PHASE EQUILIBRIA MOLECULAR TRANSPORT THERMODYNAMICS Va p o r - Liq u id E q u iIibr ia in the Acetylene- Pro pyn e Sys tern R . J. BURCH AND M. W. LEEDS Air Reduction C o . , l n c . , Murray H i l l , N. J .
v apor-liquid
equilibrium d a t a for t h e acetylene-propyne s y s t e m h a v e been obtained i n an equilibrium a p p a r a t u s des i g n e d f o r operation a t e l e v a t e d p r e s s u r e s . S e c a u s e of t h e experimental h a z a r d s of working with high c o n c e n t r a t i o n s of liquid a c e t y l e n e , t h e experimental d a t a for d i l u t e solut i o n s of a c e t y l e n e in propyne h a v e been e x t e n d e d over t h e whole range of acetylene-propyne c o n c e n t r a t i o n s by t h e Margules e q u a t i o n s (13). B e c a u s e of t h e r e l a t i v e l y high p r e s s u r e s involved, t h e a c t i v i t y c o e f f i c i e n t s (2,3,19) u s e d i n t h e Margules e q u a t i o n s were corrected for t h e nonideality of t h e v a p o r s b y e v a l u a t i o n of f u g a c i t i e s from literature d a t a for e a c h component of t h e s o l u t i o n . T h e dynamic methods for obtaining equilibrium d a t a (1,2, 6,7,10,16,18,19) h a v e c e r t a i n a d v a n t a g e s over t h e s t a t i c methods (21) a t low a n d moderately high p r e s s u r e s . However, t h e equilibrium s t i l l s u s e d i n most of t h e dynamic methods could not b e u s e d for t h e s t u d y of t h e a c e t y l e n e propyne s y s t e m a s they would b e h a z a r d o u s i n operation b e c a u s e of t h e n e c e s s i t y for c o n d e n s i n g , under p r e s s u r e , v a p o r s which were high i n a c e t y l e n e content ( 5 ) . A s t a t i c equilibrium cell w a s d e s i g n e d which r e q u i r e s only s m a l l v o l u m e s of s o l u t i o n and e l i m i n a t e s t h e major d i s a d v a n t a g e of t h e s t a t i c methods-i.e., t h e d i s t u r b a n c e of t h e equilibrium upon s a m p l i n g t h e p h a s e s . T h e cell is particularly s u i t a b l e for t h e s t u d y of p h a s e equilibria a t high p r e s s u r e s w h e r e only s m a l l volumes of e a c h p h a s e a r e required for analyses.
EXPERIMENTAL Materials. T h e propyne a n d a c e t y l e n e were manufactured by t h e Air R e d u c t i o n Co., Inc. T h e propyne w a s purified by low temperature d i s t i l l a t i o n . T h e purified product a n a l y z e d 99.95% propyne by t h e m a s s spectrometer. Cylinder a c e t y l e n e w a s freed of a c e t o n e by p a s s a g e through water scrubbing towers and drying. I n e r t s were removed from t h e a c e t y l e n e by low temperature f l a s h d i s t i l l a t i o n . S o l u t i o n s of a c e t y l e n e i n propyne w e r e prepared by p a s s i n g t h e acetyl e n e g a s i n t o liquid propyne a t low temperature.
1957
Apparatus and Procedure. T h e equilibration of t h e p h a s e s w a s c a r r i e d out i n t h e a l l - b r a s s c e l l s h o w n i n F i g ure 1. T h e lower s l e e v e , A , c o n t a i n e d a soft iron bar, B , t o which w a s a t t a c h e d a n aluminum rod, C, e x t e n d i n g upward t o t h e bottom of a 1-inch b a l l valve, D, s i t u a t e d a t t h e c e n t e r of t h e upper chamber. (The v a l v e is manufactured by t h e Rockland Sprinkler Co., Worcester, Mass.) T h e rod w a s moved v e r t i c a l l y through t h e cell by m e a n s of t h e permanent magnet, J . Perforated aluminum d i s k s , E and F , o n t h e rod allowed both t h e liquid and vapor p h a s e s t o b e s t i r r e d without transporting liquid t o t h e vapor s e c t i o n above the ball valve. T h e equilibrium cell w a s immersed i n a thermostated bath maintained c o n s t a n t t o within t 0.04 'C. T h e c e l l w a s e v a c u a t e d a n d f i l l e d under p r e s s u r e with t h e a c e t y l e n e propyne s o l u t i o n t o about 1 i n c h below t h e perforated d i s k , F , of t h e s t i r r i n g rod. Equilibrium w a s a t t a i n e d i n t h e c e l l b:i p a s s i n g rod C v e r t i c a l l y through t h e chamber by m e a n s of J (lift weight, 80 pounds). T h e magnet w a s driven by t h e slow-speed motor, PI s h o w n mounted o n t h e s q u a r e s t e e l frame above t h e equilibrium cell i n F i g u r e 2. T h e p r e s s u r e w a s measured with a S o u r d o n g a g e which h a d b e e n c a l i brated a g a i n s t a d e a d weight g a g e t e s t e r . P r e s s u r e measurements were both a c c u r a t e and p r e c i s e t o 0.014 atm. When equilibrium had b e e n maintained for a t l e a s t a 0.5hour period, as indicated by t h e c o n s t a n c y of t h e temperature and p r e s s u r e , t h e t w o p h a s e s w e r e s e p a r a t e d by c l o s ink t h e b a l l v a l v e . T h e vapor p h a s e w a s allowed t o expand i n t o a n e v a c u a t e d g l a s s bulb on t h e vacuum manifold, 0, shown i n F i g u r e 2. Approximately 1 ml. of t h e liquid p h a s e w a s forced under t h e vapor p r e s s u r e of t h e liquid i n t o t h e e v a c u a t e d s p a c e b e t w e e n v a l v e s G and H (Figure 1). After v a l v e H had b e e n c l o s e d , t h e liquid s a m p l e w a s completely flash-distilled i n t o a s e c o n d e v a c u a t e d bulb on t h e manifold. T h e liquid and vapor s a m p l e s w e r e a n a l y z e d for both a c e t y l e n e and propyne by a Perkin-Elmer infrared spectrometer. Measurements w e r e t a k e n a t c o n c e n t r a t i o n s below 15% a c e t y l e n e a t O o , 20°, and 35OC. N o measurements
CHEMICAL AND ENGINEERING DATA SERIES
3
were taken above 15% a c e t y l e n e b e c a u s e of t h e p o s s i b l e danger of s p o n t a n e o u s decomposition of t h e a c e t y l e n e a t higher concentrations and p r e s s u r e s (5).
RESULTS For i d e a l liquid solutions, t h e p a r t i a l fugacity of a component is given by Raoult's law,
-
f, =
x,rp
(1)
where f? is t h e fugacity of pure component i corrected t o t h e vapor p r e s s u r e of the solution. A measure of t h e deviation of a solution from i d e a l behavior may then b e exp r e s s e d i n terms of a n activity coefficient for e a c h component,
T h e p a r t i a l fugacity of a component i n t h e vapor p h a s e is given by t h e L e w i s and R a n d a l l rule if the v a p o r s are assumed t o form an i d e a l mixture (7,12),
-
f, = Y,f:
(3)
where f: is t h e fugacity of component i in t h e mixture and i n solution at t h e temperature and p r e s s u r e of t h e solution. Equation 2 then becomes, Ylf:
y, = -.
x,rp
(4)
For the evaluation of experimental activity coefficients from Equation 4, it w a s a s s u m e d that: (1) t h e partial molal volumes of e a c h constituent i n t h e liquid and vapor p h a s e s of t h e s o l u t i o n s were equal to their molal volumes and (2) t h e equation of s t a t e for e a c h component i n t h e vapor p h a s e Was: Figure 1. Cell for obtaining liquid-wpor equilibrium data at moderately high
(5)
PVI=RT-&P
@,
where w a s c a l c u l a t e d by graphical integration from zero p r e s s u r e to t h e vapor p r e s s u r e of the pure components and t h e s o l u t i o n s (2,9,17,22).Molal volumes of t h e pure l i q u i d s and the saturated vapors were obtained from t h e arthobaric d e n s i t i e s of a c e t y l e n e (14) and pmpyne (11). T h e vapor p r e s s u r e s of a c e t y l e n e were t a k e n from t h e d a t a of Villard (10). T h e vapor p r e s s u r e s of t h e propyne were measured i n t h e equilibrium cell and found t o agree within 0.01 atm. with t h e reported v a l u e s (8). A summary of t h e d a t a used for the c a l c u l a t i o n of t h e activity c o e f f i c i e n t s is given i n T a b l e 1. T h e experimental activity c o e f f i c i e n t s h a v e been c a l c u l a t e d from Equation 4 using t h e f u g a c i t i e s given in T a b l e 11.
Tabis I. Vapor Pisssurss, Liquid Hold Volumes, and Sscond Virimi Coefficientso of Acdyisne and Propyns
vepa. Pressme. Atrn.
Figure 2. Static vapor-liquid equilibrium cell ( N ) with o u x i l i a v apparatus for filling cell, equilibrotim and sampling phmres
4
INDUSTRIAL AND ENGINEERING CHEMISTRY
223 250
0.26 1.0
5.38 13.5
273.3
2.63
26.0
293.3 308.3
4.93
42.6 59.1
7.68
Liquid Molal "","me%
0.0561 0.0595 0.0624 0.0654 0.0679
Litas
0.0461 0.0501 0.0561 0.0650 0.0856
Second Virlal coenicirnts
. ..
0.20
2.30 2.06
0.363 0.277
0.606 0.432
0.248 0.285
T h e experimental d a t a were correlated and extended by means of t h e Margules t h r e e s u f f i x e q u a t i o n s (13), s i n c e the molal volumes of liquid prapyne a r e approximately
VOL. 2, NO. I
T a b l e II. Equilibrium Vapor-Liquid Composition Data, Calculated Fugacities, and Experimental A c t i v i t y Coefficients for Solutions o f Acetylene in Propyne Experimental Data, Mole F r a c t i o n s Prop yne
x1
Temp., OK. 250
Pressure, Atm. 13.5 1.0
273.3
26.0 2.63 3.19 3.62 3.99 5.06 5.28 42.6 4.99 5.71 6.66 7.11 7.59
0
293.3
308.3
59.1 7.68 8.47 10.53 11.60
x,
4
1.0
1.0
0
0 1.0 0.959 0.931 0.911 0.865 0.863
1.0
...
0.969 0.920 0.891
e q u a l t o t h o s e of liquid a c e t y l e n e . used in t h e form (3,23):
0.834 0.700 0.638 0.628
0.037 0.065 0.091 0,099
...
1.0 0 0.031 0.080 0.109
0.882 0.708 0.602
Ya
Y1
fa*
fi*
0.959
...
0
...
1.0
f,O
Activity Coefficients
In Vapor
11.51
1.0
...
fP
4
0 0.041 0.069 0.089 0.135 0.137
0.777 0.687 0.589 0.485 0.482
0
Corr. t o Sol. Pressure
Acetylene
0
1.0 0.963 0.935 0.909 0.901
F u g a c i t i e s of Pure Components
0.223 0.313 0.411 0.515 0.518
2.47 2.49 2.49 2.50 2.50
19.40 19.44 19.45 19.52 19.55
... ...
... ...
... ...
0.166 0.300 0.362 0.372
4.54 4.57 4.57 4.57
28.3 28.3 28.3 28.3
... ...
...
*
0.118 0.292 0.398
6.84 6.88 6.90
...
..... 35.34 35.62 35.80
20.71
...
2.47 2.96 3.32 3.56 4.50 4.66
3.10 3.50 3.85 4.84 5.04
0.952 0.958 0,910 0.972 1.00
1.04 0.967 1.08 1.09 1.12
...
31.38
... ...
...
5.49 6.35 6.75 7.19
0.978 0.970 0.961 1.01
1.07 1.26 1.15 1.15
...
4.54 5.15 5.90 6.24 6.60
...
... 8.06
... ... 0.990
9.92 10.82
1.00 0,950
41.9
6.81 7.42 8.94 9.66
...
... ...
1.16 1.34 1.32
T h e e q u a t i o n s were
-
l o g y1 = Xi [ A + 2 ( B A ) X,] limit log yi = A
T h e experimental activity c o e f f i c i e n t s g i v e n i n T a b l e I1 were u s e d to s o l v e for c o n s t a n t s A a n d B by s i m u l t a n e o u s solution of t h e e q u a t i o n s . T h e Margules e q u a t i o n s with t h e a v e r a g e v a l u e s of t h e c o n s t a n t s ( T a b l e 111) were u s e d to smooth t h e experimental activity c o e f f i c i e n t s and t o extend t h e activity coefficient d a t a over t h e whole range of a c e t y l e n e and propyne c o n c e n t r a t i o n s a t e a c h temperature. T h e c a l c u l a t e d and experimental activity c o e f f i c i e n t s a r e plotted a s a function of composition i n F i g u r e 3 for 0' and
0
0.2
0.1
0.3 0.4 0 . 5
0.6
0.7 0.8 0.9
1.0
MOLE FRACTION ( X ) Figure 3. A c t i v i t y coefficient-concentrotion curves for acetylene i n prapyne calculated from Margules equations. A, 0 . Experimental data for propyne o t 0' ond 35OC. X, m. Experimental data for acetylene a t O o and 35OC., respectively (upper curves)
W C ,
T a b l e 111. Smoothed Equilibrium Vapor-Liquid Composition Data for Acetylene-Propyne System (Correlated and extended from experimental dota and Morgules equotions) Average Margules Constants
Temp., OK. 223.2
250
273.3
Pressure, Atm. 0.483 0.930 1.39
... ...
1.46 1.92 2.41 2.91 3.94
... ...
3.42 5.11 6.93
293.3
6.13 8.62 11.28
308.3
9.10 12.19 15.66
1957
A
B
Y1
Ya
Mole F r a c t i o n Liquid-Phase
Mole F r a c t i o n Vapor-Phase
Propyne
Acetylene
Propyne
Acetylene
xi
y1
0.95 0.85 0.75
Xa 0.05 0.15 0.25
0.518 0.240 0.141
Ya 0.483 0.760 0.859
0.95 0.90 0.85 0.80 0.70
0.05 0.10 0.15 0.20 0.30
0.653 0.469 0.353 0.275 0.177
0.347 0.531 0.647 0.725 0.823
... ...
...
... ... ... .. ... ...
... ... ... ... ... ... ... ...
0.08
... ... 0.14 ...
0.03
...
1.00
...
1.00 1.00
1.083 1.082 1.075
0.95 0.85 0.75
0.05 0.15 0.25
0.732 0.438 0.284
0.268 0.562 0.716
0.06
1.00 1.00 1.00
1.156 1.147 1.130
0.95 0.85 0.75
0.05 0.15 0.25
0.771 0.491 0.330
0.229 0.509 0.670
0.23
0.10
1.00 1.00 1.01
1.272 1.261 1.247
0.95 0.85 0.75
0.05 0.15 0.25
0.801 0.536 0.368
0.199 0.464 0.632
... ... . I .
...
... ...
... ...
Activity Coefficients
*
...
...
...
...
.. ... ... ... ... I . .
CHEMICAL AND ENGINEERING D A T A SERIES
5
T h e a c t i v i t y c o e f f i c i e n t s were extended t o temperatures below t h e experimental by plotting t h e v a l u e s of A and E a g a i n s t 1/T. T h e straight l i n e s r e s u l t i n g from t h i s plot ind i c a t e d that t h e partial molal h e a t of s o l u t i o n a t infinite dilution is a c o n s t a n t over t h i s temperature interval (15, 20). I n addition, t h e intersection of t h e l i n e s with t h e a b s c i s s a a t about -2OOC. showed t h a t t h e a c t i v i t y coeffie., t h e c i e n t s below t h i s temperature a r e e q u a l t o one-i. s o l u t i o n s a r e i d e a l below -2O'C. From Equation 4 and t h e c a l c u l a t e d a c t i v i t y c o e f f i c i e n t s a t e a c h temperature, smoothed and extended equilibrium vapor and liquid compositions as well a s t o t a l p r e s s u r e s were obtained by a s e r i e s of approximations which were initiated with t h e assumption that R a o u l t ' s law in t h e u s u a l form of partial p r e s s u r e s could b e u s e d t o obtain approxi-
:i
$
10
@ IO
$ [
0-
-104
+L -SO
-60
0
1
4
-r :T--
1
TOTAL PRESSURE, ATY
Figure 5. Loci of constant vapor or liquid compositions of acetylene in propyne
mate t o t a l p r e s s u r e s . T y p i c a l smoothed equilibrium compos i t i o n d a t a and activity coefficients are given for a c e t y l e n e concentrations below 25% in T a b l e 111. T h e d a t a f r o m T a b l e 111 were u s e d t o construct a n X Y diagram at e a c h temperature ( F i g u r e 4). With d a t a obtained from t h e c u r v e s of F i g u r e 4 , t h e graph of F i g u r e 5 w a s constructed containing loci of c o n s t a n t mole fraction of a c e t y l e n e in t h e liquid and vapor p h a s e s a s a function of t h e temperature and total p r e s s u r e of t h e solutions. F o r t h e concentration region covered by F i g u r e 5 , t h e compositions of both t h e liquid and vapor p h a s e s may be obtained by interpolation in F i g ure 5 when only t h e temperature and p r e s s u r e of a mixture h a v e been measured. Ideal or nearly ideal s o l u t i o n s a r e formed a t moderate temperatures and p r e s s u r e s by homologs which a r e c l o s e l y related chemically. D e v i a t i o n s from i d e a l behavior, w h e r e they occur, a r e usually d u e t o differences i n chemical structure or in c h e m i c a l s i z e and volatility. D e v i a t i o n s from ideal behavior which a r e due t o chemical dissimilarity d e c r e a s e with i n c r e a s e i n temperature, while d e v i a t i o n s c a u s e d by differences i n molecular s i z e or volatility inc r e a s e as t h e temperature i n c r e a s e s , provided t h e p r e s s u r e becomes relatively high (4). From t h e c u r v e s of F i g u r e 3 and t h e d a t a of T a b l e 111, i t is s e e n t h a t s o l u t i o n s of acetyl e n e i n propyne d e v i a t e from i d e a l behavior a t t h e higher temperatures s t u d i e d , and approach ideal behavior as t h e temperature i s d e c r e a s e d . T h i s behavior of t h e s o l u t i o n s s u g g e s t s t h a t t h e s m a l l positive deviation of t h e s o l u t i o n s from ideality i s d u e to d i f f e r e n c e s i n molecular s i z e and volatility of t h e components.
0.9
-
- 23. 0.e
0.7
0.6
0.5
y2
0.4
0.3
NOMENCLATURE Y = activity coefficient
X = mole fraction in liquid phase Y =mole fraction in vapor phase P o = vapor pressure of pure component in atmospheres at absolute temperature T i in atmospheres V =liquid molal volume of pure component in liters per mole P =total pressure of the solution in atmospheres p= second virial coefficient of the equation of state, Pv = RT PP, where v i s the molal volume of vapor f o = fugacity of pure component at P o and T, corrected to vapor pressure of solution f l = partial fugacity of component i in liquid and vapor phases of a solution f: =fugacity of pure component i in vapor phase at temperature and pressure of solution
0.2
p i =partial pressure of component
-
0. I
-
0 0
0.1
LITERATURE CITED 0:2
013
x2
0.4
(1) Ablewhite, S. A. J., Bowden, C. H., Cooke, E. V., Chemistry & Zndustry 47, 1146 (1952). (2) Benedict, M., Johnson, C. A., Soloman, E., Rubin, L. C., Trans. A m . Inst. Chem. Engrs. 41, 371 (1945). (3) Carlson, H. C., Colburn, A. P., Ind. Eng. Chem. 34, 581
(1942).
6
INDUSTRIAL AND ENGINEERING CHEMISTRY
V O L . 2, NO. I
(4) Gsmson, 8. W., Watson, K. M., Natf. Petroleum News, Tech. Sect. 36., R 554 - - (1444). ,-- ,(5) Gilman, H., “Organic Chemistry,” vol. IV, Wiley, New York, 1953. (6) Gilmont, R., Othmer, D. F., Ind. Fng. Chem. 36, 1061 (1944). (7) Glasstone, S., “Textbook of Physical Chemistry,” Van Nostrand, New York, 1946. (8) Heisig, G. B., Hurd, C. D., J . Am. Chem. Soc. 55, 3485 (1933). (9) Karr, A. E., Scheibel, E. G., Bowes, W. M., Othmer, D. F . , Ind. E n g . Chem. 43, 961 (1951). (10) Landolt, H., “Landolt-Bornstein Physikalischchemische Tabellen,” 1895. (11) Leeds, M. W., Burch, R . J., “Orthobaric Densities of Methylacetylene,” Air Reduction Co., Inc., Rept. A-1807 (1953). (12) Lewis, G. N., Randall, M., “Thermodynamics and the Free Energy of Chemical Substances,” McGraw-Hill, New York, 1923.
(13) Margules, M., Sitzber. Akad. W i s s . Wien, Math.-naturw. K f . , Abt. rr 104. 1243 11895). (14) Mathais, E., Compt.‘rend’ 148, 1102 (1909). (15) Mertes, T. S., Colburn, A. P., Znd. Eng. Chem. 39, 787 (1947). (16) Othmer, D. F., Zbid., 35, 614 (1943). (17) Othmer, D. F., Chudgar, M. M., Levy, S. L., Ibid., 44, 1872 (1952). (18) Othmer, D. F., Morley, F. R., Zbid, 38, 751 (1946). (19) Othmer, D. F., Silvis, S. J., Spiel, A,, Ibid., 44, 1864 (1952). (20) Perry, J . H., others, “Chemical Engineer’s Handbook,” McGraw-Hill, New York, 1950. (21) Ruheman, M., “Separation of Gases,” Clarendon Press, Oxford, 1940. (22) Taylor, H. S , “Treatise on Physical Chemistry,” Van Nostrand, New York, 1931. (23) Wohl, K., Trans. Am. Znst. Chem. Engrs. 42, 215 (1946). Received for review August 25, 1956. Accepted January 3, 1957.
Saturated Liquid Phase Enthalpies for the System n- Butane-n- Heptane at Elevated Pressures MERK HOBSON AND JAMES H. WEBER D e p a r t m e n t of Chemistry and C h e m i c a l Engineering, U n i v e r s i t y of Nebraska, L i n c o l n ,
A c c u r a t e c a l c u l a t i o n s for d i s t i l l a t i o n o p e r a t i o n s require thermal a s w e l l as vapor-liquid equilibrium d a t a . A t the p r e s e n t time t h e r e a r e vapor-liquid equilibrium d a t a for a number of binary s y s t e m s for which thermal d a t a a r e una v a i l a b l e . R e c e n t l y , Stiehl, Hobson, and Weber ( 6 ) utilized a thermodynamically rigorous method, outlined by Dodge (3), by which t h e s a t u r a t e d liquid p h a s e e n t h a l p i e s of binary mixtures may b e c a l c u l a t e d from t h e differential h e a t s of c o n d e n s a t i o n and vapor p h a s e e n t h a l p y d a t a . A s t h e s a t u r a t e d vapor p h a s e e n t h a l p i e s c a n b e c a l c u l a t e d from t h e Renedict-Webb-Rubin e q u a t i o n of s t a t e (2), c o m p l e t e enthalpy composition d a t a a r e made a v a i l a b l e . T h e method of c a l c u l a t i o n h a s b e e n d i s c u s s e d thoroughly (6). T h e b a s i c r e l a t i o n s h i p s which apply t o t h e p r o c e s s of c o n d e n s a t i o n for 1 mole of liquid from a l a r g e quantity of vapor under equilibrium c o n d i t i o n s a r e
and
In t h e previous work enthalpy-composition d a t a were presented for t h e s y s t e m methane-ethane a t 200, 400, a n d 600 p o u n d s p e r s q u a r e inch a b s o l u t e and for t h e s y s t e m s ethane-n-butane and propane-n-butane a t t h e t w o lower
1957
Neb,
pressures. In t h i s work e n t h a l p y composition d a t a a r e p r e s e n t e d for t h e s y s t e m n-butane-n-heptane a t 100, 200, 300, and 400 pounds per s q u a r e i n c h a b s o l u t e . T h e vapor-liquid equilibrium d a t a and t h e volumetric behavior of t h e c o e x i s t i n g p h a s e s for t h e n-butane-n-heptane s y s t e m a r e reported by Kay (4). T h e Benedict-Webb-Rubin e q u a t i o n (2)
P = RTd
+ (B,RT
-
- A , - C , / T a P + (bRT a)d’ + aad6 + cd’/T*[(l + yd’)exp(- yd‘)]
(4)
w a s also u s e d t o c a l c u l a t e t h e s a t u r a t e d vapor volumes; t h e r e s u l t s a g r e e d with t h e experimental d a t a of Kay within *I%. T h e s i n g l e e x c e p t i o n w a s t h e c a l c u l a t e d v a l u e at t h e c r i t i c a l point a t 4 0 0 pounds per s q u a r e i n c h a b s o l u t e , 511.8’F., and 1.1%n-heptane. I n t h i s case t h e molal volume predicted by t h e equation w a s 3.6% greater t h a n t h e experimental value. A s t h e validity of t h e Benedict-Webb-Rubin e q u a t i o n w a s e s t a b l i s h e d for t h i s binary s y s t e m , t h i s r e l a t i o n s h i p w a s u s e d t o predict volumetric d a t a i n t h e s u p e r h e a t e d vapor region. Through t h e u s e of t h e c a l c u l a t e d d a t a , t h e experimental r e s u l t s of Kay (4), a n d t h e volumetric d a t a for pure n-butane (5), t h e term ( a V / d y ) , , , i n E q u a t i o n 1 c a n b e d e termined a s a function of composition along any given isotherm a t t h e p r e s s u r e under consideration. T h e partial diff e r e n t i a l must b e e v a l u a t e d accurately. T h i s is rendered difficult for t h r e e reasons: F i r s t , t h e s l o p e is determined graphically; s e c o n d , t h e s l o p e of t h e isotherm must b e determined at i t s point of i n t e r s e c t i o n with t h e s a t u r a t e d vapor curve; a n d third, a t high p e r c e n t a g e c o m p o s i t i o n s of t h e
CHEMICAL AND ENGINEERING DATA SERIES
7
