NOTES
752
XI is the mole fraction of component 1 R is the gas constant expressed in units consistent with E T is the absolute temperature The equation corrects for the effects caused by the difference in the “internal pressures” or “cohesive energy densities” of the two liquids and for the increase in entropy due to mixing molecules of unequal size. Theoretical solubilities were then calculated by inserting values for theoretical activity coeficients into equation 3. The experimental solubilities, the ideal solubilities, the theoretical solubilities, the experimental activity coefficients and the theoretical activity coefficients of uranium hexafluoride in its saturated solutions as a function of temperature are shown in Table I. .
Vol. 62
fist shown to form a solid solution by means of melting point studies18and a preliminary study of the vapor pressure-composition curve has been reported. The present investigation has been carried out in the same manner as our earlier investigation of the krypton-xenon system.6 Experimental Modifications.-The system was modified to allow operation a t lower temperatures by means of pumping on the liquid nitrogen. A solenoid valve, operated by a nitrogen vapor-pressure thermometer with electrical contacts, controlled this pumping. Another solenoid valve, operated by a krypton vapoi-pressure thermometer maintained the nitrogen level in the cryostat. It shut off the reservoir from the pumping line, and admitted helium, which forced the liquid nitrogen into the cryostat.
Results.-The procedure for obtaining and analyzing the data was exactly the same as in the previous work.6 The natural logarithm of the TABLE I partial pressure of argon us. mole fraction of argon SOLUBILITY A N D ACTIVITY COEFFICIENTS OF URANIUM is presented in Fig. 1 with the same data being HEXAFLUORIDE IN CHLORINE TRIFLUORIDE SOLUTION AS A listed in Table I. The energy of mixing parameter FUNCTION OF TEMPERATURE Composition of satd. soln., mole % UFe Ideal Theor.
Temp., OC.
Exptl.
64 60 50 40 30 20 10 0 -10 -20 -30
100.0 90.0 67.7 48.2 33.0 22.3 15.6 10.5 6.8 4.4 2.9
100.0 92.0 74.3 59.3 46.7 36.3 27.8 21.0 15.8 12.4 9.1
100.0 92.0 73.5 57.6 44.2 33.0 24.6 18.1 13.2 10.2 7.3
/
Activity coefficients of UFO Exptl. Theor.
1.00 1.02 1.10 1.23 1.42 1.63 1.78 2.00 2.32 2.81 3.14
1.00 1.00 1.01 1.03 1.06 1.10 1.13 1.16 1.20 1.22 1.25
96.2”K.
Y’
/
The exact eutectic composition could not be determined experimentally because the heat of crystallization of the very minute quantities of uranium hexafluoride was not sufficient to cause definite breaks in the warming and cooling curves ’ uranium hexafluoride. below about 4 mole % However, the eutectic composition can be calculated from the ideal solubility and the experimental activity coefficients by the method of successive approximations. The eutectic composition thus obtained is about 0.4 mole yo uranium hexafluoride. The inset in Fig. 1 illustrates the best estimate of the system at the eutectic. Acknowledgments.-The authors are indebted to G. D. Oliver and J. W. Grisard for their assistance in thermocouple calibration and for making thermal analyses on the pure materials.
/’ 89 2’K.
70.0“ K,
//’-
SOLID SOLUTION ARGON-KRYPTON FROM 70 TO 96’K.l BY J. F. WALLING* A N D G. D. HALSEY, JR. Department of Chemistry, University of Washington, Seattle 6 , Wash. Received December 88, 1867
We report here further studies of the rare-gas solid solutions. The system argon-krypton was (1) This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. A F lS(600)987. (2) Presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
02
06
04
08
Xa,,
Fig. 1.-Ln
partial pressure argon us. mole fraction argon.
(3) H. Veith and E. Schrijder, 2. physik Chem., 8179, 16 (1937). (4) J. H. Singleton and G. D. Halsey, THISJOURNAL, 68, 1011
(1954). (5) M. P. Freeman and G. D. Halaey, ibid., 60, 1119 (1956).
T
b
753
NOTES
June, 1958
TABLE I Temp.,
OK.
XAI
0.036 ,055 .088
.lo1 ,128 .186 .188 .330 .340 .461, .544 .549 .650
70.0 In
XAr
PA,
-0.0223 - .0428 .3764 .5371 .6461 ,9735 .9462 1.2698 1.2223 1.3712 1.4782 1.4584 1.5059
0.060 .087 .139 ,165 ,276 .381
0.9610 1.3455 1.7435 2.0497 2.2029 2.3052
0.293 .375 .388 .495 .540 .570 .615
83.0 In P A *
3.0963 3.2638 3.2577 3.3725 3.4388 3.4662 3.4904
XAr
89.2 In
0.009 ,019 ,024 .049 .052 .054 .066 .096 .221 .353 .463 .581
96.2 XAr
PAr
1.4386 2.1268 2.1242 2.2757 2.4027 2.8783 2.9210 3.2107 3.6354 3.8841 4.0539 4.1685
In PA,
2,7559 3.2232 3.7762 3.6205 3.9235 3,9402 4.0920 4.1449 4.1965
0.058 .080
.loo
.117 .136 ,171 .183 ,209 .221
TABLE I1 Argon at 83OK.
Krypton at 105’K.
Xenon
Ref.
a L. (cal./mole) 1840 2550 Heat of sublimation b -8.3 K(cma2/kg. X lo5) -9.9 Isothermal compressibility C 7.6 Cp(cal./deg.) 8.0 Heat capacity (constnnt pressure) d v(cm.8) 28 32 Molar volume 3.61 4.05 e 3.42 Low temp. collision diameter 180 230 e E/k 124 Equilibrium pair energy . (”) .. “Selected Values of Chemical Thermodynamic Properties,” Circular 500, Series I, National Bureau of Standards, U.s. Govt. Printing Office, p. 544-545. b The value for argon represents an extrapolation of the data while that for krypton was selected because V / K -9000 cal. which was thought to be order of magnitude correct; J . W. Stewart, Phys. .Rev., 97, 578 (1955). C K. Clusius, 2. physik. Chem., B31, 459 (1936). d L‘SmithsonianPhysical Tables,” Vol. 88, Smithsonian Institution, Washington, D. C., 1934, p. 159. e J. 0. Hirschfelder, R. B. Bird and E. L. Spotz, Chem. Revs.,4 4 , 205 (1949).
4.)
for the random-mixed model of the strictly regular solution was evaluated as before. The value WAB = 320 - 1.7T cal. per mole, with an uncertainty of 50 cal. was obtained. This value produces the solid line in Fig. 1. The dashed line is the best fit obtained with a temperature-independent WAB. The extrapolated critical temperature for phase separation is 56 i 8°K. The large uncertainty in this estimate is caused by the rather long extrapolation. Discussion of Results.-Both the entropy and energy parts of WAB are one-half the corresponding values for the krypton-xenon system. We have attempted to calculate these quantities according to several current theories, but have been hampered by the lack of good data on the pure solids, especially for xenon. We have used the “cell model” of Prigogine and Bellemans,s the “refined average potential model” of these authors and Mathot,’ and the “one liquid” and “two liquid” theories of Scott.8 The assembled data used, and their sources are presented in Table 11. The results of the computations are given in Table 111, in terms of the excess thermodynamic quantities at IL: = 0.5. If one bears in mind that all these theories are full of approximations, and that the data used are often rather poor, it is clear that the theories give a reasonable account of the krypton-xenon system. The heat term for the argon-krypton system is fairly well predicted, but all the theories fail to account for the excess entropy for this system. On (6) I. Prigogine and A. Bellemans, Disc. Faraday Soc., 16, 80 (1953). (7) I. Prigogine, A. Bellemans and V. Mathot, “The Molecular Theory of Solutions,” North Holland Publishing Co.,Amsterdam, 1957, Chapt. X. ( 8 ) R. L. Scott, J . Chem. P h y s . , 25, 193 (1956).
the other hand, as we have noted above, the simple “corresponding states” idea that the ratios of heat and entropy terms for the two systems should be the same, gives a good account of the s y ~ t e m . ~ TABLE I11 Soln. argon-krypton Temp. = 83OK. X = 0.5
Measured “Cell model” “One liquid” (‘TWO liquid” “Refined av. potential model”
Excess free energy of mixing 771
Exoesa enthalpy of mixing FI‘
(cal.jmole) (oal.j;nole)
Excess entropy of mixing S‘ (e.11.)
0.43 .14 .06 .03
45 30 41 27
42 46 30
41
31
81 53
170 113
0.85 .57
139
149
.12
80
-
.12
Soln. krypton-xenon Temp. = 105OK. X = 0.5
Measured “Cell model” “Refined av. potential model”
(9) G. D.Halsey and M. P. Freeman, Nature, 178, 431 (1950).
THE SOLUBILITY OF CALCIUM SOAPS BY JOHNTHOMAS YOKE,I11 Miami Valley Laboratories, Procler and Gamble Co., Cincinnati, Ohio Received January 6 , 1968
It has seemed worthwhile to redetermine the solubilities of calcium stearate, palmitate, laurate and oleate in water. The results of previous direct determinations1-4 are in very poor agreement. (1) J. Zink and R . Liere, 2. angew. Chem., 28,
[I] 229 (1915).
