(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 Department of Chemistry and Chemical Engineering, University of Nebraska, Lincoln,
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
0 0
4
pure components i n t h e i d e a l g a s s t a t e and unit fugacity a t OOR. w a s also s e l e c t e d a s t h e datum point for t h i s work. T h e procedure u s e d i n e v a l u a t i n g t h e term ( d & / d ~ ) ~ , ~ w a s similar t o t h e procedure u s e d for (aV,/dy)T, p . A s t h e validity of t h e Renedict-Webb-Rubin equation had been est a b l i s h e d , t h e equation i n t h e form
P=lOO PSlA P=200 P.300
H = CxlHP
+ (B,RT
- 2A, - 4C,/T2)d + (2bRT - 3a)d'/,
+
i
6 a ~ d ' / 5+ cd2/T1 [3
1
- exp(-
yd')
d2
Table 1. Enthalpy-Composition Data for n-Butane-n-Heptane System
Saturatign Temp., F.
Mole Fraction n-Butane ( 4 ) Y
Y
Enthalpy",
B. T. U. /Lb. Mole Hd
Hb
Ref.
P r e s s u r e = 100 Pounds per Square Inch Absolute
"0
0.20
0.40
0.60
0.80
1.00
MOLE FRACTION n- BUTANE (VAPOR PHASE) Figure 1. ( y
- x ) (dVc/dy)T, p y diagram for n-butonen-heptone system VS.
more v o l a t i l e component a s m a l l change i n t h e molal volume, considerably less than 1%, p r o d u c e s a very large c h a n g e in t h e s l o p e of t h e i s o b a r i c isotherm. In v i e w of t h e above, additional m e a n s were sought t o A s i m p l e plot of obtain c o n s i s t e n t ( d V G / d y ) T , p d a t a . ( d v ~ l d y ) ~ , v, a l u e s at a s i n g l e p r e s s u r e vs. y f a i l e d to yield t h e d e s i r e d r e s u l t s , b e c a u s e t h e points did not prod u c e a smooth curve. However, a plot of t h e product b' X ) ( d V G / d y ) T , p vs. y produced a smooth curve, parab o l i c i n s h a p e , for e a c h pressure. T h i s type of plot h a s an additional a d v a n t a g e b e c a u s e t h e product i s e q u a l t o zero at y = 0 and y = 1. T h i s fixed t h e t w o terminal points of , y at t h e p a r a b o l i c curve. A plot of 0. x ) ( d V ~ / d y ) ~ vs. t h e four p r e s s u r e s i n v e s t i g a t e d is given i n F i g u r e 1 t o i l l u s t r a t e t h e method which w a s u s e d t o smooth t h e s l o p e data. Figure 1 s h o w s t h a t two c a l c u l a t e d points, both i n t h e r a n g e of high n-butane compositions a n d o n e on both t h e 100 and 200 pounds per s q u a r e i n c h a b s o l u t e p r e s s u r e parameters, d e v i a t e d considerably from t h e i r r e s p e c t i v e curves. T h e smoothing t e c h n i q u e permitted t h e d e t e c t i o n of t h e s e d e v i a t i o n s . Equation 1 c a n now b e s o l v e d for t h e term AV, a s t h e other terms a r e known. Also, t h e differential h e a t of condensation, AH,, c a n b e c a l c u l a t e d f r o m Equation 2. T h e d a t a of Kay ( 4 ) were u s e d to c a l c u l a t e t h e v a l u e of t h e term ( d p / d T ) , and to obtain t h e correct temperature. T h e only enthalpy d a t a a v a i l a b l e for t h e n-butanen-heptane system a r e t h e v a l u e s for t h e pure compounds in t h e s a t u r a t e d liquid and vapor s t a t e s and t h e s u p e r h e a t e d vapor 'state (5, 7). T h e s e d a t a were u s e d i n t h i s work after they had been converted to t h e proper datum point. For convenience, t h e reference s t a t e u s e d i n (I), H = 0 for t h e
-
-
8
INDUSTRIAL A N D ENGINEERING CHEMISTRY
358 315 278.5 248 223.5 204 188 173.8 160.5 151 146
0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
0 0.380 0.628 0.773 0.856 0.908 0.944 0.969 0.985 0.996 1.00
10,673 8,338 6,615 5,338 4,370 3,658 3,045 2,502 2,070 1,732 1,310
21,186 19,330 16,198 13,951 12,558 11,650 10,965 10,405 9,954 9.560 9,227
(7,
(5)
P r e s s u r e = 200 Pounds per Square Inch Absolute 430.7 394.8 359.5 328.4 301.3 2 78.6 258.9 241.0 225.5 212.2 202.7
0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
0 0.270 0.497 0.658 0.773 0.850 0.902 0.940 0.968 0.988 1.00
16,350 12,798 10,270 8,443 7,050 5,998 5,168 4,540 4,081 3,765 3,616
24,581 22,928 20,120 17,412 15,392 13,915 12,905 12,032 11,355 10,802 10,487
(7)
(5)
P r e s s u r e = 300 Pounds per Square Inch Absolute 478.2 446.2 4 14.2 383.5 355.0 329.2 307.0 287.8 270.0 254.0 241.0
0 0.10 0.20 0.30 0.40 0.50
0.60 0.70 0.80 0.90 1.00
0 0.207 0.400 0.565 0.696 0.794 0.862 0.911 0.949 0.978 1.00
20,866 17,955 15,138 12,455 10,101 8,435 7,218 6,298 5,732 5,450 5,288
26,793 25,050 22,715 19,770 17,392 15,595 14,285 13,238 12,385 11,602 10,995
(;3
(5)
P r e s s u r e = 400 Pounds per Square Inch Gage
...
0.011 0.011 (27,380)b 0.10 0.151 23,720 26,430 24,560 0.20 0.322 19,586 21,808 0.30 0.484 15,758 0.40 0.623 13,095 19,240 0.50 0.732 11,035 17,148 0.60 0.813 9,508 15,505 0.70 0.877 8,390 14.252 13; 102 0.80 0.928 7,585 12,075 0.90 0.970 7,041 1.00 1.00 6,900 (5) 11,282 a H = 0 for pure components in i d e a l g a s s t a t e at unit fugacity and O O R . bCritical uoint Value in usrenthesis is an extraoolatad datum. 511.8 487.0 45 7.0 426.5 397.3 3 70.5 347.0 325.4 304.8 286.0 270.3
VOL. 2, NO. I
(2) and t h e method of c a l c u l a t i o n d e s c r i b e d above, enthalpy vs. composition diagrams a t 100, 200, 300, and 400 pounds per s q u a r e i n c h absolute, w e r e constructed for t h e s y s t e m n-butane-n-heptane. T h e final r e s u l t s a r e p r e s e n t e d i n T a b l e I and i n graphical form i n F i g u r e 2. T h e t a b u l a t e d v a l u e s are b e l i e v e d t o b e a c c u r a t e within t 3% a n d a r e reported t o four or five s i g n i f i c a n t figures for c o n s i s t e n c y . Although t h e s e d a t a c a n n o t b e u s e d directly to o b t a i n part i a l e n t h a l p y d a t a , they c a n b e u s e d t o c h e c k e n t h a l p i e s of mixtures o b t a i n e d through t h e u s e of partial e n t h a l p i e s or any other method.
28,000
25,000
20,000
kl
ACKNOWLEDGMENT T h e a u t h o r s w i s h t o acknowledge t h e h e l p of Donald F. Weitzel with t h e c a l c u l a t i o n s involved i n t h i s study.
I
6 15,000
5 I-
m
NOMENCLATURE
r
2x
H = enthalpy, B.t.u./lb. mole. H = 0 for a pure component in the i d e a l g a s s t a t e at unit fugacity and OOR.
10,000
H D=enthalpy of a component i n the i d e a l g a s s t a t e and unit
i
fugacity, B.t.u. Ab. mole
AHc =differential heat of condensation, B.tu./lb.
P = pressure, pounds per square inch absolute R = g a s law constant, 1.987 B.t.u./lb. mole-OR. T = absolute temperature, OR. V = molal volume, CU. ft./lb. mole d = density, lb. mole/cu. ft. x = mole fraction i n liquid phase y = mole fraction i n vapor phase A , Bo,C,, a, b, c, and y = empirical constants Webb-Rubin equation of s t a t e
5,000
0
010
0.20
030
0.40 0.50 0.60
0.70
0.00
of
Benedict-
0.90 ID0
MOLE FRACTION n- BUTANE
Figure 2. Enthalpy
mole
composition diagram for n-butanen-heptane system
VS.
w a s u s e d to c a l c u l a t e t h e e n t h a l p i e s of t h e s a t u r a t e d and superheated v a p o r s of n-butane-n-heptane mixtures. T h e n e c e s s a r y v a l u e s of H o were o b t a i n e d from (1). With t h e s e c a l c u l a t e d d a t a and t h e a v a i l a b l e information on p u r e n-butane, t h e term ( d H c / d y ) ~c,o~u l d b e e v a l u a t e d graphically. T h e s l o p e d a t a were smoothed by plotting 0.- x) ( d H ~ / d y ) vs. ~ , ~y for e a c h p r e s s u r e . Again, four p a r a b o l i c s h a p e d c u r v e s were obtained. T h e enthalpy, H,, of t h e s a t u r a t e d liquid mixtures c a n now b e c a l c u l a t e d by Equation 3. A s t h e enthalpy v a l u e s a t p o i n t s x = 0 and x = 1 a r e known, t h e H b vs. x c u r v e c a n b e completed by repeating t h e s e r i e s of c a l c u l a t i o n s for a number of differe n t c o m p o s i t i o n s in t h e vapor p h a s e .
RESULTS AND CONCLUSIONS U s i n g t h e d a t a for t h e pure components a v a i l a b l e i n t h e l i t e r a t u r e (5, 7 ) , t h e Benedict-Webb-Rubin equation of s t a t e
Subscripts G = vapor phase b =bubble point d = dew point i = a component j = total number of components
LITERATURE CITED (1) Am. Petroleum Inst. Research Project 44, T a b l e 2u-E, Carnegie Institute of Technology, Pittsburgh, Pa., 1953. (2) Benedict, M. Webb, G. B., Rubin, L. C., J . Chem. P h y s . 8, 334 (1940); 10, 747 (1942). (3) Dodge, B. F., “Chemical Engineering Thermodynamics,” p. 130, McGraw-Hill, New York, 1944. (4) Kay, W. B., Ind. Eng. Chem. 3 3 , 591 (1941). (5) Prengle, H. W., Greenhaus, L. R., York, R., Jr., Chern. Eng. Progr. 44, 863 (1948). ( 6 ) Stiehl, J. G., Hobson, M., Weber, J. H., A.I.Ch.E. Journal 2, 389-92 (1956). (7) Stuart, E. B., Yu, K. T., Coull, J., Chem. Eng. Progr. 46, 311 (1950). Received for review May 3, 1956. Accepted September 24, 1956.
Phase Equilibria in Hydrocarbon Systems Volumetric Behavior of Cyclohexane H. H. REAMER AND B. H. SAGE Colifornio Institute of Technology, Pasadena, Calif.
L i t t l e experimental information i s a v a i l a b l e concerning t h e i n f l u e n c e of p r e s s u r e and temperature upon t h e molal volume of cyclohexane. R o s s i n i ( 1 2 ) reviewed t h e availa b l e information concerning t h e p h y s i c a l p r o p e r t i e s of c y c l o h e x a n e a t atmospheric p r e s s u r e and t h e s e d a t a a r e 1957
u s e d as t h e b a s i s for e s t a b l i s h i n g t h e purity of t h e cycloh e x a n e u s e d i n t h i s investigation. G e i s t and Cannon (4), a s well as P a r k s and coworkers (8),determined a number of t h e p r o p e r t i e s of c y c l o h e x a n e a t atmospheric pressure. T h e c r i t i c a l temperature and p r e s s u r e were reported by CHEMICAL A N D ENGINEERING DATA SERIES
9
