and opposite to the internal pressure of the liquid of equal volume, were confirmed for parahydrogen and helium with a reasonable degree of certitude. It is an open question whether the hypotheses are correct in general or hydrogen and helium are particular cases.
4 I
I
i
!
Conclusions ! I
’ i
3
I!
I
’\
These hypotheses are consistent with a particular form of equations of state, able in principle t o describe the liquidsolid phase transition by a simple translation automorphism. Such equations of state seem to work reasonably Kell for a group of substances, but again it is an open problem if and how such equations can be generaljzed.
’
0’ 2
Pr :.lo
\
I I
I
Tr
I
I
Figure 6. Relation of reduced density, D,, to reduced temperature, T,, for carbon dioxide
0 0 X
Calculated b y Equation 10, where b = 55 cc./mole, and V a = 28.8 cc./mole Data of Kennedy and Thodor ( 1 9 6 0 ) Estimated from data of Grace and Kennedy ( 1 9 6 7 ) Data of International Critical Tables ( 1 9 2 8 )
where A = 4RTc, or a n adjustable parameter. Equation 11 describes reasonably well the atmospheric or low pressure liquid-solid transition data on carbon dioxide, vanadium pentoxide, iodine, and n-eicosane. No special importance should be attached to Equation 10, because numerous other formulas of the form of Equation 9 may represent as well, or even better, the liquid-solid transition. The hypotheses that the volume of the melting solid, at pressure P , is equal to the volume of the liquid at 0’ K., a t P , and that the internal pressure of the melting solid is equal
Literature Cited
Allersma, T., Hakim, R., Kennedy, T. N., Mackenzie, I. S., J . Chem. Phus. 46. 154 (1967). Bellemans, A.,“Nigam, R. ~K.,i.Chem. Phys. 46, 2922 (1967). Bernal, J. D., Proc. Roy. Soc., Ser. A, 280 (1382), 299 (1964). Bridgman, P. W. “The Physics of High - Pressures,” G. Bell and Sons, London, 1952. Cook, G. A., Dwyer, R. F., Berwaldt, 0. E., Nevins, H. E., J . Chetn. Phus. 43. 1313 (1965). Dugdale, I. S.,“Franck, J. P., Phil. Trans. 267, 1 (1964). Dwyer, R. F., Diller, D. E., Roder, N. AT., Weber, L. A., J . Cheni. Phys. 43, 801 (1965). Frisch, €1.L., Science 160, 1249 (1965). Glassford, A. P. hl., Smith, J. L., Cryogenics 6, 193 (1966). Goodwin, R. D., J . Res. Natl. Bur. Std. 70A, 241 (1966). Goodwin, R. D., Diller, D. E., Roder, H. M., Weber, L. A., J . Res. Xatl. Bur. Std., 67A, 173 (1964). Grace, J. D., Kennedy, G. C., J . Phys. Chem. Solids 28, 977 (1967). aVatl. Acad. Sci. U.S.A. 67 ’39 (1967). Hildebrand, J. H., PTOC. Hildebrand, J. H., “Solubility of Non-Electrolytes:JP Reinhold, Sew York, 1936. “International Critical Tables,” RlcGraw-Hill, New York, 1928. Kennedy, J. T., Thodos, G . .4., J . Chem. Eng. Data 6,293 (1960). Le Bas, G., Chem. AVews116, 37 (1917). Partington, J. R., “Advanced Treatise on Physical Chemistry,” Yol. 11, p. 27, Longmans, Green, London, 1955. Rushbrooke, G. S., Discussions Faraday Soc. 43, 7 (1967).
GEORGE J. AUSLAENDER Bv. Republici 291 Ploesti, Romania RECEIVED for review September 9, 1968 ACCEPTEDJune 4, 1969
CALCULATION OF PARTIAL FROM TOTAL VAPOR PRESSURES
System-C6He+CCl,F
e
CCIF,
Measurements for total vapor pressures of mixtures of benzene with Freon, CC12F.CCIF2, are used to illustrate a simple, rapid application of regular solution equations to the calculation of partial pressures from total pressures.
BENZEXE and 1,1,2-trichlorotrifluoroethane,Freon 113, were selected for a study of the solubility of gases in mixtures of two nonpolar liquids of very different solvent power. The solubility parameters of these liquids are 9.15 and 7.05 (cal./cc.)1’2, respectively. We avoided perfluorochemicals because their mixtures with alkanes are not strictly normal. We publish here our measurements of total vapor pressure of mixtures of these two liquids, because they serve 846
l&EC
FUNDAMENTALS
extraordinarily well to explain a simple, accurate method of calculating partial vapor pressures from measurements of total vapor pressures as a substitute for extremely complicated methods that have been used (Prausnitz et al., 1967; Redlich and Kister, 1949). Vapor pressures were determined in an apparatus which we designed for measuring solubility of gases (Hildebrand and Dymond, 1967). The liquids were Spectroquality. They
were degassed in the apparatus by repeated freezing and evacuating. Vapor pressures of pure Freon 113 were measured over the range of 2’ to 32’ C. They conform with a mean square deviation of 0.14% to the equation: loglo p’ = 7.6720 - 1535.29/2’ where p o is in millimeters of Hg. Our vapor pressures are a little lower than those obtained in this laboratory by Hiraoka and Hildebrand (1963)--e.g., 333.1 mm. a t 25’ C. instead of 363 mm.-but agree closely with other published data (Benning and NcHarness, 1940; Hovorka and Geiger, 1933; Riedel, 1938). The composition of each mixture was determined from its density, an accurate method in view of the large difference between the densities of the pure liquids: T h a t of benzene a t 25’ C. is 0.8736 gram per cc., that of Freon is 1.5632 grams per cc. The density-mole fraction line has a slight curvature corresponding to an excess molal volume of 0.5 cc. a t the maxitnum. Our measured total pressures in millimeters of H g a t 5’, 15’, and 25’ C. and mole fractions of benzene, 21, are given in Table I. We calculate the partial vapor pressures, pl and p z , by the regular solution equation (Hildebrand and Scott, 1962) :
RT l n y l
=
(11
v1+??(61- 6 ~ ) ~
and its conjugate equation for component 2 with subscripts reverqed. y1 = pl/pl’sl is the activity coefficient of benzene; V’S are molal volumes, 9’s are volume fractions, and 6’s are solubility parameters. Values a t 25’ C. are: C6Hs CC12F. CClF2
v, C c Mole
p‘. &Tin
6
89 4 119 9
95 2 333 1
9 15 7 05
T o calculate pl and
$12
we w i t e the above equation as
Table I. Measured Total and Calculated Total and Partial Vapor Pressures of Mixtures of C6H6and CCI2F*CCIF, pressure, I , him. Hg. C . 0 . 2 6 0 Pmeasd.
Posiod. PI o a i c d . Pzcaiod.
5 15 25 25 25 25
123.4 192.7 291.9 290.0 35.0 255.0
XI
+ log + (61 - 6?)2/4.575T log pzo + log + v&i2(6i - 62)?/4.575T
log pl = log p1O
21
log p z =
22
V1912
We first calculated values of pl and pz using 61 - 62 = 2.10 and found that total pressures, P = p l + p ~ a, t the several values of sl were as much as 10 mm. higher than the measured values. We next set 61 - 6 2 = 1.95 and obtained the partial pressures given in the last two lines of Table I. Their sums, Pcalod, in the third line from the bottom agree to 2 mm. or better with the measured total pressures on the line above. This procedure can, of course, be applied to systems for which solubility parameters are not known by estimating a probable value of 61 - 6 2 and adjusting it b y successive approximations until pl pfcalcd equals Pmeasd for several values of 2 . It is significant that this system is far from symmetrical. The excess of the total pressure over the ideal, plzl+ ~ 2 x 2 ,is maximum a t 51 = 0.675, where the respective values are 220 and 172 mm. The use of volume fractions fully compensates for the asymmetry. Partial pressures at 5’ and 15’ C. have been calculated as above with equal agreement with the measured total pressures. The junior author, for comparison, carried out with a computer the complicated calculation of p l and p2 (Prausnitz et al., 1967). His figures agreed closely with ours in Table I, which were obtained in minutes with a 60-cm. slide rule.
+
literature Cited
Benning, A. F., McHarness, R. C., Ind. Eng. Chem. 32, 497 (1940). Hildebrand, J. H., Dvmond, J. H.. IND.ENG.CHEY.Fun.o.4MEZITBLS6, 130 (196i). Hildebrand, J. H., Scott, R. L., “Regular Solutions,” p. 150, Prentice-Hall. Endewood Cliffs. N. J.. 1962. Hiraoka, H., Hildebyand, J. H., j. Phyi.-Chem. 67,916 (1963). Hovorka, F., Geiger, F. E., J . Am. Chem. SOC.6 6 , 4759 (1933). Prausnitz, J. >I., Eckert, C. A , , Orye, It. I-.,O’Connell, J. P., “Computer Calculations for Multicomponent Vapor-Liquid Equilibria,” Prentice-Hall, Englewood Cliffs, N. J., 1967. Redlich, O., Kister, A. T., J . Am. Chem. Soc. 71, 505 (1949). Riedel, L., 2. Ges. Kulte-Ind. 46, 221 (1938).
__ ---__----
R. G. L I S F O R D
0.345 0.359
0,510
0.650
0,674
0.776
118.5 184.3 278.5 278.0
106.6 165.8 250.2 250.0 61.0 189.0
92.9 145.7 221.8 223.0 72.0 151.0
90.7 142.0 215.8 216.0 73.0 143.0
78.1 123.3 188.7 187.0 76.0 111.0
118.0 183.4 276.8 277.0 47.0 48.0 231.0 229.0
falloffs:
J. H. HILDEBRAND University of California Berkeley, Calif. 94720
RECEIVED for review June 11, 1969 ACCEPTEDJuly 1, 1969 Work supported by the U.S. Atoniic Energy Commission.
VOL.
8
NO.
4
NOVEMBER
1969
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