278
Ind, Eng. Chem. Fundam. 1981, 20, 278-200
Critical States of Propane-Isomeric Hexane Mixtures Sun W. Chun,' Webster B. Kay, and Amyn S. Tela* DepaHmnt of Chemical Englneetfng, The Ohio State Universw, Columbus, Ohlo 43210
Critical states of the fwe binary systems of n-hexane, 2-methylpentane, Smethylpentane, 2,2dimethyibutane, and 2,3-dimethylbutane with propane as the common component have been measured and are presented in this paper. A simple method based on the concept of excess (critical) propetties has been used to correlate the data. The excess critical temperature and the excess critical pressure of all five systems attain a maximum value at a p proximately the same composition of propane, indicating that the position of the maxima in these curves may be a function solely of the size (and not shape) of the pure components.
Introduction The locus of critical points of mixtures defines the condition where the coexisting liquid and vapor phases become identical in their properties. It is therefore a curve of considerable interest in many chemical engineering operations. For many years, this laboratory has conducted a study of the effects of size, shape, and chemical nature of the pure components on the critical locus curve of binary systems. The present work forms part of this continuing study. Propane-isomeric hexane mixtures constitute a set of binary systems in which the sizes of the pure Components remain effectively constant but the shape of the noncommon component changes. From our experimental data, we hope to draw conclusions about the effect of shape on the critical loci of these relatively simple nonpolar mixtures. Experimental Section The apparatus and experimental procedure for the determination of critical points were similar to those used in our previous studies (Kay and Rambosek, 1953; Jones and Kay, 1967) and will not, therefore, be described here. The five research grade isomeric hexanes were obtained from Phillips Petroleum Co., who furnished the following analysis of their purity, with the most probable impurity given in parentheses: n-hexane (methylcyclopentane) 99.96%; 2-methylpentane (3-methylpentane) 99.7%; 3methylpentane (Bmethylpentane) 99.83 % ; 2,2-dimethylbutane (2,3-dimethylbutane)99.99%; 2,3-dimethylbutane (2,2-dimethylbutane)99.81%. After percolation over silica gel, the samples were thoroughly degassed by repeated freezing, pumping under vacuum, melting, and distilling cycle of operations. Research grade propane with a purity of 99.99% was also provided by the Phillips Petroleum Co. It was degassed and packaged in sealed glass ampules ready for loading into the experimental tube. As a purity check, bubble and dew point pressures at constant temperature were determined for the pure isomeric hexane samples. If the two pressures differed by more than 0.17 bar, the sample was discarded. The measured critical properties of the pure components agreed with values found in the literature, as shown in Table I. We estimate the precision of our pressure measurements to be f0.02 bar and accuracy to be f0.05 bar. The pre*School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA 30332. 'Pittsburgh Energy Technology Center, 4800 Forbes Ave., Pittsburgh, PA 15213.
Table I. Critical Properties of the Pure Compounds substance
T,, K
propane
369.72 369.96 369.96 n-hexane 507.95: 507.89 2-methylpentane 497.85 498.09 3-methylpentane 504.62 504.39 2,2-dimethylbu- 489.01 tane 489.39 2,3-dimethylbu - 500.2 3 tane 500.29
pc, bar
vc,m3 kmol''
ref
42.61 42.57 42.57 30.17 30.32 30.31 30.34 31.28 31.24 30.86 31.06 31.47 31.40
0.195 0.200 0.195 0.371 0.368 0.367 0.367 0.368 0.367 0.364 0.359 0.356 0.358
this work Rossini (1953) Beattie (1937) this work Rossini (1953) this work Rossini (1953) this work Rossini (1953) this work Rossini (1953) this work Rossini (1953)
Table 11. Critical States of Propane-Isomeric Hexane Mixtures XDroDane
0.1435 0.4437 0.6996 0.8201 0.9218
Tc, K
Pc, bar Vc, m3 kmol-I Propane t n-Hexane 496.30 35.27 0.335 468.17 44.34 0.305 431.26 49.75 0.244 409.50 49.41 0.216 387.55 46.55 0.201
Propane + 2,2-Dimethylbutane 0.1527 477.91 35.17 0.4490 450.81 43.10 0.6587 425.36 46.81 0.8205 401.93 46.98 0.9194 385.15 45.25
0.337 0.282 0.235 0.214 0.206
0.1497 0.4446 0.6488 0.8196 0.9190
Propane t 2-Methylpentane 486.49 34.77 458.19 43.68 431.97 47.79 405.45 48.00 386.58 45.77
0.339 0.277 0.240 0.212 0.199
0.1451 0.4453 0.6554 0.8336 0.8850
Propane + 3-Methylpentane 492.65 36.13 4 62.68 45.22 436.37 49.01 404.92 48.63 391.01 46.85
0.319 0.268 0.255 0.214 0.207
Propane t 2,3-Dimethyfbutane 0.1 516 488.41 36.15 0.4522 459.36 44.50 0.6508 432.05 48.37 0.8257 404.31 48.24 0.9153 387.50 46.12
0.324 0.288 0.236 0.212 0.206
cision of our temperature measurements was k0.005 K and the accuracy hO.1 K. The precision of the volume mea-
0196-4313/81/1020-0278$01.25/0@ 1981 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 20, No. 3, 1981 279
:
I
I
I
I
02
04
06
08
2
1
1 10
1
Composition Mole Fraction Propane Figure 1. Excess critical temperature vs. composition curves for the propane isomeric hexane systems. The full lines are the predicted curves using eq 7-11. Experimental points are denoted as follows: 0,propane n-hexane; 0,propane 2,2-dimethylbutane; A, propane Zmethylpentane; x, propane + 3-methylpentane; 0 , propane 2,3-dimethylbutane.
+
+
+
+
+
surements was estimated to be f0.25%, whereas the compositions were estimated to be accurate to within f0.1'31.
Results and Discussion Critical states of propane-isomeric hexane mixtures are shown in Table 11. The critical locus curves exhibit a maximum in pressure, which is characteristic of nonpolar mixtures in which the size difference between the two pure components is not too large. The relationship between the critical locus curves and differences in size, shape, and chemical nature of the Components is often more plainly discernible when the data are presented in terms of excess properties (Pak and Kay, 1972). Excess critical properties (Etter and Kay, 1961) are defined by the equation
Composition Mole Fraction Propane Figure 2. Excess critical pressure vs. composition curves for three propane isomeric hexane systems. The full lines are predicted. Experimental points are denoted as follows: 0,propane + n-hexane; 0,propane 2,2-dimethylbutane; A,propane + 2-methylpentane. The remaining two systems are omitted for clarity.
+
+
of propane-isomeric hexane systems which satisfy the boundary conditions :6 = O a t x = 1 (2) 4cE= 0 at x = 0 (3) and
-d 4-d - 0 at x = x,
= constant (4) dx These boundary conditions and the shape of the curve of the excess critical properties can be satisfied by the relationship
where,~$c is the maximum value of the excess critical propert at x. =, 2 From the boundary condition that &E = a t x = xmax,we have where 6 represents the critical temperature, pressure, or volume and x i is the mole fraction of component i. Figures 1 and 2 show, respectively, the excess critical temperature-composition and excess critical pressurecomposition diagrams of the systems studied by us. Although the curves are not symmetrical, the maxima occur a t very nearly the same composition in each of the figures. This indicates that the position (composition coordinate) of the maximum depends solely on the size of the components, whereas the height (excess property coordinate) depends on the shape (or structure) of the components. Thus, in mixtures in which the sizes of the components are the same, we would expect the maximum in :6 to occur in an equimolar mixture. As the size difference between the components increases, the maximum shifts toward a higher concentration of the smaller component (Pak and Kay, 1972). In the five systems studied here, the size differences between the two components are very nearly identical in the five binaries. Hence the maxima in the curves occur at approximately the same composition. The effect of changing the structure is then evidenced by a change in the height of each peak. In the light of these observations, general empirical equations can be derived for the excess critical properties
&,
L,
Hence, the final expression is
4Emar sinh
(
sinh
1 - Xmax
(-)
l-x Xmax
(7)
A study of a number of hydrocarbon binaries showed that x, could be related to the ratio of the sizes (molecular weights) of the components. Thus xm,[T,E] = 0.86 (MW)1/((MW)l+ (MWZI (8) x~,[P,E]= (MW,/((MW)1+ (MWZ] (9) For the propane(isomeric) hexane binaries, the magnitude of the maximum could be related to the differences in the critical properties of the pure components. Thus TE- = 0.001104(Tc~- TC# (10) PE, = 0.03838(Pc1- Pc2)2" (11)
Ind. Eng. Chem. Fundam. 1981, 20, 280-283
280
Table III. Comparison of Experimental and Predicted Excess Critical Roperties
system propane + nhexane propane t 2,2-dimethylbutane propane + 2-methylpentane propane t 3-methylpentane propane t 2,3-dimethylbutane
av abs maxabs avabs max abs error in error in error in error in TcE, K TcE, K PcE,bar PcE,bar 1.14 2.10 0.53 1.12 0.51
0.97
0.75
1.07
0.75
1.49
0.60
1.27
2.1 2
5.00
1.20
2.28
1.28
1.79
0.98
1.92
error for the five systems reported in this work.
Nomenclature A = constant P = pressure T = temperature V = volume x = composition (mole fraction) Subscripts c = critical i = component i max = maximum value
Literature Cited Beattle, J. A.; Kay, W. C.; Kaminsky, J. ' J . Am. Chem. Soc. 1937, 59,
with T,in K and P, in bar. Using eq 8-11 to obtain 4 E, and x,, we may then predict the excess critical property of these binary mixtures from a knowledge of the critical properties of the pure components. Predictions of the excess critical temperatures and pressures are summarized in Table I11 and shown in Figures 1 and 2. The excess critical volume could not be treated in the same way because ita magnitude was of the order of the experimental
1589. Etter, D. 0.;Kay, W. 8. J. Chem. Eng. Data 1961, 6, 409. Jones, A. E.; Kay, W. B. AIChE J . 1967, 13, 710. Kay, W. B.; Rambosek, (3. M. Ind. Eng. Chem. 1953, 45, 221. Pak, S. C.; Kay, W. B. Ind. Eng. Chem. Fundem. 1972, 11, 255. Rosslni, F. D. "Selected Va!ues of Physical and Thermodynamic Roperties of Hydrocarbons and Related Compounds"; Amerkan Petroleum Institute Project 44, Carnegie Press, PMsbwgh, Pa., 1953.
Receiued for reuiezu October 27, 1980 Accepted May 15,1981
Estimation of Vapor Pressures of Heavy LiquM Hydrocarbons Containing NItrogen or Sulfur by a Group-Contrtbutton Method D. R.
Edwards" and J.
M. Prausnltz
Department of Chemical Engineering, Universi& of Callfornk Berkeky, California 94720
The groupcontribution method for vapor pressures of hydrocarbons, developed by Macknick et al. (1979), based on the kinetic theory of fluids, is extended to include groups containing nitrogen or sulfur. Flrst approxlmatlons of vapor pressures in the range 10-2000 ton are possible within a factor of 2. The method should be used only in the total absence of any data since accuracy can be improved dramatically by using only one vapor-pressure datum.
Introduction
Table I. Group Contributions t o Vapor Pressure Parameters 8 and E J R . Carbon Groupsa
Vapor-pressure data are generally available for lowmolecular-weight hydrocarbons. However, as molecular weight increases, data become more scarce. Moreover, vapor-pressure data for hydrocarbons containing heteroatoms are often unavailable for even lower-molecularweight compounds. With the development of alternate energy sources, it is important to estimate vapor pressures of these types of compounds to facilitate rational process design. It is usually not possible to determine all required data experimentally. Therefore, we often extend or extrapolate limited available data through various correlations. Many vapor-pressurecorrelations exist. Most are either empirical or are based in some way on integration of the Clapeyron equation which indicates that the vapor pressure is an exponential function of temperature. Due to the semilogarithmic nature of most vapor pressure correlations, 0196-4313/81/1020-0280$01.25/0
Vwi,
carbon type aliphatic CH, aliphatic CH, aliphatic CH aliphatic C aromatic Ar=C( Ar)H aromatic Ar= C( Ar)R condensed aromatic Ar=C(Ar)cond condensed aromatic Ar= C naphthenic >CH, naphthenic >CHR
si
e,ilR, K
2.359 0.479 -2.189 -4.318 1.175
1162.7 674.0 -372.9 -1127.1 939.5
cm3/ g-mol 13.67 10.23 6.78 3.33 8.06
-0.520
583.0
5.54
-0.774
432.5
4.74
0.321
623.5
4.74
1.188 -1.936
928.0 -431.0
9.47 9.47
From Macknick et al. (1979).
0 1981 American Chemical Society
