benzene in n-Octane 190 - 116.30 195 - 126.22 200 - 136.76 205 - 147.92 210 - 159.74 215 - 172.23 220 - 185.42 225 - 199.32 230 - 213.95 235 - 229.33 240 199.61 245.50 245 217.57 262.45 250 236.75 280.22 255 257.22 298.82 260 279.02 318.27 265 302.21 338.59 270 326.85 359.80 275 353.00 381.91 280 380.70 404.94 285 410.02 428.91 291.74 C 457.40 457.40 Data for Sample BO-8 41.9 mol. % Benzene in n-Octane 190 - 120.01 195 - 130.53 200 - 141.71 205 - 153.59 210 - 166.19 215 - 179.53 220 - 193.63 225 - 208.53 230 181.29 224.25 235 198.02 240.80 240 215.94 258.22 245 235.08 276.52 250 255.50 295.74 255 277.26 315.88 37 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-8 (con't.) 260 300.41 336.99 265 325.01 359.07 270 351.11 382.15 275 378.78 406.25 280 408.07 431.40 285 439.03 457.61 290.91 C 481.50 481.50 Data for Sample BO-9 54.2 mol. % Benzene in n-Octane 190 - 134.54 195 - 146.11 200 - 158.41 205 - 171.45 210 - 185.27 215 - 199.87 220 - 215.30 225 - 231.57 230 ~ 248.72 235 - 266.75 240 238.68 285.70 245 259.78 305.60 250 282.29 326.46 255 306.26 348.31 260 331.77 371.17 265 358.86 395.06 270 387.61 420.01 275 418.07 446.04 280 450.31 473.16 285 484.38 501.40 289.53 C 519.68 519.68 Data for Sample B0-10 59.0 mol. % Benzene in n-Octane 190 195 200 138.12 150.06 162.75 38 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample B0-10 (con’t.) 205 - 176.20 210 - 190.46 215 - 205.54 220 - 221.48 225 - 238.29 230 209.30 256.01 235 228.45 274.65 240 248.92 294.25 245 270.78 314.83 250 294.08 336.41 255 318.90 359.03 260 345.28 382.69 265 373.28 407.43 270 402.99 ' 433.27 275 434.45 460.24 280 467.73 488.35 285 502.89 517.62 288.97 C 533.48 533.48 Data for Sample B0-11 69.4 mol. % Benzene in n-Octane 190 - 152.70 195 - 165.58 200 - 179.24 205 - 193.70 210 - 208.99 215 - 225.15 220 - 242.18 225 - 260.12 230 229.11 278.99 235 249.45 298.82 240 271.15 319.64 245 294.26 341.45 250 318.84 364.30 255 344.94 388.20 260 372.64 413.18 265 401.98 439.25 270 433.03 466.44 275 465.84 494.77 TABLE VII (con't.) 39 Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-11 (con't.) 280 500.48 524.27 285 537.00 554.94 288.50 C 566.54 566.54 Data for Sample B0-12 77.2 mol. % Benzene In n-Octane 190 _ 155.49 195 - 168.96 200 - 183.26 205 - 198.44 210 - 214.53 215 - 231.54 220 - 249.52 225 - 268.50 230 254.45 288.49 235 275.96 309.54 240 298.82 331.67 245 323.08 354.90 250 348.78 379.27 255 375.98 404.81 260 404.73 431.54 265 435.09 459.48 270 467.10 488.68 275 500.81 519.14 280 536.29 550.90 285 573.57 583.98 287.91 C 597.78 597.78 Data for Sample BO-13 86.8 mol. % Benzene in n-Octane 190 - 167.06 195 - 181.50 200 - 196.84 205 - 213.11 210 - 230.35 215 - 248.59 220 - 267.86 40 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-13 (con't.) 225 - 288.20 230 - 309.62 235 - 332.17 240 - 355.87 245 347.98 380.76 250 375.50 406.86 255 404.61 434.21 260 435.37 462.82 265 467.83 492.74 270 502.04 523.99 275 538.07 556.60 280 575.95 590.59 285 615.76 625.99 287.96 C 643.82 643.82 Data for Sample BO-14 88.2 mol, % Benzene in n-Octane 190 - 166.82 195 - 181.29 200 - 196.67 205 - 213.00 210 - 230.29 215 - 248.60 220 - 267.94 225 - 288.36 230 - 309.88 235 - 332.53 240 - 356.35 245 355.16 381.37 250 382.75 407.61 255 411.90 435.11 260 442.66 463.90 265 475.08 494.00 270 509.21 525.45 275 545.11 558.27 280 582.81 592.49 285 622.38 628.14 288.03 C 649.82 649.82 41 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-15 89.6 mol. % Benzene in n-Octane 190 - 172.40 195 - 187.12 200 - 202.75 205 - 219.31 210 - 236.84 215 - 255.37 220 - 274.93 225 - 295.55 230 285.60 317.26 235 308.93 340.09 240 333.66 364.06 245 359.83 389.22 250 387.49 415.58 255 416.70 443.18 260 447.49 472.04 265 479.93 502.20 270 514.05 533.67 275 549.91 566.48 280 587.56 600.66 285 627.03 636.24 288.03 C 654.74 654.74 Data for Sample BO-16 97.0 mol. % Benzene in n-Octane 190 167.14 179.66 195 182.20 195.04 200 198.25 211.36 205 215.34 228.66 210 233.50 246.98 215 252.78 266.35 220 273.20 286.79 225 294,81 308.35 230 317.66 331.05 235 341.77 354.92 240 367.18 380.00 245 393.95 406.32 250 422.09 433.90 42 TABLE VII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, psia Data for Sample BO-16 (con't.) 255 451.65 462.78 260 482.67 492.99 265 515.19 524.55 270 549.23 557.49 275 584.85 591.84 280 622.06 627.64 285 660.91 664.89 288.23 C 687.45 687.45 Figure 8 P~X Isothems for the Benzene-n-Octane System . L S . - : i : 1 ------ Uncertain Region | O Measured Bubble Point I l f A Measured Dew Point X i ^ — r - v - r : T - - j n ^ 3 rj^| ■ ! • ! S : - ' . l . 1 _^ ^ 560 V^.-i r: ■ s f _ r r r r - — . i . - j ■ j - 0 M - - - •• ; • • J.,v - I - : ' i ' I -rrTT 160 120 ° 0*1 0.2 0.3 oji 0.5 0.6 0.7 0.8 0.9 Mole Fraction Ecrscne Figure 9 P—X Isotherms for the Benzene—n-Octane System • -------Uncertain Hegion • o Measured. Bubble Point : A Measured Dev ? : .! n ~ ^ I G '- t " '" 1 - .......: | . .j. - l F ' ' % T - G G lG G j: ■ :0 jh r h i :G b iiG G G M v l-'- ■ p * | / - , til:- :• ! G:iG| G G rG - ; ■ / X vv t.= j - • : i m - X y h i G .- !:: I ' i / i - / — *mr g M !'G --T- I : : j*"’ FXr - - I Hi!.... _ ' ry\ ;. .;:-;TGgG..:;- . ;: n / s ' : 3 > n n - 0 ✓ 0 .-•! -i ■ ; I " ' b G 0 0.1 0.2 0.3 O.h- 0.5 0.6 0,7 o.i Mole Fraction Bens one Pres3urQ-Peia Figure 10 45 P-X isotherms for the Bonzene—n-Octane System Uncertain Region ® Measured Bubble Point ^ Measured Dow Point - ~ . i . i , ‘ ' ■ ' t ; ? ' ;. . ........ i-- ; ■ ! i. . ..:i , ...... . . . L ... i ; — .. . . . . . . . . . ; :... . . J C.1 0.2 0,3 o.b 0.5 0.6 0.7 0.8 0*9 Molo Fraction Bonzene Pressurc-Psi® 46 Appendix F. The composition of this sample was not deter mined with any certainty by either capillary loading or gas chromatography. The approximate composition of this sample was determined by seeing where its bubble and dew pressures fell on the smoothed curves of Figures 8 through 10. The incentive for reporting equilibrium data for a sample with a very high benzene content is to validate Kay and Hissong's suspicion that an azeotrope may exist in this region. The resulting pressure-composition diagrams show that no azeotropy is apparent over the full range of composition. Due to the nature of the P-T phase boundaries for this system, it was possible to cut many isotherms across the entire range of composition. It was not possible to do so with isobars. Because of the scarcity of tempera- ture-composition data that can be read at various pres sures, the data were not reported or plotted in this man ner . Equilibrium Ratios The smooth P-X-Y curves of Figures 8 through 10 can now be used to generate equilibrium ratios. At each pres sure level for a fixed temperature the liquid and vapor compositions which coexist at equilibrium can be read. The results in tabular form are presented in Table VIII. In the last two columns of this table are listed the 47 Temp. 220 230 240 TABLE VIII Smoothed P-X-Y Data and Calculated Equilibrium Ratios Press. psia X1 yi X2 y2 1 xi K 2 x; 115.5 0 0 1.00 1.00 1.00 120 0.010 0.169 0.990 0.831 16.9 0.840 130 0.042 0.271 0.958 0.729 6.45 0.761 140 0.090 0.352 0.910 0.648 3.91 0.712 160 0.214 0.491 0.786 0.509 2,30 0.647 180 0.335 0.620 0.665 0.380 1.85 0.572 200 0.455 0.730 0.545 0.270 1.602 0.495 220 0.577 0.820 0.423 0.180 1.42 0.426 240 0.699 0.890 0.301 0.110 1.272 0.366 260 0.820 0.946 0.180 0.054 1.152 0.300 270 0.880 0.971 0.120 0.029 1.102 0.242 284 1.00 1.00 0 0 1.00 — 136.9 0 0 1.00 1.00 — 1.00 140 0.006 0.081 0.994 0.919 13.5 0.925 150 0.032 0.207 0.968 0.793 6.465 0.820 160 0.075 0.287 0.925 0.713 3.825 0.771 180 0.174 0.420 0.826 0.580 2.418 0.701 200 0.282 0.537 0.718 0.463 1.905 0.645 220 0.391 0.640 0.609 0.360 1.638 0.591 240 0.499 0.729 0.501 0.271 1.460 0.540 260 0.606 0.810 0.394 0.190 1.336 0.482 280 0.715 0.883 0.285 0.117 1.234 0.410 300 0.8215 0.940 0.1785 0.060 1.141 0.336 320 0.935 0.984 0.065 0.016 1.051 0.246 329 1.00 1.00 0 0 1.00 — 161.3 0 0 1.00 1.00 — 1.00 170 0.017 0.119 0.983 0.881 7.00 0.896 180 0.050 0.214 0.950 0.786 4.28 0.827 200 0.142 0.354 0.858 0.646 2.493 0.753 220 0.235 0.455 0.765 0.545 1.936 0.712 240 0.329 0.549 0.671 0.451 1.669 0.672 260 0.422 0.637 0.578 0.363 1.509 0.628 280 0.515 0.720 0.485 0.280 1.398 0.577 300 0.610 0.795 0.390 0.205 1.303 0.526 320 0.702 0.861 0.298 0.139 1.226 0.466 340 0.797 0.9165 0.203 0.0835 1.150 0.411 Subscript 1 refers to benzene. Subscript 2 refers to n-octane. 48 TABLE VIII (con't.) Temp, °C 240 250 260 270 Press, psia X1 *1 x2 ?2 X1 K, -Zl X2 360 0.890 0.964 0.110 0.036 1.083 0.327 370 0.945 0.985 0.055 0.015 1.042 0.273 378 1.00 1.00 0 0 1.00 - 188.7 0 0 1.00 1.00 — 1.00 200 0.025 0.141 0.975 0,859 5.64 0.881 220 0.096 0.2625 0.904 0.7375 2.74 0.816 240 0.185 0.359 0.815 0.641 1.94 0.787 260 0.268 0.449 0.732 0.551 1.673 0.753 280 0.350 0.533 0.650 0.467 1.521 0.719 300 0.430 0.610 0.570 0.390 1.418 0.684 320 0.515 0.684 0.485 0.316 1.329 0.652 340 0.596 0.755 0.404 0.245 1.268 0.606 360 0.678 0.820 0.322 0.180 1.210 0.560 380 0.761 0.881 0.239 0.119 1.158 0.499 400 0.843 0.933 0.157 0.067 1.108 0.4265 420 0.930 0.976 0.070 0.024 1.050 0.343 434 1.00 1.00 0 0 1.00 — 219.6 0 0 1.00 1.00 — 1.00 240 0.051 0.174 0.949 0.826 3.415 0.8705 260 0.127 0,267 0.873 0.733 2.10 0.840 280 0.2025 0.349 0.7975 0.651 1.720 0.816 300 0.278 0.427 0.722 0.573 1.539 0.792 320 0.354 0.503 0.646 0.497 1.421 0.769 340 0.429 0.576 0.571 0.424 1.342 0.741 360 0.503 0.6425 0.497 0.3575 1.279 0.718 380 0.577 0.708 0.423 0.292 1.228 0.690 400 0.652 0.769 0.348 0.231 1.179 0.664 420 0.752 0.827 0.275 0.173 1.141 0.629 440 0.795 0.878 0.205 0.122 1.105 0.595 460 0.863 0.927 0.137 0.073 1.074 0.533 480 0.935 0.971 0.065 0.029 1.039 0.446 495.7 1.00 1.00 0 0 1.00 - 254.1 0 0 1.00 1.00 — 1.00 260 0.012 0.0475 0.988 0.9525 3.96 0.965 280 0.068 0.162 0.932 0.838 2.38 0.899 300 0.138 0.248 0.862 0.752 1.80 0.872 320 0.209 0.322 0.791 0.678 1.54 0.856 340 0.280 0.390 0.720 0.610 1.391 0.847 360 0.350 0.454 0.650 0.546 1.298 0.840 380 0,415 0.518 0.585 0.482 1.248 0.825 49 TABLE VIII (con't.) Temp. °C Press. psia X1 yl X2 y2 K = Za 1 X1 K = Zi 1 x2 270 (con't.) 400 0.480 0.581 0.520 0.419 1.211 0.805 420 0.545 0.642 0.455 0.358 1.179 0.786 440 0.608 0.702 0.392 0.298 1.157 0.761 460 0.671 0.760 0.329 0.240 1.131 0.730 480 0.734 0.813 0.266 0.187 1.110 0.702 500 0.797 0.864 0.203 0.136 1.082 0.670 520 0.860 0.911 0.140 0.089 1.060 0.636 540 0.922 0.953 0.078 0.047 1.032 0.602 550 0.955 0.9735 0.045 0.0265 1.020 0.589 563.5 1.00 1.00 0 0 1.00 — 280 292.4 0 0 1.00 1.00 - 1.00 300 0.016 0.044 0.984 0.956 2.75 0.972 320 0.070 0.128 0.930 0.872 1.83 0.938 340 0.1375 0.206 0.8625 0.794 1.499 0.920 360 0.2025 0.275 0.7975 0.725 1.358 0.910 380 0.2635 0.340 0.7365 0.660 1.291 0.895 400 0.324 0.400 0.676 0.600 1.236 0.887 420 0.385 0.457 0.615 0.543 1.188 0.883 440 0.446 0.514 0.554 0.486 1.150 0.878 460 0.506 0.572 0.494 0.428 1.130 0.8675 480 0.564 0.629 0.436 0.371 1.117 0.850 500 0.621 0.686 0.379 0.314 1.103 0.829 520 0.6765 0.738 0.3235 0.262 1.090 0.810 540 0.7315 0.788 0.2685 0.212 1.075 0.789 560 0.7865 0.836 0.2135 0.164 1.061 0.770 580 0.841 0.880 0.159 0.120 1.044 0,754 600 0.896 0.924 0.104 0.076 1.030 0.730 620 0.9525 0.967 0.0475 0.033 1.016 0.695 637.5 1.00 1.00 0 0 1.00 - 50 computed equilibrium ratios. In Figure 11 the equilibrium ratios are plotted against pressure at temperatures of 230, 260, and 280°C. In all cases the operating temperature is below the mini mum temperature of the critical locus. An interesting feature shown here is the behavior of the n-octane equili brium ratios. As the pressure increases, the K-ratio for n-octane decreases. As the vapor pressure of benzene is approached, these K-ratios begin to drop off rather sharp ly. At 290°C the critical locus is intersected at a pressure of 502 psia. This pressure represents a real convergence pressure. Figure 12 is the equilibrium ratio- pressure plot at 290°C. The K-ratios for benzene and n- octane converge to unity at 502 psia. This behavior is typical of most any system operating in a region where a real convergence pressure is defined. Equilibrium Ratios for the Bonsene—n-Octsne System 52 Figure 12 Ecrailibrium Ratios for the 0 Benzene-n-Octane System at 290 C Benzene Octane M * tC o ..... Fr c s s ur c~Ps ia Equilibrium Ratio. K=y/: EQUILIBRIUM DATA PROM ENTHALPIES Enthalpy Data Lenoir and co-workers (16) have measured the enthal py of benzene and six mixtures of the benzene-n-octane sys tem. These data are reported over the temperature range 380 to 700°F and for pressures up to 1400 psia. The mea surements were made using an isobaric flow calorimeter, and the uncertainty in the measurements was reported as 1.5 Btu/lb. For each mixture studied, the authors tabulated enthalpies for the saturated vapor and liquid loci. These data are not the result of direct measurements but are the observed points of discontinuity in the enthalpy-tempera- ture isobars. From these data the P-T phase boundaries were extracted over the range 390 to 550°F. Figure 13 shows the bubble point data for the six mixtures, and Fig ure 14 is a similar plot for the dew points. From both figures a series of smoothed bubble and dew pressures were read over 10°C intervals from 220°C (428°F) to 280°C (536°F). These values are listed in Table IX. Comparisons of P-X Diagrams The points from Table IX can easily be plotted on a pressure-composition diagram and compared with the direct equilibrium data measured in this investigation. This com parison is shown in Figures 15 through 17. The solid 53 Pressura-Psis 54 Figure 13 P~T Bubble Curves Generated from Enthalpy Data (16) 55 ijigure 1*+ P-T Dew Curves- Generated from Enthalpy Data (16) ! _ • ■ ! ' ■ jf I • • 1 T. 380 J-500 *+ 2C L P+0 *+60 ! -:-80 500 520 5*+C Tc-inno r atu.r e— GF 56 Temp. 2808C (536°F) 270°C (518°F) 260°C (500°F) 250°C (482°F) 240 °C (464°F) 230°C (446°F) TABLE IX Enthalpy-Based Bubble and Dew Pressures at Equal Intervals of Temperature Mole % Dew Pressure Bubble Pressure Benzene psia_________ psia_____ 27.1 359.0 384.2 44.6 401.0 444.5 67.6 491.2 522.0 77.1 518.5 547.0 85.7 563.8 600.0 93.0 598.5 612.5 27.1 311.5 341.8 44.6 349.5 391.8 67.6 430.1 467.4 77.1 463.5 492.5 85.7 494.2 527.5 93.0 532.5 548.0 27.1 268.1 301.9 44.6 305.0 344.0 67.6 373.8 413.2 77.1 409.0 439.5 85.7 436.2 462.2 93.0 468.0 484.0 27.1 229.0 263.2 44.6 264.5 299.0 67.6 322.0 360.2 77.1 356.0 386.4 85.7 382.0 404.4 93.0 409.2 423.7 27.1 - 226.0 44.6 227.2 259.8 67.6 278.0 311.9 77.1 307.1 336.5 85.7 332.0 354.0 93.0 355.8 369.3 27.1 44.6 - 224.5 67.6 238.8 270.5 77.1 263.8 291.0 85.7 286.8 308.0 93.0 307.4 320.3 57 Temp. 220°C (428°F) TABLE IX (con't.) Mole % Dew Pressure Bubble Pressure Benzene psia _____psia_____ 27.1 44.6 67.6 201.7 235.0 77.1 225.2 250.8 85.7 246.1 266.3 93.0 265.0 276.1 58 Figure 15 Comparison Between.- Equil ibrium: and Enthalpy Based Pressure-Composition Data Equilibrium Based Enthalpy Based ! : . j \ • • - i ..j - 1 : - 0,b 0.5 0.6 hole Fraction Ben: ;nc Pressttra-Psia 59 -I" | :r:1 'r!: • ' :"l r o r : /; Figure 16 Comparison Botueen Equil- 0- ibriurr and E.ithalpy Based rr Pressure—Composition Data ~U7 Equilibrium Based 411 Enthaluy Based . >.1 0,2 0,3 0 . > f - 0,5 0.6 0,7 0.3 0.9 1 Kolc Fraction Sons;one SfTfaj-oanesaJd 60 Figure 17 Comparison Between Equilibrium and Enthalpy Based Pr c s surc-Compo s it ion Data Equilibrium Based Enthalpy Based M 300 g i--r-r--; • 2u0 ii , . U ;. ; !■- I ■; ■ : ! 260 3 L _ 1 £o .r~i I- oil 0»2 0*3 O.V ' o'.5 0*6 0.7 I ole Fraction Bensons 61 curves are the smoothed results of direct equilibrium mea surements and are repeated from Figures 8 through 10. The dashed curves are the enthalpy-based equilibrium data. In general, the enthalpy-based bubble and dew pres sures lie above the equilibrium-based bubble and dew pres sures. For any temperature the bubble pressure discrepancy is no worse than about 5 psi. Below 250°C (482°F) the dis crepancies in the dew pressure curves exceed 10 psia. At 220°C (428°F) the maximum dew pressure deviation of 15 psi is observed at about 80-85 mole percent benzene. This poor agreement is understandable since the 220°C dew curve, reported in this work, is the result of a fair degree of extrapolation. No comparisons are shown at 280°C (536°F). In this case the enthalpy-based points showed excessive scatter, and smoothed curves could not be drawn with any certainty. The scatter at 280°C is most likely due to the proximity of the critical locus. It could be argued that the comparison should be made in terms of composition discrepancies at a given pres sure. Lenoir and co-workers charged their calorimeter with mixtures of precisely known composition. Therefore, the major uncertainties should be attributed to the saturation pressures and temperatures which were measured indirectly from the breaks in the cooling curves. Overall, the agreement between the two independent sets of data appears 62 to be satisfactory. It should be emphasized that the primary function of a calorimeter is to measure enthalpies directly. The associated vapor-liquid equilibrium data, derived from the enthalpies, are not measured directly but result from cross-plotting and should not be expected to be of the highest accuracy. Comparison and Analysis of Equilibrium Ratio Behavior Figure 18 shows a comparison of equilibrium ratios from the following sources at 250°C. 1. Equilibrium measurements of this work 2. Enthalpy measurements of Lenoir et al. (16) 3. Convergence pressure (Pg) nomograph of Cajander et al. (4) used in conjunction with the Acti vity Correction Chart for Mixtures Containing Aromatics (Figure 8A2.1) of the Data Book of the American Petroleum Institute (1). Since the operating temperature is below the minimum temp erature of the critical locus, the system is in a region where a real convergence pressure is nonexistent. This situation is well described in Figure 3 of a 1958 publi cation by Lenoir (15). The convergence pressure that cor rectly correlates equilibrium ratios at temperatures less than the minimum critical temperature is called the quasi convergence pressure QPg. This pressure may be thought of Figaro 18 Cbnroarison of Bauilibrim Piatics at 250°G ( h Z 2 ° U ' j Proni Y-L-E lleasurcmcnts o This "orlv 2.0 From Enthalpy lie asur orients of Lenoir et.al..(l6) Pron Convergence Pressure holograph of Capsudor ct.al. C^) With Activity Correction Values From the -0?I Data Booh (1) Oc o 100 000 300 P r c s f j ur e-P s i a 64 as the pressure where convergence of the equilibrium ratios to unity would occur if total condensation did not occur first when the pressure is raised above the vapor pressure of the more volatile component (assuming no azeotropy). In Figure 18 the equilibrium ratios of benzene must extend below unity and then turn back and approach unity again at QPg. The equilibrium ratios of n-octane must also turn back and approach unity at QPg. All of this behavior takes place above the vapor pressure of benzene and is therefore hypothetical. LIQUID PHASE ACTIVITY COEFFICIENTS FROM VAPOR-LIQUID EQUILIBRIUM DATA The thermodynamic quantity which characterizes the extent of liquid solution nonideality is the activity co efficient. The second goal of this investigation is to evaluate liquid phase activity coefficients for the ben- zene-n-octane system over the range of pressure, tempera ture, and composition measured. The first approach to this evaluation is through direct use of the measured equilibrium data. Equation of Equilibrium A vapor phase and a liquid phase are in equilibrium at the same temperature and pressure when the fugacity, fjL, of any component i in the vapor is equal to that in the liquid. Equation 3 is of little use unless the fugacities can be related to the experimentally accessible quantities x^, y^, P, and T. x^ and y^ are the component mole fractions in the liquid and vapor phases, respectively. T is the absolute temperature, and P is the total system pressure. The desired relationship between fugacities and the ex- 65 66 perimentally accessible quantities can be facilitated by the introduction of two auxiliary functions, namely, the fugacity coefficient of the component in the vapor mixture 0^ and the liquid phase activity coefficient These terms are defined by fi - 0iYl* < 4> L V L oL fi = 0 ixifi (5> OL f^ is the pure component standard state liquid fugacity at the system pressure P and temperature T. To be consis tent with this liquid phase standard state choice, the activity coefficient $ ^ must be taken at P and T also. It should be emphasized that 0^ is the .vapor mixture fu gacity coefficient of component i and is a function of pressure, temperature, and the vapor composition. Equations 3, 4, and 5 are combined, and the result ing expression is solved for the liquid phase activity co efficient. The result is Equation 6. Y i - (xj) y f - (i - j-2) <6> o V ^ is the pure component liquid phase fugacity coeffici- -.oL , ent, f^ /P. The only term in Equation 6 which is readily avail able from the experimental V-L-E data is K^, the equili- o brium ratio. Y ^ and 0^ must be evaluted from P-V-T 67 data for both the pure components and the saturated vapor mixtures. Generally speaking, the necessary pure component P-V-T data are insufficient, and mixture P-V-T data are nonexistent. Consequently, empirical correlations and / equations of state must be employed to evaluate 0^- Pure Component Liquid Fugacity Chueh and Prausnitz (5) present an empirical corre lation for computing the standard state fugacities of pure subcritical liquid hydrocarbons at zero reference pressure. This correlation is expressed by the power series. fpL(P=0) in 1 PC. = C0 + C3./TR.+ C2/Tr. + C3/Tr. + C4/Tr. (7) Pc^ and Tr^ are the pure component critical pressure and reduced temperature. The coefficients of Equation 7 are specific for a given component. The authors list the co efficients for 20 components and state that the correla tion is valid from the triple point to the critical point. Table X gives the specific coefficients for benzene and n- octane. Using Equation 7 as the basis, it is now desirable to develop the expression for the liquid standard state fugacity at the system pressure P. At a fixed temperature, the pure component fugacity is related to the pure compo nent molar volume by Equation 8. TABLE X Coefficients to Equation 7 for Benzene and n-Octane Coefficient Benzene n-Octane 0.69309 2.68502 -4.62806 0.70543 0.0 -1.80460 10.15814 -12.06327 3.60113 -0.44247 69 RTd(In fi) = V£dP (8) If Equation 8 is taken for a pure liquid phase and inte grated between zero reference pressure and the system pres sure, it becomes If Equation 9 is rearranged and divided through by P, Equation 10 results. Equation 10 is the desired expression for calculating the pure component standard state liquid fugacity at P and T. L Vi is the pure component molar liquid volume and is as- L sumed to be independent of pressure. Vi can simply be taken to be the saturated liquid molar volume at the specified system temperature. Organick et al. (18), Gornowski et al. (9), and Glanville et al. (8) have reported saturated volumetric data for benzene. Young (28) reports saturated volumetric data for n-octane. The data for both components have been plotted as a function of temperature. The results are oL L or ln fdL(P=(j) " RT i P (9) (10) 70 the smoothed curves shown in Figure 19. All of the terms for evaluating Equation 10 are now readily available. Component Fugacity in the Equilibrium Vapor Mixture At constant temperature, a component's fugacity in a vapor mixture is related to its partial molal volume by the following relationship: where RTd In fV = dP Vi - ('3v/3ni)P(T(n,(j^i) (11) If Equations 4 and 11 are combined, the result is RTd ln(^iyiP) = V± dP (12) Next, Equation 12 is differentiated with respect to pres sure at fixed temperature and composition. 'Bln#, ( ~2ln(j*iyiP)~| = [j L *3 p J T'V L T,y = 1 RT (13) Finally, Equation 13 is rearranged and integrated between the limits of the ideal gas state (P = 0) and the system pressure P, all at fixed temperature and composition. f i - * & - a dP In = T z i . i ] > Lrt i dP (14) V^,Saturated Molar Liquid Volume Cuft/Lbmole ON © a <8 w o H £ *d d © c •H r e O B° d I H fi * 1 D •P O cd fi o I S 1 . fi fi o WPQ -P ~ ” 7TT” m 333H Temperature-- °C 72 Equation 14 is the exact thermodynamic expression for the vapor mixture fugacity coefficient of component i. In order to evaluate the partial molal volume in Equation 14, an equation of state must be used because of the lack of vapor P-V-T data for benzene-n-octane mixtures. Many investigators have successfully used the Red lich-Kwong equation of state (23) to calculate the fugaci ties and enthalpies of vapor phase mixtures at relatively high pressure. The Redlich-Kwong equation is a two-con stant equation of state and is expressed as RT a . P “ V - b T°’5V(V + b) where a = 0.4278 R2T§‘5/E>c b = 0.0867 RTC/PC The compressibility factor form of the Redlich-Kwong equa tion is - H - f 1 + h 1 <1 6 > o where A = p2ip2.5 B = £- RT • u _ BP _ b h _ _ _ _ _ For mixtures, the two constants are combined on a molar basis. 73 A = I > i Ai B = ^ y iBl (17) (18) Upon using Equation 15 and the mixing rules, Equations 17 and 18, to evaluate the partial molal volume in Equation 14, the fugacity coefficient of component i in the vapor mixture becomes Equation 16 must be solved first to obtain the compressi bility factor for the entire vapor mixture. It is a cubic in Z and can have from one to three real positive roots. The root of interest is the largest positive value of Z. After Z is determined, the solution of Equation 19 for the fugacity coefficient is quite straightfoward. Activity Coefficients The means for evaluating the terms in Equation 6 have been defined. Values for are provided from Table VIII. The experimental pressure, temperature, and vapor compositions are used to evaluate 0^ with the Redlich- Kwong equation. The experimental pressure and temperature are used in conjunction with the Chueh-Prausnitz pure liquid fugacity correlation to evalute 1/?. A GE Time- Bi In 0i = (Z-l) g- - ln(Z-BP) (19) 74 Sharing computer program (CRK8) was used to perform the calculations and generate the liquid phase activity coeffi cients. Table XXV of Appendix X is a listing of this pro gram. Figures 20 and 21 are plots of the calculated vapor fugacity coefficients as a function of vapor composition for benzene and n-octane. The temperatures covered are 220, 260, and 280°C. For either component, the vapor fu gacity coefficients are below unity and decrease with either increasing benzene content or increasing tempera- tur e. Figure 22 is a plot of the calculated liquid phase activity coefficients at 220, 260, and 280°C. The activi ty coefficient behavior shown here is quite unusual. Ben zene shows a positive deviation from ideal liquid solution behavior while n-octane shows a negative deviation from ideal liquid solution behavior. At first sight, this be havior appears to be thermodynamically inconsistent. The criterion for liquid phase thermodynamic con sistency is that the activity coefficients must satisfy the appropriate form of the Gibbs-Duhem equation. At con stant temperature only, the correct form of the Gibbs- Duhem equation (25) is x^d In Q j [ = ~RT- ^ (20) 75 Figure 20 Vapor Phase Fixture Fugacity Coefficients for Benzene Calculated by the Hedlich— ICvrong equation of State ur 0.7 0.6 .r: 0.3 0.2 0.1 0.6 0,2 hole Fraction Benzene in the Vapor Fugacity Coefficient, 76 Figure 21 Vanor Phase Kirrfrura Fugacity Coefficients for ii-O.ctane Calculated by the Hcdlich- Kwong equation of State IS •H O •H tH a> o o •3-1 O *S S* * y 1/-a " * I - . - . . . . . ' - ! 1 0.1 0*0 0„2 O.b 0*6 0*8 1*0 hole Fraction Benzene in the Taror Liquid Phase Activity Coefficients ^ 78 where ^ = VL - £ * l vl L L V is the molar volume of the liquid mixture. is the molar volume of pure liquid i, all at the system tempera- L ture T and pressure P. For all practical purposes, can be taken as the saturated molar volume for species i. On a differential basis for a binary system, Equation 20 can be expressed as (21) 9 In 9 In 2 A vL 9 p X1 _ ^ xl _ T + x2 '3 T " RT 3xl Subscript 1 refers to benzene, and subscript 2 refers to n-octane. Volumetric data for the liquid phase mixtures L are not available. The only recourse is to calculate V from Equation 21 and see if a physically realistic value is obtained.. As an example, this test was performed at 220°C and X]_ = 0.455. From Figure 22 the activity coeffi cient slopes are calculated graphically to be 9ln Y i T E "9 xi _ j^-ln Y 2 -0.435 ? x] = -0.663 From Figure 9 the slope of the bubble pressure curve at 220°C and xn = 0.455 is 3P T = 170 psia/mole fraction 79 a L Now can be calculated from Equation 21. A u^1 (0.455) (-0.435) + (0.545) (-0.663) = (l0V73l)(888) (170) 4\v = -31.4 cu. ft./lb-mole The liquid phase molar volume is calculated to be L a L L L V = A v + x 1v1 + x2v2 = -31.4 + (0.455) (2.00) + (0.545) (3.6275) = -28.5 cu. ft./lb-mole The above result for is physically impossible. It shows that the calculated activity coefficients are thermody namically inconsistent. Bierlein and Kay (3) have reflected some opinions on the evaluation of the consistency of high pressure equilibrium data. They feel that, in many cases, attempts to smooth high pressure data thermodynamically usually create more uncertainty than they eliminate. Neither phase is ideal. The evaluation of Equation 14 requires very precise P-V-T data for the superheated and saturated vapor mixtures. When an empirical correlation or equation of state is used for evaluating component fugacities in a mixture, there is sometimes no way of knowing how far in error they may be. At this stage there is a strong feeling that the Redlich-Kwong equation is not properly characterizing the 80 P-V-T behavior of the equlibrium vapor phase mixture of the benzene-n-octane system in the region of the critical locus. As a result, the partial molal volume V^, needed in Equation 14, is not being predicted correctly. The suspected problem here is that the combining rules for A and B (Equations 17 and 18) work well for well behaved materials, i.e., mixtures of similar gases. It is very doubtful that these simple mixing rules work for highly nonideal systems. The analysis which follows shows a way of calcu lating activity coefficients directly from liquid phase heats of mixing derived from experimental enthalpy data. This analysis completely circumvents any treatment of the equilibrium vapor mixture. As a result, it is then possible to independently evaluate the component vapor phase mixture fugacity coefficients and shed more light on the nature of the vapor phase nonideality. LIQUID PHASE ACTIVITY COEFFICIENTS FROM HEATS OF MIXING Calculated Heats of Mixing Liquid phase activity coefficients are easily de rived from heats of mixing for the saturated liquid phase. Liquid phase heats of mixing are calculated by the expres sion A h” = hl “ xw 1h1L “ xw2h2L' Btu/lb (22) Hl is the enthalpy of the saturated liquid mixture. xw^ and xW2 are the weight fractions of benzene and n-octane in the liquid. H-^l and H2L are the pure component liquid enthalpies, evaluated at the same pressure and temperature as the mixture. As mentioned previously, Lenoir et al. (16) present experimental saturated liquid enthalpies for pure benzene and six benzene-n-octane mixtures varying in concentration from 27.1 to 93.0 mole percent benzene (20.2 to 90.1 weight percent benzene). Furthermore, enthalpies were reported for pure n-octane in another publication (17). Equation 22 has been used to calculate heats of mixing from these data. These calculations are summarized in Table XI. In Figure 23 these heats of mixing values are plotted as a function of temperature. The scatter shown here 81 82 TABLE XI Calculated Heats of Mixing from Enthalpy Data for the Benzene-n-Octane System (16) Press Psia . Temp. °F H* Btu/lb * H1 Btu/lb xwlHl Btu/lb * h2 Btu/lb *w2H2 Btu/lb Hld Btu/lb 4HM=H-Hid Btu/lb 93.0 mol. % Benzene (90.1 wt. % Benzene) 200 391.2 251.4 242.7 218.5 311.5 30.8 249.3 2.1 300 438 280.1 270.8 244 346 34.2 278.2 1.9 400 474.4 303.8 294.0 265 374.5 37.1 302.1 1.7 500 504.6 324.6 314.5 283.8 397.2 39.3 323.1 1.5 600 532.3 346.0 336.7 303.8 419.4 41.5 345.3 0.7 85.7 mol. % Benzene (80.3 wt. % Benzene) 200 395.4 261.6 245.1 196.7 314.5 62 258.7 2.9 300 442.5 290.5 273.5 219.5 349.5 68.9 288.4 2.1 400 480.3 315.6 298 239.5 379.1 74.7 314.2 1.4 500 510.7 337.2 319.2 256 402.1 79.4 335.4 1.8 600 536 358.4 340 272.8 422.5 83.4 356.2 2.2 77.1 mol. % Benzene (69.7 wt. % Benzene) 200 400.7 273.1 248.1 173.1 318 96.4 269.5 3.6 300 449.9 305.5 278 194 355 107.8 301.8 3.7 400 486.8 331 302 210.2 384 116.4 326.6 4.4 500 520.4 356.6 326.9 228 410 124.2 352.2 4.4 67.6 mol. % Benzene (58.8 wt. % Benzene) 200 408.7 285.1 253 148.9 324.2 133.9 282.8 2.3 300 459.5 319.9 284 167 363 149.8 316.8 3.1 400 495.7 345.6 308.3 181.3 391 161.1 342.4 3.2 500 528.8 371.6 333.5 196 416.7 172 368 3.6 *The enthalpy datum is 0 Btu/lb for the pure saturated liquid compo nents at -200°F. Subscript 1 refers to benzene, and subscript 2 refers to n-octane. 83 Press Psia 44.6 200 300 400 450 27.1 200 300 400 TABLE XI (con't.) Temp. hj H" “1 xwlHl H2 x w 2H2 Hid 4HM=H-Hld Btu/lb Btu/lb Btu/lb Btu/lb Btu/lb Btu/lb Btu/lb H mol. % Benzene (35.6 wt. % Benzene) 432.4 318.2 267.3 95.1 341.9 220 315.1 3.1 482.3 354.5 299.2 106.5 381 245.8 352.3 2.2 521 385.4 327.1 116.3 411 265 381.3 4.1 537.8 400.2 341.8 121.6 425 274 395.6 4.6 mol. % Benzene (20.2 wt. % Benzene) 450.9 343.1 278.5 56.4 356.1 284.2 340.6 2.5 499.3 380.1 311.5 62.9 394.1 314.5 377.4 2.7 542.2 417.5 346 70 429.8 343 413 4.5 Hsat of Mixing:, Btu/lb irv o v\ O »A ■ > * • * o"\ e r \ pi Pi A P P i i i + to S O H i 5 - » < s > 2 X :y P p p - ' t i t o S - . >* o O CO 3* rA ' - M > • -M V ■ ) ■ > H A ' m • • H . ' J"H Z t X a o 3 b0 •H O «H S i S 3 & 5 3 O «H i"H o ■p M S ^ © f f i ( X ) "T- - r ' 1 A ' - / : i A: p. ' : —h ••-f- V/“: O’ ! N t * * * a ffl, <*! o ^v-OnOtHINO : < > o 3 o t t O: v\<*v M -$\0 I'-tO O . ' i i t ■/ -p - ./ ^ 4 - / t : ■ li ■ * - ? ; i * O r - i ' ■ t f: “ a X a <3 © 85 apparently reflects the 1.5 Btu/lb uncertainty in the basic experimental data. The best visually smoothed curves possible were drawn through each series of points repre senting a fixed composition. At several temperatures vary ing from 220°C to 380°C (428°F to 536°F), heats of mixing values were read from these smooth curves. These values are listed in Table XII as a function of composition. This is the form in which these data will ultimately be used. Thermodynamic Model A thermodynamic model for the liquid phase must be available to relate heats of mixing to activity coeffici ents. Wilson (26) has proposed a very useful thermodynam ic model. On the basis of molecular considerations, he developed the following expression for the excess Gibbs free energy of a binary mixture. = - x ^ n ^ + ]X12x2) - x2ln(x2 + A21xl) (23) The activity coefficient for any component is found by the exact relation T,P,nj(j/i) (24) n^ is the number of moles of component i, and nt is the total number of moles. If Equations 23 and 24 are 86 TABLE XII Smoothed Heats of Mixing for the Benzene-n-Octane System Temperature Mole % Benzene Heat of Mixing °C in the Liquid A hm, Btu/lb 220 (428°F) 27.1 2.50 44.6 3.08 67.6 2.70 77.1 3.70 85.7 2.31 93.0 1.95 230 (446°F) 27.1 2.50 44.6 3.175 67.6 2.94 77.1 3.76 85.7 2.05 93.0 1.86 240 (464°F) 27.1 2.53 44.6 3.31 67.6 3.11 77.1 3.85 85.7 1.84 93.0 1.76 250 (482°F) 27.1 2.59 44.6 3.48 67.6 3.26 77.1 3.97 85.7 1.72 93.0 1.66 260 (500°F) 27.1 2.72 44.6 3.71 67.6 3.38 77.1 4.13 85.7 1.72 93.0 1.54 270 (518°F) 27.1 3.19 44.6 4.04 67.6 3.49 77.1 4.36 85.7 1.90 93.0 1.24 87 TABLE XII (con't.) Temperature Mole % Benzene Heat of Mixing °C in the Liquid AH m > Btu/lb 280 (536°F) 27.1 4.07 44.6 4.54 67.6 3.59 77.1 4.70 85.7 2.21 93.0 0.52 88 combined, the Wilson activity coefficient expressions for a binary system are generated. In = -In (x-^ + ^*i2x2^ + x. 12 _ /v 21 X1 + 7*12x2 ^21x1 + x2 (25) In = -ln(x2+ /^2ixi) ” xi 12 X 21 xl+ Xl2x2 ^.21X1 + x2 (26) The Wilson equations contain two adjustable parameters, ^.•^2 anc^ X 21* original derivation, Wilson related these parameters to the pure component molar volumes and to certain characteristic molecular energy differences, g^j. Orye and Prausnitz (19) give these expressions in the form Al2 = VL exP 1 1 vr A 2 1 " ~ t exp g12 ~ gll RT g12 ~ g22 RT (27) (28) As an excellent approximation the quantities (9^2 ” gll^ and (g^2 " g22^ are in<3€Pendent of temperature over a modest temperature interval. Heats of mixing, A h* 1, are related to the excess Gibbs free energy by the well known Gibbs-Helmholtz equation. 89 (29) Equations 23 and 29 are finally combined to form the ana lytical expression for the heat of mixing of a binary solu tion . 26 to fit vapor-liquid equilibrium data only. They ob tained some very good results for over one hundred com pletely miscible binary systems. Whenever they compared the ability of the Wilson model to fit data with that of the classical van Laar and Margules models, they found that the Wilson model was always as good as the other two and in many cases much better. Method of Hanks Hanks and co-workers (10) have shown that the deter mination of vapor-liquid equilibria by integrating heat of mixing measurements has great practical potential. Recent developments in heat of mixing calorimetry have made it much simpler to measure heats of mixing than to determine the x-y data experimentally. These authors have used the Gibbs-Helmholtz equation A H “ = X1 xx + ?li2x2 (g12 ‘ 9ll’ + X2 x2 +'x1X 21 <912 - *22> (30) Orye and Prausnitz (19) have used Equations 25 and 90 together with Wilson's semitheoretical liquid solution model and experimental heats of mixing to calculate iso thermal vapor-liquid equilibria for some binary systems. Basically their calculation procedure consists of regress ing Equation 30 with isothermal heats of mixing data in order to obtain the best set of molecular energy para meters, g^2 “ 9li an(3 ” ^22* T^ese parameters are then used to compute and Equations 25 and 26. If the system pressures are low enough, then the vapor phase can be taken to be ideal, and the effect of pressure on the liquid phase is negligible. For an ideal vapor phase the vapor composition is calculated by equation 31. P^ and P2 are the vapor pressures for pure components 1 and 2. Hanks et al. have used the above procedure to make some very excellent vapor composition predictions for the carbon tetrachloride-acetone and benzene-acetone systems at 45°C. Application to the Benzene-n-Octane System Over the range 220 to 280°C and 0 to 100 mole per cent benzene, system pressures vary from about 100 to 600 psia. Although the Wilson model does handle a modest (31) yl X1P1 ^1 + t1 “ X1^P2 ^2 91 variation in temperature, it does not allow for pressure variations. In the analysis to follow, the effect of pressure on the liquid phase will be ignored. With this assumption and with the degree of uncertainty in the cal culated heats of mixing, this analysis will be considered as only an approximate analysis. Basically, the method of Hanks et al. has .been ap plied to the heats of mixing data listed in Table XII. The determination of the best values of g^2 - g ^ and g^2 " %22 f°r Equation 30 is a nonlinear regression problem. An algorithm was developed to solve for these parameters. First an objective function OJ must be defined. 42 k A = 2 3 A H j c a l c . - 3=1 je x p (32) Using all 42 data points listed in Table XII, values of OJ were generated for a host of assigned values for g^2 - g ^ and g-^2 - 922* two Parameters which made an abso lute minimum were selected as the best regression con stants. The GE Time-Sharing Program CRK3 was used for these calculations (see Table XXVII of Appendix I). Figure 24 is the plot of CcJ versus the two adjustable parameters. The global minimum value is 1800 Btu/lb-mole and occurs at the following values of the two parameters. 92 Figure 2! f Dctermination of the Il'ininum Value of the Objective Function for Selection of the Best Wilson Parameters 6000 ^ g 12-gH= 1200 Btu/Lbmolell g - j 2**g22= Btn/Ltaolo 21" 5000 4000 3000 2000 S^-tS i .-r-v 4 ^1 . ; - , . ' . . . . '-'.■ITr ; ~ : i -I -i'-i- -4-i-*4- Iri -- 1” j T iivi Vlb: bffl'elT T-\ 1:1/ 4r-‘ ;; 21.',. ;t : - L ' b i x : - ' ':.., i'..z.- ■ • j '■ i Ml. . . pi. ! . 6:-: - ......I ' i -400 0 400 OOC S - j p~o22' ^ Btn/Lbznole 1 200 93 g12 - = 1200 Btu/lb-raole ^12 ” ^22 = Btu/lb-mole The best regression constants can now be used to generate smoothed heats of mixing values from Equation 30 and activity coefficients from Equations 25 and 26. Com puter Program CRK4, shown in Table XXIX of Appendix I, was used for this purpose. Figures 25 and 26 show the calculated heats of mixing curves superimposed upon the plotted points (cir cles) derived from experimental enthalpies. The experi mental points exhibit a fair degree of scatter. This is not surprising since the basic enthalpy data have an un certainty of 1.5 Btu/lb, and the heats of mixing never ex ceed 5 Btu/lb. In nearly every case, however, the calcu lated curves are within 1.5 Btu/lb of the experimental points. At 280°C (Figure 26) the point at 0.771 mole fraction benzene deviates from the curve by about 1.7 Btu/lb. Calculated activity coefficients are shown in Fig ure 27. These curves appear to be very consistent. Both components show positive deviations from ideal liquid solu tion behavior. The thermodynamic consistency of the acti vity coefficients can be shown with the Redlich-Kister area test (22) . This test is simply expressed by Equation 33. Heat o f Mixing;,Bfcu/Lb Figti.ro 2 5 Calculated Heats of riuine Prom the Wilson Ibdcl at 220 and 220°C » 0 P~r r 3.Y-o°c* i : " I ' M i i 3-0-: * r r T ; ■ ■ ; r :. J. . ■ ; r . / . ! -35-2 2p-0 : -r- r s . : ; ,©?k: - ~ U ■/ -/7~ " ft 1 . 0 ‘ v: ,,-V; :e_i . . . r ,-r:7E I '3 f: - - A.:. y; . - . v ■/ 0,0 -.! -.“1.: OnO/... Heat o f MixingsBtu/Lb Figure 26 Calculated Heatn of 1 lining From the '.illson Lodci at 260 and 2uO°C 95 m m 0 • 0 /■ , I 1 ___! . . . . . 1 0 0,2 Ojr 0„6 0,0 1.0 Folo Fraction Benzene in the Licmid .Activity Coefficient Figure 27 Liquid Phase Activity Coefficients Calculated From a Fit of the 7/ilson Hodcl to Heats of Fining Data ; • U'l ^ U t 'HR ; ! ; f: : v. f ’. :-!> j . n ! : j i f f i 0 0„2 0„C- 0,6 0* 0 1 ■ Hole Fraction Bensone in the Liquid 97 In dxx = 0 (33) This expression is valid for constant pressure and tempera ture only. However, in this analysis the effect of pres sure is being ignored. Figure 28 shows the application of this area test to the calculated activity coefficients at 260°C. The net area under the curve is reasonably close to zero. The residual area is about 2 percent of either the area above or below the zero axis. It is concluded that the activity coefficients are thermodynamically consistent. Vapor Phase Nonideality Equation 6 was previously used to calculate activi ty coefficients from experimental equilibrium ratios, pure liquid fugacities evaluated from the Chueh-Prausnitz cor relation, and vapor mixture fugacities calculated from the Redlich-Kwong equation of state. It was previously shown that this correlation predicted thermodynamically incon- o . sistent activity coefficients. The term y ^ is a pure com ponent property and is well defined. If the basic equili brium measurements are assumed to be correct, then the lack of consistency must be attributed to the inability of the Redlich-Kwong equation to properly describe the P-V-T behavior of the vapor phase mixture. In an independent analysis liquid phase activity 98 F ig u re 2o Rcdlicn-Kiater Consistency Test £or the Activity Coefficients at 260 C Froh Figure 27 0.2 0.1 ~ < ■ ivr'iT..vjSr.&izvrr. 0.6 ■ t— 0.8 0.2 0 hole Fraction Benscno in the Lin-old 99 coefficients were computed directly from liquid phase heats of mixing. In this case there was no need to char acterize the nonideality of the vapor phase. This situa tion suggests the use of the equation of equilibrium to independently calculate vapor fugacity coefficients. For this purpose Equation 6 is rearranged to form Equation 34. vL o 0 ± = k--- 1' (i = If 2) (34) From the experimental K-values of Table VIII, )/? values calculated from the Chueh-Prausnitz correlation, and activity coefficients derived from heats of mixing, values of 0^ were independently computed. Computer Program CRK7, listed in Table XXX of Appendix I, was used to per form the calculations. Figures 29 and 30 are plots of these vapor fugacity coefficients for benzene and n-octane as a function of vapor composition with temperature as the parameter. Quantitatively these curves are quite different than the curves predicted by the Redlich-Kwong equation in Figures 20 and 21. The vapor fugacity coefficients of benzene go through characteristic maxima. At 280°C the 0i for benzene rises to a maximum value of about 1.3. For n-octane the curves rise rather sharply at concentrations exceeding 0.90 mole fraction benzene in the vapor. An interesting feature shown here is that the 0^ values for benzene Fugacity Coefficient 100 Figure 29 Vapor Phase 'nocture Fugacity Coefficients for Benzene as Derived From lie at s of lihcing -Q- W f f l o 0,2 ' j > 0 C, o • - 0.» o • ' > » - 'i»0 I'olc Fraction Bensons in the Vanor Fugacity Coefficient Figure 30 101 Vapor Phase lli.uiure Fugacity Coefficients for ir-Cctoneas Derived From Iieats of Fixing 1 ..8 if R 0.6 0.2 0.6 0.8 1.0 Ible Fraction Benzene in the Vapor 102 generally increase with increasing temperature while values for n-octane decrease with increasing temperature. Although the activity coefficients derived from heats of mixing are only approximate, the resulting vapor mixture fugacities at least reveal a trend and show that the vapor phase of the benzene-n-octane system in the cri tical region is highly nonideal. As mentioned previously, the Redlich-Kwong equation of state is not properly char acterizing the P-V-T behavior of the equilibrium vapor phase. It is suspected that the simple mixing rules (Equations 17 and 18) are inadequate for this system. It is very unlikely that the appropriate vapor mixing rules could be developed without the availability of some very precise P-V-T data for both the saturated and superheated vapor mixtures. The saturated P-T data are provided in this work. SUMMARY In this investigation, the liquid and vapor P-T phase boundaries of pure benzene, pure n-octane, and six teen benzene-n-octane samples were measured over the tem perature range of 190 to 290°C (critical region). The critical locus of this system has a characteristic minimum temperature of 287.9 C at approximately 81 to 82 mole per cent benzene. In the region of its critical locus, the benzene-n-octane system exhibits total liquid phase mis- cibility and forms no azeotropes over the full composition range. Pressure-composition isotherms were constructed from the basic P-T phase boundaries. From these isotherms the liquid and vapor compositions which coexist at equili brium could be determined at various pressure levels. Finally, the equilibrium ratios were calculated and re ported in Table VIII. The direct phase boundary measurements of this in vestigation have been compared with the corresponding phase boundaries derived from the enthalpy measurements of Lenoir et al. (16) for the benzene-n-octane system. The comparisons were made in terms of pressure-composition isotherms over the range 220 to 270°C. At any temperature, the bubble pressure discrepancy was no worse than 5 psi. 103 104 Below 250°C, the worst discrepancies in the dew pressures varied between 10 and 15 psi. Overall, the comparisons were considered satisfactory. Another primary goal of this study was to evaluate liquid phase activity coefficients for the benzene-n- octane system over the range of pressure, temperature, and composition measured. Two different methods were illus trated for calculating liquid phase activity coefficients. With the first method activity coefficients were calculated directly from the measured equilibrium data through use of the equation of equilibrium. The Redlich-Kwong equation of state was used to compute the vapor mixture fugacity coefficient of each component and thus characterized the nonideality of the equilibrium vapor phase. The resulting activity coefficients turned out to be thermodynamically inconsistent. The second approach involved the use of liquid phase heats of mixing which were derived from the experimental enthalpy data reported by Lenoir et al. (16). The method of Hanks et al. (10) employs the Wilson model to calculate liquid phase activity coefficients directly from heats of mixing. Basically the method of Hanks et al. was used in the second approach. In this analysis, the effect of vari ations in pressure on the liquid phase was assumed to be negligible. With this assumption and with the degree of 105 uncertainty in the calculated heats of mixing (at least 1.5 Btu/lb), the calculated activity coefficients were con sidered as only approximate values. These activity coeffi cients turned out to be thermodynamically consistent. This second approach to evaluating activity coeffi cients completely circumvents treatment of the vapor phase. This situation immediately suggested the use of the equation of equilibrium to independently calculate vapor mixture fugacity coefficients. The resulting fuga city coefficients revealed that the vapor phase of the benzene-n-octane system in the critical region is highly nonideal and is not being characterized properly by the Redlich-Kwong equation. This observation accounted for the lack of thermodynamic consistency in the activity co efficients calculated by the first method. It is concluded that the simple mixing rules (Equa tions 17 and 18) are not adequate for calculating the characteristic Redlich-Kwong vapor mixture constants A and B. It is very unlikely that correct mixing rules could be developed without the availability of some very precise P-V-T data for both the saturated and superheated'vapor mixtures. REFERENCES 1. API Technical Data Book - Division of Refining, New York (1966). 2. Bender, P., G. T. Furukawa, and J. R. Hyndman, Ind. Eng. Chem., 44., 387 (1952). 3. Bierlein, J. A., and W. B. Kay, Ind. Eng. Chem., 45., 618 (1953). 4. Cajander, B. C., H. G. Hipkin, and J. M. Lenoir, J. Chem. Eng. Data, J5, No. 3, 251 (1960). 5. Chueh, P. L., and J. M. Prausnitz, Computer Calcula tions for High-Pressure Vapor-Liquid Equilibria, Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1968) . 6. Ellis, S. R. M., A New Equilibrium Still and Binary Equilibrium Data, Trans. Inst. Chem. Engrs., 30., 58 (1952). 7. Elshayal, I. M., and B. C. Y. Lu, Isothermal Vapor- Liquid Equilibria for the Binary System Benzene-n- Octane, J. Applied Chem. (London) , 18^, 277 (1968) . 8. Glanville, J. W., and B. H. Sage, Ind. Eng. Chem., 41, 1272 (1949). 9. Gornowski, E. J., E. H. Amick, Jr., and A. N. Hixon, Ind. Eng. Chem., 39., 1348 (1947). 10. Hanks, R. W., A. C. Gupta, and J. J. Christensen, Ind. Eng. Chem. Fund., 10., 504 (1971). 11. Hayworth, K. E., Ph.D. Dissertation, Univ. Southern California, Los Angeles (1969). 12. International Critical Tables, JL, 53 (1926). 13. Kay, W. B., and D. Hissong, The Critical Properties of Hydrocarbons - I. Simple Mixtures, API 32nd Mid- Year Meeting (1967). 14. Kay, W. B., Ind. Eng. Chem., .30, 459 (1938). 106 107 15. Lenoir, J. M., A.I.Ch.E. Jr., 4, No. 3, 263 (1958). 16. Lenoir, J. M., K. E. Hayworth, and H. G. Hipkin, Enthalpies of Benzene and Mixtures of Benzene with n-Octane, J. Chem. Eng. Data, _16, No. 3, 280 (1971) . 17. Lenoir, J. M., D. R. Robinson, and H. G. Hipkin, Enthalpies of Mixtures of n-Octane and n~Pentane. J. Chem. Eng. Data, _15, No. 1, 26 (1970). 18. Organick, E. I., and W. R. Studhalter, Chem. Eng. Prog., 44, 847 (1948). 19. Orye, R. V., and J. M. Prausnitz, Ind. Eng. Chem., 52, 18 (1965). 20. Popovics, S., A Method for Evaluating How Well Ob served Data Fit the Line Y=X, Materials Research and Standards ASTM, 2* 195 (1967). 21. Rebert, C. J., Ph.D. Dissertation, The Ohio State University (1955). 22. Redlich, O., and A. T. Kister, Ind. Eng. Chem., 40, 345 (1948). 23. Redlich, O., and J. N. S. Kwong, Chemical Reviews, 44, 233 (1949). 24. Sieg, L. , Chem. Ing. Tech., 22.< 322 (1950). 25. Van Ness, H. C., Classical Thermodynamics of Non- electrolvte Solutions, MacMillan Co., New York (1964). 26. Wilson, G. M., J. Amer. Chem. Soc., 8.6, 127 (1964). 27. Young, S., Stoichiometry, Longmans Green and Co., New York (1918). 28. Young, S., J. of the Chem. Soc., 11_, 1145 (1900). A P P E N D I C E S 108 APPENDIX A Sample Preparation and Experimental Procedure General Hayworth (11) presents an extensive discussion on the techniques of sample preparation and phase boundary measurement employed in this research. Therefore, this information is only briefly discussed here. Loading Sample Tube The experimental tubes used were made of Pyrex glass with the approximate dimensions shown in Figure 31. The overall sequence of loading a sample tube is as follows: 1. Degas all fluids. 2. Transfer a known amount of each fluid to the sample tube. 3. Trap the sample with a stem of mercury. 4. Remove the sample tube from the loading apparatus and transfer it to the compressor block. The loading apparatus is shown schematically in Fig ure 32. This figure is a reproduction of Figure 29 from Hayworth (11). Basically, it is a vacuum still in which it is possible to degas the experimental fluids, and also transfer known amounts of each fluid by distillation. The 109 t 600 r n r n 1 0 0 r n m ) i !i/ m l no PITlEX PR EC 131017 30HE CAPILLARY TUBE 2m." i. D*. 8n£a C. PYREX 1-L1IE TAPERED JOIITT Figure 31 Experiment cl Tub? TRANSFER MANIFOLD i n 20 23 33 32 » I 29 Figure 32 Schematic of Loading Apparatus 111 112 sample tube assembly 13, 14, and 15 is attached with a stainless steel ball placed at the bottom of the tube. A cold trap, bulb 23, is attached and an acetone-dry ice bath, 33, is placed around it. Mercury is placed in bulb 16 and will ultimately be used to confine the final sample in the tube. The entire system is pumped down with the aid of a vacuum pump and mercury diffusion pump operating in series. During the pumping down of the apparatus the degassing of the hydrocarbons is accomplished. This consists of dis tillation of the hydrocarbon from bulb 20 to bulb 19 (or 21 to 22) with valve 4 closed and valve 6 opened (or 5 closed and 7 opened). After a transfer from one bulb to the other, the hydrocarbon is kept in a solid state by placing a dry ice-acetone bath (31 or 32) around it, and valve 4 (or 5) is opened to the vacuum to draw off the re leased gases, then closed again. This type of operation is carried out several times assuring the removal of all non-condensables. With all fluids degassed, the next step is to trans fer a known quantity of each to the sample tube. The measurement of the amount of each component transferred is done with a fine capillary tube, 17. The calibration of tube 17 is covered in Appendix B. The method of select ing the amount of each component is covered in Appendix C. 113 The capillary is kept at a constant temperature by placing a water bath, 30, around it. This water bath is maintained at approximately 8 to 15°C. The vacuum manifold is used to adjust the desired height of the liquid level, and a cathetoraeter is used to make the precise measurement of the liquid level to within .+0.005 cm. The above procedure is followed for each component successively transferring them to the sample tube. The sample tube tip is immersed in a dry ice-acetone bath in order to promote this transfer. When all components are in the sample tube, mercury is poured into the sample tube from the mercury bulb, 16. Sufficient mercury is poured into the tube to completely fill it. The vacuum is broken by removing the mercury bulb from the system, and the sample tube is then removed from the apparatus. The sample is now ready to be placed in the compressor block. Complete Data Collecting Apparatus Figure 33 is a schematic diagram of the entire ap paratus as assembled for use. This figure is a reproduc tion of Figure 31 from Hayworth (11). This equipment and the procedures employed were basically those developed by Young (27) and Kay (14), and used after modification by Rebert (21). The sample tube is held in a compressor block filled with mercury, and the block, in turn, is con nected to a hydraulic-pressure oil compressor used to T H E R M O C O U P L E LEADS 114 T O V A C U U M F l i . D r . A D W E I G H I G A ' J C j c f c . 3 T c .F f rrr COT! c a r;- O IL CCf c= RVOCOUPLE -VACUUM MANOMETER SAMPLE PRESSURE GAUG i r — l ___ [ V r : ] f^Q3 BULBS FOR M INUTE PRESSURE VARIATION WIT HIM THERMOSTAT & — V.'iRE HANGERS P 0 P . STIRRING MAGNET SAMPLE TUS MERCURY LEV= INDICATOR STIRRING MAGNET THERMOSTAT ERCURY ES50R -0 CO, VACUUM RESERVOIR (2 -5 GALLON DOTTLES) ■ T Z 7 T Z 7 BOILER RESI5TA PRESSOR B LOCI' 115 balance the pressure developed by the sample. The mercury level (mercury-oil interface) was held constant by adjust ing the level in the mercury level indicating cylinder. The mercury level was observable by means of a single probe which made contact with the mercury and was connected to a flashlight bulb and transformer. The tube was heated to a constant temperature by the condensing vapor of one of a series of organic liquids, which was confined in a vacuum- jacketed thermostat surrounding the tube. During the course of this investigation, it was necessary to use two boiling fluids, benzophenone and diphenyl ether. By vary ing the pressure within the thermostat, the boiling point of the liquid is changed; therefore, the condensing vapor and sample temperatures are changed. The thermostat is only partially silvered, allowing the operator to observe the state of the sample. By varying the pressure at a given temperature, the bubble point and the dew point can be established. In this manner the phase boundaries can be traced. The pressure in the system was indicated by a Bourdon pressure gauge with a range of 0 to 1500 psig. The temperature was determined by means of an iron-con- stantan thermocouple in conjunction with a potentiometer and galvonometer. The calibration of the thermocouple system and pressure gauge is described in Appendix B. 116 To hasten the attainment of equilibrium, the sample was stirred by means of a 400 series stainless steel ball inside the experimental tube. The ball was moved within the sample by means of a small cylindrical permanent mag net which surrounded the sample tube. This magnet was hung inside of the vapor thermostat on stainless steel wires which were suspended from a steel carrier. This steel carrier was itself moved by a cylindrical permanent magnet outside the system. In order to observe the phase changes taking place within the sample tube, a light was mounted directly be hind the tube. This light was connected to a variac so that the intensity of the light could be changed. To check critical phenomena, a small movable light source was used to observe both transmitted and incident light effects. APPENDIX B Calibration of Equipment Pressure Gauge The Bourdon pressure gauge was periodically cali brated against a dead weight tester up to a pressure of 800 psig in increments of 100 psi. Figure 34 is a typical deviation chart showing the results of a single calibra tion. In no case did the deviation ever exceed +1 psi. This error is well within the claimed accuracy of +0.1% of the full scale reading. As a result, the gauge correc tion was ignored in the calculation of the absolute sample pressure. Thermocouple The thermocouple used in this investigation con sisted of a 24-gauge iron and constantan wire with fiber glass insulation. It was standardized against condensing water, naphthalene, and benzophenone using a melting ice reference junction. The results of the standardization are summarized in Table XIII. Table XIV lists the equa tions used to obtain the true boiling temperatures of the calibration fluids. These equations are taken from the International Critical Tables (12) and are valid for baro metric pressures ranging between 680 and 780 mm Hg. To 117 Deviation=*Psi Figure 3*f Pressure Gauge Deviation Chart 118 0 200 1)00 600 oOO Gauge Reacling-Psig 119 TABLE XIII Thermocouple Deviation Data Substance Condensing Water Condensing Naphthalene Condensing Benzophenone -E0 emf Barometric Thermocouple Press. mv________mm Hg 5.230 11.751 16.558 753.3 752. A 750.6 True Temp. °C Ec emf Chart mv 99.75 5.230 217.52 11.726 305.29 16.602 Deviation E0 — Ec mv 0.000 +0.025 -0.044 120 TABLE XIV Summary of Equations for Obtaining True Boiling Temperatures of Standard Calibration Fluids 1. Steam 100.000 + 47.164 LOg10 (^fo) t 1 - 0.1727 Log 10 2. Naphthalene c = 217.96 + 56.668 L o ^ 1 - 0.2075 LOg10 3. Benzophenone 305.90 + 52.981 Log10 Im ) 1 - 0.194 Log 10 ( 76o) where t is in °C P is in mm Hg. 121 convert from millivolts to temperature, Tables XIX and XX of Appendix E were used. These were prepared from the table given by Rebert (21). Figure 35 is a plot of the deviation of the true EMF of the thermocouple from the standard chart against observed EMF. This figure was utilized to correct all ex perimental EMF readings in order to ascertain the true sample temperature. Sample Measuring Tube The technique of calibrating the sample measuring tube has been described by Hayworth (11). For the sake of completeness it will be repeated here. The precision-bore capillary tube that was used for measuring the quantity of each component in a sample mix ture was calibrated to determine its volume as a function of its length from the tip. Measurements were made of the length and temperature of known masses of mercury in the tube and of the height of the mercury meniscus. To the calculated volume of mercury was added a volume compliment of the mercury meniscus based on the assumption that the meniscus was a segment of a sphere. For convenience in subsequent use, these data were reduced to the form of a linear equation by application of the metho: of least squares with the following result. Figure 35 Tiiernocouple Deviation Chart 122 0.03 0.02 0,01 0.00 0.01 ■ 0,0 r * 2 6 7 r \ o 9 10 11 12 13 I1 * 15 16 17 30-xhc-rno couple Do ading-mv 123 V = 0.004675L - 0.000114 where V is the liquid volume in cc. L is the liquid length in cm. The total volume of the sample measuring capillary in cluding the volume Up to the closed valve was determined by filling the volume with mercury. This volume was found to be 5.99 cc. APPENDIX C Calculation of Sample Composition from the Capillary Loading Technique From the capillary loading measurements made on the individual components, the apparent sample composition was calculated in a manner shown in Table XV for sample BO-14. The individual items in the table have the following signi ficance . 1. The temperature of the water bath surrounding the sample measuring capillary tube. 2. The vapor pressure of the individual components at the temperature of the bath (Figure 36). 3. The density of the liquid of the individual components at the temperature of the bath (Figure 37). 4. Cathetometer reading of top of the liquid level in capillary. 5. Cathetometer reading of bottom of liquid in capillary. 6. Difference of items 4 and 5 giving the length of liquid in capillary. 7. The calculated volume of liquid. 8. The calculated number of gram-moles of component contained in the remainder of the volume of the 124 Vapor Pressure-mm Hg Figure 36 Vapor Pressures of Benzene end n-Octane at Loading Temperatures 10 12 1^ 16 10 20 Temper at ur e-°C Figure 37 Density of Liquid Benzene and n-Octane at Loading Tenneratures 0,90 0,88 0.80 <3 0*78 S v . : -,:,:, L_tULU 0.76 W S i S T - T ; o 0,/2 O.60 0.66 V; - } - : 0 Tensc r atur g C 128 measuring tube assembly at its saturation vapor pressure and temperature assuming ideal gas behavior. 9. The moles of liquid portion of component. 10. Total moles of components. Sum of 8 and 9. 11. Total moles in sample. 12. Composition mole percent. During the actual preparation of a binary sample, it would be too tedious to determine the above for each component as it was being loaded. Since the sample mea suring capillary is a constant volume tube, it was possible to calculate the component weight for a given length at a given temperature. These component weights could then be plotted as a function of liquid length with temperature as the parameter. Figure 38 is an example of one of these loading charts. With such a chart, the rapid determina tion of the correct liquid stem of the component to give the required weight of the component for the particular sample was possible. Once the sample was loaded, the ex act numerical composition was computed by the method pre viously described. Component VJeight-Gm-molee x 10 F ig u r e 38 Component Weight as a Function of Liquid Length in Measuring Capillary it: ' I ' : f ! I ■ ’ ■ !lrh-!r L U irU 11'i i ! : : j i : i : \ i F j ' i : ! r r ' ' ili.L :;i! :<v.cx4 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.6 Liquid Length-cm APPENDIX D Determination of Sample Compositions by Gas Chromatography Gas Chromatograph In this investigation it was necessary to check the compositions calculated from the capillary loading tech nique. This check was done with the use of a Hewlett- Packard 7620A thermal conductivity gas chromatograph. In order to get the proper peak resolution and sensitivity for the benzene-n-octane system, the following chromato graphic operating conditions were employed. 1. The separating column (6 ft. long and 1/8 inch o.d.) was packed with 10% UCW-98, 80-100S. 2. The operating temperatures were Item Temperature,°C Injection port 150 T.C. oven 150 Column oven 100 3. The thermal conductivity detector operated at a bridge current of 150 MA. 4. The helium carrier flowrate was 30 cc/min. 5. One f&Jt liquid samples were injected with a standard 1 0 Hamilton syringe. Figure 39 shows a typical chromatogram for the benzene- n-octane separation. For a given sample, three to four 130 131 Figure 39 Typical Chromatogram for the Bcnnene-n-Octane System 132 such scans were run and the average area percent calcu lated . Calibration In order to relate peak area percent and mole per cent, benzene-n-octane mixtures of known composition were prepared gravimetrically and analyzed on the chromatograph. The plotted circles on Figure 40 are the results of this calibration. The calibration data were successfully fitted to the hyperbolic form! v - A +. ,■§* * “ 1 + CX where X is the area percent of benzene in n- octane Y is the mole percent of benzene in n- octane Table XVI shows a GE Time-Sharing program which determines the least squares fit of the above equation. Table XVII shows the program output for the calibration data in question. Listed are the best regression constants, a comparison between actual and predicted compositions, and calculated Popovics' statistical parameters showing the overall goodness of fit. These results show that the fit is quite good. The final calibration relationship be comes: Y-Mole Percent Benzene Figure Vo Benzone-n-Octane Gas Chromatograph Calibration 133 0 - Calibration Data Y = A + BX 1 ■ + CX A = O.T16303 3 =■ 1 . ^ 6 9 0 ^ C = 0.00^-9097h r 100 80 60 l: - C hhr-'y •&; ' ' & 20 m m m n . /-HpT -pizi f — 1- - - r .r ■ ■ ' ’ [ : . ' ■ ! . /. i ' • -4rj— -fir: .1 1 :- . £i~ E 4 - . ^ ' i ’ 1: : 0 20 J - f O 60 80 X-lrca' Percent Benzene 100 2 01 f'l AC 50) , r< 50) , l(. 53) » SC 30) 5 READ N TABLE XVI 10 FJR I = 1 TJ N 1 5 REAi) XC I ) , / 20 n e x t i G.E T z m e - S h a r i n g P r o g r a m 25 l e t i>i=3 f o r H y p e r b o l i c F i t 30 LET D2=0 35 LET 03=0 40 LET J « 0 45 LET 05=0 50 LET 06=0 55 LET D7=0 60 FOR I = 1 TJ N 65 LET 01= 01 + XCI ) 73 LET 02= 02 + T< 1) 75 LET D3= D3 + X C I ) * y C I ) S O LET 04= 04 + X 3 5 LET 0 5= 05 + C X C i ) * 7 C I ) ) f 2 9 0 LET 06= 06 + XC1 ) * T C I ) * y c I ) 9 5 LET 07= 07 + X C I) * X C I> 100 NEXT I 105 LET 0= N*C 0 4 * 0 4 - 0 7 . 0 5 ) -D1 K 03*D4-D1 *0 5 ) + 03*C 07=03-01 * 04) 110 LET 41= D2*C D 4 * D 4 - 0 7 * D 5 ) -D 3 * < 0-4*03-0 1 *Do)+D6+C 0 7 * 0 3 - 0 1 * 0 4 ) 1 15 LET A= AJ/D 120 LET B 1 = N* C 0 6 * 0 4 - 0 3 *1)5)-D 1* C Do*D3 -D5* 0 2 )+ 03* < 03* D3-D2 * 04) 125 LET B= 9 1 / 0 130 LET C= CM*A+B*01-02>/O3 135 PRINT " A " , " 0 " , "C" 140 PRINT A . 8 . C 145 PRINT " X ” , ’’r - E X P ” # •,r-CALC'’> '’SDEV" . 1 50 FOR I = 1 TJ N 155 LET E C I ) = CA*B*X CI) > / C 1+ C * <C I ) ) 1O0 LET 5 C I) = ( < EC 1 ) - i C1 ) ) / ycI ) ) * 103 165 P R U T XC I >,rc I ) , ZC L > , SC I ) 170 M EX T I 175 LET 0=0 133 LET H=0 13 5 LET J =0 190 LET K=0 195 LET L.--0 200 LET f > = 0 205 LET P1=0 2 13 LET P2=3 2 1 5 FOR 1= 1 TO M 223 LET G= 0 + TCI) 2 2 5 LET rl= ri + EC 1 ) 2 33 LET J= J + Y C I ) * Y C t ) 2 3 5 LET K = K + Y C I ) * / < I ) 240 LET L= L + CI C I ) - Y C I) ) r 2 2 45 NEXT I 253 LET 31= SQRCL/N) 2 5 5 LET S2= S l/( r !/M ) 260 LET B2= C N *K - GM ) / < N * J - Ci* G) 2 6 5 LET A2= rl/N -B2+CG/N) 2 70 FOR 1= 1 TO M 2 75 LET «= (*♦ C32-:-rC i ) *4g-YC I ) ) r2 2TD LET Pi = P! < i‘ C ' ) -H / >;) f 2 23 3 'i-EXT ■ 290 LET F= SORC1 - ( 5 1 < 3 1 ) / < CM/M>+CP1/M ) ) ) 29 5 LET 09= G-rl 300 PAINT "S£F"," RSEF'’," F "» "OF" 305 PRINT S I. 52. F. 03 9 99 END 31? OATA 1 7 . 3 . 3 3 . 5.51* 7-47. 1 0 .4 6. 14.30# 1 9 . 0 3 . 3 * 7 1 . 12*32 3 15 OATA 2 1 . 3 4 . 3 0 . 12. 77.9 4,3 3 . 3 . 8 6- 3 . 9 3 * 3. 69. 3. 77. 2. 6 4 . 9 . 7 3 .3 5 320 DATA 51 >6, 61 • £» 4 6. 7, 5 6 . 2 , 3 7 * 6. 4 7 . 0 . 2 1 . 4 3 , 2 9 . 4 , 3 1 . 6s. 41 . 1 3 2 5 DATA 33 • 36, 9 2. ? . 55. 6, 6 d- 3. 9 7. 0 5, 93 . I___________ .. . . 134 135 TABLE XVII Output to Hyperbolic Fit Program 310 DATA 19*3 . 33* 5. 51* 7. 473 13-46* 1 4. 00* 1 9 .t)3*-3* 71* 1 2 . 8 2 i 3 15 DATA 2 1 . 3 4 . 3 0 - 12. 77.6 4 , 6 3 . 6 , 6 6 . 5 * 9 0 . 3* 69. 5* 7 7 . 2 . 6 4 .9 * 73 -3 5 ' 3 2 0 DATA 5 1 • 6 * 6 1 . 2 > 46. 7* 3 6 . 2 * 3 7 . 6* 4 7 . 0 * 2 1 • 4 3 * 2 9 . 4 * 31 • 65*41> 1 3 2 5 DATA 3 5 . 3 5 . 9 2 . 0 , 33. 3* 6 5 . 3 . 9 7 . 0 3 * 9 6 . 1 | 3 3 0 DATA 0 . 0 * 0 . 0 . 1 0 3 . 0 . 1 0 0 . 0 I USED 1 . 50 UNI TS. CftKO 19:4 2 20 TUE 1 2 / 1 4 / 7 1 . 1 13303 1 . 43904 4 . 9 0 9 7 4 E - 0 3 T-E^P T-CAUC °?oD EV 3 . 8 3 5. 31 3.71338 3 . 7 0 0 1 4 7. 47 10. 46 10.8 437 3 - 6 63 49 14 19.03 1 9 .61 6 3 3 . 0 3 1 9 I 3 . 7 1 12.32 12-3511 - 2 - 0 9 7 4 9 2 1 . 3 4 30. 12 23 . 3 69 6 - 4 . 1 5 1 3 3 7 7 .3 4 3 3 .3 3 3 . 9 439 .17 17 57 6 6*3 90. 3 9 0. 709 6 . 2 3 1 6 2 3 69. 5 77. 2 7 7 .2 4 7 6 6. 16412 E 64.9 7 3 .3 5 7 3 .3 7 6 2 .0 3 5 7 3 3 51 . 6 61.2 61. 393 .3 2 35 3 9 46. 7 56.2 56. 6642 .3 2 5 9 77 3 7 - 6 4 7 47. 3627 .7 7 1 7 6 2 2 1-45 2 9 . 4 2 9 . 0 0 3 7 - 1. 34795 3 1-6 5 41.1 4 0 .8 9 2 505964 3 3 - 3 5 92 9 1-3379 - . 17619 bS- 5 63.3 6 3 .0 3 73 - . 43 1 526 9 7 .0 5 9.3 . 1 9 7 . 9 35 - . 1 4 7 3 2 d i v i s i o n er z e ro in 160 ; OVER PLOW IN 160 - 0 0 '. 113333 • 1 3 0 is:'.! ? 4 9 6 SEE P S " , r r " . 3 9 438 7 7. 34u49t>w3 *9 99 927 - 5. 73 9 60 L+ 7 6 - - 3 3040 1 .0 ; - - I - 4<i3 6E-03 USED 4 . 3 3 L U IIS . 136 0.118303 + 1.48904X Y = 1 + 0.00490974X Figure 40 shows this equation plotted against the observed calibration points. This equation is very useful for calculating unknown compositions from the chromatographic peak area analyses. APPENDIX E Determination of True Temperature and Pressure of Sample For each observed point, the following information was recorded: 1. EMF of the thermocouple. 2. Pressure reading of the gauge. 3. Level of the mercury column in the experimental tube. 4. Phase boundary being observed. The model data correction sheet and temperature interpola tion charts (Tables XIX and XX) taken from the work of Hayworth (11) were used to simplify the application of corrections to the basic data. Table XVIII shows a sample of this data. The primary measurements are indicated by asterisks. The significance of the items in Table XVIII are as follows: * 1. The EMF generated by the thermocouple. 2. The deviation of the actual EMF of the thermo couple from the reference nomograph (Appendix B, Figure 35) as determined by standardization. 3. The value of the corrected EMF. 4. The value of the temperature as indicated to the nearest 0.1 millivolt (from Table XIX). 137 138 TABLE XVIII Sample Data Reduction Sheet Data Reduction on Sample BO-14 Temperature correction: *1. Observed EMF (mv) 14.655 2. - Correction (mv) -(-.017) 3. True EMF (mv) 14.672 4. Temperature to nearest 0.1 mv (cC) 269.26 5. Interpolated temperature increment (°C) 1.30 6. Temperature (°C) 270.56 Pressure correction: *7. Relative mercury head (mm) 736 8. - Reference correction (mm) -90 9. Hydrostatic head (mm) 646 10. Hydrostatic head (psi) 12.48 11. Mercury vapor pressure (psi) 2.42 12. Total negative correction (psi) 14.90 *13. Gauge reading (psi) 530 14. - Correction (psi) 0 15. Gauge pressure (psig) 530 16. Barometric pressure (psi) 14.62 17. Absolute pressure at gauge (psla) 544.62 18. + Total negative correction (psi) +(-14.90) 19. Absolute sample pressure (psia) 529.72 *20. Phase boundary observed bubble point TABLE XIX Reference Chart for Iron-Cons tantan Thermocouple Millivolts vs °C mv 0.0 0.1 0.2 0.3 0.4 0 0.00 2.02 4.04 6.05 8.05 1 19.94 21.90 23.86 25.81 27.76 2 39.36 41.28 43.19 45.10 47.01 3 58.38 60.26 62.14 64.02 65.89 4 77.08 78.93 80.78 82.63 84.48 5 95.53 97.37 99.20 101.03 102.86 6 113.83 115.65 117.47 119.29 121.11 7 132.03 133.85 135.67 137.49 139.30 8 150.16 151.97 153.78 155.59 157.40 9 168.26 170.07 171.88 173.69 175.50 10 186.36 188.17 189.98 191.79 193.60 11 204.46 206.26 208.06 209.86 211.66 12 222.46 224.26 226.06 227.86 229.66 13 240.46 242.26 244.06 245.86 247.66 14 258.46 260.26 262.06 263.86 265.66 15 276.46 278.26 280.06 281.86 283.66 16 294.46 296.26 298.06 299.86 301.66 17 312.46 314.26 316.06 317.86 319.66 18 330.46 332.26 334.06 335.86 337.66 19 348.46 350.26 352.06 353.86 355.66 20 366.46 368.25 370.04 371.83 373.62 0.5 0.6 0.7 0.8 0.9 Ave. T/0.1 10.05 12.04 14.02 16.00 17.97 2.00 29.70 31.64 33.58 35.51 37.44 1.94 48.91 50.81 52.71 54.60 56.49 1.90 67.76 69.63 71.50 73.36 65.22 1.87 86.33 86.17 90.01 91.85 93.69 1.85 104.69 106.52 108.35 110.18 112.01 1.83 122.93 124.75 126.57 128.39 130.21 1.82 141.11 142.92 144.73 146.54 148.35 1.81 159.21 161.02 162.83 164.64 166.45 1.81 177.31 179.12 180.93 182.74 184.55 1.81 195.41 197.22 199.03 200.84 202.65 1.81 213.46 215.26 217.06 218.86 220.66 1.80 231.46 233.26 235.06 236.86 238.66 1.80 249.46 251.26 253.06 254.86 256.66 1.80 267.46 269.26 271.07 272.86 274.66 1.80 285.46 287.26 289.06 290.86 292.66 1.80 303.46 305.26 307.06 308.86 310.66 1.80 321.46 323.26 325.06 326.86 328.66 1.80 339.46 341.26 343.06 344.86 346.66 1.80 357.46 359.26 361.06 362.86 364.66 1.80 375.41 377.20 378.99 380.78 382.57 1.79 irtv 139 140 5. The interpolated fraction of the temperature to the nearest 0.001 millivolt (from Table XX). 6. The true temperature of the sample. * 7. The height of the mercury meniscus in the ex perimental tube above an arbitrary datum plane near the base of the compressor block. 8. A constant correction for the difference in hydrostatic head between the datum plane near the base of the compressor block and the center of the Bourdon tube in the pressure gauge. 9. The contribution to the pressure indicated on the gauge by the hydrostatic head in mm Hg. Sum of 7 and 8. 10. Same as 9 except in psi. 11. The contribution to the pressure indicated on the gauge by the vapor pressure of mercury in the experimental tube (Table XXI). 12. Total negative correction for hydrostatic head and vapor pressure of mercury. Sum of 10 and 11. ij|« 13. Actual gauge reading. 14. The deviation of the actual1 pressure of the system from the pressure deviation chart (negligible). 15. True gauge pressure. TABLE XX Interpolation Chart for Iron Constantan Thermocouple for A t of 1.80°C/0.1 mv mv 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 o.oos 0.00 0.02 0.04 0.05 0.07 0.09 0.11 0.13 0.14 0.16 0.01 0.18 0.20 0.22 0.23 0.25 0.27 0.29 0.31 0.32 0.34 0,02 0.36 0.38 0.40 0.41 0.43 0.45 0.47 0.49 0.50 0.52 0.03 0.54 0.56 0.58 0.59 0.61 0.63 0.65 0.67 0.68 0.70 0.04 0.72 0.74 0.76 0.77 0.79 0.81 0.83 0.85 0.86 0.88 0.05 0.90 0.92 0.94 0.95 0.97 0.99 1.01 1.03 1.04 1.06 0.06 1.08 1.10 1.12 1.13 1.15 1.17 1.19 1.21 1.22 1.24 0.07 1.26 1.28 1.30 1.31 1.33 1.35 1.37 1.39 1.40 1.42 0.08 1.44 1.46 1.48 1.49 1.51 1.53 1.55 1.57 1.58 1.60 0.09 1.62 1.64 1.56 1.67 1.69 1.71 1.73 1.75 1.76 1.78 0.10 1.80 141 TABLE XXI Mercury Vapor Pressure Chart for Experimental Range psia vs °C °c 150 160 0 0.06 0.08 1 2 3 4 5 6 7 8 9 170 0.12 0.12 0.13 0.13 0.14 0.14 0.15 0.15 0.16 0.16 ISO 0.17 0.18 0.18 0.19 0.20 0.21 0.21 0.22 0.23 0.23 190 0.24 0.25 0.26 0.27 0.28 0.28 0.29 0.30 0.31 0.32 200 0.33 0.35 0.36 0.37 0.39 0.40 0.41 0.42 0.44 0.45 210 0.46 0.48 0.49 0.51 0.52 0.54 0.56 0.57 0.59 0.60 220 0.62 0.64 0.66 0.68 0.70 0.73 0.75 0.77 0.79 0.81 230 0.83 0.86 0.88 0.91 0.93 0.96 0.99 1.01 1.04 1.06 240 1.09 1.12 1.15 1.19 1.22 1.25 1.29 1.32 1.35 1.39 250 1.43 1.47 1.52 1.56 1.60 lr65 1.69 1.73 1.78 1.82 260 1.86 1.91 1.96 2.02 2.07 2.12 2.18 2.23 2.28 2.33 270 2.38 2.45 2.51 2.58 2.64 2.71 2.77 2.84 2.90 2.97 280 3.03 3.11 3.19 3.27 3.34 3.41 3.49 3.57 3.65 3.73 290 3.82 3.91 4.00 4.10 4.19 4.28 4.38 4.47 4.56 4.66 300 4.75 4.87 4.99 5.10 5.22 5.34 5.45 5.56 5.68 5.80 310 5.92 6.05 6.19 6.32 6.46 6.59 6.72 6.86 6.99 7.12 320 7.25 7.41 7.57 7.73 7.89 8.05 8.21 8.37 8.53 8.69 330 8.85 9.04 9.23 9.42 9.61 9.80 9.99 10.18 10.37 10.56 340 10.75 10.97 11.20 11.42 11.64 11.87 12.09 12.31 12.54 12.76 350 360 12.98 15.50 13.23 13.48 13.74 13.99 14.24 14.50 14.75 15.00 15.25 142 143 16. Barometric pressure. 17. Absolute pressure of the gauge. 18. Total negative correction. Sum of 10 and 11. 19. Absolute sample pressure. ' f t 20. Boundary observed. APPENDIX F Reduced Experimental Data The data on the phase boundaries for samples of fixed composition are presented in Table XXII as they were originally observed and corrected for known devia tions of the measuring instruments. Each set of data is listed in order of increasing benzene concentration. Vapor pressures for pure benzene and n-octane are reported as the mean values of the bubble and dew pressure at the specified experimental tempera ture. The critical point is indicated by the letter C next to the experimental temperature. 144 145 TABLE XXIX Reduced Experimental Data Temp. Dew Pressure Bubble Pressure Mean Pressure °C psla psla______ psla_____ Data on Benzene 279.59 634.01 636.69 635.35 283.77 666.05 668.40 667.23 286.47 686.76 688.70 687.73 287.58 696.58 698.65 697.62 288.39 703.92 705.09 704.50 288.99 709.84 710.57 710.20 289.44 C 712.73 712.73 712.73 233.58 - 350.13 - 246.20 410.20 414.76 412.48 254.99 460.45 465.94 463.20 265.79 531.49 534.97 533.23 276.26 609.89 612.89 611.39 192.08 - 186.24 — 201.94 - 219.65 — 213.15 - 258.97 — 221.83 - 295.83 — Data on n-Octane 279.41 287.11 290.99 289.05 283.26 303.79 306.69 305.24 288.77 329.15 332.31 330.73 293.42 350.13 351.91 351.02 294.64 355.51 357.32 356.42 295.58 359.88 361.71 360.80 296.21 C 362.77 362.77 362.77 289.78 333.08 335.67 334.38 232.76 141,98 146.05 144.02 246.63 176.36 180.64 178.50 255.04 201.88 206.26 204.07 264.53 231.90 235.90 233.90 274.01 268.01 271.79 269.90 206.40 - 93.90 _ 215.48 - 109.28 — 225.27 123.00 128.60 125.80 192.44 - 70.98 202.54 - 86.38 — 212.74 - 103.77 — 146 TABLE XXII (con't.) Temp. Dew Pressure Bubble Pressure Mean Pressure °C psla psia_______ psla_ Data on n-Octane (con’t.) 225.59 126.70 129.03 127.87 239.31 157.73 162.19 159.96 250.67 187.05 191.31 189.18 Temp. °C Dew Pressure, psla Bubble Pressure, psla Data for Sample BO-1 2,71 mol. % Benzene in n-Octane 279.95 282.17 285.12 288.56 290.81 292.57 293.60 294.66 295.58 C 294.93 233.49 245.59 254.95 265.44 269.67 275.00 191.35 202.16 213.30 222.01 Data on Sample B0-2 6.59 mol. % Benzene in n-Octane 277.83 281.43 283.44 297.75 306.49 321.16 334.69 346.40 354.66 359.49 368.31 372.61 369.27 203,44 238.38 253.91 272.87 304.60 313.41 327.69 340.43 351.28 358.66 364.56 370.52 372.61 154.62 186.76 213.89 247.93 263.19 283.37 76.78 93.18 112.02 130.90 298.51 310.20 320.40 312.21 325.00 333.85 147 TABLE XXII (con't.) Temp. °C Dew Pressure, psla Bubble Pressure, psla Data on Sample BO-2 (con't.) 287.87 340.85 352.49 290.88 357.41 366.80 292.64 365.24 373.66 294.93 380.31 383.53 295.43 C 382.15 382.15 234.32 - 169.05 245.12 . - 197.23 253.42 204.23 221.46 264.83 240.59 258.50 270.14 262.49 278.69 275.69 285.36 299.86 294.14 374.90 380.53 191.45 - 85.75 201.76 - 101.66 211.89 - 119.51 221.36 - 139.37 Data on Sample BO-3 14.1 mol. % Benzene in r,-Octane 278.31 281.25 284.27 286.22 288.21 290.43 291.83 293.06 294.01 293.52 232,59 244.53 252.86 264.38 274.28 200.10 210.46 221.18 319.04 332.34 346.03 357.34 369.60 379.89 388.20 397.07 402.87 399.0 158.02 191.70 217.59 258.35 296.98 126.57 336.93 349.23 362.52 372.88 382.74 391.58 397.49 403.39 402.87 182.92 215.61 241.28 280.76 318.19 111.04 130.41 153.21 TABLE XXII (con't.) 148 Temp. °C Dew Pressure, psla Bubble Pressure, psia Data on Sample BO-4 17.9 mol. % Benzene in n-Octane 280.13 332.79 354.29 283.43 348.38 368.07 287.17 366.86 383.85 289.13 380.55 394.70 291.46 393.11 404.50 292.34 400.97 309.50 292.73 404.82 411.49 293.76 C 411.59 411.59 293.16 406.85 231.12 - 182.35 243.95 - 217.49 252.34 - 245.18 263.64 258.28 285.23 272.33 290.78 318.77 192.60 - 98.96 203.25 - 117.33 213.53 - 138.70 222.75 - 159.04 Data on Sample B0-5 20.2 mol. % Benzene in n-Octane 279.63 282.85 286.27 289.37 291.20 292.41 293.24 C 232.86 244.13 252.66 264.00 269.05 274.91 285.37 190.74 202,32 212.42 222.15 337.23 354.41 369.39 391.92 402.68 409.38 417.63 283.21 311.45 367.42 357.26 371.57 385.29 403.63 413.50 417.43 417.63 188.72 222.94 250.58 291.62 311.34 335.00 383.32 97.83 118.22 139.60 161.92 149 TABLE XXII (con't.) Temp. °C Dew Pressure, psla Bubble Pressure, psla Data on Sample BO-6 24.4 mol. % Benzene In n-Octane 282.71 359.43 380.11 285.12 372.10 390.42 287.44 387.22 402.25 290.21 402.30 415.56 291.51 412.56 423.47 292.46 420.81 426.96 293.24 C 425.55 425.55 232.85 - 195.09 243.58 - 225.82 252.97 - 256.51 263.27 - 294.09 268.72 285.65 317.82 278.71 338.79 360.69 272.82 305.16 336.07 190.54 - 100.31 202.29 - 121.20 212.58 - 143.58 221.45 - 164.40 Data on Sample B0-7 34.8 mol. % Benzene In n-Octane 278.40 370.59 397.68 281.70 388.33 413.95 284.43 403.44 426.22 287.17 421.08 441.00 288.93 431.44 449.41 290.12 439.76 454.84 290.99 447.11 459.30 291.74 C 457.40 457.40 232.85 - 218.68 243.30 211.15 255.36 252.90 247.21 . . . . . . 2J37.00 262.64 291.27 326.62 271.67 334.85 366.13 198.47 - 134.67 209.68 - 159.54 220.10 - 184.86 150 Table xxii (con't.) Temp. °C Dew Pressure, psla Bubble Pressure, psla Data on Sample BO-8 41.9 mol. % Benzene in n-Octane 280.49 408.70 435.08 282.92 423.00 446.42 286.49 445.55 465.14 288.12 457.41 474.52 289.37 467.22 480.46 290.63 476.05 483.92 290.91 C 481.50 481.50 232.85 186.87 232.65 245.00 239.62 274.29 253.60 272.98 307.96 263.90 318.70 352.49 272.78 360.44 394.50 192.17 - 124.20 204.96 - 153.10 214.97 - 180.45 225.70 - 209.76 Data on Sample BO-9 54.2 mol. % Benzene in n-Octane 279.86 283.20 285.44 287.26 288.12 288.38 288.92 289.53 231.64 243.07 253.19 262.85 272.69 190.76 201.76 212.52 221.90 445.92 466.55 484.20 499.02 506.37 512.35 516.23 519.68 252.72 297.81 343.51 398.14 473.21 490.92 503.78 515.12 519.60 519.68 253.26 295.94 338.04 382.62 434.07 136.78 162.18 192.05 220.39 151 TABLE XXII (con't.) Temp. °C Dew Pressure, psla Bubble Pressure, psla Data on Sample B0-10 59.0 mol. % Benzene in n-Octane 280.46 468.43 490.91 282.06 478.30 500.80 284.56 496.00 514.60 287.06 515.25 529.45 287.82 522.17 534.40 288.54 527.60 - 288.97 C 533.48 533.48 228.26 200.80 248.05 240.80 250.32 295.73 249.32 293.51 331.95 261.14 354.91 386.82 268.41 393.30 423.94 274.07 426.88 453.63 200.10 - 162.58 211.21 - 194.44 220.66 - 223.78 Data on Sample BO-11 69.4 mol. % Benzene in n-Octane 279.95 498.51 524.97 281.61 510.81 536.30 282.89 520.19 543.70 284.71 533.97 553.61 286.31 544.77 561.97 286.97 549.78 566.43 287.96 557.65 570.35 288.09 561.56 288.50 C 566.54 566.54 232.23 236.90 285.00 244.17 290.96 335.18 252.34 330.31 372.37 262.10 384.04 422.94 271.23 439.31 471.47 275.54 463.94 494.21 191.01 - 155.60 201.54 - 183.50 212.76 - 217.34 222.28 - 250.18 TABLE XXII (con't.) 152 Temp. °C Dew Pressure, psla Bubble Pressure, psia Data on Sample BO-12 77.2 mol. % Benzene In n-Octane 277.52 280.24 282.36 285.10 286.86 287.37 287.91 232.59 243.99 251.82 261.83 271.79 194.50 205.06 215.28 225.99 516.83 533.02 551.23 571.93 587.88 593.80 597.78 265.40 317.58 356.99 413.73 478.40 534.64 550.94 566.25 584.55 596.68 600.10 597.78 297.61 348.80 385.50 439.61 498.59 166.67 199.05 232.41 272.71 Data on Sample B0-13 86.8 mol. % Benzene in n-Octane 280.22 282.33 284.35 286.13 287.30 287.62 287.96 232.94 240.86 247.91 257.78 267.87 274.21 191.93 200.39 209.75 221.96 574.03 591.78 608.53 624.31 637.16 637.04 643.82 364.22 423.26 482.37 525.20 591.22 606.58 621.41 633.79 642.69 643.82 321.18 356.97 391.74 448.86 509.88 552.01 172.78 197.71 229.58 274.88 153 TABLE XXII (con't.) Temp. °C Dew Pressure, psla Bubble Pressure, psla Data on Sample BO-14 88.2 mol. % Benzene in n-Octane 270.56 514.98 529.72 277.86 565.26 576.34 282.15 595.74 605.64 283.75 609.54 618.92 286.40 633.14 639.73 287.01 639.59 644.76 287.44 641.52 647.72 287.86 643.42 - 288.03 C 649.82 649.82 232.20 - 318.14 245.30 359.26 379.81 253.92 402.54 426.02 264.06 464.65 485.05 260.89 444.93 - 193.44 • - 176.75 208.66 - 225.58 220.07 - 267.94 Data on Sample BO-15 39.6 mol. % Benzene in n-Octane 268.86 503.79 525.69 274.30 541.31 559.35 279.09 578.79 595.02 281.77 598.51 611.88 283.61 613.29 624.77 285.26 629.08 639.67 286.38 639.41 647.59 287.24 646.30 653.56 287.84 652.71 657.07 288.03 C 654.74 654.74 231.42 294.86 322.04 243.09 351.99 377.75 252.43 391.26 424.42 263.05 462.81 486.98 191.05 - 175.69 210.02 - 237.43 221.80 - 280.74 154 TABLE XII (con't.) Temp. °C Dew Pressure, psia Bubble Pressure, Data on Sample BO-16 97.0 mol. % Benzene - in n-Octane 281.41 631.70 638.89 282.80 642.08 650.82 284.79 659.88 665.64 285.62 665.71 670.99 286.45 672.61 677.91 287.08 677.55 682.36 287.44 682.51 686.32 287.86 685.45 688.80 288.23 C 687.45 687.45 228.76 312.34 322.54 229.43 314.43 325.60 238.21 357.45 366.34 248.45 412.42 421.50 258.34 467.82 477.11 268.14 532.19 540.60 274.86 580.65 588.23 191.17 175.95 187.66 201.52 199.94 214.60 211.91 238.85 252.95 222.26 276.94 294.77 194.57 179.27 -■ APPENDIX G Discussion of Errors Pressure and Temperature The experimental accuracy of the basic temperature measurements is believed to be within +0.05°C. The Bourdon pressure gauge employed in this investigation was marked in 1 psi increments from 0 to 1500 psig. The observed pres sures could easily be read and corrected with an uncertain ty of +1 psi. This was certainly true for the bubble point observations. For dew points, however, the combina tion of experimental accuracy of the actual measurements plus the ability to detect the phase boundary itself re sulted in a wider tolerance of probably about +2 psi. In general, the greatest accuracy occurred at high temperature and pressure for both bubble and dew points. The accuracy of the measured critical points is al most solely dependent upon operator's errors. Since the P-T envelopes for the benzene-n-octane system exhibit an insignificant retrograde region around the critical, the observation of the critical pressure and temperature was rather sharp. In addition, the very good agreement be tween the observed critical points of this work and Kay and Hissong's observed critical points (13) gives a high degree of confidence. 155 156 Composition There are several contributions which must be con sidered in estimating the precision of the experimental compositions. From the capillary loading measurements, the composition could be calculated within +0.1 mole per cent benzene. The uncertainties in the compositions de termined by gas chromatography are estimated to lie between +0.1 and +0.5 mole percent benzene. The two contributions to error in this case are the degree of reproducibility in the GC scans and the goodness of fit of the GC calibra tion equation. Finally, the composition correction curve, Figure 2, can be read to the nearest 0.5 mole percent or better. Overall, it can be said that the estimated ac curacy of the final reported compositions is no worse than +0.5 mole percent and definitely not better than j+0.1 mole percent. ^ - APPENDIX H Purity of Fluids Used Benzene The benzene employed in this research was prepared by taking a part of the center cut of a distillation of a batch of Thiophene Free Analytic Reagent Grade Benzene from Mallinkrodt Chemical Works. The column used was a standard Oldershaw laboratory still with 48 trays and a reflux ratio of about 50:1. The center cut was reached when the overhead temperature remained constant at 80.1°C. n-Octane The n-octane employed was obtained from C. F. Braun and Co. It was distilled in the same manner as the ben zene. The center cut was reached when the overhead temper ature remained constant at 124.6°C. The primary impurities in the n-octane are believed to be some or all of the isomers of n-octane. The exact identity of these isomers is virtually impossible to determine. Vapor Pressures and Criticals A very stringent indication of the degree of purity of the hydrocarbons is the measurement of vapor pressure. 158 As shown previously, Figure 5 is a comparison of the vapor pressures measured in this work with other literature data. Table III shows comparisons for the critical properties. The overall agreement for both hydrocarbons is good. APPENDIX I Listing of Computer Programs and Printouts Tables XXIII through XXXI represent a complete set of listings and printouts for the computer programs em ployed in this research. Each program is referred to in the main body of the text. These programs were written in the BASIC language (Beginner's All-Purpose Symbolic Instruction Code) and run on a General Electric Time-Sharing Computer. A terminal at C. F. Braun and Co. was used. 159 160 TABLE XXIII Listing of GE Time-Sharing Program CRK1 !2 DIM TC5 0 ) * P C 5 0 )> X C 5 0 ) . I t 5 3 ) » R ( 5 0 ) * SC 50) : 5 READ N '10 FOR 1=1 TO N 15 READ T C I ) , P C I ) 20 NEXT I 2 5 LET C=0 30 LET D=0 3 5 LET E=0 40 LET F1=0 45 FOR 1= 1 TO N 50 LET X C I) = 1/< T C I ) + 2 7 3 ) 5 5 LET Y C I) = LO GC P C I ) ) 60 LET C= C + XCI ) 6 5 LET D= D + Y d ) 70 LET E= E + X C I ) * Y C I > 75 LET F I = FI * X d ) * X C I > 8 0 NEXT I 8 5 LET A = C N * E - C * D ) / C N * F l - O C ) 9 0 LET 8= ( D /N ) -A *C C /N > 9 5 PRINT ' ^ " # " 0 " 100 PRINT A.B 101 PRINT "T.»C"#‘,P -E X P ,,* ,,P-CALC:*,* ,,*DEV/m 102 FOR 1= 1 TO N 103 LET R < I )= E X P C A *X C I)+ B ) 104 LET S < I ) = C < RCI ) - P d ) ) /PC I ) ) * 100 105 PR IN T T C I ) , P C I ) , R C I ) * S C I ) 106 NEXT I 107 LET G=0 108 LET H =0 109 LET J = 0 1 10 LET K = 0 1 1 t LET L. = 0 1 12 LET M = 0 1 13 LET P 1 =0 1 14 LET P2=0 1 15 FOR 1= 1 TO N 1 1 6 LET G= G V/ CL + 1 17 LET H= H + R C I) 1 IS LET J= J + P C I > * P C I ) 1 19 LET K= K + PC I ) + R C I ) 120 LET L= L + C RC I ) -PC I ) M 2 121 NEXT I 122 LET S l= SQRCL/N) 123 LET S2= S l / C H / N ) 124 LET 91= < N * X -G * H > /C N * J - G JlG) 125 LET Al= H/N - 3 ! * ( G / M J 126 FOR i~ 1 TO N 127 LET M= M + ( B 1 * P ( I ) + A l - P d ) ) » 2 123 LET P l= P I + C R C I ) - H / N ) » 2 !l 29 NEXT I 130 LET F= SORC1 - C S 1 * S 1 ) /C C M /N ) + CP1/ N > ) ) 131 LET D1= G-H 132 PRINT "S E F "> "R S £ F ',» ',F,’j "D F " 133 PR IN T S 1> S 2 >F t DI 161 TABLE XXIV Sample -Printout for Program CRK1 Dew Curve A B - 4 9 5 2 .3 1 1 4 .7 9 6 1 T»C P- EXP P-CALC #D£V 2 8 2 .7 1 3 5 9 . 4 3 3 59. 4 - 8 . 3 4 0 6 4 E - 0 3 2 3 5 . 12 3 7 2 . 1 3 7 3 . 5 . 3 7 6 1 7 3 28 7 . 4 4 38 7 . 2 2 38 7. 474 6 . 5 6 0 7 7 E - 0 2 29 0 . 2 1 4 0 2 . 3 4 0 4 . 68 5 . 59 28 1 6 2 9 1 • 5 1 4 1 2 . 5 6 4 1 2 * 9 6 3 9« 7 6 S 3 9 E - 0 2 2 9 2 . 4 6 4 2 0 .8 1 4 1 9 . 0 9 5 - . 4 0 7 6 4 2 C ^ 2 9 3 -2 4 4 2 5 . 5 5 4 2 4 . 18 1 - . 3 2 1 6 3 3 268 . 72 2 8 5 . 6 5 2 3 5 . 5 14 - 4 . 7 6 7 8 4 E - 0 2 2 7 8 * 7 1 ■ 3 3 8 . 79 3 3 6 - 9 1 3 - . 5 54039 2 7 2 . 8 2 3 0 5 . 1 6 3 0 5 .8 0 9 • 2 1 2 6 5 3 SEF RSEF F DF 1 .2 9 0 4 9 3* 4788 6 E -0 3 . 9 9 9 6 0 7 3 . 6 6 8 9 8 E - 02 Bubble Curve A B - 3 7 3 4 . 1 7 1 2 -6 5 5 7 T .C P - EXP P-CALC 0DEV 2 3 2 -7 1 3 3 0 .1 1 3 7 3 . 4 2 2 - . 4 4 4 0 2 4 2 8 5 . 1 2 39 0 . 4 2 3 8 9 - 5 6 3 - - 2 1 9 4 2 3 2 8 7 . 4 4 4 0 2 . 2 5 4 0 0 . 5 0 4 - . 4 3 4 1 3 6 2 9 0 .2 1 4 15* 56 4 1 3 . 3 4 6 - . 4 1 2 5 6 5 2 3 2 - 3 5 1 9 5 .0 9 1 9 5 .1 3 2 2 . 1 6 3 0 5 E - 02 2 4 3 - 5 8 2 2 5 - 8 2 2 2 7 . 4 6 8 . 7 2 9 8 2 2 5 2 . 9 7 2 5 6 .5 1 2 5 3 - 8 0 1 - 8 9 3 2 9 1 2 6 3 . 2 7 2 9 4 -0 9 29 6. 61 1 . 3 5 7 1 6 2 6 3 . 7 2 3 1 7 - 8 2 318 • 135 9 . 9 0 1 3 7 E - 0 2 2 7 3 -7 1 3 6 0 .6 9 3 6 0 . 4 2 8 - 7 . 2 6 6 8 1 E - 0 2 2 7 2 - 8 2 3 3 6 . 0 7 3 3 5 -0 4 1 - . 3 0 6 0 9 2 19 3 . 5 4 1 3 3 .3 ! 9 9 - 4 7 2 5 - . 3 3 4 3 9 5 232 - 29 1 2 1 .2 121*39 3 . 1 39 332 £ 1 2 -5 3 1 43 • 1 4 3 - 3 3 4 - . 13 6 6 53 2 2 1 . 4 5 1 6 4 .4 164..59 4 - 1 1 7 7 2 6 SEF RSEF F OF 1 .3 1 4 9 1 4 . S 0 7 3 3 E - 0 3 .9 9 9 9 2 1 1. 12 S3 7 152 TABLE XXV Listing of GE Time-Sharing Program CRI<8 3 DIM P I 9 0 ) * X 190 ) / Y l 9 0) 5 READ P l , T l * P 2 * T 2 10 READ N. T. Vis V 2.G 1 .G 2 15 FOR 1 = 1 TO N 2 0 READ P 1 I ) » X 1 I ) « Y 1 I ) 2 5 NEXT I 3 0 LET U* 1 T + 2 7 3 - 1 6 ) * 1-8 3 5 LET T3= U /T l <40 LET C 1 = 0 . 69 309 + 2 . 68 5 0 2 / T 3 - 4. 6 2 8 0 6 / < T 3 * T 3 ) 45 LET C2= 0 . 7 0 5 4 3 / 1 T3»3) 50 LET F l = P1*EXPC C1 + C2) 55 LET T 4= U/ T2 60 LET C3= - 1 . 8 0 4 6 0 * 1 0 . 158 1 4 / T 4 - 12. 0 6 3 2 7 /1 T 4 * T 4 ) 65 LET C4= 3 . 6 0 1 1 3 / 1 T 4 * 3 ) - 0 . 4 4 2 4 7 / 1 T4t 4) 70 LET F2 = P2*EXP1C3+C4) T 5 LET A I = < 0 . 4 2 7 8 * 1 T 1 *2 . 5 ) / l P l * » 0 - 5 3 3 LET A2= 1 0 . 4 2 7 3 * 1 T 2 f 2 . 5 ) / ! P 2 * t U » 2 . 5 ) ) ) 10 . 5 3 5 LET B 1 = 0 . 0 8 6 7 * T 1 /1 P 1 * U ) 9 0 LET 82 = 0 . 0 8 6 7 * T 2 /1 P 2 * U ) 95 FOR 1 = 1 TO N 100 LET A= Y 1 1 >* A 1 ♦ C ! - Y * A a 195 L ET B= Y 1 I > * 8 1 ♦ 1 1 - Y 1 I ) ) * B £ 1 10 LET Z= 1 . 0 0 0 i 115 LET H 1= Z - Z / 1 Z - B * P I I ) ) + I A * A ) * P ( I ) / 1 Z + B * P 1 I ) ) I 120 LET H2= l + C 8 * P ) T 2 ) - t A * A ) * P t I > / < Z * B * P l I > ) » 2 j 125 L ET Z l = Z - H 1 /H 2 l 130 LET E= A B S ( Z - Z l ) ■ 135 I F £ * 1 • 0 E -5 THEN 150 140 LET Z = Z1 145 GO TO I I 5 150 LET J l = 1 Z 1 - 1 > * 1 B 1 / B > - L 0 G 1 Z 1 - 8 * P 1 I ) > 1 55 LET J2 = - 1 1 A * A ) / B ) * 1 2 + t A 1 / A ) - B 1 / B ) * L 0 G 1 l + B * P ' 160 LET G3= EXPt J 1 * J 2 ) ' • 165 LET G4= 1 Z 1 - 1) *1 B 2/B ) -L 0 G ( Z 1 ~B* PI I ) ) 170 LET G5= - I t A * A ) / B ) * 1 2 * 1 A 2 / A ) - B 2 / B ) * L 0 G 1 I + B * P U > / Z 1 > 175 LET G6= EXP1 G4+G5) 130 LET F3= 1 F 1 / P 1 I ) ) * E X P 1 V ! * P t I ) / t 1 0 . 7 3 1 * U > ) 135 L E T F A- 1 F2/P1 I > ) * E X P t V2*P1 1 ) / 1 1 0 .73 1 *1 1)) 1 199 LET W1= C Y t I ) * G 3 )/1 X 1 1 ) * F 3 > 195 LET L2= t ( l - Y ( ! ) ) * G 6 ) / ; ( | - X ( i ) ) * F 4 ) 2 2 0 PR IN T Pi I i> G3» G6> Z! 2 0 5 PRINT F3*F4»W1,W2 2 1 0 NEXT I 999 END TABLE XXVI Sample Printout for CRK8 2 2 0 DATA 2 2 5 DATA 2 3 0 DATA 2 3 5 DATA 2 4 0 DATA KEY READY RUN 7 1 2 . 73. 1 0 1 2 . 7 . 3 6 2 . 7 7 . 1 0 2 4 .9 1 0 . 2 2 3 . 2 . 3 . 6 2 7 5 . B 0 0 . 8 0 0 1 2 0 . 0 . 0 1 0 . 0 . 169. 1 3 0 . 0 . 0 4 2 . 0 . 2 7 1 * 1 4 0 . 0 . 0 9 0 . 0 - 3 5 2 . 160 0 - 2 1 4 . 0 - 49 1. 180. 0 - 33 5. 0 . 6 2 0 . 2 0 0 . 0 . 45 5 . 0 . 7 3 0 . 2 2 0 . 0 . 577 0 - 8 2 0 . 2 4 0 . 0 . 6 9 9 . 0 . 8 9 0 . 2 6 0 . 0 - 8 2 0 . 0 . 9 4 6 * 2 7 0 . 0 . 8 8 0 . 0 . 9 71 I CRK8 2 3 t 08 20 TUE 0 3 / 1 4 / 7 2 ? ' 120 4 , ~ - 9 3 3 7 7 1 ?£. = • 8 3 3 5 9 7 2 —.8 2 4 2 4 1 M ° - l . 798 72 lA*'. 779 646 yi'8. 77331 > £ = .8 9 7 4 7 9 130 • 9 2 4 2 2 4 . 8 2 0 9 5 6 • 3 2 1 5 1 9 1 . 6 6 3 3 5 . 7 2 2 4 1 9 3 . 5 3 4 1 3 . 8 6 4 7 5 4 140 . 9 1 5 4 1 2 . 8 0 8 648 . 8 17 3 14 1. 54325 . 6 7 3 3 7 7 2 . 3 1 2 4 7 __ . 8 5 5 1 3 5 160 .8 9 8 4 1 1 . 7 8 5 1 5 3 . 8 0 8 9 8 9 1 .3 6 0 4 2 .5 9 3 7 1 1 . 5 1 5 2 •3 5 6 3 9 8 180 .8 3 1 7 1 5 . 7 6 3 5 0 1 . 8 0 3 1 0 2 1 . 2 1 4 3 5 . 5 3 1 7 7 7 1 . 3 4 3 7 9 . 3 2 0 4 3 2 203 • 8 6 5 3 19 . 7 4 3 1 6 2 . 7 9 7239 1 .0 9 7 5 1 .4 8 2 2 5 3 1 . 2 657 . 7 6 3 4 3 4 2 2 0 . 8 5 3 7 0 6 ♦ 72 3601 . 7 9 0 4 4 4 1 . 0 0 1 9 4 .4 4 1 7 6 3 1 . 2 0 6 6 4 . 6 9 700 6 2 40 • 8 3 6 2 2 . 7 0 4 2 4 6 . 7 8 1 6 7 1 . 9 2 2 3 0 7 . 4 3 8 0 5 1 . 1 5 4 4 . 6 3 0 7 2 2 60 . 8 2 2 1 1 6 . 68 502 1 . 7 7 1 4 3 . 8 549 43 .3 7 9 541 1. 10936 . 5 4 1 4 6 270 • 3 1 5 1 5 7 . 6 7 5 5 3 6 , 7 6 6 0 3 4 .3 25309 . 3 56379 1 . 0 9 0 2 3 . 4 4493 2 164 TABLE XXVII Listing of GE Time-Sharing Program CRK3 1 READ N 2 D IN X C 9 0 ) , H C 9 0 ) , T ( 9 0 ) , V C 9 0 ) , W( 9 0) 4 FOR 1= 1 TO N 5 READ X ( I ) , H ( I ) , T ( n > V ( I ) » W ( I ) 6 NEXT X 7 FOR G l= 1000 TO 2000 STEP 200 10 FOR G2 = - 4 0 0 TO 1200 STEP 200 15 LET S1=0 2 0 FOR 1 = 1 TO N 3 0 LET Y = 1 - X C I ) 3 5 LET 7 S . 1 * X C I ) + 1 1 4 . 2 * Y 4 0 LET R= 4 5 LET U= C T C I ) + 2 7 3 . 1 6 ) * 1 . 8 5 0 LET L 1 = ( W C I J / V C I ) ) * EX PC-G1/C 1 .9 8 7 * U )) 5 5 LET L 2= C VC I ) / W C 1) ) * EXPC -G2/C 1. 98 7 * U) ) 60 LET Q= X C I ) * C Y * L 1 ) * G 1 / C X C I ) + L 1 *Y ) 65 LET Z = Y * C X C I ) * L 2 ) * G 2 / C Y + L 2 * X 7 0 LET S I = SI + ABSCQ+Z-R) 7 5 NEXT I 8 0 PRINT G1, G2, SI 8 5 NEXT G2 9 0 NEXT G 1 100 DATA 42, 0 . 2 7 1 , 2 . 72, 2 6 3 , 2. 39 0 , 4. 21 13, 0 . 4 4 6 , 3. 71, 2 6 0 , 2* 3 9 0 , 4 . 2 1 13 105 DATA 0 . 6 7 6, 3 - 3 8 , 2 6 0 , 2 . 3 9 0 , 4 . 2 1 13, 0 . 77 1 , 4 . 13, 2 6 0 , 2* 390, 4 - 2 1 1 3 1 10 DATA 0 . 8 57, 1 . 72, 2 6 0 , 2 . 39 0, 4 .2 1 13, 0 . 9 3 0 , 1 . 54, 2 6 0 , 2 . 390, 4. 2 1 1 3 115 DATA 0 . 2 7 1 , 2 . 5 0 , 2 3 0 , 2 . 0 7 2 , 3 . 7 3 8 4 , 0. 446, 3 . 175, 2 3 0 , 2 . 0 7 2 , 3 . 733 4 1 20 DATA 0 . 67 6, 2 . 9 4, 2 3 0 , 2 . 0 72, 3. 733 4, 0. 7 71, 3- 76, 2 3 0 , 2 . 0 7 2 , 3. 738 4 125 DATA 0 . 8 5 7 , 2 . 0 5 , 2 3 0 , 2 . 0 7 2 , 3 . 7 3 3 4 , 0 . 9 30, 1. 8 6, 2 3 0 , 2 . 0 7 2 , 3 . 733 4 1 30 DATA 0 . 2 7 1 , 2 . 5, 2 2 0 , 2, 3 . 62 7 5 , 0 . 4 4 6 , 3. 03 , 2 2 0 , 2, 3. 6 2 7 5 , 0 . 676, 2 . 70 135 DATA 2 2 0 , 2 , 3 . 627 5 , 0 . 7 7 1 , 3 . 7 0 , 2 2 0 , 2 , 3. 6 2 7 5 , 0. 3 57, 2 . 3 1 , 2 2 3 , 2 , 3 • 6275 140 DATA 0 . 9 3 0 , 1 .9 5 , 2 2 0 , 2 , 3 . 6 2 7 5 , 0 . 2 7 1 , 2 . 5 3 , 2 4 0 , 2 . 170, 3 . 8 6 2 3 145 DATA 0 . 4 4 6 , 3 . 3 1 , 2 4 0 , 2 . 1 7 0 , 3 . 8 3 2 3 , 0- 676, 3 . 1 I , 2 4 0 , 2 . 170, 3 . 8 8 2 3 1 50 DATA 0 . 7 7 1 , 3 . 8 5, 2 4 3 , 2 . 1 70, 3 . 3 3 2 3 , 0 . 8 57, 1 . 8 4 , 2 4 0 , 2 . 1 70, 3 . 8 3 2 3 155 DATA 0 . 9 3 0 , 1 . 7 6 , 2 4 0 , 2 . 1 7 0 , 3 - 8 3 2 3 , 0 . 2 7 1 , 2 . 59, 2 5 3 , 2 . 2 6 2 , 4 . 0 3 1 7 1 60 DATA 0 . 4 4 6 , 3 . 43, 2 50, 2 . 2 6 2 . 4 . 0 3 1 7, 0. 676, 3 . 2 6 , 2 5 0 , 2 . 2 62, 4 . 0 3 1 7 1 65 DATA 0 . 7 7 1 , 3 . 9 7 , 2 5 0 , 2 . 2 6 2 . 4. 03 17, 0 . 8 57, 1. 72, 2 50, 2 . 2 6 2 , 4• 03 1 7 170 DATA 0 . 9 3 0 , 1 . 6 6 , 2 5 3 , 2 . 2 6 2 , 4 . 0 317, 0. 2 71 , 3. 19, 2 7 0 , 2 . 5 50, 4 . 4 5 4 2 17 5 DATA 0 , 4 4 6 , 4 . 0 4 , 2 7 0 , 2 . 553, 4. 45 42, 3. 67 6, 3 . 49, 2 70, 2- 553, 4. 4542 133 DATA 0 . 7 71, 4. 3 6 , 2 7 0 , 2. 553, 4 . 4 5 4 2 , 0 . 8 5 7 , 1 . 9 0 , 2 7 0 , 2 . 553, 4. 4542 13 5 DATA 0 . 9 3 0 , 1 . 2 4 , 2 70, 2 . 550, 4. 4542, 0. 27 1, 4 . 0 7 , 2 3 0 , 2 . 8 2 4 , 4 -8 1 7 1 190 DATA 0 . 4 4 6 , 4. 5 4 , 2 3 0 , 2 . 8 2 4 , 4 . 8 1 7 1 , 0. 676, 3 . 5 9 , 2 3 0 , 2 - 8 2 4 , 4 . 8 1 71 1 95 DATA 0 . 7 71, 4 . 7 0 , 2 3 0 , 2 . 8 2 4 , 4 .8 1 71, 0 . 8 57, 2 . 21, 2 3 0 , 2 . 8 2 4 . 4 . 3 1 71 2 0 0 DATA 0 . 9 3 0 , 0 . 5 2 , 2 3 0 , 2 . 8 2 4 , 4 . 8 171 9 9 9 END ______________________ TABLE XXVIII Printout for Program CEK3 1 2“ ^22 CO 1000 - 4 0 0 61 69 • 05 1000 -2 0 0 48 9 9 . 96 1000 0 3 7 5 0 . 6 4 ' 1000 2 00 2 7 6 6 . ■ 1000 400 2 1 0 9 . 0 3 ' 1000 600 1 8 2 1 .6 6 10B0 8 0 0 1 8 3 9 .7 8 1000 1000 1 9 5 3 *3 8 ■ 1000 1200 2 0 9 1 - 2 1 . 1200 - 4 0 0 5 2 5 8 .0 8 : 1200 - 2 0 0 3 9 8 9 . 8 3 . 1200 0 2 8 5 1 . 5 4 . 1200 200 2 0 5 9 - 8 3 ' : 1200 400 1 8 0 4 . 26 *Iininrin . 1200 600 1 9 2 5 . 0 4 , 1200 8 0 0 211 1.99 ! 1200 1000 2 3 0 2 . 3 5 ; 12W0 1200 2 5 3 3 . 7 6 1400 - 4 0 0 4 5 0 2 - 6 . : 1400 - 2 0 0 3 2 3 4 . 3 5 i . 1400 0 2 2 0 2 . 4 4 : ; 1430 2 0 0 188 7 .4 9 : 1400 400 1 9 8 6 . 75 i 1 400 600 2 2 1 4 . 19 1400 8 0 0 2 4 4 6 - 8 6 ! 1400 I000 2 7 1 0 . 4 2 1400 1200 30 5 3 .8 6 1 600 - 400 389 1 -1 6 1 600 -200 8 6 2 9 .06 ■ 1 600 0 2 0 4 6 . 0 7 j 1 600 2 00 2 bb9 . 06| 1 600 40 0 2 2 8 1 . 9 21 1 000 600 5 31 * 72 1 600 8 0 0 2 8 0 4. 5i i 1 O n V 1000 3 1 7 1 - 3 1 j . 1 600 1 200 3 5 5 8 . 4* 1 10 00 -400 3 4 1 3 . 0 3 j jo 00 - 2 0 0 2 4 2 7 . 5 1: ; 1000 a 2 08 2* 36 j 1800 2 u0 2 2 0 5- 1 6 i i » 0 « 400 e. Oiy / « 12 ; 1O00 600 d O jt). 9 lt$ 00 800 3 l 30* e 1000 ; 000 j j5 b- 6 2 . 10 00 1233 39 5 4 . 63 2 0 0 0 - 4 0 3 3 1 3 9 . 2 3 : 2000 - 2 0 0 2 4 0 2 . 4 4 > 2000 0 2 1 8 9 . 3 2 * 2000 2 0 0 2 4 2 1 . 3 4 : 2000 4 00 2 7 3 9 . 6 6 ; 2000 600 3 0 9 1 . 1 2 2000 8 0 0 3 4 2 4 . 7 1; 2000 1 0 0 0 38 43 -2 8 2000 1 2 0 0 4 2 7 1 .1 9 166 TABLE XXIX Listing of GE Time-Sharing Program CRK4 and a Sample Printout for 260°C 2 PRINT "X C 6" j " H E " / "GAMMAC 6"/ "GAMMAC8"* ” GE" 3 READ 1. V I. V2, G l , G2 7 LET T l = C T + 2 7 3 . 1 6 > * 1 . 8 15 LET L l = C V 2 /V 1> *E X P C -G 1 /C t . 9 S 7 * T l ) > L2= C V I/V 2 )+ E X P C -G 2 /C 1 .987*T1.» > X = 0 TO 1 STEP 0 .1 Y= 1 -X M= 7 8 . 1 * X + I 1 4 . 2*Y CX*Y*L H>G 1J/CX +Lt*Y J C Y * X + L 2 * G 2 )/C Y + L 2 *X ) ( 0+ V > /M C - 1 . 9 3 7 *T 1 )*C X *L 0 G C X + L 1#Y) + Y+LOG< Y+L2*X> > G0 = G/M A=-LOGC X + L 1*Y) B= Y + C L 1 /C X + L 1 * Y )-L 2 /C L 2 + X * Y > > P l = EXPCA+B) C= -LOGC Y+L2+X ) D= - X + C L 1 / C X + L 1 * Y ) - L 2 / c L 2 * X + Y n P2 = EX PC C+DJ H / P 1 / P 2 / G 0 LET FOR LET LET LET LET LET LET LET LET LET LET LET LET LET 0 = V= H - G= 20 2 5 30 3 5 40 4 5 50 55 57 60 65 70 75 8 0 8 5 9 0 PR IN T X 9 5 NEXT X 9 9 9 END KEY READY 100 DATA 2 6 0 / 2 . 3 9 0 . 4 . 2 1 1 3 * 1 2 0 3 /4 0 0 RUN CRX4 1 4 :4 6 2 0 SAT 0 3 / 0 4 / 7 2 XC6. HE . /J, GAMMAC6 GAMMAC8 ' 0 0 ' 1 .8 2 7 0 2 1 • 1 1 . 128 62 1. 6699 7 1 .0 0 4 7 9 • 2 2 . 0 3 0 3 5 1 .5 3 2 7 1 .0 2 0 1 9 « 3 2 . 8 3 7 5 1 ! . 4132 1. 3 4326 « A 3 . 3 7 3 7 I . 30 9 37 1 . 3 9 2 1 4 • 5 3 . 6 7 7 6 6 !.2 2 1 5 1 1 . 1 5 6 5 6 • 6 3 . 70168 1 .1 4 7 3 4 1 . 2 4 3 9 . 7 3 - 4 0 9 3 2 1 .0871 1 .3 8 1 -8 2 . 74 69 4 1 .0 4 1 2 3 1 .5 7 2 7 8 . 9 1 . 6 4 3 2 1 .0 1 1 1 6 1. S 59 69 1. 5 . 4 6 2 5 I E - 08 1 2 . 3 0 9 72 GE 0 '//- .9 5 8 4 3 3 8 0 7 3 4 522 65 0 7J69 426*2 S313 1 3 . 3 3 0 1 3 2 . 7 4 6 6 1 1 -6 8 0 9 1 5 . 2 9 5 3 6 E - 03 157 TABLE XXX Listing of GE Time-Sharing Program CRK7 2 DIM P C 90>,X C 90>,Y C 90> 3 READ P 1 , T l,P 2 » T2 5 READ N , T , V I . V 2 . G l , G 2 2 0 FUR 1= 1 TO N 2 5 READ P C I ) , X C I ) , Y C 1 > 3 0 NEXT I 3 5 LET U= C T + 2 73. 16) * 1 .8 3 7 LET 0= E X P C C - 3 7 0 9 . 9 1 / C T + 2 7 3 . 1 6 ) ) + 1 3 . 1644) 38 LET R= EXPCC- 4 2 2 4 . 3 7 / C T + 2 7 3 . 1 6 ) > + 1 3 . 3 1 5> 4 0 LET T3= U / T l 45 LET A= 0 . 6 9 3 0 9 + 2 . 6 3 5 0 2 / T 3 - 4 . 6 2 3 0 6 / C T3*T3) 50 LET B= 0 . 7 0 5 4 3 / C T 3 t 3) 5 5 LET F l= C P l * E X P C A + 8 ) ) * E X P C V 1 * 0 /C 1 0 . 7 3 I * U > > 6 0 LET T4= U /T 2 6 5 LET C= - 1 .8 0 4 6 0 + 1 0 . 1 5 8 1 4 / T 4 - 12. 0 6 3 2 7 /C T 4 * T 4 ) 7 0 LET D= 3 -6 0 1 1 3 / C T 4 t 3 ) - 0 . 4 4 2 4 7 / C T 4 + 45 7 5 LET F2= CP2+EXPCC+D) ) + EXPC V2+R/C 1 0 . 7 3 1 * U ) 5 8 0 LET L 1 = C V 2 /V I5 + EXPC-U1/C I .9 S 7 + U 5 ) 8 5 LET L2= < V 1 / 925 * EXPC - G2/ C 1 .9 3 7+ U> ) 9 0 FOR 1= 1 TO N 9 5 LET Z = l-XC 15 100 LET £1= - L J G C X C I) + L 1 * Z ) 1 05 LET E2= Z * C L 1 / C X C I >+ L 1* Z ) - L 2 / C L 2 * X C I 5 + Z>5 110 LET P3= EXPCE1 + E2) 115 LET E3= - L O G C Z + L 2 * X ( I ) ) 120 LET E4= -XC I 5 kC L 1/C X C I5+L 1 + Z 5 - L 2 / C L 2 + X C I 5+ Z ) 5 125 LET P4= EXPC E3+E4) 130 LET C l= EXPCV1 + C P C I)-Q > /C 1 '0 . 731-MJ5) 135 LET C2= EXPCV2+CPC 1 5 -R 5/C 10. 731 * U) 5 140 LET F3= C F 1/ PC I J ) *C 1 145 LET F 4= C F2/P C I 5 5 *C 2 "1 5 0 LET S l = CF3 + P3 + X C I ) > / Y C I 5 155 LET S2= C F 4 * P 4 « Z ) / C 1- Y C I )5 160 PRINT PCI 5 , S I , S2 1 65 PRINT F 1 . F 2 . F 3 . F 4 ■170 PRINT P 3 . P 4 . C 1 . C 2 17 5 NEXT I 2 2 0 Qa TA 712- 73. 1012. 7. 3 6 2 . 77. 1024. V 2 2 5 DATA I 7 . 5 5 0 . 2 - 3 2 4 . 4 . 8 1 7 1 . 2 3 0 0 . 2 0 0 2 30 DA frt 3 0 0 . 0 . 0 1 6. 3. 0 4 4. 320. 0. 07 0 . 0 . 123. 3 40. 0. 1 3 7 3. 0 • 20 6. 3 50 2 3 5 DATA 0 . 2 0 2 5 . 0 . 2 75. 3 3 0 . 0 . 2 6 3 5 . 0 . 3 4 0 , 4 0 0 . 0 . 3 2 4 . 0 . 4 0 0 . 420 2 40 DATA 0 . 3 8 5 , 0 . 457. 4 4 0 . 0 . 446. 0. 514, 4 6 0 . 0- 50 6, 0 . 572, 4 3 0 , 0- 564 2 45 DATA 0 . 629. 500, 0. 621 . 0 . 63 6, 5 2 0 , f). 67 65, 0. 7 3 6 , 540, 0 . 73 I S, 0 . 786 2 5 0 DATA 5 6 0 , 0 . 73 6 5 , 0 . 6 3 6 , 6 6 0 , 0 . 8 4 1, 0 . 3 3 0 , 600, 0 . 8 9 6 , 0 . 9 2 4 2 5 5 DATA 6 2 0 , 0 . 9 52 5 , 0 . 9 67 9 99 END 168 TABLE XXXI Sample Printout for Program CRK7 F ~ 120 2 0 0971 $x.~ * 9288 66 : f / = 2 2 3 . 3 1 1 f/= -9 3 .3 9 66 ^°=1 • 793 72 ^ “ . 779 646 (Tf j- 1 .3 3 3 2 4 . K - 1 . 0 0 0 3 5 < S / - . 9 6 6 5 7 3 0 2 = 1 . 0 0 1 7 2 130 ........................ • 47193 1 . 9 5 0 1 9 2 2 3 .3 1 1 9 3 . 3 9 6 6 1 . 6 6 3 3 5 . 7 2 2 4 1 9 1 . 8 3 0 3 4 __________ 1 .0 0 0 3 3 .9 63 6 04____________1 .0 0 555 140' " '. 6920 63 . 9 49552 2 2 3 . 3 1 ! 9 3 - 3 9 6 6 1 .5 4 8 2 5 . 6 7 3 3 7 7 1. 743 26__________ 1 . 0 0 4 1 4 __________ . 9 7064___________1. 009 33 160 . 9 2 5 2 6 5 . 9 3 9 6 7 1 2 2 3 .3 1 1 9 3 . 3 9 6 6 1 . 3 6 0 4 2 . 59371 I 1-5 6 0 4 9 ___________ L-JL2_.49.j4____________ . 9 7 4 72 4 __________ 1*0 1 7 1 130 ."92339 1 . 9 9 2 0 1 3 2 2 3 -3 1 1 9 3 . 3 9 6 6 1 . 2 1 4 3 5 . 5 3 1 7 7 7 1. 40731___________ U 0 6 5 9 ? ____________ -9 7 3 3 2 6___ ________ 1. 02 4 8 3 .. 200 . 3 7 6 3 8 6 !• 10359" 22 3 * 311 93 - 39 6 6 1 -0 9 7 51 . 48 2 253 1 .2 3 1 14___________ 1. 1337 _____________ . 9 8 2 9 4 5 ___________ 1-0 3 2 7 1 2 23 . 3 29 59 3 1 .2 3 9 21’ 2 2 3 -3 1 1 9 3 . 3 9 6 6 1 . 0 0 1 9 4 . 441763 I . 1 7669 1. 2 4 1 8 2 ____________ .9 3 7 0 3 1 ___________1 . 04061 243 .’ 79 3183" f- 57 52 4 2 2 3 - 31 1 9 3 . 3 9 6 6 . 9 2 2 3 0 7 . 4 2 3 0 5 j 1-09 5 1-4 1078 ______-_9 9_12 3 5 ____ _____ L^0-5.?56_ j 2 6 0 " ” ■."763371........... " ’ 2 . 1 2 3 6 7 ’ [ 22 3 . 31 1 9 3 . 3 9 6 6 - 8 5 4 9 4 3 . 379541 1 -0 3 68 4 1 *6 7 8 6 1 6 ___________1 j l 0. ? . 4 ? 6 _ ! 270 ........ ’ " .7 6 2 5 5 9 ” " 2 . 3 4 0 3 6 | 223 . 311 93 . 39 6 6 . 8 2 5009 . 3 6 63 79 1 1 .0 1 7 2 1 1 - 8 7 1 3 . 9 9 7 4 9 3 1 .0 6 0 6 1

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Creator Koppany, Charles Robert (author)

Core Title Vapor-Liquid Equilibria For The Benzene - N-Octane System Near The Regionof The Critical-Locus

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, chemical,OAI-PMH Harvest

Format dissertations (aat)

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Lenoir, John M. (committee chair), Choudhury, P. Roy (committee member), Rebert, Charles J. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-767262

Unique identifier UC11363486

Identifier 7300745.pdf (filename),usctheses-c18-767262 (legacy record id)

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Document Type Dissertation

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

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