INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
816
the same form as Equation 3 for a binary system. Ioffe (3) and others, working with nonvolatile systems, have also observed that mixing individual hydrocarbons into mixtures gives the same form of curve as binary systems. Thus, n-butane-naphtha systems might be expected to show the same pattern of behavior as simple binary systems. The effect of the molecular xeight of the second component on volume changes in light hydrocarbon-hydrocar bon systems 1s marked (6). However, the similarity between the volume changes in the n-butane-benzene and n-butane-cyclohexane systems suggests that the structure of the second component is not important. To confirm this view, further work on mixing n-butane with other types of hydrocarbons of about the same molecular weight as benzene and cyclohexane would be needed.
Table 111. V o l u m e C h a n g e s on lliixing T\ eight Fraction BenCyclozene hexane
nButane 0.090 0.180 0.391 0.648 0.812 0.096 0.196 0.425 0.673 0 834 0.262 0.413
0.910 0,820 0,608
0.352 0.188 0 0 0 0 0 0.396 0.194
Table IV.
O
F.
60 80 100 120 140
0 0 0 0 0 0.904 0.804 0.575 0.327 0.166 0.342 0.393
BO 0’ F. -0.18 -0.29 -0.44 -0.38 -0.22 -0.21 - 0 40 -0.61 -0.56 -0.32 - 0 10 -0.39
Volume Changes Wr a t 80 0’ 100 0’ 120 0’ r. F. F. -0.23 -0.30 -0.39 -0.45 -0.60 -0.74 -0.58 -1.04 -0.78 -0.48 - 0 65 - 0 . 8 7 -0.29 -0.54 -0.40 -0.27 - 0 35 - 0 . 4 4 -0.50 -0.82 -0.77 -0.74 -0.92 -1.14 -0.68 -0.84 -1.04 -0.40 -0.50 -0.64 -0.25 -0.42 -0.61 -0.57
110 0’ F. - 0.90 -0.86 -1.36 -1.14 -0.71 -0.53 -0.94 -1.40 -1.29 -0.80 -0.81
P e r c e n t a g e \‘olume C h a n g e s €or T e r n a r y Mixtures Mixture 2
Mixture 1 Predicted -0.10 -0 14 -0.25 -0.28 -0.44 -0.42 -0.61 -0.63 -0.81 -0.86
Obsd.
Predicsed -0.41 -0.56
Obsd. -0.39 -0,57
Diff. -1-0.04 +0.03 +0.02 t0.02 +0.05
Diff. -0.02 -0.01
T a b l e Y.
COMPRESSIBILITIES
Av
10.0
‘E
(9)
- 7.0
n here Ti, is the volume of liquid in the pycnometer a t 7 atm
,
and AT’ is the change in volume when the pressure is raised from 7.0 to 10.0 atm. a t constant temperature. The experimental error depends on the magnitude of the compressibility and ranged from about 4 to 9 X low6atm.-’. For each mixture the compressibilities were fitted by t h e method of least squares to equations of the form
+ b ( t - t l ) Jr c ( t -
?iY
2:
Compressibility, p, in atm. -I, 7%-ascalculated from
p = -- 1x V?
C o n s t a n t s for E q u a t i o n 10
Weight Fraction Constants Difference“ nBenx 104 Eiatane zene al$ o‘+. XTTZL 1.0 1.75 1 . 9 2 6 0 . 6 =tl 0 0 267 +2 0 0 90 60.0 0 0 0.46 -0.03 1.0 0 1.0 101 0 0.52 0.08 57.9 0 +1 0,090 0 99 -1 0.52 0.02 5 8 . 5 +1 0.910 0.180 0 111 0 . 4 8 +1 0.26 58.7 & 1 0.820 0 142 0 0 0,391 0.77 0.30 5 9 . 7 0.609 0 193 0,648 1.06 0.82 6 2 . 2 &1 0.352 0 216 1.37 1.23 56.4 0 0.812 0.188 0.904 111 -1 0 0.53 0.20 60.2 & l 0.096 0.804 126 +2 0.51 0.40 60.8 k 1 0 0.196 0.575 160 0.425 -1 0 0.84 0.44 67.0 J 1 0.327 180 0 1.07 0 . 9 3 52.5 & 1 0.673 0 834 0 166 216 1.26 1 . 3 0 55.0 i l 0 +2 0,262 0.342 128 0.65 0 . 2 4 62.3 i l 0.396 a Obser T,ed c o m p r a;sibility minus c,ompressibility from Equation 10.
,“,Y,“,‘zi
Equation 5 , as is often done to represent the excess free energy of more symmetrical systems (4,8, 9 ) .
p = a
Vol. 48, No. 4
11’12
(10)
There t is temperatuie in O F and a, b, c, and tl are constant$ given in Table V. Equation 10 xvas used to calculate the deviations of the compressibilities from ideality-i.e., p - Po, n-heie Z&. These deviations the ideal compressibility is PO = Z,pi n’ere directly proportional to the per cent volume changc.9 within the accuracy of the measurements
+
p - PO = k ( % volume change)
(11)
where k is a constant independent of tempeiature, pressure, and composition in the range studied, and per cent volume change is given b y Equations 3 and 4. The k for the ?e-butane-benzene system, 77 X 10-6 atin.-’. gives an average deviation from experiment of 3 X atm.-’ and a maximum deviation of 9 X 10-6 atm.-’. The k for the n-butane-cyclohexane system 61 X 10-6 atm.-’ gives an average deviation from experiment of 4 X 10-6 atm.-l and a maximum deviation of 12 x 10-6 atm.-’
ACKNOWLEDG3IENT
The author thanks Herman S. Seelig for valuable suggestions made during the course of this work. REFERENCES
Am. Petroleum Inst., “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons,” BPI Project 44, Car-
negie Press, Pittsburgh, Pa., 1953. Dorsey, N. E., “Properties of Ordinary Water Sub.tance,” p. 243, Reinhold, New York, 1940. Ioffe, B. V.,Zhur. Priklad. Khim. 22, 1263 (1949). Redlich, O., Kister, A. T., IND.ENG.CHEM. 40, 345 (1948). Reeves, E. J., Petroleum Refiner 31, 154 (1952). Sage, B. J., Lacey, TI’. X., Trans. Am. Inst. Mining M e t . Engrs. 136 (1940). Scatchard, G., Chem. Revs. 44, 17 (1949). Scatchard, G., Ticknor, L. B., J . Am. Chem. SOC.74, 3724 (1952). Scatchard, G., TT-ood, S. E., Mochel, J. hf., Ibid., 62, 712 (1940) Scatchard, G., Wood, S. E., XIochel, J. XI.,J . Phgs. Chem. 43, 119 (1939). Thiele, E. W., Kay, W. B , ISD. EXG.CHEM.25, 894 (1933). Wood, S. E., Austin, A. E., J . Am Chem. SOC.67, 480 (1945). IT’ood, S. E., Brueie, J. P., Ibid., 65, 1891 (1943). Wood, S. E., Gray, J. A., 111,I b z d . , 74, 3730 (1952). RECEIVED for review Beptember 6, 1955. ACCEPTEDNovember 30, 1955. Division of Industrial a n d Engineering Chemistry, 126th Meeting, A C S , S e w York, S. Y . , September 1954.
COiYCLUSIONS
For mixing n-butane into constant-composition mixtures of benzene and cyclohexane, Equation 8 can be reduced to
% volume change
= 21(1
- &)(a + bZi)
(12)
where 21 is the volume fraction of n-butane, and a and b are functions of al+ bl.2, a ~ b1,3, , a2.3, b2.3 and 2 2 / 2 8 . Equation 12 has
Correction I n the article “Volumetric and Phase Behavior in the Nitric Acid-Water System” [C. H. Duffy, W H. Corcoran, B. H. Sage, IKD, EKG.CHEII. 48, 431 (1956)] the legends for Figures 3 and 5 m r e interchanged. Figure 5 now appears on page 432 and Figure 3 on page 433.
