Volumetric and Phase Behavior
of Propene-1-Butene System G. H. GOFF, P. S. FARRINGTON, AND B. H. SAGE Calqornia Institute of Technology, Pasadena, Calif,
A
s
as were discussed earlier. T h e volumetric behavior of four mixtures of propene LTHOUGH a large The composition of the dewand 1-butene was determined experimentally at seven a m o u n t of experipoint gas was investigated mental information relating temperatures between 40' and 280' F. for pressures up to by the withdrawal under 10,000 pounds per square inch. The compositions and t o the volumetric and phase isobaric, isothermal condibehavior of h y d r o c a r b o n specific volumes of the coexisting phases have been estabtions of a portion of the gas systems has become availlished throughout the two-phase region at temperatures phase of an equilibrium able, no work on binary oleabove 40' F. Equilibrium constants for propene and 1heterogeneous mixture. The finic systems is reported in butene were computed and are reported as functions of method of analysis used the literature. Since prostate. The results are presented in graphical and tabular . was similar to that empene and 1-butene are oleform. ployed in the study of the fins of importance as raw methane+-butane s y s t e m materials in the synthetic (14). A sample of approximately 1gram of a gas phase was withchemical industry, the volumetric and phase behavior of the drawn into a highly evacuated glass bulb having a volume individual components of the propene-1-butene system has been known with an uncertainty of 0.15%. The temperature of the investigated in some detail. The behavior of propene has been bulb was maintained within 0.2' of 90 'F. by means of an agitated established at pressures ( 3 ) up to 10,000 pounds per square inch air bath. The pressure which was approximately atmospheric throughout the temperature interval between 40" and 460" F. within the glass bulb after temperature equilibrium had been Recent measurements ( 11 ) have established the volumetric attained was measured by a mercury-in-glass manometer. and phase behavior of 1-butene a t pressures up to 10,000 pounds The relative elevations of the mercury in the arms of the manomper square inch in the temperature interval between 100' and eter were established by a vertical-component cathetometer. 340" F. The vapor pressures of 1-butene a t 40" and 7 0 " F. It is believed that the uncertainty in the pressure measurement are recorded in the literature ( 6 ) . In addition, other experimendid not exceed 0.03%. The outlet of the bulb was closed after t a l results are reported in the literature for propene (5, 16, the attainment of equilibrium, and the glass bulb was removed 17, 18) and for 1-butene ( 1 , 7 , IS). These data serve to estabfrom the air bath and conditioned for weighing with a nearly lish the volumetric and phase behavior of propene and 1-butene identical tare bulb. The sample bulb was weighed, using the with sufficient accuracy for the present investigation. tare, and the change in weight was determined by substitution. METHODS Air buoyancy corrections for the variations in weight resulting from changes in the barometric pressure were not necessary since The specific volumes of four different mixtures of propene and the two bulbs were of nearly identical volume. The uncertainties 1-butene were determined at seven systematically chosen temin specific weight arising from the conditioning and weighing peratures between 40" and 280" F. for pressures up to 10,000 of the sample bulb are believed to be within 0.060/,. pounds per square inch. (All pressures referred to are expressed Since hydrocarbon mixtures a t atmospheric pressure do not as pounds per square inch absolute.) The work was restricted strictly follow the behavior of ideal solutions (8), i t was necessary t o a maximum temperature of 280" F. as a result of a previous to employ experimental P-V-T (pressure-volume-temperature) investigation of 1-butene ( 1 1 ) which reported significant demeasurements relating to the volumetric behavior of the propenecomposition of this compound above 300" F. No deterioration 1-butene system to permit the calculation of the mole fraction of a was observed in the present study. The method involved component from the measured specific weight. It is believed the use of apparatus and procedures which have been described that the over-all uncertainty in the experimental phase data i n the literature (16). I n order, to obtain temperatures below resulting from the above-mentioned procedures is within 0.25%. 100" F., the basic equipment was modified by the addition of a As a check on the method, analyses were made of dew-point gas refrigeration unit. The low viscosity oil was circulated from the of known composition, and the agreement was within 0.2%. oil bath over a refrigeration heat exchanger and returned to the Duplicate samples of dew-point gas were withdrawn for each bath. The gravimetric techniques employed in the preparation analysis, and the average result is the value reported. The of the experimentally studied mixtures probably did not cause average mean deviation was 0.2% except when difficulty arose uncertainties greater than 0.001 mole fraction in the reported in withdrawing the samples. composition of the mixtures. Uncertainties in the temperature The specific volume of the dew-point gas was ascertained from measurements are believed not to exceed 0.08 O F. relative to the volumetric data obtained in the gaseous and two-phase regions international platinum scale. The magnitude of the pressure in for the series of experimental mixtures. To obtain values of t h e working sections was established within 0.2 pound per square dew-point specific volume a t 40" and 70" F. at which temperainch or within 0.05%, whichever uncertainty is the larger. The tures no volumetric data were available in the gaseous region, total volume of the sample was determined with an uncertainty it was necessary t o extrapolate curves of constant composition of about 0.1% a t the largest volumes and of less than 0.3% at the on residual volume-pressure plots. The dew-point pressures smallest. were obtained from isothermal curves on pressure-composition The study of the heterogeneous equilibrium of the propene-ldiagrams. The compressibility factor was found t o be a useful butene system was made with the apparatus employed for obfunction in smoothing the dew-point and bubble-point volumetric taining the volumetric data. The equilibrium pressure and data. temperature were established with nearly the same uncertainties
735
INDUSTRIAL AND ENGINEERING CHEMISTRY
736
condensation from dew point to bubble point was 0.8 pound per square inch. The 1-butene was prepared by dehydration of n-butanol with activated alumina as a catalyst. A description of the apparatus, the procedure employed, and the method of purification used may be found in the literature (11). The maximum change in vapor pressure a t 130" F. for any of the lots of 1-butene during an isothermal condensation from dcw point to bubble point was 0.7 pound per square inch. The time of storage of the 1-butene was held to a minimum to reduce the possibility of an isomerixation to 2-butene.
0 3
0.045 Y cc
t-
? 0 040
g
U
w 0.035
I
3 >
0 u
Vol. 42, No. 4
0.030
EXPERIMENTAL RESULTS
Lo
I
1 500
250
750 PRESSJRE
1000
1250
15C0
I750
I
POUNDS PCR SQUARE I N C H
Figure 1. Experimental Results in Vicinity of Bubble Point for 3Iixture of Propene arid 1-Butene Containing 0.8174 Mole Fraction 1-Butene
The constants used in the calculations associated with the preparation of these experimental data had the follonkg values: universal gas constant, 10.73185 (pounds per square inch) (cubic feet per pound mole) per R., thermodynamic tempcrawre in R., 459.69' F., the molecular weight of propene, 42.079, and of 1-butene, 56.105. Throughout, all calculations, care was exercised to ensure that the combination of analytical and graphical procedures TTas such that the accuracy of the primary data was not significantly impaired by any smoothing operations employed. O
MATERIALS
The propene employed in this investigation was obtained from the Phillips Petroleum Company and had an analyzed purity of greater than 0.995 mole fraction propene. Further purification of the propene was carried out by fractionation at, atmospheric pressure in a column packed Trith small glass helices. A reflux ratio of approximately 40 to 1 \vas used, and the first tent,h and the last fifth of the material were discarded in the course of fractionation. Several lot's of purified propene were prepared during the course of the investigat,ion. The maximum change in vapor pressure a t 100" F. found in the course of an isothermal
1.00
Figure 1 presents an illustrative set of experimental results for a state near the bubble point of a niixture containing 0.8174 mole fract,ion 1-butene. The density of the experimental points indicated in this diagram is typical of the measurements made on other mixtures. Redetermination of the volume of a sample exposed to the highest temperature used during a series of measurements gave no evidence of thermal decomposition of the hydrocarbon. The effect of change of composition within the propene-lbutene syst,em a t 160" F. is portrayed in Figure 2. Smoothed values of the compressibility factor are used to describe the volumetric behavior, and the bubble-point, locus and the dcwpoint locus are indicated for the s-stem. The discontinuity in the first derivative of the compressibility fact'or with respect to pressurc a t constant temperature is apparent a t the phase boundaq-. Since propene and 1-butene are adjacent members of a honiologous series, they would be expected to form nearly ideal solutions (8). The volumetric behavior of the propene-1-butene system is compared with calculated ideal values in Figure 3. The volume of an ideal mixture may be calculated from the relationship T'A
= TLsVz
+
72eT'l
(1)
where V " is the specific volurne of the pure component in t,hc same phase a t the same pressure and temperature. The ordinatr for Figure 3 is defined by the equation:
The volumes of liquid mixtures at, 10,000 pounds per square inch deviate less from the calculated values than do the volumes of gaseous mixtures rtt 100 pounds per square inch. The specific volumes and compressibility factors of the four experimental mixtures of propene and l-but,ene are recorded in Table I. The smoothed data have been interpolated to cvcn values oi pressure. I n Table I1 the volumetric results ai'e presented as molal volumes, and the experimental compositions have been interpolated to even values of mole fraction for
0.90
5 aeo U
2
F.
t 2
m 0.70 VI
a 1
8 0.60
100
200 PRESSURE
300 400 POUNDS PER SQUARE INCH
Figure 2. Effect of Change of Composition within Propene-1-Butene System at 160" F.
MOLE F R I C T I O N I-BUTEIIL
Figure 3. Deviation of Volumetric Behavior from Ideal Solution for Propene-1-Butene Mixtures at 160" F.
INDUSTRIAL AND ENGINEERING CHEMISTRY
April 1950
convenience in use. The specific volume and the pressure at bubble point and dew point are recorded for each of the mixtures in Table I. The experimentally determined compositions of the dew-point gas and the bubble-point liquid are shown graphically in Figure 4. All of the bubble-point states were ascertained from discontinuities in the first derivative of the isothermal volume-pressure relation. The composition of the dew-point gas was established from discontinuities in the first derivative of the isothermal compressibility factor-pressure relation, supplemented by analyses of samples of the gas phase withdrawn from heterogeneous mixtures as discussed earlier.
TABLE I.
SINGLE-PHASE VOLUMETRIC
BEHAVIOR OF
737
Figure 5 presents a pressure-temperature diagram for the propene-1-butene system. The dew-point and bubble-point curves of the experimental mixtures as well as the vapor pressure curves for the pure components ( 3 , l l )are shown. The properties in the critical region have been estimated only since insufficient experimental data were available in this region to determine the critical behavior. The estimated critical properties, shown by dashed lines in Figures 4, 5 , and 6, are based on the critical behavior of the paraffin analog (IO). It is believed t h a t the critical envelope was established within narrow limits so that less than 3y0 uncertainty exists in the critical values recorded. F O U R EXPERIMENTAL pI/IIXTURES O F
PROPEE;E--I-BUTENE
(Figures in parentheses are dew-point or bubble-point pressures expressed a8 pounds per square inch) Pressure, Lh./Sq. Inch Ahs.
Dew point Bubble point 0 14.7 20 30 40 50 60 80 100 125 150 200 300 400 500 600 800 1000 12.50 1500 1750 2000 2250 2500 2750 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000
Dew point Bubble point 0 14.7 20 30 40 50 60 80 100 125 150 200 300 400 500 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000
CompressiCompressiSp. Volume, bility Sp. Volume, bility Cu. Ft./Lb. Factor Cu. Ft./Lb. Factor Temperature, 40' F. 1-Butene, 1-Butene, -0,1705 mole fraction--0.3315 mole fraction-1.815 (60.0) 0,02874 (82.8)
.....
8.039 5.860 3.845 2.8336 2.2238
.....
0.903 0.0197 1.000 0.9796 0.9719 0.9565 0.9399 0.9220
....
....
0.2039 0.0298 0.0357 0.0476 0.0712 0.0948 0.1182 0.1415 0.1878 0.2339 0,2909 0.3473 0.4034 0.4591 0.5142 0.5689 0.6232 0,6777 0.7845 0.8900 0.9945 1.0975 1.3011 1.5011 1.6990 1.8934 2.0864 1-Butene, 7 - 0 . 6 9 0 5 mole fraction-3.280 (29.7) 0.9403 0.02695 (43.6) 0.0113 ..... 1.000 6.848 0.9713 4.976 0.9606
.....
.... ....
0.0130 0.0156 0.0208 0.0260 0.0324 0.0389 0.0517 0.0775 0.1030 0.1285 0.1539 0.2045 0.2548 0.3173 0.3792 0.4409 0.5021 0,5634 0.6240 0.6846 0.7445 0.8639 0.9815 1.0981 1.2133 1 .4409 1.6655 1.8880 2.1075 2.3263
2.3155 (45.6) 0.02814 (70.5)
.....
7.627 5.554 3.635 2.6714
.....
0.9201 0.1729 1,000 0.9768 0.9679 0.9502 0.9311
..
0.02804 0:0i96 0.02802 0.0244 0.02800 0.0305 0.02799 0.0366 0.02796 0.0487 0.02790 0.0729 0.02785 0.0971 0,02779 0.1211 0.02774 0.1450 0.02763 0.1926 0.02752 0.2398 0.02741 0.2986 0,02730 0.3568 0.02719 ' 0.4146 0.02708 0.4719 0,02698 0.5290 0.02688 0.5856 0.02678 0.6417 0.02670 0.6980 0.02652 0.8088 0.02634 0.9181 0.02616 1.0258 0.02600 1,1328 0.02570 1.3437 0.02545 1.5524 0.02518 1.7553 0.02495 1,9567 0.02475 2.1567 1-Butene, 7 - 0 . 8 1 7 4 mole fraction-3.626 (26.1) 0.945 0.02659 (34.9) 0.0093
.....
0.9698 0.9584
0: 62659 0.02658 0.02657 0.02656 0.02654 0.02663 0.02651 0.02647 0.02643 0.02637 0.02633 0.02628 0.02619 0.02612 0.02601 0.02591 0.02583 0.02576 0.02569 0.02561 0.02554 0.02546 0.02531 0.02515 0.02500 0.02487 0.02461 0.02442 0.02424 0.02404 0.02390
0.0106 0.0133 0.0159 0.0212 0.0265 0.0331 0.0397 0.0529 0.0792 0.1053 0.1315 0.1574 0,2092 0.2608 0.3246 0.3881 0.4513 0.5144 0.5772 0.6393 0.7013 0.7627 0.8845 1.0045 1.1233 1.2416 1.4744 1.7068 1.9363 2.1604 2.3864
....
.
Compressibility Factor
CompressiSI,. Volume, bility Cu. Ft./Lh. Factor Temperature, 70' F. 1-Butene, 1-Butene, --0,1705 mole fraction---0.3315 mole fractionDew point 1.060 (103.6) 0.859 1.363 (78.8) 0.8830 Bubble point 0.03013 (130.6) 0.0308 0.02942 (111.3) 0.0269 0 ..... 1 ,000 ..... 1.000 0.9830 14.7 8.551 8.118 0.9806 20 0.9767 6,243 5.921 0.9734 30 0.9646 4.110 3.891 0.9595 40 0.9519 3.042 2.8743 0.9451 50 2.4000 0.9387 2.2628 0.9300 60 1.9711 0.9252 1.8539 0.9144 0.8962 1.4321 80 ,.... .... 1.1057 100 ..... 0.8650 125 ..... .... 0.02941 0 : 0302 150 0.03013 0.0354 0.02939 0.0362 200 0.03010 0.0353 0.02935 0.0483 300 0.02998 0.0704 0.02925 0.0721 400 0.02990 0.0936 0.02916 0.0959 500 0.02981 0.1166 0.02907 0.1195 0.02971 0,1395 600 0.02899 0.1430 0.02955 800 0.1849 0.02883 0.1896 0.02938 0.2298 1000 0.02866 0.2356 0.02919 0.2854 1250 0.02848 0.2926 0.02900 0.3403 1500 0.02830 0.3490 0.02883 0.3947 1750 0.02815 0.4050 0.02867 2000 0.4486 0.02800 0.4603 0.02850 0.5016 2250 0,02788 0.5151 0.02835 2500 0.02773 0.5617 0 * 5544 0.02821 2750 0.6069 0.02761 0.6241 0.02808 3000 0.6590 0.02750 0.6782 0.02784 3500 0.7623 0.02729 0.7852 0.02763 4000 0.8646 0.02710 0,8911 0.02743 4500 0.9656 0.02691 0.9954 0.02725 1,0659 5000 0.02675 1.0995 1,2626 0.02690 6000 0.02641 1.3026 0.02659 7000 1.4561 0.02610 1.5018 0.02630 1.6459 0.02579 1.6960 8000 0,02602 1.8320 9000 0.02553 1.8888 0.02574 2.0136 0.02530 2.0797 10000 1-Butene, 1-Butene, --O, 8174 mole fraction-7 - 0 . 6 9 0 5 mole fraction1.9702 (50.6) 0.9078 2.158 (45.0) 0.914 Dew point 0.0180 0.02760 (57.4) 0.0149 Bubble Doint 0.02795 (70.9) 1,000 ..... 1,000 0 7.039 0.9743 14.7 7.292 0.9758 5.308 0.9666 5.121 0.9646 20 3.346 0.9456 3.473 0.9488 30 2.4560 0.9253 2.5527 0.9298 40 1.9976 0.9095 ..... 50 60 0 : 02795 0 : 0204 0 : 0208 80 0.0259 0.02793 0.0254 100 0,0324 0.02791 0.0318 125 0.0389 im 0.02790 0.0381 ~~. 0.0517 0.02786 0.0607 200 0.0774 0.02780 0.0759 300 0.1030 0.02774 0.1010 400 0,1284 0.02767 0.1260 500 0.1538 0.02760 0.1508 600 0.2042 0.02749 0 2003 800 0.2543 0.02737 0.2492 1000 0.3165 0.02723 0.3099 1250 0.3782 0.02710 0.3702 1500 0.4394 0.02697 0.4298 1750 0.5003 0.02685 0.4890 2000 0.5608 0.02674 0.5479 2250 0.6207 0.02664 0.6064 2500 0.6804 0.02653 0.6643 2750 0.7392 0,02644 0.7223 3000 0.8571 0.02626 0.8369 3500 0.9735 0.02610 0.9506 1.0889 0.02595 1.0633 1.2028 0.02580 1.1746 1.4264 1.3932 0.02550 1.6483 0.02523 1.6082 1.8657 0.02499 1.8204 2.0811 0.02476 2.0291 2.2944 0.02456 2.2364 (Continued on page 758) Sp. Volume, Cu. Ft./Lb.
.....
1,000
6.609 4.799
Pressure Lb./Sq. Inch. Abs
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
738
Vol. 42, No. 4
OF FOUR E X P E R I M E N T a L hfIXTURES O F PROPANE-~-BUTENE (Continueii) TABLE I. SINGLE-PHASE VOLUMETRIC BEHAVIOR
Pressure, Lb./Bq. Inch Abs.
Sp Volume C;. Ft./Lb:
Compressibility Factor
Sp. Volume, Cu. Ft./Lb.
Compressibility Factor
Temperature, 100’ F. 1-Butene, 1-Butene, 7-0.3315 mole fractionA. 1705 mole fraction-0.8752 (124.4) 0.847 0.8086 0 . 6 7 6 7 (161.4) Dew point 0.03090 (166.9) 0.0401 0.0461 Bubble point 0.03185 (195.3) . . . . . 1.000 1.000 ..... 0 8.604 0.9837 0.9856 9.058 14.7 6.285 0.9778 0.9803 6.621 20 4.142 0.9666 0.9704 4.369 30 3.070 0,9554 0.9603 3.243 40 2.4268 0.9440 0,9501 2.5667 50 1.9974 0.9324 0.9398 2.1157 60 1.4595 0,9083 0.9184 1.5507 80 1,1346 0.8827 0.8968 1.2100 100 . . .. .... 0.8647 0,9344 125 .... 0.8282 0,7458 150 0 . Q3iji5 0.0480 0.0471 0.03184 200 0.03073 0.0717 0.0704 0.03170 300 0.03061 0.0953 0.0935 0.03 156 400 0.03050 0.1186 0.1163 0.03142 500 0.03039 0.1419 0.1390 0.03129 600 0.03017 0.1878 0 1838 0.03104 800 0.02997 0.2332 0,2281 0.03081 1000 0 2827 0.02974 0.2892 0,03055 1250 0.02952 0.3445 0.3366 0,03030 1500 0.02931 0,3990 0.3896 0.03007 1750 0.4420 0.02913 0.4532 0.02985 2000 0.4939 0,02895 0.5067 0,02965 2250 0.5451 0.02878 0.5597 0,02945 2500 0.5961 0.02863 0.6125 0.02928 2750 0 6466 0,02911 0.02847 n . 6645 3000 0,7468 0,02882 0.02820 0,7679 3500 0.02857 0,02795 0.8698 0.8461 4000 0 9442 0.02834 0.02774 0.9711 4500 0.02753 1 ,0709 1 ,0406 0.0281 1 5000 1.2305 0.02715 1.2673 0.02770 6000 1.4169 0.02679 1.4589 0.02734 7000 1.5992 0.02645 1.6462 0.02700 8000 1.7777 0.02615 1.8309 0.02668 9000 1.9516 0.02636 0.02586 2.0118 10000 1-Butene, 1-Butene, ,-0.6905 mole fraction---0.8174 mole fraction1.3622 (72.3) 0.878 1.2501 (80.8) 0 8705 Dew point 0.02865 ( 8 9 , 4 ) 0.0273 0,0228 Bubble point i0.02920 (108.4) n ..... 1.000 1.000 7.734 0,9796 7:467’ 0.9783 14.7 5.639 0,9720 5.442 0.9702 20 3.704 0.9676 3.570 0.9546 30 40 2.7344 0.9426 2.6319 0.9388 50 .. 2.1511 0.9270 2.0674 0.9215 1.7604 0.9103 1.6888 0.9032 60 1 ,2652 0.8723 80 ..... .... .... 0.02866 0.0255 100 0 : b i b is 0.0314 125 0.02863 0.0319 0,0377 0,02915 0.02861 0.0383 150 0.02910 0.0502 0.02889 0.0510 200 0.02900 0,0750 0.02848 0.0762 300 0.02890 400 0.0996 0.02840 0.1013 ~. 0.02881 0.1241 0.02882 500 0.1262 0.02873 0.1486 600 0.02826 0 . 1311 0.02856 0,1969 0.02810 0,2004 800 0.02841 0,2449 1000 0.02796 0.2492 0.02824 0,3042 1250 0.02782 0.3100 0.02806 0.3628 1500 0,02768 0 3701 0.02790 0.4208 1750 n . 02753 0.4295 0.02775 0.4783 2000 0.02740 0.4885 0.02761 0.5354 2250 0.02726 0.5468 0.02749 0.5923 2500 0.02714 0.6048 0,02737 0,6487 2750 0.02703 0.6626 0,7049 0.02726 3000 0.02693 0.7202 0.8160 0.02705 3500 0,02674 0,8343 0.9256 0.02685 4000 0.02656 0.9470 1.0343 0.02667 4500 0.02638 1.0582 1.1419 sono 0.02650’ 0.02618 1.1669 0.02616 1,3528 6000 0.02588 1.3842 0.02585 1.5595 7000 0.02559 1.5968 0,02558 8000 1,7637 0.02534 1.8071 0.02532 1.9640 9000 0.02609 2.0129 2.1615 0,02508 10000 0.02488 2.2179 ~
The compositions and specific volumes of the coexisting phases are recorded as a function of pressure and temperature in Table 111. These results were interpolated graphically from the experimental measurements already discussed. The “gasliquid equilibrium constant” was computed from the compositions of the coexisting phases and the values are recorded in Table 111. Figure 6 shows a plot of the equilibrium constants for propene and I-butene as a function of pressure. The product of pressure and equilibrium constant was chosen as a coordinate in order to provide a magnified scale for the plotting of equilibrium constants. From a combination of Raoult’s ( I d ) and Dalton’s laws the following relation obtains:
Pressure, Lb./Sq. Inch Abs.
CompressiCompreasiSp. T’olume, bility Sp. Volume, bility Cu. Ft./Lb. Factor Cn. Ft./Lb. Factor Temperature, 160’ F. 1 Butene, 1-Butene, 7-0.1705 mole fraction--0.3315 mole fra ction0.3709 (276.3) 0.7200 0 6643 Dev point 0.2864 (346 9) 0.0824 0 0965 0.03509 (334.3) Bubble point 0 03705 (389 7) 1.000 ..... 1.000 0 0.9880 9,568 0.9894 10.068 14.7 0.9837 0.9855 7.369 7,000 20 0.9785 0,9782 4.876 4.628 30 3.630 0,9673 3.442 0.9708 40 0.9591 2.8814 2.7300 0.9634 50 0.9508 2.2554 2.3823 0.9558 60 xn 1.6619 0.9342 1.7581 0,9405 1.3829 0.9247 0.9172 1.3053 100 0.8953 1.0821 0.9045 1.0194 125 0.8726 0,8834 0.8279 0,8807 150 0.8379 0.8222 0.5851 0,6266 200 0.03698 0,3640 0.7302 ..... .... 300 0.0979 0.0989 0.03483 400 0.1211 0.1219 0.03448 0.03646 000 0.1441 0.1448 0.03417 0.03601 600 0.1890 0.1887 0.03363 0.03527 800 0.2331 0.2318 0.03318 0,03466 1000 0.2878 0.2845 0.03404 0.03236 0,03277 1250 0.3411 0.3361 0.03351 I500 0.03306 0.3869 0.03202 0.3937 1750 0.03167 0.4451 0,03267 0.03232 0.4369 2000 0.03137 0.4863 0.4959 2250 0.5351 0.03110 0.5467 0.03201 2500 0.6833 0.03084 0.5959 0.03172 2730 0.6311 0,6448 0.03146 0,03059 0.03019 3000 0,7424 0.03099 0.7253 3500 0.03089 0.8182 0,02950 0.02984 0.8387 4000 0,9096 0.9328 0.0302.? 4.500 1.0000 1.0259 0.02920 0.02991 5000 0.02985 1,1775 1.2091 0.02824 0.02868 6000 1.3509 1.3890 0.02842 0.02886 7000 1.5203 1.5638 0,02782 8000 1.7340 0.02742 0.02802 1.6863 9000 0.02703 1.8992 0.02765 1,8489 10000
.....
__
I-Butene, --0.6905 mole fraction-0.5428 (184.1) 0.7778 Dew point 0.0566 Bubble point 0,03233 (224.9) ..... 1.000 0 8.612 0.9851 14.7 6.293 0,9797 20 4.152 0.9G95 30 3.081 0.9591 40 2.4374 0.9486 50 2.0084 0.9380 60 1,4712 0.9161 80 1,1476 0.8933 100 0.8868 0.8628 125 0.7133 0,8328 150 ..... 200 0.03215 0:0761 300 0.03192 0.0994 400 0.03173 0.1235 500 wnn 0.03153 0.1473 ... 0.1942 0.03119 800 0.2407 0.03092 1000 0.03062 n . 2979 12.50 0.03031 0.3539 1500 0.4096 0,03007 1750 0.4644 0.02983 2000 0.5191 0.02964 2230 0.02948 0.5731 , 2500 0.6261 0,02925 2750 0.6788 0.02907 0.02874 3000 0.7830 3500 0,8852 0.02843 4000 0.9860 0.02815 4500 1,0859 0.02790 .>ooo 1.2811 0.02743 6000 1,4728 0.02670 0,02703 7000 I , 6626 8000 1.8481 9000 0,02638 2.0300 0.02608 10000
P:
=
1-Butene, 7 - 0 8174 mole fraction0,7920 0 ,6009 (163.7) 0 ,03156 (190.6) 0.0484
PKR,k
.....
8.320 6.078 4.007 2,9713 2.3494 1.9346 I . 4148 1.1015 0.8483 0.6755 0.03153 0.03133
1.000
0.9843 0.9786 0.9678 0,95G8
0,9457 0.9345 0.9112
0.8868 0.8837 0,8137 0.0508
0.0757 0.1003 0.1247 0.03099 0,1490 0.03084 0.1068 0.03056 0.2442 0.03033 0,3022 0.03003 0.3595 0,02977 0.02953 0.4160 0,4719 0.0293 1 0,8277 0.02913 0,02898 0,5827 0.02879 0.6374 0.02863 0.6915 0,02833 0.7983 0.02805 0.9033 0,02779 1.0068 0.02755 1.1090 0.02713 1.3105 0.02673 1.5075 0.02645 1.7036 0.02614 1.8941 2.0852 0.02590 ( C o n t i n u e d o n page 730) 0.031 15
(31
I n the above expression P i is the vapor pressure of component k , P is the prevailing pressure, and K is the ratio of the mole fraction of component k in the gas phase to the mole fraction in the coexisting liquid phase. For each component this equation gives a horizontal line in Figure 6. Comparison of the experimental curves with the straight line shows the deviation of the system from the laws of Raoult and Dalton. COMPARISONS
Figures 7 and 8 present a comparison of the behavior of the components in the propene-1-butene system with their behavior
April 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
739
TABLE I. SINGLE-PHASE VOLUMETRIC BEHAVIOR OF FOUR EXPERIMENTAL MIXTURESOF PROPANE-~-BUTENE (Continued) CompressiCompressibility Sp. Volume, bility Factor Cu. Ft./Lb. Factor TemDerature. 220' F. 1-Butene, 1-Butene, -0.1705 mole fraction-4.3315 mole fraction.. .... 0.1488 (543.7) 0.5183 Dew point 0.04598 (594.5) 0.1751 Bubble point .. .... 0 ..... 1,000 ..... 1.000 11.073 0.9921 0.9911 14.7 10.527 8.113 0.9892 0.9879 20 7.710 5.109 5.379 0.9838 0.9818 30 4.012 0.9783 0.9757 40 3.808 3.191 0.9728 0.9696 50 3.027 2,6442 0.9672 0.9635 2.5067 60 xn 1.9601 0.9560 0.9512 1.8560 -_ 1.5493 0.9445 0.9388 1.4654 100 1 ,2203 0.9300 0.9230 1.1526 125 0.9439 1.0007 0.9151 0.9070 150 0.7254 0,8844 0.6822 0.8741 200 0.4478 0,8189 0.8020 0.4173 300 0.3054 0.7447 0.7156 0.27925 400 0.18620 0.2158 0.6577 0.5964 500 0.04570 0.1478 0.5406 0.1757 600 0.04681 0,2283 0.2096 0.04090 800 0,04242 0.2586 0.2500 0.03903 1000 0.03992 0.3042 0.2899 0.03748 1250 0.03844 0.3515 0.3507 0.03650 1500 0.03743 0.3993 0.4001 0.03569 1750 0.03658 0.4460 0.4487 0.03502 2000 0.03588 0.4922 0.4960 0.03441 2250 0.03396 0.03530 0.5380 0.5439 2500 0.03480 0.5834 0.03352 0.5906 2750 0.03435 0,6282 0.03313 0.6367 3000 0.03357 0.7163 0.03247 0.7280 3500 0.03293 0.8030 0.03191 0.8177 4000 0.03236 0.8878 0.03143 0.9061 4500 0.03187 0.9715 0.9930 0.03100 5000 0.03106 1.1361 0.03028 1.1639 6000 0.03042 1.2982 1,3323 0.02971 7000 0.02986 1.4563 0.02921 1,4970 8000 0.02936 1.6109 0.02870 1.6547 9000 0.02893 1.7637 0,02828 1.8117 10000 1-Butene, 1-Butene, --0,6905 mole fraction---0,8174 mole fraction0.2794 (324.2) 0.6650 Dew point 0.2458 (365.4) 0.6375 0.03622 (357.3) 0.0950 Bubble point 0.03777 (413.1) 0,1107 0 ,.... 1.000 ..... 1.000 0.9891 14.7 9.483 9.163 0.9885 0.9851 0.9843 20 6.940 8.704 4.434 0.9776 0.9763 30 4.592 3.298 0.9699 0.9684 40 3.417 2.6165 0.9624 0.9603 2.7122 50 0,9547 2,2422 2.1621 0.9523 60 0.9392 1.6543 1.5935 0.9358 80 1.2517 0.9234 0.9188 1.3011 100 0.9030 0.8970 1.0180 0.9776 125 0.7940 0.8821 0.8743 0.8286 150 0.8376 0.5902 0.5618 0.8247 200 0.7326 0.3441 0.3186 0.7016 300 0.03595 0.1056 400 0.03543 0 : 03669 0,1300 500 0.03498 0.1541 600 0.03640 0.03426 0.03544 0.2012 800 0.2472 0.03368 0.03470 1000 0.03308 0.3035 0.03400 1250 0.03256 0.3585 0.03340 1500 0.03213 0.03290 0.4127 1750 0.4661 0.03175 0.03246 2000 0.5188 0.03141 0.03208 2250 0.03110 0.03173 0,5707 2500 0.6223 0.03083 0.03141 2750 0.03059 0.031 13 3000 0.6736 0.7741 0.03013 0.03062 3500 0.02973 0.8729 0.03018 4000 0,9702 0.02937 0.02979 4500 0,02945 1.0662 0.02905 5000 0.02850 0.02886 1.2552 6000 1.4393 0.02801 0.02835 7000 1.6208 0.02760 0.02793 8000 1.7996 0.02724 0.02753 9000 0.0271 5 1.9724 0.02687 10000 Pressure Lb./Sq: Inch Abs.
Y
Sp. Volume, Cu. Ft./Lb.
in an ideal solution (8)and in coexisting phases following Raoult's (12) and Dalton's laws. I n each of these figures the following ratio of the equilibrium constant, as obtained from experiment and from Raoult's law, is presented as a function of the composition of the liquid phase for propene and 1-butene, respectively.
In addition, the ratio of the equilibrium constant as established by experiment to that estimated from the behavior of an ideal solution (8)has been presented. The latter ratio was established from the following expression which is based on the concepts of
Pressure Lb./Sq: Inch Abs.
Dew point Bubble point 0 14.7 20 30 40 50 60 80 100 125 150 200 300 400 500 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3500 4000 4500 5000 6000 7000 7000 9000 10000
CompressiCompressibility Sp. Volume, bility Factor Cu. Ft./Lb. Factor Temoerature. 250° F. 1-Butene, - 4 . 3 3 1 5 1-Butene, mole fraction-- 4 . 1 7 0 5 mole fractionSp Volume C;. Ft./Lb:
..... ....
I
.....
11.575 8.484 5.629 4.202 3.345 2.7742 2.0602 1.6316 1.2886 1.0597 0.7731 0.4849 0.3390 0.2494 0.1873 0.09743 0.05405 0.04579 0.04250 0.04070 0.03935 0.03823 0.03740 0.03670
. I . .
....
1.000 0.9932 0.9907 0.9860 0.9813 0.9766 0.9719 0.9623 0.9526 0.9404 0.9281 0.9027 0.8494 0.7917 0.7282 0.6560 0.4551 0.3156 0.3342 0.3722 0.4159 0.4595 0.5022 0.5459 0.5893 0.6322 0.7171 0.8001 0.8823 0.9634 1,1210 1.2764 1.4298 1.5812 1.7283
0.03609 0.03509 0.03426 0.03358 0.03300 0.03200 0.03123 0.03061 0.03009 0.02960 1-Butene, --0.6906 mole fractionDew point 0.1560 (497.7) 0.5278 Bubble point 0.04356 (540.8) 0.1601 1,000 0 0.9906 9:gis' 14.7 0.9872 7.263 20 0.9808 4.810 30 0.9743 3.584 40 0.9677 2.8477 50 0.9612 2.3570 60 0.9479 1.7432 80 0.9343 1.3747 100 0.9171 1.0794 125 0.8822 0.8994 150 0,6345 0.8624 200 0.3827 0.7804 300 0,24953 0.6784 400 500 0 : iiio 600 0,2124 800 0,2451 1000 0,3093 1250 0.3619 1500 0.4134 1750 0.4641 2000 0.5140 2250 0.6633 2500 0.6118 2750 0.6598 3000 0.7548 3500 0.8480 4000 0.9396 4500 1.0300 5000 1.2083 6000 1.3821 7000 1.5529 8000 1.7207 9000 1.8861 10000
.....
.....
11.006 8.064 5.348 3.989 3.174 2.6308 1,9514 1.5437 1.2174 0,9998 0.7274 0.4530 0.3134 0.22518 0.16105 0.05629 0.04529 0.04157 0.03957 0.03818 0.03719 0.03644 0,03578 0,03522 0.03471 0.03386 0.03315 0.03255 0.03202 0.03116 0.03050 0.02993 0,02892 0.02941
1 ,000 0.9923 0.9895 0.9843 0.9790 0.9737 0.9685 0.9578 0.9471 0.9337 0.9201 0.8925 0,8338 0.7691 0.6908 0.5929 0,2763 0.2779 0.3188 0.3642 0.4099 0.4563 0 . 5030 0,5488 0.5942 0,6389 0.7271 0.8135 0,8987 0.9823 1.1471 1.3099 1.4690 1.6240 1.7743
1-Butene, --0.8174 mole fraction-0.1827 (442.0) 0.5678 0.04050 (472.5) 0,1345 ..... 1.000 9.583 0.9901 7.016 0.9865 4.645 0.9797 3.460 0.9729 2.7481 0.9660 2.2737 0.9591 1.6802 0.9450 1.3238 0.9307 1.0381 0.9123 0.8471 0.8933 0.6064 0.8526 0.3603 0.7600 0.22710 0.6386 0.04000 0.1406 0.03885 0.1639 0.03726 0.2095 0.2544 0.03619 0.03520 0.3093 0.03443 0.3631 0.03383 0.4162 0.03332 0.4685 0.03287 0.5199 0.03246 0.5705 0.0321 1 0.6208 0.03179 0.6705 0.03120 0.7677 0.03070 0.8633 0.03026 0.9573 0.02989 1.0507 0.02925 1.2338 0.02887 1.4109 0.02819 1.5855 0.02778 1.7577 0.02740 1.9263 (Concluded on page 740)
such a solution and the fact that the fugacity of a component is the same in coexisting phases (9).
(5)
It is apparent from a consideration of Figures 7 and 8 that the propene-1-butene system does not differ greatly from the behavior of a n ideal solution. This would be expected as a result of the small deviations from additive volume shown in Figure 3. The corresponding values of the equilibrium constants based on experimental measurement, Raoult's and Dalton's laws, and ideal solutions have been recorded in Table IV. The experi-
740
INDUSTRIAL AND ENGINEERING CHEMISTRY $'OLUMETRIC BEHAVIOR O F FOUR EXPERIMENTSL MIXTURES TABLE I. SINGLE-PHASE
OF
PROPASE-~-BUTEXE (Concluded)
CompressiCompressiSp. Volume bility Sp. Volume, bility Cu. Ft./Lb: Factor Cu. Ft./Lb. Factor Temperature, 280' F. 1-Butene, 1-Butene, --0.6905 mole fraction7-0.8174 mole fractionDew point Dew point ..... .. . 0 1015 (590.0) 0.404 Bubble point Bubble point .. 0.0566 (610.5) 0.233 0 ..... 1.000 0 ..... 1.000 1.000 0,9920 0.9915 14.7 11.483 0,9934 14.7 10.351 I O , 003 7,583 0.98QO 0.9884 8,418 0.9910 7.327 20 20 5.027 30 0.9835 0.9826 5,586 0.9865 4.856 30 3,749 40 40 0.9779 0,9767 4.171 0.9820 3.620 0,9723 3.321 0.9775 2,9820 50 50 2,8786 0,9708 2.4705 2,7548 60 0,9666 0.9648 0.9730 60 2.3841 0.9551 0.9527 2,0469 0.9639 1.8309 1.7657 80 80 1.4469 0.9435 0,9404 1.6221 0.9549 1.3942 100 100 1,2820 1.1394 125 125 0.9288 0.924G 0.9433 1.0987 1,0553 0,9340 150 150 0.9136 0,9085 0.9318 0,8980 0.7714 0,6767 200 200 0.8825 0.8748 0.9082 0,6485 0.8157 0.4864 0.8589 0.4170 0.28368 0.3958 300 300 0.8009 0,3424 0.7400 0.8062 400 400 0.26465 0.7141 0.19870 0.6479 0.7481 0.25416 500 0.6013 500 0.17S32 0.19313 0.13258 0.5187 0.6821 GOO GOO ..... .... 0.2472 0.5131 0.10896 0.04739 800 800 0.04240 0,2288 0.2761 0,3633 0.06172 0.04234 0,03975 1000 1000 0.2681 1250 0.3213 0,3858 0.04838 0.03942 0.03785 1250 0.3191 0,04403 1500 0.3700 0.3888 0.03783 0.03663 1500 0,3706 0,4290 0.04164 0,03606 0.03687 1750 1750 0.4208 0.03573 0,4217 0.04001 2000 2000 0.4703 0.4710 0.03505 0,4728 0.03891 0.5153 2250 2250 0,5220 0,03633 0.5183 0.03440 0.5637 0,03792 2500 0,03470 2500 0,5580 0,03390 0.5716 0.03713 2750 0.6197 0.03417 0.03341 2750 0.6011 0.6128 3000 0.03645 0,6679 0,03371 0,03301 3000 0.6437 0.6595 3500 0.03293 0 7279 0,03533 0.7630 0.03232 3500 0.7516 4000 0.03229 0,03444 0.8563 4000 0.8423 0.8109 0 , 0 3 174 4500 0.03370 0.9485 0.03174 0.03126 4500 0.9314 0.8927 0.03125 0,03308 0,9736 5000 1,0387 1.0192 0.03080 5000 0,03206 1.1914 1.1323 6000 0.03045 1.2161 0.03008 6000 0.03128 1.3603 1.2889 0.02940 0.029so 7000 7000 1.3881 1.5254 1.4429 0,02924 8000 0.03064 1.5594 0.02890 8000 1,5923 0.02873 9000 0.03006 1,7270 0.02845 1.6861 9000 0.02953 1,7383 1.8411 0,02828 10000 0,02800 10000 1,8886 Figures in parentheses are dew-point or bubble-point pressures expressed as pounds per square inch. Pressure, Lb./Sq. Inch Abe.
CompressiCompressiSp. Volume, bility Sp. Volume, bility Cu. Ft./Lb. Factor Cu. Ft./Lb. Factor Temperature, 280' F. 1-Butene, 1-Butene, --0,1705 mole fraction--0,3315 mole fraction-
Vol. 42, No. 4
.....
Pressure, Lb./Sq. Inch 4bs.
....
f
.
.
.
..
.
.....
TABLE 11. MOLALVOLUMESFOR SISGLE-PHASE REGIOX OF PROPEPI'E-~-BCTESE SYSTEM Pressure, Lb./Sq. Inch Abs.
200 400 600 800
1000 1250 1500 1750 2000 2250 2500
2750 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000 200 400 GOO 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3500 4000 4500 5000 6000
7000 8000 9000 10000
Volumes, Cu. Ft./Lb. Mole 1-Butene, Mole Fraction
0.2 0.4 Temperature, 4O0 F. 1,2819 1,3210 1.2761 1.3153 1 ,2702 1.3105 1.2648 1.3082 1.2594 1.3005 1.2952 1.2545 1,2905 1.2478 1.2857 1,2424 1.2809 1,2378 1.2762 1.2321 1.2709 1,2267 1.2637 1.2217 1,2628 1,2182 1,2647 1,2087 1,2471 1 ,2002 1.2390 1,1922 1.2318 1,1841 1.2180 1,1698 1.2056 1,1572 1.1932 1.1456 1.1827 1.1348 1.1741 1,1253 Temperature, 70° F. 1.3844 ,3444 1.3768 . ,3363 1.3687 ,3273 1.3615 . ,3206 1.3534 ,3125 1.3448 ,3044 1.3372 . ,2955 1.3296 . ,2887 1,3229 ,2811 1.3162 ,2739 1.3110 ,2672 1.3052 . ,2609 1.3005 ,2655 1,2909 . ,2452 1.2824 ,2358 1.2733 .2268 1.2657 . ,2187 1,2604 . ,2034 1.2356 ,1886 1.2213 ,1761 . ,1635 1.2089 ,1509 1.1989
0.6
0.8
1.3654 1,3593 1.3533 1.3492 1.3452 1,3396 1,3346 1,3295 1,3260 1.3215 1.3169 1.3119 1.3088 1.3013 1,2942 1,2866 1.2798 1,2664 1.2538 1.2422 1,2326 1.2245
1.4135 1.4071 1.4029 1.3981 1.3943 1.3885 1.3831 1,3789 1.3751 1.3714 1.3666 1.3634 1.3581 1.3512 1,3432 1.3346 1,3277 1.3138 1.3032 1.2936 1.2829 1 ,2974
1.4229 1.4169 1.4093 1.4043 1.3967 1.3891 1.3815 1.3740 1.3674 1.3619 1,3568 1.3512 1.3467 1.3376 1,3290 1,3209 1.3139 1.2982 1.2836 1.2705 1.2588 1.2482
1 4663 1 ,4599 1.4535 1 ,4476 1 ,4423 1,4348 1.4290 1.4231 1.4178 1.4124 1.4066 1 ,4023 1 ,3959 1,3874 1,3789 1.3709 1.3623 1.3469 1.3346 1.3213 1.3096 1 ,2995
Pressure Lb./Sq.' Inch Abs. 200 400 600 800 1000 1250 1500 1750 2000 2250
2500 2750 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000 200 400 GO0 800 1000 1250 1500 1750 2000 2250 2500
2750 3000 3500 4000 4500 5000 6000
7000 8000 9000 10000
--
Volumes, Cu. Ft./Lb. Mole1-Butene, Mole Fraction
0.2 0.4 Temperature, loo0 F.
1.4207 1 4540 1,4081 1,4435 1.3961 1 ,4331 1 4230 1.3837 1.3788 1,4140 1.3646 1,4030 1.3829 1 3930 1.3430 1,3830 1 3754 1,3336 1 ,3672 1.3242 1 ,3596 1.3161 1,3085 1 ,3529 1,3458 1,3008 1,2883 1,3343 1 ,2770 1 ,3215 1 ,3119 1 ,2667 1 ,3019 1 ,2569 1 ,2847 1.2384 1,2223 1,2676 1,2618 1.2070 1.1927 1,2380 1,1788 1,2247 Temperature, 160' F.
,...
1.6414 1.6006 1.5678 1.5427 1.6166 1 ,4942 1 ,4749 1.4574 1 ,4426 1,4287 1.4161 1.4040 1,3838 1,3667 1.3506 1.3366 1.3115 1.2900 1,2707 1,2327 1.2348
....
1 ,6276 1 . 6000
1.5771 1.5580 1.5404 1,5222 1,5070 1.4917 1.4784 1.4664 1.4545 1.4431 1,4249 1.4087 1.3930 1.3792 1,3548 1.3339 1,3148 1,2962 1,2786
7
0.6
0.8
1.4896 1,4790 1,4694 1,4603 1,4522 1,4426 1.4330 1 ,4240 1.4169 1 .4093 1,4028 1 ,3967 1.3906 1.3795 1,3679 1,3588 1.3497 1.3321 1.3154 1.3013 1.2871 1.2745
1 5270
1.5169 1 . 5095
1 ,5009
1 ,4935 1.4855 1,4775 1.4700 1.4626 1,4556 1.4487 1.4428 1,4370 1.4274 1.4172 1.4082 1,3986 1.3815 1,3655 1,3522 1.3389 1 ,3277
INDUSTRIAL AND ENGINEERING CHEMISTRY
April 1950
74 1
FOR SINGLE-PHASE REGION OF TABLE 11. MOLALVOLUMES
PROPENE-I-BUTENE SYSTEM(Concluded)
Pressure, Lb./Sq. Inch Abs.
Volumes Cu. Ft./Lb. Mole l-ButeAe, Mole Fraction Temperature, 220’ F.
200 400 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000
.... .... ..~.
2.0391 1.8708 1.7684 1,7083 1,6638 1,6275 1.5970 1.5732 1.5512 1.5319 1.4973 1 ,4695 1,4444 1,4228 1.3869 1,3600 1.3353 1.3120 1.2931
.... ....
....
2.0616 1.8794 1,8093 1,7464 1.7068 1.6691 1.6429 1.6162 1.5957 1,5761 1,5575 1.5284 1.5046 1.4817 1.4621 1.4288 1.4035 1.3801 1.3568 1.3367
:
1 9295 1.8719 1,8335 1.8015 1.7680 1.7413 1.7173 1.6971 1.6790 1.6614 1,6470 1,6336 1.6091 1.5873 1.5676 1,5505 1,5206 1.4951 1.4727 1.4535 1.4338
Temperature, 250’ F. 200 400 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000
.... .... ....
4.041 2.3331 2.0139 1.8811 1.8034 1.7473 1.6998 1,6652 1,6347 1.6073 1.5642 1.5283 1.4978 1.4731 1.4296 1.3954 1.3676 1.3447 1.3209
.... ..
,3883 ,0583 ,9204 ,8408 ,7836 ,7383 ,7054 ,6772 ,6524 ,6291 ,5919 ,5585 ,5327 ,5089 ,4703 ,4402 ,4140 ,3901 ,3677
.... ....
2 13293 2.0794 1.9638 1.8895 1,8360 1.7926 1,7547 1.7269 1,7017 1.6800 1.6588 1.6249 1.5946 1.5714 1.5492 1.5123 1.4825 1.4583 1.4351 1.4154
2.0883 1,9945 1.9364 1.8836 1.8415 1.8090 1.7813 1.7568 1.7349 1,7141 1.6976 1,6662 1.6396 1.6150 1.5963 1.5617 1.5297 1.6041 1.4828 1.4631
.... .... ....
....
Temperature, 280° F. 200 400 600 800 1000 1250 1500 1750 2000 2250 2500 2750 3000 3500 4000 4600 5000 6000 7000 8000 9000 10000
....
....
.... .... ....
1
1
0.0
0.2
Figure 4.
1
1
1
0.4
0.6
MOLE FRACTION
I-BUTENE
0.8
IQ
Pressure-Composition Diagram for Propene1-Bu tene System
When a binary system follows Raoult’s and Dalton’s laws this relationship may be expressed in the following form which applies t o isothermal conditions :
(7)
600
1
- 500 W
U
a
mental information available concerning the influence of pressure and temperature on the specific volume of propene (3) and 1butene ( 1 1 ) was employed to establish the fugacity of these compounds. The latter information was utilized t o obtain the values of the equilibrium constants based on ideal solutions. Experimental data were taken from the same sources (3, 1 1 ) concerning the vapor pressure of propene and 1-butene required for the calculation of equilibrium constants based on the laws of Raoult and Dalton. The information presented in Figures 7 and 8 permits a n additional comparison of the actual behavior with that predicted from the laws of Raoult ( 1 2 ) and Dalton and from ideal solutions (8). The basic relationship of Gibbs ( 4 ) and Duhem ( 2 ) for the propene-1-butene system is as follows:
5
400
a W a v1
2 300 3
2 U W
3
200
v)
in W
a
P
100
1 50
Figure 5.
1
J
1
1
100 150 TEMPERATURE
200
250
OF
Pressure-Temperature Diagram for Propene1-Butene System
INDUSTRIAL AND ENGINEERING CHEMISTRY
742
I n an ideal solut,ion the analogous expression for isothermal conditions becomes: d_In YI.3
dx,
- d In Y Z , ~ = 0
3 - - - -dXa n
4
TABLE 111. Ternperature,
F.
(8)
40
Mole Fraction 1-Butene Liquid Gas 1.000 1.000 0.674 0.887 0.436 0.743 0.291 0.600 0.199 0.467 0.126 0.336 0.071 0.207 0.027 0,086 0.000 0.000 1,000 1.000 0.943 0.983 0.888 0.698 0.793 0.531 0.319 0.606 0.188 0.429 0,216 0.080 0.017 0.006 0.000 0.000 1.000 1.000 0.880 0 . 702 0,746 0.491 0.587 0.329 0.440 0.213 0.129 0.284 0.144 0.062 0.000 0.000 1,000 1.000 0.930 0.970 0.781 0.608 0,604 0.410 0.272 0.440 0.166 0.284 0.142 0.082 0.000 0.000
Pressure, Lb./Sq. Inch Abs. 21.9Q 30
_-
A0
50 60 70 80 90 97.5b 38.Za 40 50 60 80 100 125 I50 152.lb 62.ja 80 100 125 150 175 200 227.3b 142.ga 150 200 250 300 350 400 456.6b
Equations 7 and 8 are specific in their application t o the conditions a t the phase boundary and do not include the restraint of constancy of pressure indicated io in Equation 5 . This follows since the so-called activity coefficient, y ( 9 ) , for the cases of Raoult's law and ideal solutions is independent of pressure. This is indicated by the defining relationships 100 of Equations 4 and 5 , respectively. Likewise, as is shown in Equation 7, this coefficient as defined by Equation 5 is independent. At a temperature of 100" F. the average disagreement of the first equality of Equation 7 expressed in 160 Brigg's logarithm a t compositions of the liquid phase from 0.20 to 0.80 mole fraction propene was 0.0596 whereas a t 160" F. it was 0.0753. In comparison with the behavior of ideal solutions described by Equation 8 the corresponding deviations were 0.0090 and 0.0043, respectively. Insufficient information was available to permit the application of Equation 6 to the data. The deviations from Equations 7 and 8 indicate quantitatively the differences in the actual behavior from the laws of Raoult and Dalton and from the characteristics of an ideal solution. ACKNOWLEDGMENT
This investigation was conducted as a result of fellowships received from the Socony-Vacuum Corporation. The advice
Vol. 42, No. 4 PROPERTIES OB COEXIsTlNG
Volume, Cu. Ft./Mole Liquid Gas 1.464 232.6 1.423 166.6 1.407 125.5 1.374 101.4 1,342 85.69 1.316 72.26 1.286 61.24 1.263 52.56 1.249 47.25 1.526 137.2 1.520 130.2 1,507 102.7 1, ,470 84.84 1.428 62.33 1.395 48.92 1.351 38.00 1.315 30.84 1.313 30.33 1.583 85.53 1.551 65.53 1.524 51,66 40.72 1.489 1.469 32.87 1.437 27.47 1.412 23,42 1.396 19.85 1.735 37.79 1,726 35.56 1.685 23.55 1.658 19.66 1.641 13.02 1.640 10.69 1.650 10.13 1.676 8,421
EZonstants uilibrium Propene 3.954 2,908
2.190 1.772 1.502 1.315 1,171 1,064 1,000 3.521 3,364 2 . 700 2.264 1.730 1.420 1.174 1.011 1.000 3.136 2.472 2,002 1.625 1.382 1.218 1.096 1 ,000 2,500 2.337 1,791 1.491 1 299 1.165 1,070 1,000
1-Butene 1.000 0,789 0.587 0.485 0.426 0.375 0.341 0.316 0.303 1.000 0.959 0.783 0.670 0,526 0.439 0.370 0.333
0,330 1.000
0,798
0,658 0 560 0.494 0,454
0.431 0.411 1.000 0,959 0.778 0.679 0.619 0.585 0.574 0.581
and assistance obtained from W. N. Lacey and H. IS. Reamer are greatly appreciated. NOMENCLATURE
d f
total derivative = fugacity K = equilibrium constant In = natural logarithm n = weight fraction of a component in the system nk = mole fraction of component k in a phase or system P = pressure, pounds per square inch absolute P" = vapor pressure of component V = specific volume, cubic feet per pound =
l.0C
0.9:
?
: 8 f E
0.91
0.8
0
0 < 0.8
0.7
Figure 6. Product of Equilibrium Constant and Pressure for Propene and 1-Butene in Propene-1-Butene System
Figure 7.
Ratio of Equilibrium Constant for 1-Butene in Propene-1-Butene System
INDUSTRIAL AND ENGINEERING CHEMISTRY
April 1950
743
(4) Gibbs. Works.” Vol.and 7 New “Collected York, Longmans, Green -I
PHASES IN PROPENE-~-BUTENE SYSTEM Volume Mole Fraction Cu. Ft./Mole 1-Butene Gas ’ Liquid Liquid Gas F. 18.07 1.948 1.000 1.000 220 282. 1.942 16.57 0.954 0.917 300 1.938 13.45 0.834 0.735 350 1.950 11.oo 0.720 0.600 400 1.957 9.079 0.610 0.490 450 1.973 7.771 0.508 0.399 500 2.020 6.760 0.411 0.324 550 6.935 2.184 0.320 0.255 600 2.298 5.200 0.276 0.224 625d 2.539 4.752 0.232 0 . I96 650d 2.906 4.182 0.188 0,172 675” 3.559 2.944 0.180 0.172 680d 3.109 3.109 0.176 0.176 681.5Cpd 2.132 12.46 1.000 1.000 250 381. 1.975 11.47 0.961 0.938 400 2.157 9.468 0.796 0.860 450 2.176 8.012 0.686 0.766 500 2.288 6.753 0.593 0.674 550 2.263 6.268 0.519 0.585 600 2.340 6.023 0.550 0.491 620d 2.589 5.792 0.467 0.515 640d 2.928 5.415 0.447 0.479 66Od 3.293 3,625 0.446 0.453 675d 3.377 3.377 0.449 0.449 676.2C9d 2.523 7.445 1.000 1.000 280 50Ba 2.448 7.040 0.966 0.952 525 2.364 6.334 0.920 0.893 550 2.443 5.700 0.871 0.834 580 2.851 5.166 0.835 0.797 600d 3.332 4.515 0.801 0.771 620d 3.485 4.336 0.793 0.770 625d 3.666 3.666 0.783 0.783 630Csd C Critical state. a Vapor pressure of I-butene. d Estimated values in oritical region. b Vapor pressure of propene.
Temperature,
Pressure, Lb./S Inch Aqds.
Co., 1931. (5) Gilliland and Scheeline, IND.ENG. CEEM.,32, 48 (1940). (6) Hachmuth, H a n s o n , a n d S m i t h , Trans. Am. I n s t . Chem. Engrs., 42, 975 (1946). (7) Lamband Roper, .J. Am. Chem. Soc., 62,806 (1940). (8) Lewis, Ibid., 30, 668 (1908). (9) Lewis and Randall, ” T h e r m o d y namics and Free Energy of Chemical Substances,” p. 254, New York, McGraw-Hill Book Co., 1923. (10) Nysewander, Sage, and Laoey, IND. ENG. CHEM.,32, 118 (1940). (11) Olds, Sage, and Lacey, Ibid., 38, 301 (1946). (12) Raoult, Z. physik Chem., 2, 353 (1888). (13) Roper, J. Phys. Chem.,44, 835 (1940). (14) Sage, Hicks, and Lacey, Ibid., 32, 1085 (1940). (15) Sage and Lacey, Trans. Am. I n s t . Mining Met. Engrs., 136, 136 (1940). (16) Seibert and Burrell, J. Am. Chem. Soc., 37, 2683 (1915). (17) Vaughan and Graves, IKD. ENG. CHEM.,32, 1252 (1940). (18) Winkler and Maass, Can. J . Research, 9 , 610 (1933).
Equilibrium Constants Propene 1-Butene 1.000 0.961 0,880 0.834 0.803 0.786 0.790 0.797 0.810 0.843 0.914 0.956 1.000 1.000 0.976 0.926 0.896 0.880 0.887 0.894 0.908 0.933 0.984 1.000 1.000 0.986 0.970 0.958 0.954 0.962 0.972 1.000
1.918 1.817 1.590 1.428 1.309 1.221 1.141 1.096 1.072 1.047 1.020 1.009 1,000 1.652 1.592 1.453 1.342 1.245 1.159 1.130 1.098 1.061 1.013 1.000 1.443 1.400 1.347 1.283 1.231 1.152 1.108 1.000
RECEIVED July 11, 1949
= mole fraction of component k in liquid phase
I k = mole fraction of component IC in gas phase y fik
= activity coefficient = chemical potential of component
T A B L EIV.
k, B.t.u./mole
Pressure, Lb./Sq. Inch Abs.
Subscripts 3 = propene 4 = 1-butene gas phase ideal solution IC = either component 1 = liquid phase R = Raoult’s law
LITERATURE CITED
(1) Coffin and Maass, J . Am. Chem. Soc., 50, 1427 (1928). (2) Duhern, Compt.rend., 102, 1449 (1886). (3) Farrington and Sage, IND. ENG.CHEM., 41, 1734 (1949).
...
2:925 2.227 1.809 1.531 1.185 1.000
3:250 2.438 1.950 1.625 1.219 1.000
62.5b 80 100 125 150 200 227.3C
1.000 0.798 0.658 0.560 0.494 0.431 0.411
Temperature, looo F. 1.000 1.000 3.136 0.811 0.781 2.472 0.677 0.625 2.002 0.572 0.500 1.625 0.505 0.417 1.382 0.438 0.312 1.096 . 1.000
..
2:378 1.946 1.602 1.376 1.096 1.000
21841 2.273 1.818 1.515 1.136 1,000
142.9b 150 200 250 300 400 456.6O
1.000 0.959 0.778 0.679 0.619 0.574 0.581
Temperature, 160° F. 1.000 1.000 2.500 0.963 0.953 2.337 0.785 0.714 1.791 0.685 0.572 1.491 0.626 0.476 1.299 0.578 0.357 1.070 .. 1.000
2:i& 1.753 1.472 1.289 1.072 1.000
3:044 2.283 1.826 1.522 1.142
282.66 300 350 400 500 600 681.5d
1,000 0.961 0.880 0.834 0.786 0.797 1.000
525 550 580 600 620 630d 100
200 PRESSURE
so0 M O 400 POUNDS PER SQUARE INCH
600
Figure 8.
Ratio of Equilibrium Constant for Propene in Propene-1-Butene System
... ... ... ... ... .
I
d
.
1.000 0.986 0.970 0.958 0.954 0.962 1IO00
Ideal
...
...
...
.
Temperature, 220° 1.000 1.000 0.963 0.942 0.884 0.807 0.830 0.706 0,773 0.565 0.763 0.471
...
..
,
Temperature, 280° 1.000 1,000 0.979 0.964 0.962 0.920 0.946 0.872 0.938 0.843 0.930 0.816
...
.. .
1.000
F. 1.918 1.817 1.590 1.428 1.221 1.096 1,000
1:892 1.683 1.529 1.323 1.195
. ..
... ...
.. ...... ... ... ,
F. 1.443 1.400 1.347 1.283 1.231 1.152 1.000
1.’724 1.672 1.616 1.582 1.552
.,.
Experimental values based on propene-1-butene system. of 1-butene. Vapor pressure of propene. Critical state.
b Vapor pressure 0
Experimental
Temperature, 40” F. 3.954 ... 2.908 ... ... 2.190 ... ... 1.772 1.502 1.172 1.000
506 b
L
Propene Raoult’s law
Raoult’s law
80 97.50
Superscripts ‘ = pure substance
1-Butene Experimentala
Ideal
21.9a 30 40 50 60
11
COMPARISON OF EQUILIBRIUM CONSTANTS OF PROPENE--I-BUTENE
...
... ., .
... .. ... ,
...
