Prediction of Finite Concentration Behavior from Infinite IJCPE Vol.11 No.3 (September 2010) 33 Iraqi Journal of Chemical and Petroleum Engineering Vol.11 No.3 (September 2010) 33 - 46 ISSN: 12010-4884 PREDICTION OF FINITE CONCENTRATIONBEHAVIOR FROM INFINITE DILUTION EGUILIBRIUM DATA Prof Dr. Mahmoud O. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad Chemical Engineering Department – University of Nahrin ___________________________________________________________________________________ ABSTRACT Experimental activity coefficients at infinite dilution are particularly useful for calculating the parameters needed in an expression for the excess Gibbs energy. If reliable values of γ∞1 and γ∞2 are available, either from direct experiment or from a correlation, it is possible to predict the composition of the azeotrope and vapor-liquid equilibrium over the entire range of composition. These can be used to evaluate two adjustable constants in any desired expression for G E. In this study MOSCED model and SPACE model are two different methods were used to calculate γ∞1 and γ∞2 _______________________________________________________________________________________________ INTRODUCTION Activity coefficients at infinite dilution have many uses, some of them: calculating the Vapor Liquid Equilibrium for any mixture, finding the azeotrope composition and pressure; and the estimation of mutual solubility. These calculations are carried out by finding the two adjustable parameters of any desired expression for GE (Wilson [1], NRTL [2] and UNTQUAC [3] equations. Wilson equation has two adjustable constants λ12 and λ21 (energy parameters) where they can be found from the γ∞ by solving the equations for the two component simultaneously. But NRTL or UNIQUAC equations have three parameters. For NRTL equation parameters are τ12, τ21 and α22 where α12 is related to the non randomness in the mixture, the others are considered as energy parameters. The UNIQUAC equation contains three parameters, u12 and u21 adjustable binary energy parameters and the third parameter is considered as coordination number designated as Z. All parameters for activity coefficient equations (Wilson, NRTL and UNIQUAC) for most binary mixtures are not available in the literature. Hence, another method was advocated to calculate these parameters which Iraqi Journal of Chemical and Petroleum Engineering University of Baghdad College of Engineering Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 34 serve to calculate the activity coefficient at infinite dilution γ∞. Several methods were developed for the measurement of activities coefficients at infinite dilution (γ∞). The most important methods are: gas- liquid chromatography (GLC), non-steady-state gas-liquid chromatography, differential ebulliometry, static methods and the dilutor method. The simple experimental method for rapid determination of activity coefficients at infinite dilution is based on gas-liquid chromatography. Principal aim of this work is to adopt the activities coefficients at infinite dilution for finding the parameters of different models (i.e., Wilson, NRTL, and UNIQUAC) which are not easy to find. The other aim is to evaluate the uses of the activities coefficients at infinite dilution (γ∞) and the methods that can be used and compare between them. Mosced model Mosced (modified separation of cohesive energy density) is a model proposed by Thomas and Eckert [4] for predicting limiting activity coefficients from pure component parameters only. It is essential]y an extension of regular solution theory to polar and associating systems. The extension is based on the assumption that forces contributing to the cohesive energy density are additive. Those forces included are dispersion, orientation, induction, and hydrogen bonding. The five parameters associated with these forces are the dispersion parameters. A list of the parameters for 15 substances at 20 0C is given in [5]. In a binary mixture, the activity coefficient for component 2 at infinite dilution is calculated from: 12 1 )2121 1 2 21 2 2 2 12 21 2 2 )(()( )(ln d qq RT V                    (1) aaaa V V V V d                   1 2 1 2 12 1ln (2) 4.0 293 293        T T  8.0 293 293 ;        T T  8.0 293 293 ;        T T  (3) TTPOL  011.0 (4)       25.1023.0exp4.24.3168.0 tooPOL   (5) Where POL=q4 [1.15 -1.15 exp (-0.020 τ 3 T)] + 1 (6) And where τ = 293/T (T in Kelvin). Subscript 0 refers to 20°C (293 K), and subscript T refers to system temperature aa = 0.953 — (0.00968)( τ2 2 + α2 β2) (7) where τ, α2 and β are at system temperature T. Space model A predictive method for estimating γ ∞ is provided by the solvatochromic correlation of Bush and Eckert (2000) [6] through the SPACE equation. SPACE stands for Solvatochromic Parameters for Activity Coefficient Estimation. The SPACE formulation for solvent 1 is:        effeffeff RT V 2121 2 21 2 21 2 2ln    936.0 1 2 936.0 1 2 1ln                   V V V V (8) The dispersion terms are calculated as functions of the molar refractivity index (nD): Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 35            2 1 2 2 D D n n k (9) Where constant k is 15.418 for aliphatic compounds, 15.314 for aromatics, and 17.478 for halogen compounds [6]. R is 1.987,1 is in Kelvin, and V is in cm/mol. The polarity and hydrogen-bond parameters for the solvent are ; 1 * 11 1 V BA KT     ; 1 111 1 V DC KT     1 111 1 V FE KT     (10) Parameters 2eff , 2eff, and β2eff are for the solute. Subscript eff means they are normalized such that limiting activity coefficients for a solute in itself must be unity. Calculation of these quantities requires both solvent and solute parameters for the solute.   33.1 * 2 * 1 2222 KTkT oo eff     (11)   20.1 21 2222 KTkT oo eff     (12)   95.0 21 2222 KTkT oo eff     (13) ;; 2 * 22 2 V BA where H     ; 2 222 2 V DC H     2 222 2 V FE H     (14) ; 2 * 21 2 V BA and KT o     ; 2 121 2 V DC KT o     2 121 2 V FE KT o     (15) Parameters are given in [6] for 15 components. Superscription 0 means that properties for the solute in its solvent - like state Calculation of Activity coefficients at Infinite dilution The calculation that carried out by using MOSCED and SPACE models is shown in Table 1 noting that the experimental data are extracted from literatures. The overall average deviation results show that SPACE model equation gives better results than Mosced model equation. Space is similar to MOSCED, but reduces the three adjustable parameters of each component to 0 and adds 7 adjustable parameters per functionality of compound. Thus, for a database containing 100 different solvents, MOSCED will have 300 parameters (i.e, equivalent to 3 parameters for each solvent) while, SPACE has about 100 parameters. The main advantage of SPACE over MOSCED is the prediction of activities coefficients of compounds that were not in the original database provided they have the same functionality as others in the database as well as the required solvent and solute parameters. The SPACE method is probably the best universal available method for estimating activities coefficients at infinite dilution. Calculation of the Uses of Activity Coefficient at in finite Dilution Steps of Calculation for Azeotropic Composition and Pressure: a. Determining the parameters of the activity Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 36 coefficient equations (Wilson, NRTL, and UNIQUAC) from experimental γ∞. b. Calculating of the vapor pressure of pure component at specified temperature using Wagner equation ―see Appendix A‖. c. At Azeotrope the relation volatility (12) is one, hence according to modified Rault's law 2 1 1 2    sat sat P P (16) d. Substitution of ln( γ1/ γ2 )with the activity coefficient model used. e. Solving the composition (x1 and x2) by trial and error. f. Calculation of activity coefficient at the azeotropic composition. g. Calculation of azeotropic pressure by the following equation sat i az i az PP  (17) Table 1 Experimental and Calculated γ ∞ 1 and γ ∞ 2 by using MOSCED and SPACE modes System T o C Experimental data By MOSCED model By SPACE model γ ∞ 1 γ ∞ 2 γ ∞ 1 γ ∞ 2 γ ∞ 1 γ ∞ 2 Acetone— Acetonitrile 45 1.05 1.04 1.105 1.1 0.9954 1.0061 Acetone—Benzene 45 1.65 1.52 1.48061 1.3809 1.4475 1.5476 Acetone —Carbon tetrachioride 45 3.00 2.15 2.64655 2.0804 2.5052 2.1490 Acetone—Methyl acetate 50 1.32 1.18 1.0417 1.0376 1.044 1.0472 Acetone —nitro methane 50 0.94 0.96 1.0377 1.0362 1.0499 0.7709 Acetonitrile — Benzene 100 3.20 3.00 2.3056 2.0093 2.9103 2.3198 Acetonitrile — nitro methane 40 0.96 1.00 0.9839 0.9838 0.9173 0.9691 Benzene—n-heptane 30 1.35 1.82 1.55136 1.95156 1.3591 1.8565 Carbon tetrachioride - Acetonitrile 60 5.66 9.30 5.2169 7.0278 4.4317 8.816 Chloroform—Methanol 50 2.00 9.40 3.23174 5.34556 2.1859 7.7311 Ethanol—Benzene 45 10.6 4.45 13.9057 4.6284 12.9898 5.1616 n-Hexane—Benzene 69 1.68 1.49 1.73638 1.4944 1.6637 1.3251 n-Hexane—Methylcyclopentane 69 1.17 1.03 1.01697 1.01402 1.0795 1.0668 Met hylcyclopenane—Benzene 72 1.47 1.34 1.5328 1.44367 1.2499 1.161 Nitroethane—Benzene 25 2.78 1.91 2.20598 1.72945 2.2299 1.8874 Nitromethane — Benzene 25 3.20 3.72 4.00663 3.064 3.5746 3.2465 Nitro methane — Benzene 45 3.20 3.40 3.42507 2.67778 3.2797 2.9901 2-Nitropropane - carbon tetrachioride 25 3.24 1.92 4.73716 2.54479 4.7714 2.1122 Over all average absolute deviation 0.5794 0.5799 0.4526 0.3042 Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 37 Table 2 Calculated and experimental azeotrope composition and pressure using Wilson equation of one and two parameters models (γ ∞ 1 and γ ∞ 2) System T o C 12 X1 wt% at azeotrop e exp. X1 wt% at azeotrope cal. with one parameter. X1 wt% at azeotrope exp. cal. with two parameters P az Exp. (bar) P az cal. with one parameter. (bar) P az cal. with two parameters (bar) Acetone – Carbon tetrachloride 45 0.47 91 92.62 83.0338 0.6842 1 0.7045251 0.68578 Acetone – Chloroform 50 0.3 22.9 23.6269 19.2754 0.6066 2 0.6117064 0.59379 Acetonitrile - Benzene 45 0.47 30.7 30.2309 31.9997 0.3706 4 0.3752523 0.38272 Carbontetrachlorid e - Acetonitrile 45 0.47 84.5 82.1122 84.1988 0.4948 9 0.4544587 0.49205 Chloroform - Methanol 50 0.47 87.8 87.9172 90.8768 0.8359 8 0.7432916 0.83946 Methyl cyclopentane - Benzene 72 0.47 91 84.9816 93.8899 0.6986 1 1.026725 1.01761 Nitromethane - Benzene 25 0.47 6.4 4.44970 6.326 0.1302 6 0.1273378 0.12777 System T o C 12 X1 wt% at azeotrop e exp. X1 wt% at azeotrope cal. with one parameter X1 wt% at azeotrope exp. cal. with two parameters P az Exp. (bar) P az cal. with one parameter. (bar) P az cal. with two parameters (bar) Nitromethane - Benzene 45 0.47 9.6 6.89904 9.8254 0.3039 8 0.3011422 0.30282 Nitromethane - Carbontetrachlorid e 45 0.4 10.6 8.44299 9.7866 0.4039 7 0.3863205 0.39316 n-Hexane - Benzene 69 0.47 99.8 87.4161 95.1542 0.7666 0 1.030297 1.02179 %Over All Average Absolute Deviation 3.053157 2.4917 0.077836 0.062145 Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 38 While, when we apply similar calculation procedure but with NRTL equation the following results are obtained Table 3. Table 3 Calculated and Experimental Azeotrope Composition and Pressure Using NRTL Equation of One and Two Parameters γ ∞ 1 and γ ∞ 2 System T o C 12 X1 wt% at Azeo. Exp. X1 wt % at Azeo. Cal. with One Parameter X1 wt % at Azeo. Cal. with Two Parameters PExp. (bar) P az Cal. with One Paramete r (bar) P az Cal. with Two Parameters (bar) Acetone - Carbon tetrachloride 45 0.47 91 88.258 7 90.8 107 0.68421 0.70284 0.684 72 Acetone - Chloroform 50 0.3 22.9 26.7476 25.7412 0.60662 0.59908 0.59934 Acetonitrile - Benzene 45 0.47 30.7 17.5476 30.0615 0.37064 0.32809 0.35051 Carbonleirachiori de - Acetonitrile 45 0.47 84.5 80.4428 84.3994 0.49489 0.43264 0.49401 Chloroform - Methanol 50 0.47 87.8 91.365 7 90.3624 0.83598 0.69886 0.86534 Methyl cyclopentane - Benzene 72 0.47 91 91.7786 93.7580 0.69861 1.00296 1.00203 Nitromethane - Benzene 25 0.47 6.4 8.1236 6.7034 0.13026 0.12 795 0.12 773 Nitromethane - Benzene 45 0.47 9.6 12.5 794 9.5541 0.30398 0.30424 0.30265 Nitromethane - Carbontetrachlori de 45 0.4 10.6 13.8429 10.7995 0.4039 7 0.41330 0.40086 n-hexane - Benzene 69 0.47 99.8 99.9238 99.9208 0.76660 1.01256 1.01257 %Over all Absolute Average deviation 2.4917 0.97596 0.08303 0.061452 When UNIQAC model is applied the results will change to: Table 4 Calculated and Experimental Azeotrope Composition and Pressure Using UNIQUAC Equation of One and Two Parameters γ ∞ 1 and γ ∞ 2 System T o C 12 X1 wt% at Azeo. Exp. X1 wt % at Azeo. Cal. with One Parameter X1 wt % at Azeo. Cal. with Two Parameters PExp. (bar) P az Cal. with One Parameter (bar) P az Cal. with Two Parameters (bar) Acetone - Carbon tetrachloride 45 0.8 91 90.55 75 90.8730 0.6842] 0.6842 7 0.68408 Acetone - chloroform 50 3.9 22.9 24.2491 22.9058 0.60662 0.6871 0.59263 Acetonitrile - Benzene 45 0.65 30.7 30.7088 30.7092 0.3 7064 0.15446 0.38309 Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 39 Carbontetrachioride - Acetonitrile 45 1.4 84.5 84.4917 84.5021 0.49489 0.01852 0.505 12 Chloroform - Methanol 50 0.01 87.8 8 7.8072 89.8536 0.83598 0.88632 0.85041 Methyl cyclopentane - Benzene 72 0.01 91 89.2809 93.8282 0.69861 1.00765 1.00202 Nitromethane - Benzene 25 6 6.4 3.3 7393 6.3678 0.13026 0.12 714 0.13016 Nitromethane - Benzene 45 3.5 9.6 5.28095 9.5828 0.30398 0.30020 0.30789 Nitromethane - carbontetrachloride 45 2.5 10.6 6.60830 10.7628 0.4039 7 0.3 7879 0.40511 n-hexane - Benzene 69 0.36 99.8 99.6282 99.8332 0.76660 1.01256 1.01255 %Over all Absolute Average deviation 1.50436 0.52713 0.133212 0.06057 Vapor Liquid Equilibrium Calculation The Vapor Liquid Equilibrium (VLE) data can be calculated from the activities coefficients at infinite dilution (γ∞1, γ∞2) for any binary system. The equations of Vapor Liquid Equilibrium are calculated using suitable equation of state (EOS). Peng Robinson equation of state [7] is selected to calculate VLE since it is the more reliable equation for the calculation. The VLE data for 13 systems has been calculated by using Wilson, NRTL and UNIQUAC equations for one parameter and two parameters. Experimental Data From the experimental data can be determined the accuracy of any calculation and this can be done by calculating the deviation between the experimental data and the calculated results. The experimental data for Vapor Liquid Equilibrium obtained from literature for 13 systems are shown in Table 5: Table 5 Vapor liquid equilibrium Systems data System P(mmHg) or T in ( O C) No. of data points Reference 1 Benzene (1) - Acetonitrile (2) T= 70 21 8 2 Methanol (1) - Water (2) P= 760 26 9 3 Acetone(1)-Carbon tetrachloride (2) P =450 24 10 4 Hexane (1) - Benzene (2) P=735 11 11 5 Acetone (1) - Benzene (2) P= 738 10 12 6 Acetone (1) - Water (2) P=760 13 13 7 Methelcyclopentane (1) - Benzene (2) P= 760 15 14 8 Benzene (1) - Heptane (2) P= 760 18 15 9 Acetone (1) - Benzene (2) T=45 11 16 10 Acetone (1) - Acetonitrile (2) T=45 10 17 11 Acetonitrile (1) - Nitro methane (2) T=60 10 18 12 Nitro methane (1) - Carbon tetrachloride (2) T==45 12 19 13 Carbon tetrachloride (1) - Acetonitri/e(2) T=45 13 20 Steps of Calculation of VLE Data 1. Calculating the parameters of the activity coefficient equations (Wilson, NRTL and UNIQUAC) from experimental γ∞. 2. For each point of the VLE data (x1) the following steps were taken a.Finding the pure-component saturated vapor pressure Psat1, Psat2 at temperature of that point using Wagner equation appendix ―A‖. Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 40 b.Calculating the constants of the e~} nation at that temperature corresponding to that point c.Calculating the activity coefficients (γ∞1, γ∞2) at that point from the employed equation (Wilson, NRTL or UNIQUAC) d.Calculating VLi from Rackett eqtiation which has the form: 2857.0 )1( Tr CC sat i ZVV   (18) e.Solving the following equation where ɸ i sat and ɸi V must be calculated using Peng — Robinson equation of state.            RT PPV PVxPy sat i L isat i sat iii V ii )( exp (19) f. Calculating y1 from the following equation                     RT PPV P Px y sat i L i V i sat i sat iii i exp   (20) These steps are repeated for each point of VLE data (for each x1) by preparing suitable computer program. Steps of Investigation for VLE Calculation The steps of investigation were carried out on 13 different systems some of them are Isothermal and the others are Isobaric by the three models of Wilson, NRTL, and UNIQUAC models and the following results are obtained: Table 6 Average absolute deviation for VLE calculation when Wilson, NRTL, and UNIQUAC models are applied for the following systems: System P(mmHg) or T ( O C) No.of data points Wilson NRTL UNIQUAC Parameters One Two Parameters One Two Parameters One Two Benzene (1) - Acetonitrile (2) Isothermal T=70 21 0.019294 0.019044 0.02 7988 0.017167 0.016661 0.0161 63 Methanol (1) - Water (2) Isobaric P=760 26 0.032758 0.02 1413 0.024775 0.020513 0.019821 0.015083 Acetone(1) - Carbon tetrachioride (2) Isobaric P=450 24 0.007259 0.003249 0.038627 0.020761 0.003735 0.002005 Hexane (1) - Benzene (2) Isobaric P=735 11 0.0233 79 0.00672 7 0.018 786 0.00 7361 0.053490 0.006812 Acetone (1) - Benzene (2) Isobaric P=738 10 0.018799 0.008494 0.011519 0.020163 0.008019 0.7854 Acetone (1) - Water (2) Isobaric P=760 13 0.012 764 0.010586 0.020921 0.012743 0.011605 0.7809 Methelcyclopentane (1) - Benzene (2) Isobaric P=760 15 0.004823 0.003538 0.011235 0.006554 0.003601 0.004110 Benzene (1) - Heptane (2) Isobaric P=760 18 0.098944 0.004573 0.014158 0.006411 0.005809 0.004804 Acetone (1) - Benzene (2) Isothermal T=45 11 0.004832 0.003964 0.031053 0.007277 0.004547 0.003527 Acetone (1) - Acetonitrile (2) Isothermal T=45 10 0.00 7607 0.007518 0.00 7776 0.00 7738 0.007467 0.00 7153 Acetonitrile (1) - Nitro methane (2) Isothermal T=60 10 0.025060 0.003938 0.007455 0.005826 0.004469 0.003910 Nitromethane (1) - Carbon tetrachloride (2) Isothermal T=45 12 0.009516 0.007698 0.034571 0.006849 0.012256 0.005957 Carbon tetrachloride(1) – Acetonitrile (2) Isothermal T=45 13 0.042118 0.005674 0.018375 0.0183 75 0.019538 0.017218 %Over all Average Absolute Deviation 194 0.023627 0.008186 0.022892 0.012134 0.013155 0.007877 Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 41 Also; the results of application of Wilson, NRTL, and UNIQUAC relations can be represented on a graph for range of composition for a selected systems which are taken as a sample of calculation for one and two parameters as follows: Fig. 2 VLE for Acetone-Carbon tetrachloride at P=450mmHg by using different models of two parameter Fig. 1 VLE for Acetone-Carbon tetrachloride at P=450mmHg by using different models of one parameter Fig. 4 VLE for Benzene – Acetonitrile at T=70oC by using different models of Two parameter Fig. 3 VLE for Benzene – Acetonitrile at T=70oC by using different models of one parameter Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 42 Fig. 5 VLE for Acetone-Carbon tetrachloride at P=450mmHg by using Wilson models of one and two parameters Fig. 6 VLE for Acetone-Carbon tetrachloride at P=450mmHg by using NRTL models of one and two parameters Discussion The principle aim in this work is to show if it is possible to use the activities coefficients at infinite dilution to find the parameters of different models. It was suggested two modem methods for calculating the activities coefficients at infinite dilution (γ∞), MOSCED method (modified separation of cohesive energy density) and SPACE method (Solvatochromic Parameters for Activity Coefficient Estimation). The two equations are applied to 18 systems and SPACE model gives better results than MOSCED equation. This work presents the evaluation of the uses of activities coefficients at infinite dilution, γ∞, to calculate the parameters of different equations: Wilson, NRTL and UNIQUAC. One of the uses is azeotropic calculation where it is applied for Fig. 7 VLE for Acetone-Carbon tetrachloride at P=450mmHg by using UNIQUAC models of one and two parameters Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 43 10 different binary systems from the experimental γ∞ and the results when compared with the experimental data for azeotrope at the same temperature show as nearly as good if using the actual parameters of the equations. The other use is the calculation of Vapor Liquid Equilibrium data where it applied for 13 different binary systems (194 data points) from the experimental γ ∞ and the results also show as high accuracy as if using the actual parameters of the equations. From these calculations IJNIQUAC model gives the highest accuracy than the other models (Wilson, NRTL). In the system that only one γ ∞ is available one parameter equation is used for Wilson, NRTL and UNIQUAC equation which it gives result closer accuracy to the two parameters equation. For more details and comparison for all systems which are investigated in this work you can see appendix ―B‖ The results which appeared in the previous Tables with their absolute deviations show 1. The most important two methods for calculating the activities coefficients at infinite dilution are SPACE method and MOSCED method. And it was found that SPACE method is better than MOSCED where SPACE gives Average Absolute Deviation 0.4526, 0.3042 for γ ∞ 1 and γ ∞ 2 respectively and MOSCED equation give Average Absolute Deviation equal to 0.5794, 0.5 799 for ‗y‘ respectively. 2. One of the uses of activities coefficients at infinite dilution is the calculation of azeotropic properties (azeotropic composition and pressure). The equations used are Wilson, NRTL and UNIQUAC where UNIQUAC equation gives better results than NRTL and Wilson equations. 3. The other uses of activities coefficients at infinite dilution is the calculation of VLE and the same equation are used (Wilson, NRTL and UNIQUAC).UNIQUAC equation also gives the best results than the others. 4. In the system that has only one γ ∞ available, the use of one parameter equation gives result with accuracy near to the two parameters equation which is accepted. Conclusions 1. SPACE and MOSCED are good estimated methods to predict or calculate values of parameters which serve the calculation of activity coefficients at infinite dilution (γ ∞ ). 2. Wilson equation of two parameters is the easier method to calculate activity coefficients at infinite dilution (γ ∞ ) since it contain only two parameters. While, NRTL and UNIQUAC models contains three adjustable parameters which make the program which designed to calculate the parameters more difficult. 3. When the obtained parameters applied to calculate activity coefficients at infinite dilution (γ ∞ ) and then calculate vapor liquid equilibrium, azeotropic composition and pressure good agreement with the experimental data are obtained for all applications. 4. When Wilson model is applied; the affect of increasing adjustable parameters from one to two parameters will be appeared in azeotropic composition calculation; while it would not had a great affect in the calculation of azeotropic pressure. The same thing is happened when NRTL and UNIQUAC equations are applied for the calculation. 5. The comparison between the Wilson, NRTL, UNIQUAC equations for azeotropic composition and pressure calculation; UNIQUAC equation gives best results Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 44 comparing with the experimental data than NRTL and Wilson equation which gives the less accurate results. 6. Wilson, NRTL, and UNIQUAC models are applied to calculate VLE for thirteen different binary mixtures with 194 data points at different temperatures gives very good accuracies for one parameter and excellent results for two parameters i.e. increasing the number of parameters will increase the accuracy. 7. Also, like the calculation of azeotropic composition and pressure the two parameters model gives better results compared with the one parameter models for Wilson, NRTL, and UNIQUAC equations with slightly different accuracies. UNIQUAC, NRTL, and Wilson models give reasonable accuracy comparing with the experimental data for one and two parameters when VLE calculation is adopted. 8. The calculated results show that prediction of VLE from activity coefficients at infinite dilution (γ ∞ ) when SPACE and MOSCED models adopted are excellent. 9. For azeotropic calculation of composition and pressure a very good results are obtained for two parameters models especially for UNIQUAC model. While; reasonable results are obtained for one parameter model. Also, UNIQUAC gives more accurate results when compared with Wilson and NRTL equations. References 1. G. M. Wilson, J. Am. Chem. Soc.: 8~, 127 (1964). 2. .H. Renon and J. M. Prausintz, Aich J.:14,135(1968). 3. J. M Smith, H. C. van Ness ―Introduction to Chemical Engineering Thermodynamics‖ 5 th edition (1996). 4. Thomas, B. R., and C. A. Eckert: md. Eng. Chem. Process Des. Dev. 23:194 (1984). 5. Bruce B. Poling, Prausenitz J. M., 0‘connell J. P.: The Properties of Gases and Liquids‖ (1987). 6. Bruce B. Poling, Prausenitz J. M., 0‘connell J. P.: The Properties of Gases and Liquids‖ (2001). 7. D. Y. Peng and D. B. Robinson, md. Eng. Chem. Fundam.: 15, 59 (1976). 8. Jean — Plerre Monfort, J. Chem. Eng. Data, Vol. 28, No. 1, 24-27 (1983). 9. PER DALAGER, J. Chem. Eng. Data, Vol. 14 No.3, 298-30 1 (1969). 10. Bachman K. C., Simons E. L.: md. Eng. Chem. 44, 202 (1952). 11. Tonberg G. 0., Johnston F.: md. Eng. Chem. 25, 733 (1933). 12. Tailmadge J. A., Canuar L. N.: md. Eng. Chem. 46, 1279 (1954). 13. York R., Holmes R. C.: md. Eng. Chem. 34, 345 (1942). 14. Griswold J., Ludwig E. E.: md. Eng. Chem., 35, 117 (1943). 15. Brzostowski W.: Bull. Acad. Polon. Sci. Ser. Chim. 8, 291 (1960). 16. Brown I., Smith F.: Austr. J. Chem. 10, 423 (1957). 17. Brown I., Smith F.: Austr. J. Chem. 13, 30 (1960). 18. Brown I., Smith F.: Austr. J. Chem. 8, 62 (1955). 19. Brown I., Smith F.: Austr. J. Chem. 8, 501 (1955). 20. Brown I., Smith F.: Austr. J. Chem. 7, 264 (1954). Appendix “A” Wagner equation to calculate pure component vapor pressure Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 45 Equation ―1‖ ln (P/Pc) = (1-x) -1 [Ax + B x 1.5 + Cx 3 + Dx 6 ] where x=1-(T/ Tc) (A-1) Equation ―2‖ lnP=A- (B/T) ± Cln(T) +DP/T 2 (A-2) Component A B C D Eq. no. Acetone -7.45514 1.2)2 -2.43926 -3.3559 1 Acetonii~rile 40.774 5392.43 -4.357 2615 2 Benzene -6.98273 1.33213 -2.62863 -3.33399 1 Carbon tetrachioride -7.07139 1.71497 -2.8993 -2.49466 1 Chloroform -6.95546 1.16225 -2.1397 -3.44421 1 Water -7.76451 1.45838 -2.7758 -1.23303 1 Methanol -8.54796 0.76982 -3.10850 1.54481 1 Methylcyclopentane -7.15937 1.48017 -2.92482 -1.98377 1 n-Heptane -7.67468 l.37068 -3.53620 -3.20243 1 n-Hexane -7.46765 1.44211 -3.28222 -2.50941 1 Nitromethane -8.41688 2.76466 -3.65341 -1.01376 Nomenclature P pressure T temperature V volume Z Compressibility factor x Mole fraction in the liquid phase y Mole fraction in the gas or vapor phase R gas constant EOS Equation of state nD Refractive index C, D, E, and F Equation constants G Gibbs free energy R Gas constant f Fugacity u UNIQUAC parameter x Mole fraction in liquid phase y Mole fraction in vapor or gas phase Latinic symbols γ Activity coefficient ɸ Fugacity coefficient  NRTL parameter β Proportionality factor λ Wilson parameter calculated from energy parameter ξ Parameter calculated by an equation π Parameter in SPACE MODEL Subscript 0 System at 1 atmosphere and 20 o C 1 Component one in the system 2 Component two in the system C critical i Component ―i‖ r Reduced condition T System temperature Superscript ∞ Infinite dilution sat Saturation ˄ Physical property of component in the solution or mixture V Vapor phase L Liquid phase az Azeotropic condition Prof Dr. Mahmoud 0. Abdullahil; Dr. Venus M Hameed*; Basma M. Haddad IJCPE Vol.11 No.3 (September 2010) 46 E Excess KT Solvent state H Solute state التنبؤ بتصرف المواد عنذ تراكيز محذدة في التخفيف الالنهائي لمعلوماث التعادل الفيزيائي بسمت موفق حذاد . م.م, فينوس مجيذ حميذ. د.م, محمود عمر عبذ اهلل. د.أ :الخالصت  نحساب انمعامم انضشوسَة نمححىي انطاقة انفائض انحش نگثس " انمخحثشٌ عىذ انحخفُف انالوهائٍ مهم وضشوسٌ جذا E G . ارا كان نذَىا قُم مىثىقة نكم مه  21 , ًسىاء كاوث هزي انقُم محسىتة مه انحجاسب او مه انعالقات جؤدٌ ان انضغط وانىسة نكم مه انسائم و انثخاس كزنك جمكىىا مه حساب كمُات انحىاصن نكم azeotropeامكاوُة اسحىحاج عىذ وقطة انـ هزا َفحح انمجال نحساب . مه انسائم و انثخاس عىذ ظشوف انحشغُم E G. و MOSCEDأخحُش مىدَم كم مه . (Wilson, NRTL, UNIQUAC)قذ طثقث فٍ هزا انثحث نحساب ثىاتث كم مه SPACE نحساب كم مه  21 ,