Al-khwarizmi Engineering Journal Al-Khwarizmi Engineering Journal, Vol.4 , No.1 , pp 8-16, (2008) Effect Of Polar Component(1-Propanol) On The Relative Volatility Of The Binary System N-Hexane - Benzene Dr. Khalid Farhod Chasib Al-Jiboury Chemical Engineering Department University of Technology (Received 11 April 2007 ; accepted 4 October 2007))) Abstract: Vapor-liquid equilibrium data are presented for the binary systems n-hexane - 1-propanol, benzene - 1-propanol and n-hexane – benzene at 760 mm of mercury pressure. In addition ternary data are presented at selected compositions with respect to the 1-propanol in the 1-propanol, benzene, n- hexane system at 760 mmHg. The results indicate the relative volatility of n-hexane relative to benzene increases appreciably with addition of 1-propanol. Keywords: Vapor-Liquid Equilibria, Relative volatility, Polar component. Introduction The rapid growth of the petrochemical industry has led to the wide application of extractive distillation as a means of separating closely boiling compounds. One of the problems in the field of extractive distillation is to find a quantitative method of assessing solvents, in terms of the physical properties of the constituents, in order to select the most efficient solvent for a particular process. The aim of the present study was to determine experimentally the effect of polar components on the relative volatility of binary systems. The binary system studied in this work was composed of n-hexane and benzene. These hydrocarbons are difficult to separate because of closeness of boiling points. 1-propanol was used as a solvent. Vapor-Liquid Equilibria of the binary systems n-hexane – benzene, n-hexane - 1-propanol, benzene - 1-propanol, and of the ternary system n-hexane – benzene- 1-propanol was determined at 760 mm of mercury absolute, using a modified Colburn recirculating still. The change in relative volatility of n-hexane relative to benzene, in the presence of 1-propanol, was calculated. Experimental Section Chemicals n-hexane, 99 mole % (min.) grade, was obtained from Phillips Petroleum Co., the reagent grade benzene was obtained from Merck and Co., and the Baker analyzed reagent grade 1-propanol was obtained from Baker Chemical Co. Table 1 compares the literature (Marc, 1998) and experimental values of physical properties of these materials. Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Ö !! Table 1 Properties of Materials Physical Property n-Hexane Benzene 1-Propanol Experimental Literature Experimental Literature Experimental Literature Refractive Index nD 30 1.36996 1.36949 1.49469 1.49460 1.38146 1.38160 Density, 30 g/cm-3 0.65043 0.65026 0.86839 0.86829 0.7962 0.7960 Boiling point, 760 mmHg, oC 68.8 68.74 80.1 80.1 97.25 97.29 Antoine Constants, where log P = A – [B / ( C + t )] , P = mmHg, t = oC A 6.87773 6.89745 7.99733 B 1171.53 1206.35 1569.70 C 224.366 220.237 209.5 Apparatus A modified Colburn recirculating equilibrium still Fig 1 was used to obtain the vapor-liquid equilibrium data. The modifications and the general procedure have been reported in (Colburn, A.P., 1984). The mixture is introduced into the equilibrium apparatus via the filler tube of the storage vessel, where the liquid mixture in the reservoir is heated to boiling by a housing heating mantle. The circulation caused by vapor bubbles ensures even heating and mixing, where the heating mantle ensures that the number of vapor bubbles remains constant and that the mixture is heated uniformly. The ascending vapor bubbles thoroughly mix the entire volume of liquid, thus preventing a concentration gradient from forming and the boiling liquid from over-heating. When the vapor bubbles (A) pass the funnel-shaped constriction of the Cotrell pump they carry a large quantity of non-vaporized liquid (B) to the Phase divider (phase separator). Here, the vapor-liquid mixture pours over the thermocouple protection tube. The splashguard which becomes wider higher up, prevents liquid splashes from being vaporized, which would complicate establishment of stationary equilibrium. To prevent partial condensation on the glass walls of the phase divider (phase separator) the equilibrium apparatus is equipped with an evacuated glass mantle consisting of two panes. In the phase divider the vapor phase (A) and the liquid phase (B) are separated. The liquid phase (B) drains off laterally to the sampling port at which it can be sampled through the septum of the screw cap without having to open the apparatus. Sampling via a glass syringe also prevents contamination of the sample. To condense the vapor residues present in the liquid phase (B), the outlet flows into a small vessel, on which a Liebig cooler is mounted. The vapor (A) flows through the phase divider and a lateral outlet to the Dimroth cooler where it condenses. The condensate (A) drips down in a curved tube, which also terminates at a sampling port. The liquid (B) and condensate reflux (A), each arms fitted with a siphon, flow into a common tube. This enables remixing of the two phases before they are returned to the reservoir. The tube extends into the reservoir and ends inside it with its opening facing upward. The liquid rising in the middle of the reservoir draws the returned sample out of the tube and heats it. Temperature were measured using a Copper – Constantan thermocouple and a Type K Leeds & Northrup potentiometer. A Bausch & Lomb precision refractometer was used to measure the refractive index of the vapor and liquid samples using a sodium D line light source. A Cottrell boiling point apparatus was used to check the purity of the compounds and to calibrate the equilibrium still thermocouple. The accuracy of the refractometer was tested by the test pieces supplied by Bausch & Lomb Inc. Pressure was measured to within ± 0.5 mm of mercury using a calibrated mercury manometer. Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Î Í !! Fig.1. Flow diagram for equilibrium apparatus. Procedure The procedures for determining vapor- liquid equilibrium data for the three binary systems were essentially those described below. For each of the binary hydrocarbon systems, refractive index calibration curves were obtained with samples of 12 to 15 different known concentrations at 30 oC. The compositions of vapor and liquid samples were read from the calibration curves. In the case the ternary system, three mixtures of n-hexane – benzene in the mole ratios of 25 to 75, 50 to 50, and 75 to 25 were used. 1-Propanol was added to each of the above mixtures to give equivalent mole fractions of 0.33, 0.50, 0.67, 0.75, and 0.80 in the ternary mixture. These mixtures were subjected to equilibrium distillation in the modified Colburn recirculating still and the vapor and liquid samples were obtained. The 1-propanol in these samples was extracted with water. The hydrocarbon layer was dried overnight by adding crystals of Drierite, which removed any traces of water remaining in the hydrocarbon mixture. The composition of the added agent- free samples was determined in the refractometer maintained at 30 oC. Discussion Of Results Experimental activity coefficients for the components in the binary mixture were calculated by the following equation (Prausnitz et.al., 1980). Px Py ii Tii i   (1) The fugacity coefficient i, was calculated using the PR equation of state, which have the form (Sytryjeck et.al., 1986): 2 11ln                      cc T T n T T m (2) Where m and n are two empirical factors for each pure component, their values given in Table 2 (Sytryjeck et.al., 1986). Table 2. m and n (PR) factors equation of state compound PR – EOS m n 1-Propanol 1.1505 0.8075 Hexane 0.7939 0.4116 Benzene 0.6671 0.4723 axkkka O ijijiaijaijaij                1 (3) ))((  jjaaa iiij O  ,  i iji j j axxA (4) 33131 21                           bb xkkkb ji ijibijbijbij (5)  i ii BxB (6)                              BZ BZ b B axaB ABZZb B i ij i i j j 414.0 414.2ln2 828.2ln1ln (7) Where                                   n n bb n jiiji j k kj kj j j bb kkxxbbxB kjjk 1 1 33131 2 1 2 b bb kkxx n i ibibi j j j jj                              1 33131 2 (8) The vapor -liquid equilibrium data for the three binaries are reported in Tables 3 to 5 and shown graphically in Figures 2 to 7. Our results are compared to literature data (Chen, S. et.al., 2003) Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Î Î !! Table 3 Vapor-liquid equilibrium data for Hexane–Benzene system at 760 mmHg. Temp. oC Experimental Calculated xH yH H B H B 77.6 0.073 0.140 1.46 1.00 1.53 1.00 75.1 0.172 0.268 1.28 1.03 1.36 1.02 73.4 0.268 0.376 1.22 1.05 1.25 1.05 72.3 0.372 0.460 1.12 1.11 1.16 1.08 70.9 0.462 0.540 1.09 1.15 1.11 1.12 70.1 0.585 0.644 1.06 1.18 1.06 1.18 69.4 0.692 0.725 1.03 1.26 1.03 1.24 69.1 0.792 0.807 1.01 1.32 1.01 1.29 69.0 0.828 0.838 1.00 1.34 1.01 1.32 68.9 0.883 0.888 1.00 1.35 1.00 1.35 68.8 0.947 0.950 1.00 1.36 1.00 1.39 68.8 0.962 0.964 1.00 1.36 1.00 1.40 Table 4 Vapor-liquid equilibrium data for Hexane–1-propanol system at 760 mmHg. Temp. oC Experimental Calculated xH yH H 1-P H 1-P 89.6 0.024 0.256 6.04 1.03 6.17 1.00 82.3 0.060 0.490 5.46 1.01 5.25 1.01 74.6 0.144 0.662 3.67 1.01 3.74 1.05 71.9 0.236 0.728 2.81 1.02 2.73 1.13 71.2 0.262 0.716 2.53 1.15 2.52 1.16 70.7 0.370 0.760 1.97 1.20 1.90 1.34 68.4 0.476 0.786 1.67 1.39 1.53 1.55 67.7 0.620 0.800 1.33 1.85 1.32 2.01 67.0 0.752 0.836 1.18 2.41 1.09 2.63 66.4 0.784 0.856 1.18 2.49 1.06 2.82 66.2 0.904 0.916 1.10 3.30 1.01 3.71 65.8 0.954 0.952 1.10 3.85 1.00 4.17 67.2 0.975 0.97 1.05 4.32 1.00 4.40 Table 5 Vapor-liquid equilibrium data for Benzene –1-propanol system at 760 mmHg. Temp. oC Experimental Calculated xB yB B 1-P B 1-P 92.8 0.049 0.142 1.99 1.07 2.34 1.00 88.4 0.104 0.296 2.22 1.12 2.21 1.01 84.8 0.180 0.436 2.10 1.14 2.04 1.02 82.1 0.254 0.530 1.97 1.17 1.88 1.04 79.7 0.398 0.622 1.62 1.33 1.61 1.13 77.4 0.504 0.680 1.47 1.46 1.44 1.24 76.5 0.642 0.728 1.27 1.78 1.25 1.49 76.2 0.764 0.774 1.15 2.31 1.12 1.94 76.1 0.792 0.776 1.11 2.59 1.10 2.11 76.3 0.834 0.812 1.10 2.70 1.06 2.39 76.9 0.916 0.864 1.04 3.75 1.02 3.24 78.2 0.956 0.916 1.01 4.16 1.01 3.89 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mole Fraction of Hexane 66 68 70 72 74 76 78 80 82 T E M PE R A T U R E , C o T-x-y Curves Liquid phase experimental data Liquid phase literature data Vapor phase experimental data Vapor phase literature data   Fig.2. Boiling Point - Composition Curve for Hexane – Benzene at 760 mmHg. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mole fraction of Hexane 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 A ct iv it y C oe ff ic ie nt ,  Calculated Experimental Fig.3. Activity Coefficient - Composition Curve for Hexane – Benzene at 760 mmHg. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mole Fraction of Hexane 60 65 70 75 80 85 90 95 100 T E M PE R A T U R E , C o T-x-y Curves Liquid phase experimental data Liquid phase literature data Vapor phase experimental data Vapor phase literature data   Fig.4. Boiling Point - Composition Curve for Hexane – 1- Propanol at 760 mmHg. Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Î Ï !! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mole fraction of Hexane 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 A ct iv it y C oe ff ic ie nt ,  Calculated Experimental Fig.5. Activity Coefficient - Composition Curve for Hexane – 1- Propanol at 760 mmHg. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mole Fraction of Benzene 74 76 78 80 82 84 86 88 90 92 94 96 98 T E M PE R A T U R E , Co T-x-y Curves Liquid phase experimental data Liquid phase literature data Vapor phase experimental data Vapor phase literature data   Fig.6. Boiling Point - Composition Curve for Benzene – 1- Propanol at 760 mmHg. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Mole fraction of Benzene 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 A ct iv it y C oe ff ic ie nt ,  Calculated Experimental Fig.7. Activity Coefficient - Composition Curve for Benzene – 1- Propanol at 760 mmHg. The data were correlated by the NRTL activity coefficient equations (Chen, S. et.al., 2003).                      2 1212 1212 2 2121 21 21 2 21 G ln Gxx τG xx Gτxγ (9)                      2 2121 2121 2 1212 12 12 2 12 G ln Gxx τG xx Gτxγ (10)  τexp 1212 -αG  (11)  τexp 2121 -αG  (12) The values of the constants in the correlation were evaluated by using the maximum likelihood principle method providing a mathematical and computational guarantee of global optimality in parameter estimation that provides the best fit to measured data. The objective function in nonlinear parameter estimation problems is given below (Anderson et.al., 1978; Prausnitz et.al., 1980):                                                     M N y i j i j i j i j TPi j ec x ece i c i e i c i yyxxTTPP S 1 1 2222 22 22  (13) Where the superscripts c and e indicate calculated and experimental values, respectively, the 2 are the estimated variances of the corresponding variables, and the sum is taken over all M experimental data, and N is the number of compounds in the mixtures. The standard deviation assumed were (Marc et.al., 1998; Lu et.al., 1989): P = 0.5 mmHg T = 0.1 oC x = 0.001 mole fraction y = 0.005 mole fraction A listing of optimized interaction parameters for NRTL activity coefficient model studied is shown in Table 6 for all binary systems. Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Î Ð !! Table 6 Optimized interaction parameters for binary systems. System    Hexane – Benzene 466.2 269.3 0.292 Hexane – 1-Propanol 822.7 174.8 0.412 Benzene- 1-Propanol 296.9 212.6 0.405 The values of activity coefficients calculated by NRTL equations are also given in Table 3 to 5. A defined deviation between the calculated and experimented activity coefficients was evaluated by the formula (Anderson et.al., 1978):   1)-( 2/122 - n nkk  (14) k = deviation of experimental activity coefficients values from calculated values. n = number of experimental points  = defined deviation of k from a mean value of k The deviations are as follows: H – B H – 1-P B – 1-P H B H 1-P B 1-P 0.029 0.023 0.101 0.137 0.112 0.188 Maximum and minimum values of the activity coefficients were calculated to show the limits of the experimental deviations. The refractometer error for the n-hexane – benzene and benzene - 1-propanol system was within 0.001 mole fraction and for the n-hexane - 1- propanol system, 0.005 mole fraction. Pressure errors were within ± 0.5 mm of Hg and temperature errors were within ± 0.1 oC.      C.P.x .P.y γ O T -tat- 100010 500010 11 1 max   (15)      C.P.x .P.y γ O T tat 100010 500010 -- 11 1 min   (16) The defined deviation between the experimental activity coefficients and the max and min values calculated by equation 14, in the range of x = 0.15 to x = 0.85, are as follows: H – B H – 1-P B – 1-P H B H 1-P B 1-P  m ax  0.022 0.006 0.034 0.048 0.009 0.013  m in  0.006 0.016 0.026 0.053 0.005 0.012 The defined deviation over the full range will be larger because of the influence of the high error in the end values of ’s. It may be seen from Table 3 to 5 that the deviation between the calculated (Equation 9 to 12) and experimental values of ’s is maximum in the middle range and this deviation depends on the type of equation applied for calculation the ’s. It is not necessary that the defined deviation between calculated and experimental ’s be between  max  and  min  values as they are only deviations due to experimental errors. McDermott-Ellis test method (McDermott et.al., 1965) was applied to the activity coefficient – composition data of the binaries. According to McDermott-Ellis test method, two experimental points a and b are thermodynamically consistent if the following condition is fulfilled: D < Dmax (17) The local deviation D is given by      N i iaibibia xxD 1 lnln  (18) In this method, it is recommended the use of a fixed value of 0.01 for Dmax if the accuracy in the measurement of the vapor and the liquid mole fraction is within 0.001. The local maximum deviation, Dmax, due to experimental errors, is not constant, and is given by              N i ibibiaia ibiamax y yxyxxxD 1 1111       NN i ibia i iaib P P xxx 11 lnln2               N bi a ibia t ttxx 1 11 (19) Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Î Ñ !! Table 7 Results of Thermodynamic Consistency test. System D Dmax 1-Propanol – Hexane 0.0243 0.026 Hexane – Benzene 0.0161 0.021 1-Propanol – Benzene 0.0274 0.029 1-Propanol – Hexane – Benzene 0.0321 0.035 In accordance with the criterion of the test the data were found to be consistent. The experimental data for all the three binaries show that they are non–ideal in nature. (Tongberg et.al., 1992), studying the equilibrium of n-hexane – benzene, reported no separation obtainable at concentration above 97 mole % hexane. This is consistent with the observation made in this investigation. The n-hexane – 1-propanol and benzene – 1-propanol systems evidence minimum boiling azeotropes. It is indicated by the interpolation of the data that n-hexane – 1- propanol form an azeotrope at 95 mole % hexane at 65.8 oC, and the benzene – 1- propanol form an azeotrope at 77.5 mole % benzene at 76 oC The variation of the relative volatility with the concentration of the solvent in the ternary system is reported in Table 8 and shown in Figure 8. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Mole fraction of 1-Propanol in the mixture 1.2 1.6 2.0 2.4 2.8 R el at iv e V ol at il it y ,  12 1 2 3 Fig 8 Effect of 1-propanol on relative volatility of binary system n-hexane – benzene at 760 mmHg Table 8 Variation of relative volatility with solvent concentration for ternary system n-hexane – benzene- 1-propanol at 760 mmHg Pressure Binary mixture Mole fraction 1-propanol in mixture Temperature oC Mole fraction 1-propanol free basis )/( BH xH ' xB ' x P-1 xH y H xB y B 0.25 0.75 0.00 0.33 0.50 0.67 0.75 0.80 74.1 27.0 74.3 78.7 82.3 84.8 0.21 0.193 0.172 0.156 0.154 1.36 0.326 0.346 0.332 0.325 0.327 0.300 0.79 0.807 0.828 0.884 0.846 0.864 0.674 0.654 0.668 0.675 0.673 0.709 1.82 2.21 2.39 2.60 2.67 2.72 0.50 0.50 0.00 0.33 0.50 0.67 0.75 0.80 71.2 67.5 70.2 75.2 80.3 83.0 0.428 0.424 0.400 0.396 0.375 0.368 0.528 0.574 0.572 0.593 0.580 0.574 0.572 0.576 0.600 0.606 0.625 0.632 0.472 0.426 0.423 0.407 0.429 0.426 1.50 1.83 2.00 2.23 2.30 2.31 0.75 0.25 0.00 0.33 0.50 0.67 0.75 0.80 69.4 66.3 68.2 72.8 78.2 80.7 0.684 0.681 0.632 0.658 0.635 0.605 0.724 0.776 0.744 0.776 0.766 0.746 0.316 0.324 0.378 0.342 0.365 0.395 0.276 0.224 0.256 0.224 0.234 0.251 1.31 1.63 1.71 1.80 1.88 1.92 x'= Solvent free basis Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Î Ò !! Conclusion The data show that the greatest change of relative volatility is obtained at higher concentration of the solvent. As the vapor and liquid samples were extracted with water, it was ensured by laboratory tests that the solvent–free hydrocarbon concentration did not change because of the different solubilities of the hydrocarbons in water. Also, it was found that the drying agent, Drierite, had no selective absorption capacity for the hydrocarbon mixture involved. Nomenclature ai Combining rule coefficient aij Mixing rule coefficient O ija Mixing rule coefficient A Cohesion parameter of cubic equation of state bi Combining rule coefficient B Covolume term (parameter) of the cubic equation of state Bi Combining rule coefficient ijk a Interaction coefficient of equation of state ijkb Interaction coefficient of equation of state m Temperature dependent correlation parameter n Temperature dependent correlation parameter nD Refractive index P Equilibrium pressure of the system, MPa Pi Vapor pressure of pure component i MPa T Temperature, K TC Critical temperature, K xi Mole fraction of component i in liquid phase yi Mole fraction of component i in vapor phase z Compressibility factor Greek Litters  Temperature dependency of the attractive term of equation of state  Relative volatility  Activity coefficient  Standard deviation  Density 2 Estimated variance  Fugacity coefficient References Anderson, T. F., D. S. Abrams, and E. A. Grens. Evaluation of parameters for Nonlinear Thermodynamic Models, AIChE J., 24, 20. 1978. Chen, S,. and Yan, C., “Vapor-Liquid Equilibrium Calculations of Azeotropic Mixtures Using the Peng-Robinson Equation of State and Various Activity coefficients models”, J. Chem. Eng. of Japan, 27, 512-516, 2003, Internet Resources, available at http://www.scej.org/ronbun/JCEJe/ e27_0512.html. Colburn, A.P, Ind. Eng. Chem., 35, 666, 1984 Lu, B. C. and M. Kato, The use of Two- Parameter Equation of State for Predicting Vapor-Liquid Equilibria, Int. Chem. Eng. Symp. , 56, 57. 1989 Marc, J. A., Martin, J. P. and Thamas, F. T., “Thermophysical Properties of Fluid, An introduction to their prediction”, Imperial College Press, first reprint, 1998. McDermott, C., Ellis, S. R. M., “A Multicomponent Consistency Test”, Chem. Eng. Sci., 20, 293, 1965. Prausnitz, J. M., C. A. Eckert, R. V. Orye, and J. P. O’Connell. Computer Calculations for Multicomponent Vapor-Liquid and Liquid- Liquid Equilibria, Prentice Hill, Englewood Cliffs, New Jersey, 1980. Sytryjeck, R. and J. H. Vera, An Improved Peng Robinson Equation of State for Pure and Mixture, J. of Chem. Eng., 64, 323, 1989. Tongberg, C.O., Johnston, F., Ind. Eng. Chem., 25, 734, 1992 Khalid Farhod Al-khwarizmi Engineering Journal ,Vol.4, No.1 PP 8-16 (2008) Î Ó !! بنزین –نظام الثنائي ھكسان على التطایریة النسبیة لل) بروبانول- ١(تأثیر المركب القطبي !!!!! ! ! !!!!œ!!! ! !! !!! !! !!!! ! !!! !!!!! ! !! !Š! !! !! !!!!!Ÿ! !Š!!!! : الخالصة ان –تم عرض بیانات إتزان بخار ة ھكس زین -١ –سائل لألنظمة الثنائی انول، بن ان -١ –بروب انول و ھكس ي –بروب زین ف بن غط ق ٧٦٠ض م زئب ى . مل بة إل ارة بالنس ز مخت ي لتراكی ام الثالث ات النظ رض بیان م ع ك ت ى ذل افة إل ام -١باإلض ي نظ انول ف -١بروب د إزدادت . ملم زئبق ٧٦٠بروبانول، بنزین، ھكسان في ضغط زین ق ى البن بة ال ان بالنس بیة للھكس النتائج أشارت الى إنھ التطایریة النس .بروبانول-١عند إضافھ بصورة ملموسة !! n D 30 P x P y i i T i i i f g = 2 1 1 ln ú ú ú û ù ê ê ê ë é + ú ú û ù ê ê ë é = - - c c T T n T T m a a x k k k a O ij i ji a ij a ij a ij ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ - + - = 1 ) )( ( a a j j a a a i i ij O = å å = i ij i j j a x x A 3 3 1 3 1 2 1 ÷ ÷ ÷ ø ö ç ç ç è æ + ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ - + - = b b x k k k b j i i ji b ij b ij b ij å = i i i B x B ( ) ( ) ÷ ÷ ø ö ç ç è æ ú ú ú ú û ù ê ê ê ê ë é - - - - - = - + ¢ ¢ F å B Z B Z b B a x a B A B Z Z b B i ij i i j j 414 . 0 414 . 2 ln 2 828 . 2 ln 1 ln å å å = = = ú ú ú û ù ê ê ê ë é ÷ ÷ ÷ ø ö ç ç ç è æ + ÷ ÷ ø ö ç ç è æ - - ÷ ø ö ç è æ + = ¢ n n b b n ji ij i j k k j k j j j b b k k x x b b x B kj jk 1 1 3 3 1 3 1 2 1 2 b b b k k x x n i i b i b i j j j j j - + å = ú ú ú û ù ê ê ê ë é ÷ ÷ ÷ ø ö ç ç ç è æ + ÷ ÷ ø ö ç ç è æ - 1 3 3 1 3 1 2 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 M o l e F r a c t i o n o f H e x a n e 6 6 6 8 7 0 7 2 7 4 7 6 7 8 8 0 8 2 T E M P E R A T U R E , C o T - x - y C u r v e s L i q u i d p h a s e e x p e r i m e n t a l d a t a L i q u i d p h a s e l i t e r a t u r e d a t a V a p o r p h a s e e x p e r i m e n t a l d a t a V a p o r p h a s e l i t e r a t u r e d a t a l n 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 M o l e f r a c t i o n o f H e x a n e 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 A c t i v i t y C o e f f i c i e n t , g C a l c u l a t e d E x p e r i m e n t a l 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 M o l e F r a c t i o n o f H e x a n e 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 T E M P E R A T U R E , C o T - x - y C u r v e s L i q u i d p h a s e e x p e r i m e n t a l d a t a L i q u i d p h a s e l i t e r a t u r e d a t a V a p o r p h a s e e x p e r i m e n t a l d a t a V a p o r p h a s e l i t e r a t u r e d a t a l n 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 M o l e f r a c t i o n o f H e x a n e 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 6 . 0 7 . 0 8 . 0 A c t i v i t y C o e f f i c i e n t , g C a l c u l a t e d E x p e r i m e n t a l 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 M o l e F r a c t i o n o f B e n z e n e 7 4 7 6 7 8 8 0 8 2 8 4 8 6 8 8 9 0 9 2 9 4 9 6 9 8 T E M P E R A T U R E , C o T - x - y C u r v e s L i q u i d p h a s e e x p e r i m e n t a l d a t a L i q u i d p h a s e l i t e r a t u r e d a t a V a p o r p h a s e e x p e r i m e n t a l d a t a V a p o r p h a s e l i t e r a t u r e d a t a l n 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 M o l e f r a c t i o n o f B e n z e n e 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 5 . 0 A c t i v i t y C o e f f i c i e n t , g C a l c u l a t e d E x p e r i m e n t a l ( ) ú ú û ù ê ê ë é + + ÷ ÷ ø ö ç ç è æ + = 2 12 1 2 12 12 2 21 2 1 21 21 2 2 1 G ln G x x τ G x x G τ x γ ( ) ú ú û ù ê ê ë é + + ÷ ÷ ø ö ç ç è æ + = 2 21 2 1 21 21 2 12 1 2 12 12 2 1 2 G ln G x x τ G x x G τ x γ ( ) τ exp 12 12 - α G = ( ) τ exp 21 21 - α G = å å = ï ï ï þ ï ï ï ý ü ï ï ï î ï ï ï í ì = ÷ ÷ ø ö ç ç è æ - + ÷ ÷ ø ö ç ç è æ - + ÷ ø ö ç è æ - + ÷ ø ö ç è æ - = M N y i j i j i j i j T P i j e c x e c e i c i e i c i y y x x T T P P S 1 1 2 2 2 2 2 2 2 2 s s s s ( ) 1) - ( 2 / 1 2 2 - n n k k å å = w ( ) ( ) ( ) ( ) C . P . x . P . y γ O T - t at - 1 0 001 0 5 0 001 0 1 1 1 max + + = ( ) ( ) ( ) ( ) C . P . x . P . y γ O T t at 1 0 001 0 5 0 001 0 - - 1 1 1 min + + = ( ) ( ) å = - + = N i ia ib ib ia x x D 1 ln ln g g ( ) å = ÷ ÷ ÷ ø ö ç ç ç è æ + + + + D = N i ib ib ia ia ib ia max y y x y x x x D 1 1 1 1 1 ( ) å å = + = D + D - + N N i ib ia i ia ib P P x x x 1 1 ln ln 2 g g ( ) å = ÷ ÷ ÷ ø ö ç ç ç è æ + + D + N b i a ib ia t t t x x 1 1 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 M o l e f r a c t i o n o f 1 - P r o p a n o l i n t h e m i x t u r e 1 . 2 1 . 6 2 . 0 2 . 4 2 . 8 R e l a t i v e V o l a t i l i t y , a 1 2 1 2 3 ) / ( B H a x H ' x B ' x P - 1 x H y H x B y B O ij a ij k a ij k b Correlation for Fitting Multicomponent Vapor-Liquid Equilibria Data and Prediction of Azeotropic Behavior Al-khwarizmi Engineering Journal Al-Khwarizmi Engineering Journal, Vol.4 , No.1 , pp 8-16, (2008) Effect Of Polar Component(1-Propanol) On The Relative Volatility Of The Binary System N-Hexane - Benzene Dr. Khalid Farhod Chasib Al-Jiboury Chemical Engineering Department University of Technology (Received 11 April 2007 ; accepted 4 October 2007) Abstract: Vapor-liquid equilibrium data are presented for the binary systems n-hexane - 1-propanol, benzene - 1-propanol and n-hexane – benzene at 760 mm of mercury pressure. In addition ternary data are presented at selected compositions with respect to the 1-propanol in the 1-propanol, benzene, n-hexane system at 760 mmHg. The results indicate the relative volatility of n-hexane relative to benzene increases appreciably with addition of 1-propanol. Keywords: Vapor-Liquid Equilibria, Relative volatility, Polar component. Introduction The rapid growth of the petrochemical industry has led to the wide application of extractive distillation as a means of separating closely boiling compounds. One of the problems in the field of extractive distillation is to find a quantitative method of assessing solvents, in terms of the physical properties of the constituents, in order to select the most efficient solvent for a particular process. The aim of the present study was to determine experimentally the effect of polar components on the relative volatility of binary systems. The binary system studied in this work was composed of n-hexane and benzene. These hydrocarbons are difficult to separate because of closeness of boiling points. 1-propanol was used as a solvent. Vapor-Liquid Equilibria of the binary systems n-hexane – benzene, n-hexane - 1-propanol, benzene - 1-propanol, and of the ternary system n-hexane – benzene- 1-propanol was determined at 760 mm of mercury absolute, using a modified Colburn recirculating still. The change in relative volatility of n-hexane relative to benzene, in the presence of 1-propanol, was calculated. Experimental Section Chemicals n-hexane, 99 mole % (min.) grade, was obtained from Phillips Petroleum Co., the reagent grade benzene was obtained from Merck and Co., and the Baker analyzed reagent grade 1-propanol was obtained from Baker Chemical Co. Table 1 compares the literature (Marc, 1998) and experimental values of physical properties of these materials. Table 1 Properties of Materials Physical Property n-Hexane Benzene 1-Propanol Experimental Literature Experimental Literature Experimental Literature Refractive Index 1.36996 1.36949 1.49469 1.49460 1.38146 1.38160 Density, 30 g/cm-3 0.65043 0.65026 0.86839 0.86829 0.7962 0.7960 Boiling point, 760 mmHg, oC 68.8 68.74 80.1 80.1 97.25 97.29 Antoine Constants, where log P = A – [B / ( C + t )] , P = mmHg, t = oC A 6.87773 6.89745 7.99733 B 1171.53 1206.35 1569.70 C 224.366 220.237 209.5 Apparatus A modified Colburn recirculating equilibrium still Fig 1 was used to obtain the vapor-liquid equilibrium data. The modifications and the general procedure have been reported in (Colburn, A.P., 1984). The mixture is introduced into the equilibrium apparatus via the filler tube of the storage vessel, where the liquid mixture in the reservoir is heated to boiling by a housing heating mantle. The circulation caused by vapor bubbles ensures even heating and mixing, where the heating mantle ensures that the number of vapor bubbles remains constant and that the mixture is heated uniformly. The ascending vapor bubbles thoroughly mix the entire volume of liquid, thus preventing a concentration gradient from forming and the boiling liquid from over-heating. When the vapor bubbles (A) pass the funnel-shaped constriction of the Cotrell pump they carry a large quantity of non-vaporized liquid (B) to the Phase divider (phase separator). Here, the vapor-liquid mixture pours over the thermocouple protection tube. The splashguard which becomes wider higher up, prevents liquid splashes from being vaporized, which would complicate establishment of stationary equilibrium. To prevent partial condensation on the glass walls of the phase divider (phase separator) the equilibrium apparatus is equipped with an evacuated glass mantle consisting of two panes. In the phase divider the vapor phase (A) and the liquid phase (B) are separated. The liquid phase (B) drains off laterally to the sampling port at which it can be sampled through the septum of the screw cap without having to open the apparatus. Sampling via a glass syringe also prevents contamination of the sample. To condense the vapor residues present in the liquid phase (B), the outlet flows into a small vessel, on which a Liebig cooler is mounted. The vapor (A) flows through the phase divider and a lateral outlet to the Dimroth cooler where it condenses. The condensate (A) drips down in a curved tube, which also terminates at a sampling port. The liquid (B) and condensate reflux (A), each arms fitted with a siphon, flow into a common tube. This enables remixing of the two phases before they are returned to the reservoir. The tube extends into the reservoir and ends inside it with its opening facing upward. The liquid rising in the middle of the reservoir draws the returned sample out of the tube and heats it. Temperature were measured using a Copper – Constantan thermocouple and a Type K Leeds & Northrup potentiometer. A Bausch & Lomb precision refractometer was used to measure the refractive index of the vapor and liquid samples using a sodium D line light source. A Cottrell boiling point apparatus was used to check the purity of the compounds and to calibrate the equilibrium still thermocouple. The accuracy of the refractometer was tested by the test pieces supplied by Bausch & Lomb Inc. Pressure was measured to within ± 0.5 mm of mercury using a calibrated mercury manometer. Fig.1. Flow diagram for equilibrium apparatus. Procedure The procedures for determining vapor-liquid equilibrium data for the three binary systems were essentially those described below. For each of the binary hydrocarbon systems, refractive index calibration curves were obtained with samples of 12 to 15 different known concentrations at 30 oC. The compositions of vapor and liquid samples were read from the calibration curves. In the case the ternary system, three mixtures of n-hexane – benzene in the mole ratios of 25 to 75, 50 to 50, and 75 to 25 were used. 1-Propanol was added to each of the above mixtures to give equivalent mole fractions of 0.33, 0.50, 0.67, 0.75, and 0.80 in the ternary mixture. These mixtures were subjected to equilibrium distillation in the modified Colburn recirculating still and the vapor and liquid samples were obtained. The 1-propanol in these samples was extracted with water. The hydrocarbon layer was dried overnight by adding crystals of Drierite, which removed any traces of water remaining in the hydrocarbon mixture. The composition of the added agent-free samples was determined in the refractometer maintained at 30 oC. Discussion Of Results Experimental activity coefficients for the components in the binary mixture were calculated by the following equation (Prausnitz et.al., 1980). (1) The fugacity coefficient i, was calculated using the PR equation of state, which have the form (Sytryjeck et.al., 1986): (2) Where m and n are two empirical factors for each pure component, their values given in Table 2 (Sytryjeck et.al., 1986). Table 2. m and n (PR) factors equation of state compound PR – EOS m n 1-Propanol 1.1505 0.8075 Hexane 0.7939 0.4116 Benzene 0.6671 0.4723 (3) , (4) (5) (6) (7) Where (8) The vapor -liquid equilibrium data for the three binaries are reported in Tables 3 to 5 and shown graphically in Figures 2 to 7. Our results are compared to literature data (Chen, S. et.al., 2003) Table 3 Vapor-liquid equilibrium data for Hexane–Benzene system at 760 mmHg. Temp. oC Experimental Calculated xH yH H B H B 77.6 0.073 0.140 1.46 1.00 1.53 1.00 75.1 0.172 0.268 1.28 1.03 1.36 1.02 73.4 0.268 0.376 1.22 1.05 1.25 1.05 72.3 0.372 0.460 1.12 1.11 1.16 1.08 70.9 0.462 0.540 1.09 1.15 1.11 1.12 70.1 0.585 0.644 1.06 1.18 1.06 1.18 69.4 0.692 0.725 1.03 1.26 1.03 1.24 69.1 0.792 0.807 1.01 1.32 1.01 1.29 69.0 0.828 0.838 1.00 1.34 1.01 1.32 68.9 0.883 0.888 1.00 1.35 1.00 1.35 68.8 0.947 0.950 1.00 1.36 1.00 1.39 68.8 0.962 0.964 1.00 1.36 1.00 1.40 Table 4 Vapor-liquid equilibrium data for Hexane–1-propanol system at 760 mmHg. Temp. oC Experimental Calculated xH yH H 1-P H 1-P 89.6 0.024 0.256 6.04 1.03 6.17 1.00 82.3 0.060 0.490 5.46 1.01 5.25 1.01 74.6 0.144 0.662 3.67 1.01 3.74 1.05 71.9 0.236 0.728 2.81 1.02 2.73 1.13 71.2 0.262 0.716 2.53 1.15 2.52 1.16 70.7 0.370 0.760 1.97 1.20 1.90 1.34 68.4 0.476 0.786 1.67 1.39 1.53 1.55 67.7 0.620 0.800 1.33 1.85 1.32 2.01 67.0 0.752 0.836 1.18 2.41 1.09 2.63 66.4 0.784 0.856 1.18 2.49 1.06 2.82 66.2 0.904 0.916 1.10 3.30 1.01 3.71 65.8 0.954 0.952 1.10 3.85 1.00 4.17 67.2 0.975 0.97 1.05 4.32 1.00 4.40 Table 5 Vapor-liquid equilibrium data for Benzene –1-propanol system at 760 mmHg. Temp. oC Experimental Calculated xB yB B 1-P B 1-P 92.8 0.049 0.142 1.99 1.07 2.34 1.00 88.4 0.104 0.296 2.22 1.12 2.21 1.01 84.8 0.180 0.436 2.10 1.14 2.04 1.02 82.1 0.254 0.530 1.97 1.17 1.88 1.04 79.7 0.398 0.622 1.62 1.33 1.61 1.13 77.4 0.504 0.680 1.47 1.46 1.44 1.24 76.5 0.642 0.728 1.27 1.78 1.25 1.49 76.2 0.764 0.774 1.15 2.31 1.12 1.94 76.1 0.792 0.776 1.11 2.59 1.10 2.11 76.3 0.834 0.812 1.10 2.70 1.06 2.39 76.9 0.916 0.864 1.04 3.75 1.02 3.24 78.2 0.956 0.916 1.01 4.16 1.01 3.89 Fig.2. Boiling Point - Composition Curve for Hexane – Benzene at 760 mmHg. Fig.3. Activity Coefficient - Composition Curve for Hexane – Benzene at 760 mmHg. Fig.4. Boiling Point - Composition Curve for Hexane – 1- Propanol at 760 mmHg. Fig.5. Activity Coefficient - Composition Curve for Hexane – 1- Propanol at 760 mmHg. Fig.6. Boiling Point - Composition Curve for Benzene – 1- Propanol at 760 mmHg. Fig.7. Activity Coefficient - Composition Curve for Benzene – 1- Propanol at 760 mmHg. The data were correlated by the NRTL activity coefficient equations (Chen, S. et.al., 2003). (9) (10) (11) (12) The values of the constants in the correlation were evaluated by using the maximum likelihood principle method providing a mathematical and computational guarantee of global optimality in parameter estimation that provides the best fit to measured data. The objective function in nonlinear parameter estimation problems is given below (Anderson et.al., 1978; Prausnitz et.al., 1980): (13) Where the superscripts c and e indicate calculated and experimental values, respectively, the 2 are the estimated variances of the corresponding variables, and the sum is taken over all M experimental data, and N is the number of compounds in the mixtures. The standard deviation assumed were (Marc et.al., 1998; Lu et.al., 1989): P = 0.5 mmHg T = 0.1 oC x = 0.001 mole fraction y = 0.005 mole fraction A listing of optimized interaction parameters for NRTL activity coefficient model studied is shown in Table 6 for all binary systems. Table 6 Optimized interaction parameters for binary systems. System    Hexane – Benzene 466.2 269.3 0.292 Hexane – 1-Propanol 822.7 174.8 0.412 Benzene- 1-Propanol 296.9 212.6 0.405 The values of activity coefficients calculated by NRTL equations are also given in Table 3 to 5. A defined deviation between the calculated and experimented activity coefficients was evaluated by the formula (Anderson et.al., 1978): (14) k = deviation of experimental activity coefficients values from calculated values. n = number of experimental points  = defined deviation of k from a mean value of k The deviations are as follows: H – B H – 1-P B – 1-P H B H 1-P B 1-P 0.029 0.023 0.101 0.137 0.112 0.188 Maximum and minimum values of the activity coefficients were calculated to show the limits of the experimental deviations. The refractometer error for the n-hexane – benzene and benzene - 1-propanol system was within 0.001 mole fraction and for the n-hexane - 1-propanol system, 0.005 mole fraction. Pressure errors were within ± 0.5 mm of Hg and temperature errors were within ± 0.1 oC. (15) (16) The defined deviation between the experimental activity coefficients and the max and min values calculated by equation 14, in the range of x = 0.15 to x = 0.85, are as follows: H – B H – 1-P B – 1-P H B H 1-P B 1-P  max  0.022 0.006 0.034 0.048 0.009 0.013  min  0.006 0.016 0.026 0.053 0.005 0.012 The defined deviation over the full range will be larger because of the influence of the high error in the end values of ’s. It may be seen from Table 3 to 5 that the deviation between the calculated (Equation 9 to 12) and experimental values of ’s is maximum in the middle range and this deviation depends on the type of equation applied for calculation the ’s. It is not necessary that the defined deviation between calculated and experimental ’s be between  max  and  min  values as they are only deviations due to experimental errors. McDermott-Ellis test method (McDermott et.al., 1965) was applied to the activity coefficient – composition data of the binaries. According to McDermott-Ellis test method, two experimental points a and b are thermodynamically consistent if the following condition is fulfilled: D < Dmax (17) The local deviation D is given by (18) In this method, it is recommended the use of a fixed value of 0.01 for Dmax if the accuracy in the measurement of the vapor and the liquid mole fraction is within 0.001. The local maximum deviation, Dmax, due to experimental errors, is not constant, and is given by (19) Table 7 Results of Thermodynamic Consistency test. System D Dmax 1-Propanol – Hexane 0.0243 0.026 Hexane – Benzene 0.0161 0.021 1-Propanol – Benzene 0.0274 0.029 1-Propanol – Hexane – Benzene 0.0321 0.035 In accordance with the criterion of the test the data were found to be consistent. The experimental data for all the three binaries show that they are non–ideal in nature. (Tongberg et.al., 1992), studying the equilibrium of n-hexane – benzene, reported no separation obtainable at concentration above 97 mole % hexane. This is consistent with the observation made in this investigation. The n-hexane – 1-propanol and benzene – 1-propanol systems evidence minimum boiling azeotropes. It is indicated by the interpolation of the data that n-hexane – 1-propanol form an azeotrope at 95 mole % hexane at 65.8 oC, and the benzene – 1-propanol form an azeotrope at 77.5 mole % benzene at 76 oC The variation of the relative volatility with the concentration of the solvent in the ternary system is reported in Table 8 and shown in Figure 8. Fig 8 Effect of 1-propanol on relative volatility of binary system n-hexane – benzene at 760 mmHg Table 8 Variation of relative volatility with solvent concentration for ternary system n-hexane – benzene- 1-propanol at 760 mmHg Pressure Binary mixture Mole fraction 1-propanol in mixture Temperature oC Mole fraction 1-propanol free basis 0.25 0.75 0.00 0.33 0.50 0.67 0.75 0.80 74.1 27.0 74.3 78.7 82.3 84.8 0.21 0.193 0.172 0.156 0.154 1.36 0.326 0.346 0.332 0.325 0.327 0.300 0.79 0.807 0.828 0.884 0.846 0.864 0.674 0.654 0.668 0.675 0.673 0.709 1.82 2.21 2.39 2.60 2.67 2.72 0.50 0.50 0.00 0.33 0.50 0.67 0.75 0.80 71.2 67.5 70.2 75.2 80.3 83.0 0.428 0.424 0.400 0.396 0.375 0.368 0.528 0.574 0.572 0.593 0.580 0.574 0.572 0.576 0.600 0.606 0.625 0.632 0.472 0.426 0.423 0.407 0.429 0.426 1.50 1.83 2.00 2.23 2.30 2.31 0.75 0.25 0.00 0.33 0.50 0.67 0.75 0.80 69.4 66.3 68.2 72.8 78.2 80.7 0.684 0.681 0.632 0.658 0.635 0.605 0.724 0.776 0.744 0.776 0.766 0.746 0.316 0.324 0.378 0.342 0.365 0.395 0.276 0.224 0.256 0.224 0.234 0.251 1.31 1.63 1.71 1.80 1.88 1.92 x'= Solvent free basis Conclusion The data show that the greatest change of relative volatility is obtained at higher concentration of the solvent. As the vapor and liquid samples were extracted with water, it was ensured by laboratory tests that the solvent–free hydrocarbon concentration did not change because of the different solubilities of the hydrocarbons in water. Also, it was found that the drying agent, Drierite, had no selective absorption capacity for the hydrocarbon mixture involved. Nomenclature ai Combining rule coefficient aij Mixing rule coefficient Mixing rule coefficient A Cohesion parameter of cubic equation of state bi Combining rule coefficient B Covolume term (parameter) of the cubic equation of state Bi Combining rule coefficient Interaction coefficient of equation of state Interaction coefficient of equation of state m Temperature dependent correlation parameter n Temperature dependent correlation parameter nD Refractive index P Equilibrium pressure of the system, MPa Pi Vapor pressure of pure component i MPa T Temperature, K TC Critical temperature, K xi Mole fraction of component i in liquid phase yi Mole fraction of component i in vapor phase z Compressibility factor Greek Litters  Temperature dependency of the attractive term of equation of state  Relative volatility  Activity coefficient  Standard deviation  Density 2 Estimated variance  Fugacity coefficient References Anderson, T. F., D. S. Abrams, and E. A. Grens. Evaluation of parameters for Nonlinear Thermodynamic Models, AIChE J., 24, 20. 1978. Chen, S,. and Yan, C., “Vapor-Liquid Equilibrium Calculations of Azeotropic Mixtures Using the Peng-Robinson Equation of State and Various Activity coefficients models”, J. Chem. Eng. of Japan, 27, 512-516, 2003, Internet Resources, available at http://www.scej.org/ronbun/JCEJe/ e27_0512.html. Colburn, A.P, Ind. Eng. Chem., 35, 666, 1984 Lu, B. C. and M. Kato, The use of Two-Parameter Equation of State for Predicting Vapor-Liquid Equilibria, Int. Chem. Eng. Symp. , 56, 57. 1989 Marc, J. A., Martin, J. P. and Thamas, F. T., “Thermophysical Properties of Fluid, An introduction to their prediction”, Imperial College Press, first reprint, 1998. McDermott, C., Ellis, S. R. M., “A Multicomponent Consistency Test”, Chem. Eng. Sci., 20, 293, 1965. Prausnitz, J. M., C. A. Eckert, R. V. Orye, and J. P. O’Connell. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria, Prentice Hill, Englewood Cliffs, New Jersey, 1980. Sytryjeck, R. and J. H. Vera, An Improved Peng Robinson Equation of State for Pure and Mixture, J. of Chem. Eng., 64, 323, 1989. Tongberg, C.O., Johnston, F., Ind. Eng. Chem., 25, 734, 1992 تأثير المركب القطبي (1-بروبانول) على التطايرية النسبية للنظام الثنائي هكسان – بنزين د. خالد فرهود قسم الهندسة الكيمياوية الجامعة التكنولوجية الخلاصة : تم عرض بيانات إتزان بخار – سائل للأنظمة الثنائية هكسان – 1-بروبانول، بنزين – 1-بروبانول و هكسان – بنزين في ضغط 760 ملم زئبق. بالإضافة إلى ذلك تم عرض بيانات النظام الثلاثي لتراكيز مختارة بالنسبة إلى 1-بروبانول في نظام 1-بروبانول، بنزين، هكسان في ضغط 760 ملم زئبق. النتائج أشارت الى إنه التطايرية النسبية للهكسان بالنسبة الى البنزين قد إزدادت بصورة ملموسة عند إضافه 1-بروبانول. � EMBED PBrush ��� 1 PAGE 9 _1237405551.unknown _1237452542.unknown _1237469451.unknown _1237469660.unknown _1263752029.unknown _1237469538.unknown _1237469559.unknown _1237469579.unknown _1237469521.unknown _1237469324.unknown _1237469349.unknown _1237453004.unknown _1237406053.unknown _1237408494.unknown _1237405994.unknown _1058895914.unknown _1060789742.unknown _1237370783.unknown _1237404980.unknown _1060789743.unknown _1173207870 _1060688046.unknown _1060789639.unknown _1060688094.unknown _1060680737.unknown _1058446222.unknown _1058469767.unknown _1058470572.unknown _1058470696.unknown _1058465160.unknown _1055534564.unknown _1056362361.unknown _1055533940.unknown _1055534325.unknown _1055525244.unknown