January 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
In the three systems tested using phenol, toluene, methylcyclohexane, and iso-octane the data were of such nature as to preclude any definite appraisal of the accuracy of the prediction. The binary data were sparse and not too consistent, so that very little credibility could be placed on the parameters obtained. The multicomponent data showed points which were considerably scattered. Drickmer et al. ( S ) , from whose paper the bulk of the data was taken, could not get good correspondence between their binary data and their extrapolated ternary data. The only conclusive result of these later systems was the ability of the prediction to get better results than Raoult’s law calculations. Vapor pressure data for the pure components used in the systems tested in this paper were obtained from Stull (10), Perry (IC), and the “Handbook of Chemistry and Physics” (IO). CONCLUSIONS
In general, the method of prediction given in this paper warrants further investigation, based on systems which have data of euch character that the results of the tests would be conclusive. Further work is being done to simplify the calculation procedure for the prediction of ternary systems. NOMENCLATURE
C , = coefficient for equation of Othmer plot g = total excees free energy of a system divided by 2.303RT 0, = partial molal a for comDonent i
8::
rtli parameter for component z in the activity coefficient power series expression in terms of component j P = pressure of system p , = partial pressure of component i in vapor phase p: = vapor pressure of pure component i p: = vapor pressure of reference material at same temperature as system 7 = integer representing number of a parameter in the activity coefficient power series expression S, = exponent for the equation of Othmer plot x, = mole fraction of component i in homogeneous system, liquid phase y 7 = mole fraction of component j in vapor phase at]= relative volatility of component i compared to component j a!> = ideal relative volatility =
a{ = yi = yzl =
199
relative volatility deviation = y I / y l = a i , p : / p : activity coefficient of component i in homogeneous system activity coefficient of component i in binary system i-j expressed as a power series in terms of x1 LITERATURE CITED
(1) Carlson, H. C.,and Colburn, A. P., IND. ENO.CHEM.,34, 581 (1942). (2)Cornell. L.W..and Montonna. R. E.. Ibid.. 25. 1331 (1933). (3j Drickmer, H G., Brown, G. G., and White, R: R., Trans. ’Am. Inst. Chem. Engrs., 41, 555 (1945). (4) Gilmont, R., Weinman, E A,, Kramer, F., Miller, E., Hashmall F.,and Othmer, D. F., IND. ENG.CHEM.,42, 120 (1950). (5)Griswold. J., and Dinwiddie. J. A.,Ibid., 34, 1188 (1942). (6)Harrison, J. H., and Berg, L:, Ibid., 38, 117 (1946). (7)Hausbrand, E., “Principles and Practice of Industrial Distillation.” New York, John Wiley & Sons, 1925. (8) Herrington, E. F. G., Research, 3, 41 (1950). (9) Hildebrand, J. H.,“Solubility of Non-Electrolytes,” 2nd ed., p. 65,New York, Reinhold Publishing Corp.. 1936. (10) Hodgman, C. D., editor, “Handbook of Chemistry and Physics,” 28th ed., Cleveland, Chemical Rubber Publishing Co., 1944. (11)b a r , J. J., Van, 2.physik. Chem., 72,723 (1910):83,599(1913). (12) Margules, M., A k a d . Wiss. Wien. Math. .Vaturzc. Klasse II, 104, 1243 (1895). (13) Othmer, D.F.,IND.ENG.CHEM.,32, 841 (1940). (14) Perry, J. H.,editor, “Chemical Engineers’ Handbook.” 2nd ed., New York, McGraw-Hill Book Co., 1941. (15) Quiggle, D.,and Fenske, M R., J. Am. Chem. SOC.59, 1928 (1937). (16) Redlich, O.,and Kister, A. T., IND.ENG.CHEM.,40,345 (1948). (17) Reinders, W., and blinjer, C. H. de, Rec. trav. chim., 59, 369 (1940). (18) Scatchard, G.,Trans. Faradall SOC.,33, 160 (1937). (19)Scatchard, G.,and Hamer, W. J., J . Am. Chem. Soc.. 57, 1805 (1935). (20) Stull, D. R.,IND. ENG.CHEM.,39, 517 (1947). (21) White, R. R.,Trans. Am. Inst. Chem. Engrs., 41,539 (1945). (22) Wohl, K., Ibid., 42,215 (1946). R E C E I ~ Efor D review September 5 , 1952. ACCEPTED July 23, 1953. Presented before the Division of Industrial and Engineering Chemistry at the 118th Meeting of the AMERICAN CHEMICAL SOCIETY, Chicago, Ill. MEterial supplementary t o this article has been deposited Document 4097 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the document number and b y remitting $1.25 for photoprinb or $1.25 for 35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
=
Volumetric Behavior of Isopentane REGINALD ISAAC, KUN LI, AND L. N. CANJAR Carnegie Institute of Technology, Pittsburgh, Pa,
T
HE only extensive compressibility data available on isopentane (2-methylbutane) were obtained by Young (8)in 1894. As work done in this laboratory (6) and by other investigators ( 2 , 3, 7) on n-pentane indicated that the measurements of Young ( 9 ) are inaccurate, it became necessary to remeasure the P-V-T properties of isopentane so that present knowledge of the compound would be complete and accurate. Beattie, Douslin, and Levine ( 1 ) have recently measured the compressibilities of neopentane (2,2-dimethyl propane). With this lyork complete information on all the pentanes is now available. The apparatus and method employed in this investigation have been described by Cherney, Marchman, and York (b), who modified the original design by J. A. Beattie of the Massachusetts Institute of Technology. A modification of their technique (6) is necessary when the sample to be measured is a liquid a t room temperature. The charging technique used in this investigation differed only slightly from that described by Li and Canjar (6). The isopentane used for these measurements was an American
Petroleum Institute research sample which was already sealed under vacuum in a glass ampoule. Charging the glass ampoule directly into the compressibility bomb eliminated several possible sources of error due to air leaks. The API research sample of isopentane has a purity of 99.89 f 0.05 mole % and was made available for this investigation by the American Petroleum Institute Research Project 44 a t the Carnegie Institute of Technology from the series of 4PI research samples of hydrocarbons purified by the American Petroleum Institute Research Project 6. The volumetric behavior of isopentane was studied by Young (8) using the capillary glass tube method over a range of temperatures from 10’ to 280” C. and a pressure range up to 1000 pounds per square inch absolute. I n this investigation the data have been extended to cover a wider range of pressures (150 to 3100 pounds per square inch absolute). The temperature range extended from 212’ to 572’ F. The data include four isotherms in the liquid region and five isotherms in the superheated region.
INDUSTRIAL AND ENGINEERING CHEMISTRY
200
Vol. 46, No. 1
TABLEI. P-V-T DATAFOR ISOPENTANE P , Lb./Sq. Inch
d , Lb.-Mole/ Cu. Foot
P,Lb./ Sq. Inch
212°,F.
152.78 522.39 891.99 1266.35 1631.21 2037.67 2370.43 2759.61 3109.64
390.91 393.95 396.62 399.74 402.41 405.46' 405.46'' 421.72 522.51 892.07 1289.48 1631.24 2000.84 2372.84 2737.08 3109.65
257' F. 0.4388 0.4472 0.4540 0.4601 0.4654 0.4700 0.4747 0.4816
0.08804 0.09002 0.09209 0.09427 0.09654 0.0991:b 0.3326 0.3364 0.3541 0.3837 0.4011 0.4118 0.4211 0.4291 0.4358 0.4420
516.68 560.80 602,24 648.86 702.65 775.36 837.70 970.41 1261.17 1630.72 2000.29 2364.71 2736.23 3109.05
455.63 485.99 012.80 538.50 562.20 584.27 601.34 648.04 920.14 1329.60 1716.33 2009.37 2370.36 2739.96 3109.55
0.3919 0.4046 0.4184 0.4287 0.4369 0.4441 0.4501 0,4554 0.4607
0.08798 0.1014 0.1162 0.1361 0.1644 0.2070 0.2380 0.2798 0.3389 0.3696 0.3868 0.3968 0.4068 0.4141 0.4227
TABLE 11. VAPORPRESSURES AND SATURATED LIQUID DENSITIES T,' F. 257 302 347
Vapor Pressure Lb./Sq. Inch Ads. 174.61 271.49 405.46
d, Lb.-iMole/
P Lb/
Cu. Foot
Si. Inch
0.08752 0.1014 0.1163 0.1363 0.1647 0.2075 0.2392 0.2816 0.3242 0.3519 0.3698 0.3830 0.3938 0.4029
633.77 702.06 772.27 860.26 979.26 1057.95 1165.79 1370.66 1628.79 2039.54 2367.83 2820.45 3106.96
Saturated Li uid Density, Lb.-MoleyCu. Foot 0.4276 0.8913 0.3326
d, Lb.-Mole/ Cu. Foot
527O F.
437' F.
0,08782 0.1014 0.1165 0.1367 0.1655 0.1850 0.2097 0.2477 0,2811 0.3147 0.3338 0.3530 0.3628
482O F. 575.61 631.45 687.99 755.68 842.29 970.66 1082.27 1313.55 1629.88 2006.34 2369.09 2730.62 3108.28
392' F.
302' F. 279,81 522.63 891.22 1261.81 1631.42 1932.02 2370.62 2740.23 3126.88
P , Lb.-/Sq. Inch
Cu. Foot
347' F. 0.4290 0,4654 0.4710 0.4759 0,4804 0.4849 0.4883 0.4920 0.4953
522.64 89.20 1270.57 1631.41 2001.01 2352.55 2740.23 3109.83
d , Lb.-Mole/
0
0 08787 0.1014 0.1164 0.1365 0.1651 0.2087 0.2405 0.2835 0.3169 0.3417 0.3588 0.3718 0,3829
572' F.
I
690.79 771.38 855.94 965.60 1118.65 1270.28 1626.69 1996.13 2365.63 2799.06 3104.69
0.08777 0.1014 0.1165 0.1369 0.1660 0.1938 0.2470 0.2830 0.3085 0.3301 0.3422
Vapor pressure.
b Saturated vapor density, 0
Saturated liquid density.
TABLE IV, COMPARISON OF VAPORDENSITIES OF ISOPEKTANE) Pressure, Lb./Sq. Inch 562.20 584.27 601.34 648.04
Vapor Densities, Lb.-Mole/Cu. Foot Young This Pc-ork 0.1722 0.1645 0,2070 0.2187 0.2426 0.2380 0.2768 0.2798
TABLE V. COMPARISON OF VAPORPRESSURES OF ISOPENTANB TABLE 111. COMPARISON OF LIQUIDDENSITIES OF ISOPENTANE Pressure Lb./Sq. In& Abs. 279.81 522.63 891.22
1302' F. (150' C.)] Liquid Densities, Lb.-Mole/Cu. Foot This work Young 0.3857 0.4001 0.4151
0.3919 0.4040 0.4184
F. (" C.) 257 (125)
302 (150) 347 (175)
Vapor Pressure, Lb./Sq. Inch Abs. Young This work 171.06 174.61 271.4% 266.92 398.85 405.46
TABLEVI. RESIDUALS FROM B-W-R ( P o a l o d . - P o b s d . ) ISOPENTANE Density, Lb./Cu. Foot
FOR
One sample of 17.174 grams was used to cover the entire range of 0.1 0.2 0.3 pressures and temperatures. The pressure a t a density of 0.08T, F. Lb./Sq. Inch Abs. 8036 pound-mole per cubic foot and 347' F. was measured a t the 392 12.5 7.0 25.1 437 21.0 6.3 39.0 beginning and the end of the work to determine if any decomposi482 23.0 19.5 57.5 tion had occurred. No change in pressure was observed. 527 28.5 39.0 83.5 572 36.5 55.6 109.0 A summary of the experimental data is given in Table I. The vapor pressure and saturated liquid densities a t three TABLEVII. SMOOTHED COMPRESSIBILITY FACTOR FOR ISOPENTANE temperatures are given in Table 11. (Compressibility factor, P V / R T ) The densities of saturated liquids were Pressure, Temperature, F. Lb./Sq. not measured directly but obtained by Inoh Abs. 200 250 300 350 400 450 500 550 600 extrapolating experimental data to the 0.7678 0.8056 0.8260 400 0.1222 0.1175 0.1181 0.5729 0.7901 0.7835 0,8078 450 0.1361 0.1312 0.1320 0.4690 vapor pressure. Although this extra0.7141 0.7628 0.7410 500 0.1501 0.1480 0.1507 0.1672 0.6873 0.7413 0.7740 550 0.1643 0.1622 0.1648 0.1802 polation is accurate for liquid densities, 0.6617 0.7195 0.7550 600 0.1791 0.1769 0.1790 0.1933 0.6365 0.7019 0.7428 650 0.1932 0.1910 0.1930 0.2069 large uncertainties appear in the satu0.6125 0.6845 0.7298 700 0.2083 0.2050 0.2070 0.2195 rated vapor volume when determined 0.6631 0.6510 0.7082 800 0.2374 0.2338 0.2351 0.2458 0.5250 0.6205 0.6843 0.2710 0.2619 0.2623 900 0.2660 in this way. Hence the saturated vapor 0.4965 0.5952 0.6658 0.2972 1000 0.2948 0.2901 0.2900 0,5026 0.5605 0.6277 1500 0,4375 0.4275 0.4229 0.4249 volumes are not reported. The maxi0.5891 0.6213 0.6618 0.5510 0.4985 0.6601 2000 0.5777 0.6851 0.7046 0.7305 mum uncertainty in the reported 2500 0.7148 0.6919 0.6761 0.6681 0.7845 0.7945 0.8070 3000 0,8485 0.8211 0.8002 0.7865 values of density is estimated to be Table VI1 does no! hare t h e sanie accuracy as the original data listed iri Table I. Addition211 uncer0.27%. The uncertainty is considertainties exist due to IIiterpolation and extrapolatiori. ably less a t the lower densities.
-
January 1954
20 1
INDUSTRIAL AND ENGINEERING CHEMISTRY
Liquid and vapor densities are compared with those of Young (8) in Tables I11 and IV. A comparison of vapor pressures is given in Table V. It is evident that considerable differences exist between the data of Young and those obtained in this laboratory. The disagreement in vapor pressure data is in the same direction and of the same order of magnitude as that observed in Young’s data on n-pentane when compared with the work of Beattie, Douslin, and Levine ( 9 ) and the work done in this laboratory (6). It can be concluded then, that the information presented here is more reliable. Benedict, Webb, Rubin, and Friend ( 4 ) have fitted an equation of state to the data of Young (8). This equation therefore also deviates from the compressibility data presented here. I n general, the pressures calculated by the equation of state are higher than the observed pressures, Table VI gives a few of the residuals from the Benedict-Webb-Rubin equation in the superheated region. The residual is defined as the calculated pressure minus the observed pressure. No attempt was made to adjust the original equation as presented by Benedict, Webb, Rubin, and Friend.
BENEDICT-WEBB-RUBIN EQUATION FOR ISOPENTANE
P
= RTd
+ (BoRT-Ao-Co/T*)d2+ (bRT-a)d3 + aad6 + $ [(l+ydZ)e-Yd2]
Bo
b
= 2.56386 A0 = 4825.36 Co X 10-6 = 21336.7 P = lb./sq. inch
a
c X 10-6
= 17.1441 = 226902
136025.0 d = 1b.-mole/ou. foot =
a X 102 = 6987.77 y X 102 = 1188.07
R = 10.7335 T = degrees Rankin
LITERATURE CITED
(1) Beattie, J. A., Douslin, D. R., and Levine, S. W., J. Chem. Phya., 20,1619 (1952). (2) Beattie, J. A., Levine, S. W.. and Douslin, D. R., J . Am. Chem. Soc.. 73. 4431 (1951). (3) Ibid.i74,4778(1962).’ (4) Benedict, M.,Webb, G . B.,FRubin, L. C , , and Friend, L., Chem. Eng. Progr., 47,419 (1951). 15) Chernes, B. J., Marchman. H.. and York, R., IND.ENG.CHEM., 41. 2653 (1949). (6) Li, Kun, and Canjar, L. N., Chem. Eng. Progr. Symposium Series No. - -. 7. 49 ~- (1963). . /
(7) Sage, B. H., Lacey, W. N., and Schaafsma, J. G., IND.ENQ. CHEM.,27,48 (1935). (8) Young, S., Proc. Phys. Soe. (London),13, 602 (1894-95). (9)Young, S.,J . Chem. SOC.(London), Trans.,71,446 (1897). RECEIVED for review June 5, 1953.
ACCEPTEDSeptember 17, 1953.
Single-Constant Linear Equation for Vapor-Liquid Equilibria in Binary Systems R. S. NORRISH AND G. H. TWIGG Research and Development Department, The Distillers Co., Ltd., Great Burgh, Epsom, Surrey, England
T
HE importance of vapor-liquid equilibria for the design of
distillation columns has directed much attention to the derivation of algebraic expressions for smoothing experimental data, checking the internal consistency of the results, and predicting complete equilibrium curves from a minimum of experimental points. Unfortunately, most of the equations, including the well-known Margules and Van Laar relations, are valid only for conditions of constant temperature, whereas the great majority of distillations are carried out under conditions of constant total pressure. These semitheoretical equations based on the GibbsDuhem equation suffer from the further practical disadvantage that their use requires conversion of the experimental equilibrium results to activity coefficients to give a nonlinear plot and subsequent reconversion to x,y data, involving an accurate knowledge of the boiling point as a function of composition. More recently, entirely empirical linear equations have been proposed by Clark (8)which accurately relate vapor to liquid compositions for many systems a t constant pressure and do not require a knowledge of the boiling points. These equations, however, involve three and sometimes four arbitrary constants. The equation now proposed is linear, is immediately applicable to experimental equilibrium measurements at constant pressure without knowledge of the boiling point curve, contains only one arbitrary constant, and has been verified for 25 different constantpressure systems involving a wide range of chemical types. The equation does not apply to systems containing water as one component. EMPIRICAL EQUATIONS
Z is a function of x and y only, defined by the equation:
where K is the ratio of the molar latent heat of vaporization of the lorer to that of the higher boiling component. When experimental values of 2 a t constant pressure are plotted against xl,it is found that the points lie on a straight line: 2 = Mzt
+c
(2)
where .W and C are constants for a given system a t a given total pressure. Equation 2 has been verified for the 25 systems listed in Table I, and Figure 1 shows some typical plots. The apparently large deviations a t the ends of some of the lines correspond to comparatively small errors in the equilibrium data, as the sensitivity of Z to changes in x and y is a t a minimum near the middle of the plot and increases rapidly to infinity a t the ends. For example, an error in x of 0.001 mole fraction results in an error in 2 of 0.004 a t x = 0.5, but of 0.1 at z = 0.01. In particular, apparent deviations in the systems heptane-methylcyclohexane and 2,2,4-trimethylpentane-methylcyclohexane can be shown to be within the probable analytical error and apparent deviations in the plot for chloroform-cyclohexane disappeared completely when the materials were dried through silica gel and precautions taken to exclude atmospheric moisture from the still (see Figure 2 and Table 11). The only systems tested which did not give linear plots were those containing water as one component. It is not known why aqueous systems show anomalous behavior, but it is probably significant that because of the low
