EXCESS THERMODYNAMIC FUNCTIONS OF METHYL ACETATE-METHANOL AND METHYL ACETATE-ETHANOL SYSTEMS*
ISAMU NAGATA, TATSUHIKO OHTA AND TAKESHI TAKAHASHI** Department of Chemical Engineering, KanazawaUniversity, Kanazawa, Japan
Isothermal vapor-liquid equilibrium data are presented for methyl acetate-methanol system at 35° and 45°C and for methyl acetate-ethanol system at 45° and 55°C. Excess enthalpy data for the two systems are obtained at 45°C. Simultaneous fit of these thermodynamic quantities was successfully accomplished by using the NRTL equa- tion whose parameters were assumed to be a linear function of temperature.
Table 1 Physical properties of compounds Introduction Compound Bp[-C] Density at Refractive The work presented here forms part of a programme 25-C index at 25-C to determine excess Gibbs functions and excess nD Methyl acetate 56.8 0.9273 1.3588 enthalpies for mixtures of alcohols with esters. 56.9 (ll) 0.9279 (ll) 1.3587 (5) Methanol 64.7 0.7865 1.3265 Experimental 64.65(1) 0.78653(ll) 1.32663(12) Ethano1 78.3 0.7852 1.3591 Material. Methanol was distilled twice in a 78.3 (ll) 0.7851 (ll) 1.35929(ll) glass column packed with McMahon packings. s Ethanol was refluxed over calcium oxide and then fractionated in the same column. Methyl acetate mined by density or refractive index measurements. was refluxed with acetic anhydride for six hours and Densities of methyl acetate-ethanol mixture were then distilled through a packed column. The distil- obtained by using Sprengel-Ostwald phycnometers late was shaken with anhydrous potassium carbonate (capacity ca. 10 cm3) fitted with capillary arms of and redistilled. The physical properties of purified internal diameter 1 mm. The temperature of a materials are compared with the literature values water thermostat was controlled at 25° i 0.1°C. in Table 1. The pycnometers were calibrated using distilled water. Procedure. Isothermal vapor-liquid equilibrium Weighingwas done on a Shimadzubalance within data was obtained using a Jones still4). The boiling i 0.0001 g of observed value. The vapor and liquid temperature was maintained within +0.05°C of samples of methyl acetate-methanol were analyzed designated temperature and measured with a copper- by refractive index measurements at 25° ^ 0.1°C. constantan resistance thermometer, which was cali- A Shimadzu Pulfrich refractometer was used for this brated against a standard mercury thermometercali- purpose. The tolerance of the measurements was brated by the National Research Laboratory ofMetrol- less than ± 0.0001. ogy5 Tokyo. The equilibrium pressure was measured Calorimetry. A calorimeter consists of a glass using a mercury manometer. The height of the mixing cell with two compartments in its upper half mercury level was read off by a cathetometer with and a side arm. The two liquids to be mixed are an accuracy of i 0-1 mm.The atmospheric pressure confined separately, and in the complete absence of and room temperature were recorded for each ex- vapor spaces in the compartments since mercury perimental run and necessary corrections were added filled the rest of the cell and the arm. The cell was to observed reading of pressure4}. In all cases mounted in a sealed plastic cylinder immersed in a measurements were taken only after the boiling tem- water thermostat with inner and outer baths controlled perature had remained constant for at least one hr. separately. Mixing was brought about by inverting The composition of equilibrium mixtures was deter- the cylinder. The temperature of the cell was kept ＊ Received on March3，1972 within ^ 0.005°C of specified temperature. The ＊＊ Department ofNuclear Englneerlng，Nagoya Uni－ temperature change was detected from graphical VerSlty，Nagoya extrapolation of resistance values obtained from a
VOL. 5 NO. 3 1972 :i3: 227 Table 2 Vapor-liquid equilibrium data for the binary systems
X , 2/i P [m m H g ] A 7 i g E Zh /* Z/P * * [% ] [c a l/m o l] M e t h y l A c e t a t e ( l ) - M e t h a n o l ( 2 ) a t 3 5 - C 0 .0 1 1 0 . 0 5 4 2 1 8 . 4 3 .2 6 2 1 .0 0 0 0 .9 8 1 0 .9 8 1 7 .8 7 - 0 . 0 0 2 1. 2 1 0. 0 2 4 0 . 1 0 3 2 2 9 .6 2 . 9 9 5 1 . 0 0 9 0 . 9 8 0 0 . 9 8 0 2 1 .4 3 - 0 . 0 0 9 1. 2 7 0 . 0 5 0 0 . 1 8 1 2 4 8 . 9 2 .7 3 4 1 .0 2 4 0 .9 7 8 0 .9 7 8 4 4 . 6 7 - 0 . 0 1 8 1. 2 6 0 . 2 0 8 0 . 43 1 3 1 0. 6 1 . 9 4 3 1 . 0 5 9 0 . 9 7 4 0 . 9 7 3 1 1 2 .3 2 - 0 . 0 1 2 - 0 . 9 4 0 .3 2 2 0 . 5 2 2 3 3 4 .3 1 . 6 3 3 1 . 1 1 6 0 . 9 7 2 0 . 9 7 1 14 2 .14 0 . 00 1 - 0 . 7 9 0 . 3 8 9 0 . 5 5 0 3 4 4 .6 1. 4 6 7 1. 2 0 0 0 .9 7 1 0 .9 7 0 1 59 . 5 3 - 0 . 0 0 7 - 0 . 4 5 0 . 4 52 0 . 5 8 5 3 5 2. 8 1. 3 7 4 1. 2 6 2 0 .9 7 0 0 .9 6 9 16 6 . 0 7 - 0 . 0 0 1 0 . 00 0 .5 2 5 0 . 61 9 35 9 . 0 1. 2 7 3 1 .3 6 0 0 .9 7 0 0 .9 6 8 1 6 6. 9 1 0 . 0 0 0 0 . l l 0. 6 5 1 0 .6 8 2 3 6 5 . 8 . 1 5 2 1 . 5 7 3 0 . 9 7 0 0 . 9 6 8 1 5 3 . 04 0 . 00 3 0. 3 7 0 .7 2 2 0 .7 1 7 36 5 . 2 1 . 0 9 0 1 . 7 5 4 0 . 9 7 0 0 . 9 6 8 1 3 3. 7 6 0 . 0 0 0 0. 01 0 .7 8 0 0. 7 5 2 3 6 3 . 0 1. 0 5 2 1 .9 3 1 0 .9 7 0 0 .9 6 8 1 1 2 . 88 - 0 . 0 0 2 - 0 . 2 8 0. 8 6 1 0 .8 2 3 35 8 . 9 1 . 0 3 2 2 . 1 5 7 0 . 9 7 0 0 . 9 6 8 8 1. 9 0 0 .0 0 5 0 .0 4 0 .9 0 5 0 . 8 6 0 3 5 3. 0 1 . 0 0 9 2 . 4 5 6 0 . 9 7 1 0 . 9 6 8 5 7 . 46 - 0 . 0 0 2 - 0 . l l 0 . 9 3 3 0 . 8 9 3 3 4 4 .7 0 . 9 9 4 2 . 6 0 1 0 . 9 7 1 0 . 9 6 9 3 5 .5 1 - 0 . 0 0 2 - 1. 1 8 M e t h y l A c e t a t e ( l ) - M e t h a n o l ( 2 ) a t 4 5 - C 0 . 02 1 0 . 0 9 6 3 6 0 . 7 3 . 3 5 9 0 . 9 9 4 0 . 9 7 3 0 . 9 7 3 1 2 .5 3 0 . 0 0 7 2 . 00 0 . 0 4 9 0 . 1 7 1 3 8 5. 6 2 . 7 3 6 1 . 0 0 1 0 . 9 7 1 0 . 9 7 1 3 2 .0 4 - 0 . 0 0 7 0 . 87 0 . 0 8 9 0 . 2 45 4 1 6 . 8 2 .3 2 8 1 .0 2 7 0 .9 6 9 0 .9 6 9 6 2 . 61 - 0 . 0 2 2 0 .3 8 0 . 1 6 7 0 . 3 5 9 4 5 9 . 0 1 . 9 9 6 1 . 0 4 6 0 . 9 6 6 0 . 9 6 6 9 6 . 6 2 - 0 . 0 1 8 - 0 . 3 1 0 . 2 3 5 0 . 4 33 4 8 8 . 8 . 8 1 7 1 . 0 7 0 0 . 9 6 4 0 . 9 6 3 12 1.5 7 - 0 . 0 0 6 0 . 40 0 . 3 4 5 0 . 5 1 0 5 1 7 . 4 1 . 5 4 0 1 . 1 4 1 0 . 9 6 2 0 . 9 6 1 14 8 . 6 7 0 . 0 0 0 0 .4 9 0 . 41 7 0 . 5 4 8 5 3 0. 7 1. 4 0 3 1 .2 1 1 0 .9 6 1 0 .9 6 0 15 9 . 8 4 0 . 0 0 0 0 .6 8 0 .4 9 1 0 . 5 89 5 4 0. 7 1 . 3 0 4 1 . 2 8 4 0 . 9 6 1 0 . 9 5 9 16 2 .7 8 0 . 0 05 0 .8 2 0 . 5 6 9 0 . 6 23 5 4 8. 7 .2 0 7 1 .4 10 0 .9 6 0 0 .9 5 8 16 1. 3 7 0 . 00 1 1. 0 9 0 . 65 5 0 . 6 6 6 5 5 1. 9 1 . 1 2 7 1 . 5 6 9 0 . 9 6 0 0 . 9 5 8 14 7 .9 1 0 . 0 0 0 1. 0 5 0 . 7 4 7 0. 7 2 2 5 4 9 . 6 . 0 6 7 1 . 7 7 4 0 . 9 6 0 0 . 9 5 8 1 2 2 .4 7 0. 0 0 1 0. 8 8 0 . 8 3 4 0. 7 8 5 5 3 8 . 0 1 . 0 1 9 2 . 0 4 8 0 . 9 6 1 0 . 9 5 9 84 . 9 2 - 0 . 0 0 2 0. 1 8 0 . 9 1 0 0 . 8 66 5 2 1.5 1 .0 0 0 2 .2 8 5 0 .9 6 2 0 .9 5 9 4 6 . 76 0 .0 0 2 - 0 .2 1 M e t h y l A c e t a t e ( l ) - E t h a n o l ( 2 ) a t 4 5 - C 0 . 0 2 8 0 . 1 7 8 2 0 8 . 8 2 . 7 3 8 1 . 0 0 0 0 . 9 8 5 0 . 9 8 2 1 8 .9 3 - 0 . 0 0 6 0 .9 2 0 . 1 12 0. 4 2 8 2 8 0 . 9 2 .2 0 3 1 .0 1 8 0 .9 8 0 0 .9 7 6 6 6. 8 7 - 0 . 0 1 8 - 1.2 6 0 . 3 9 8 0 . 6 9 6 4 1 5. 7 . 4 7 6 1 . 1 6 6 0 . 9 7 0 0 . 9 6 4 1 5 7 . 14 0 . 0 0 2 0 . 79 0 . 46 3 0 . 7 2 0 4 2 9. 1 1. 3 5 4 1. 2 4 1 0 .9 6 9 0 .9 6 2 16 2 .5 9 - 0 . 0 0 1 0 .2 1 0 . 50 2 0 . 7 3 6 4 3 9 . 0 1 . 3 0 5 1 . 2 9 0 0 . 9 6 8 0 . 9 6 2 1 65 . 0 9 0 . 0 0 0 0 . 56 0 . 5 6 4 0 . 75 7 4 5 3 . 2 .2 3 2 1 .3 9 8 0 .9 6 7 0 .9 6 0 16 7. 13 - 0 . 0 0 1 1. 0 6 0 .6 4 7 0 .7 9 1 4 6 3.2 1 . 1 4 6 1 . 5 1 7 0 . 9 6 7 0 . 9 5 9 14 8 . 9 6 0 . 0 0 2 0 .2 2 0 . 7 6 5 0 . 8 3 7 4 7 7 . 4 1 . 0 5 6 1 . 8 2 8 0 . 9 6 6 0 . 9 5 8 1 1 6. l l 0 . 0 0 0 - 0 . 1 9 0 . 7 89 0 . 8 4 9 4 8 0 . 9 1 . 0 4 6 1 . 9 0 0 0 . 9 6 5 0 . 9 5 8 1 0 8 . 0 5 0 .0 0 1 - 0 . 0 4 0 .8 5 9 0 . 8 8 6 4 8 7 . 9 1. 0 1 6 2 .1 7 6 0 .9 6 5 0 .9 5 7 7 8 . 2 2 0 . 0 0 0 0 .0 1 0 . 93 7 0 . 9 42 4 9 5 . 0 1. 0 0 4 2 .5 12 0 .9 6 4 0 .9 5 6 3 9 . 3 7 0 . 0 0 2 0 .6 1 M e t h y l A c e t a t e ( I ) - E t h a n o l ( 2 ) a t 5 5 - C 0 . 0 2 5 0 . 14 2 3 2 1 .3 2 .6 0 1 0 .9 8 8 0 .9 8 0 0 .9 7 6 8. 0 2 - 0 . 0 0 1 0 . 58 0 . 0 5 0 0 . 2 48 3 6 1. 1 2 .5 4 6 0 .9 9 6 0 .9 7 7 0 .9 7 3 2 7 .8 7 0 . 0 0 4 1. 7 7 0 . 10 5 0 . 3 7 9 4 2 2 .4 2 . 1 5 9 1 . 0 1 6 0 . 9 7 3 0 . 9 6 8 6 1. 9 5 - 0 . 0 1 0 0 . 68 0 . 16 6 0 .4 8 1 4 7 7. 1 1. 9 5 0 1 .0 2 5 0 .9 7 0 0 .9 6 4 8 5 . 5 3 - 0 . 0 0 6 0 . 33 0 . 2 4 4 0 . 5 6 3 5 2 9 .7 1. 7 18 1. 0 5 2 0 .9 6 7 0 .9 6 0 1 1 1. 15 - 0 . 0 0 3 - 0 . 0 3 0 .3 6 5 0 . 6 4 8 5 8 8 .6 . 4 6 3 1 . 1 1 6 0 , 9 6 3 0 . 9 5 6 1 3 5 .8 8 0. 0 0 2 - 0 . 1 8 0 . 4 5 4 0 . 6 90 6 2 0 . 6 1. 3 18 1 .2 0 2 0 .9 6 1 0 .9 5 3 1 4 7. 0 5 0. 0 0 1 - 0 . 1 8 0 . 5 3 6 0. 7 2 6 6 4 5 . 1 1. 2 19 1 .2 9 6 0 .9 6 0 0 .9 5 1 1 4 7 .6 5 0 . 0 0 2 - 0 . 0 8 0 . 6 12 0 . 7 5 6 6 6 2 .8 1 . 1 4 1 1 . 4 1 6 0 . 9 5 9 0 . 9 5 0 1 4 0 .5 4 0. 0 0 0 - 0 .2 1 0 . 6 93 0 . 7 9 3 6 7 8 . 1 1 . 0 8 0 1 . 5 5 1 0 . 9 5 8 0 . 9 4 9 1 2 2 .6 3 0 . 0 0 2 - 0 . 4 3 0 . 7 6 8 0 . 8 2 8 6 9 1. 0 1 . 0 8 6 1 . 7 3 6 0 . 9 5 7 0 . 9 4 8 1 0 1. 1 0 0. 0 0 2 - 0 . 4 0 0 . 8 4 0 0 . 8 7 0 6 9 9 . 5 .0 0 7 1 .9 2 5 0 .9 5 6 0 .9 4 7 7 2. 0 0 0 . 0 0 4 - 0 . 5 1 0 . 9 1 4 0 . 9 24 7 0 7. 1 0 . 9 9 3 2 . 1 1 5 0 . 9 5 6 0 . 9 4 6 3 7.7 1 0 .0 0 6 - 0 . 1 6
^=2/exptl-2/calc ** ^P=P(Pexptl-Pcalc)XlOO/Pexptl
calibrated thermistor mounted in the mixing cell. piViP^iXiPi^exp^
Vil{P-PjS RT Further details on the apparatus and the experimental (1) technique have been published previously6). where §uyuPi\v\,yi and P are, respectively, the Thermodynamic Analysis of Experimental Data vapor-phase fugacity coefficient, vapor mole fraction, vapor pressure, partial molar volume, liquid-phase A fundamental equation expressing equilibrium activity coefficient of component i and the total relation between liquid and vapor phase is pressure. Under normal pressure the partial molar
228 :i4) JOURNAL OF CHEMICAL ENGINEERING OF JAPAN M E T H Y L A C E T A T E ( I ) - M E T H A N O U 2 ) M E T H Y L A C E T A T E ( I ) - E T H A N O L ( 2 )
.0 en o n_ m < o > Q < > - 0 . 8 0 .8 UJ I- 2 0 - C < ; LU I- I<- 3 0 -C LU I- o LU 4 0 -C < g o .6 0 . 6 V ^ T >- m S M h- I UJ h- 5 LJ EXP E R IM EN T AL 2 li_ 0 .4 蝣2 0-C BE KA RE K O 0 . 4 o - 3 0-C BEK A REK 2 z o o - 4 0-C BE KA RE K I- I- 一 蝣50 -C SEV ER NS o o < r 0 .2 O 3 5-C TH IS W O R K 0 . 2 O F X P E R IM F N T A L 4 5 -C u_ > 4 5-C TH IS W O RK LU �' E X P E R IM E N T A L 5 5 -C LU _ 1 I CA LC UL AT ED o C A L C U L A T E D o 2 2
o o 0 . 2 0 . 4 0 . 6 0 . 8 . 0 0 . 2 0 . 4 0 . 6 0 . 8 o M O L E F R A C T IO N O F M E T H Y L A C E T A T E IN L IQ U ID M O L E F R A C T I O N O F M E T H Y L A C E T A T E IN L I Q U I D
Fig. 1 Binary x-y diagram for the methyl acetate- Fig. 2 Binary x-ydiagram for the methyl acetate-etha- methanol system nol system
M E T H Y L A C E T A T E ( I ) - M E T H A N O L ( 2 )
M E T H Y L A C E T A T E ( I ) - E T H A N O L ( 2 ) 4 . I . J . I ｻ T -.
� � I I I 蝣 I � I � 4 5 - C 3 3 5 5 - C �
2 � 2 � K
fk ｣ i I LU K . I o I . I . I . I . I- li_ I � I � I � I � u - 4 z 4 I � I � I � I � LU LjJ o o o u _ > 3 5 - C h- 3 ^ 3 u s 4 5 - C > � o h- o o � < 2 t 2
> h - 1 o < I
I I . I . I . I
0 . 2 0 . 4 0 . 6 0 . 8 I . 0 0 . 2 0 . 4 0 . 6 0 . 8 0 M O L E F R A C T I O N O F M E T H Y L A C E T A T E M O L E F R A C T I O N O F M E T H Y L A C E T A T E ｮ E X P E R IM E N T A L E X P E R I M E N T A L C A L C U L A T E D C A L C U L A T E D
Fig. 3 Activity coefficient-composition diagram for the Fig. 4 Activity coefficient-composition diagram for the methyl acetate-methanol system methyl acetate-ethanol system volume is taken to be equal to the molar volume of pure liquid, and fugacity coefficient may be obtained ln&=-4-Eyi£ij -ln- Pv v j=\ from the virial equation truncated after the second (2) term The molar volume of the gas mixture, v, is given by VOL. 5 NO, 3 1972 :i5: 229 Table 3 Parameters of NRTL equation and root-mean square deviations for binary data
System Cx C2 C3 Dx D2 D3 100Jy P Ah [cal/mol] [cal/mol] [cal/mol-°K] [cal/mol-°K] [°K-1] [%] [cal/mol] Methylacetate(l)- 493.99 488.52 0.635676 0.2704 -2.9157 0.000203 O8~ 0.8 4.0 methanol(2) Methyl acetate(l)- 478.63 577.71 0.572297 -1.4620 -3.2553 0.000454 0.5 0.6 4.0 ethanol(2)
Table 4 Heat of mixing data for the binary systems
Temp. [°C]Methyl Acetate%2 hE(l)-Methanol[cal/mol] J/z* (2)[cal/mol] Methyl%2 AcetatehE [cal/mol](l)-EthanolM* [cal/mol](2)
25.00 0.0134 17.66 -0.75 0.0765 1 18.22 - 1.52 0.0269 34.23 - 1.71 0.1207 169.42 -4.06 0.0391 48.92 -2.02 0.3080 305.30 -2.17 0.0474 57.45 - 3.27 0.4037 335.64 3.89 0.0537 65.22 -2.69 0.4584 338.03 2.88 0.0761 89.46 -2.44 0.5054 335. 16 2.58 0.2142 192.47 - 1.66 0.5559 328.00 3.54 0.3132 228.81 -0.78 0.6037 316.29 4.50 0.4089 238.32 -3.47 0.7047 266.12 -3.03 0.5100 232.44 -3.72 0.8013 206.35 -0.80 0.5655 227.30 1.02 0.8470 166.41 -3.44 0.6088 221.09 5.53 0.9043 1 13.28 - 1.67 0.7063 181.37 -0.94 0.8034 133.32 -3.41 0.8762 95.65 1.85 0.9539 37.41 -0.98 35.00 0.1087 123.60 - 1.46 0.1084 160.51 -3.14 0.2221 206.52 2.04 0.2107 260.39 - 3.42 0.3139 239.61 0.05 0.3423 335.88 1.82 0.3341 243.91 -0.46 0.4014 348.78 0.59 0.3648 246.30 -3.57 0.5046 347.1 1 -3.76 0.4072 256.81 2.69 0.5548 337.07 -5.77 0.4277 253.46 - 1.40 0.5945 327.28 -5.07 0.4531 253.94 -0.74 0.6071 323.70 -4.57 0.5117 253.22 3.39 0.6875 291.21 -2.41 0.5570 248.68 6.55 0.7599 252.51 à" 3.1 1 0.6062 233.25 3.12 0.8739 153.77 1.18 0.6086 230.79 1.33 0.9321 87.70 - 1.05 0.7068 190.66 - 3.74 0.7989 148.14 -0.56 0.8184 134.76 -2.61 0.8936 84.38 - 3.52 45.00 0. 1043 127.93 4.91 0.0989 162.02 6.65 0.21 15 207.98 3.44 0.2074 276.63 6.74 0.31 10 249.64 1.76 0.2945 326.56 - 1.12 0.4086 263.02 -2.92 0.3983 356.66 -6.96 0.5054 264.45 0.55 0.5142 369.80 2.44 0.6081 236.91 -6.09 0.6056 349.02 3.17 0.7067 201.72 -4.75 0.6986 310.08 7.45 0.7099 201.77 -3.26 0.8018 230.43 1.61 0.7542 201.74 18.45 0.8994 83.85 -5.12 0.9513 42.88 -2.90 M =hEGXVtl-hEc
equation8). The NRTL equation is found to be Pv successfully applicable to partially miscible as well
Jl=1+- ViVjBij=1j=l (3) RT 22 as completely miscible systems. The second virial coefficients are calculated by a The excess Gibbs free energy, gE, and the activity correlation of O'Connell and Prausnitz7). The vapor coefficient of the NRTL equation are expressed as pressure data of the pure componentswere taken from follows. the literature1>5>8). The concept of local composition proposed by RT -XlX\ x1+x2G21 +'x2+xiGi2~) {4) Wilson13) prompted Renon and Prausnitz to their Inrt=*|Fr21( r'V-y+r-r^-si <5) derivation of the nonrandom two-liquid (NRTL) LV.*1+a;oG21 / (x-,+x,GnfJ
230 (16. JOURNAL OF CHEMICAL ENGINEERING OF JAPAN nr_^,2r_ ( G12 V_l ^21^21 I (c\ } 111/2-$1 ^12 I i 7S j T"7 ; 7S-VK (O) correlated with the NRTL equation having tem- perature-dependent parameters over a range of where T12={gl2-g22)/RT; r21={g21-gn)IRT; G12= exp temperature 25° to 55°C. (-a12r12); and G2i=exp(-a12r21). Acknowledgement The NRTLequation involves three adjustable param- The authors are grateful to the Computer Center, Osaka eters 02i-#ii> 012-022? and a12. It is reasonable University, for the use of its facilities. Yoshio Nakayama to assume that these parameters are temperature- and Hitoshi Kobayashi assisted experimental work. dependent2}. In this investigation the three param- eters are assumedto be a linear function of tempera- Nomenclature ture. Btj = second virial coefficient [m//mol] (ki-9n=C1+A(^-273. 15) Ch C2= values of (921-9n) and (^12-^22) at 0°C ?i2-fe=C2+A(T-273. 15) [cal/mol] C3 =valueofa12at0°C
«12 (7) =C3+Z)3(T-273. 15) (8) (9) D1, D2= coefficients of temperature change of (021-011) Then the heats of mixing, hE, are calculated from the and (012-022) [cal/mol-°K] excess Gibbs free energy data by differentiation of Dz = coefficient of temperature change of a12 ^K"1] the NRTL equation using the well-known Gibbs- gE = excess Gibbs free energy [cal/mol] 9ij = energies of interaction between an i-j pair of Helmholtz relation. molecules [cal/mol] R L d(l/T)'Ap,x [W) Gij = coefficient as defined by Gtj = exp(-ol12tij) hE = heat of mixing [cal/mol] hE= x1X2exp(-a12T21) FA_ ^12^21^1 P\ = saturation pressure of pure componenti [atm] ^!+^2exp(-a12r2i)L\ xlJrX2exp(-a12T21) P = total pressure [atm] X(Ci-273.15A)+ T2lxiDfRT2 1 Q = objective function ^i+^2exp(-a12T21)J R = gas constant [1.987 cal/mol-°K] T = absolute temperature [°K] _^ ^!o;2exp(-a12r12) |~A_ ^12^12^2 Vf = partial molar liquid volume of component i #2+#iexp(-al2Tl2)L\ x2+o;1exp(-a12r 12, [m//mol] v = molar volume of vapor mixture [m//mol] x (C2-273. 15A) ^2+^iexp(-«:12r12)J+-*j&JMll- 1 (ii) xt = liquid-phase mole fraction of component i yi = vapor-phase mole fraction of component i The constants C's and Z)'s were determined by
Conclusion Pure1964Organic Compounds", Vol. II, Elsevier, NewYork, 12) Weissberger, A., E. S. Proskauer, J. A. Riddick and Experimentally determined excess Gibbs free ener- E. E. Toops, Jr.: "Organic Solvents", 2nd ed., Inter- gies and excess enthalpies of mixtures ofmethyl acetate science, New York, N.Y., 1955 with methanol and ethanol are simultaneously well 13) Wilson, G.M.: J. Am. Chem. Soc, 86, 127 (1964) VOL, 5 NO, 3 1972 å 17: 231