Jan. , 1958
SOLUBILITY OF RAREGASESIN METHYLCYCLOHEXANE
Calibrations.-All solutions were prepared from recrystallized reagent grade salt and distilled water.4 The sodium and potassium chloride solutions were made up by weight. The concentrations of the ammonium chloride and potassium bromide solutions were determined by potentiometric titration against silver nitrate which had previously been standardized against both the NaCl and the KCl solutions. Agreement between duplicate titrations was always within 0.05%. Concentrations a t 500 and 1000 atmospheres were calculated from those a t one atmosphere by using the Tait equation.b The cross-sectional area A was found by direct measurement of the bore of the tube with a comparator, the measurement being made while the cell was immersed in a mixture of its own refractive index (3 : 1 = xy1ene:n-octanol). This procedure was checked on a short length of precision bore tubing of the approximate diameter of the cell; agreement was within 0.1% between the diameter as measured across the flattened end of the tube in air, and the diameter as measured by the above described immersion scheme. The measuring part of the cell was also found to have a uniform diameter, within 0.1%. The diameter of the cell was taken as 4.058 mm. and the cross-sectional area was therefore determined to be 0.1294 The other variables in eq. 2 were found in the ways described in the previous paper.2 The length, I , in the present cell was calculated to be 10.50 em. The average time during which current flowed throuqh the cell was 209.94 seconds for the present set of experiments. About 30 seconds were allowed for measuring resistance before the direct current was switched on again. Errors and Limitations of the Method.-The present results are probably subject to a somewhat higher error than the previous ones. The crosssectional area is known'at best t o about 0.2%, while it could be found t o 0.1% for the smaller diameter tubes.2 Furthermore, any contaminants introduced during the somewhat complicated procedure for filling the cell become a more serious (4) L. G. Longsworth,ibid., 67, 1185 (1935). ( 5 ) R. E. Gibson, ibid., 66, 4 (1934); B. B. Owen, J . Chem. Ed., 81, 59 (1944).
89
source of error as the solution becomes more dilute. Adding in errors attributable t o measuring the other quantities in eq. 2, we can expect a total error of about 0.6%. The sensitivity of the entire method decreases with the conductivity of the salt solution under study. If the resistance of a 0.02 N solution of electrolyte, CA, in the cell is R1, and the resistance a t the end of the run, with CdA, between the probes, is R,, then the change in resistance per centimeter of motion of the boundary is about (R, - R1)/lO. Each resistance reading is obtained to * l O ohms. This corresponds to an uncertainty in boundary position of 100/(Rz - Rd. For potassium chloride, this amounts to 0.004 em., but for sodium chloride, the uncertainty is increased to more than 0.009 em. An experiment on lithium chloride was abandoned because the over-all change in resistance was only 1000 ohms, which meant that the boundary could not be located to better than 0.1 em.
*
Results and Discussion The transference numbers measured at one atmosphere all check the literature values to 0.2% or better. Figures 1, 2, 3 and 4 show clearly that the transference numbers of the cations of all four salts studied decrease with pressure. The magnitude of the decline is about 2% per thousand atmospheres for 0.02 N solutions of KCI and NHdCI, almost 3% over the same pressure range for the 0.02 N NaCl solution, and less than 1 % for the 0.02 N KBr. For the last solution, it is quite apparent that the pressure coefficient of the potassium ion transference number is larger in absolute magnitude in the first half of the pressure range investigated than in the second (Fig. 3). Comparison of the present results with those of Wall and Gi1112suggests that the K + transference number in aqueous KC1 solutions is relatively independent of concentration from 1 to 1000 atmospheres (Fig. 1). For sodium chloride solutions (Fig, 2), on the other hand, the transference number increases with decreasing concentration, but the magnitude of the increase is about the same a t all pressures studied.
T H E SOLUBILITY OF HELIUM, NEON, ARGON, KRYPTON AND XENON I N METHYLCYCLOHEXANE AND PERFLUOROMETHYLCYCLOHEXANE' BY H. LAWRENCE CLEVER, J. H. SAYLOR AND P. M. GROSS Contribution from the Department of Chemistry, Duke University, Durham, North Carolina Received Augual 8. 1967
Rare gas solubilities have been determined at one atmos here total pressure and temperatures of about 16, 30 and 43" in methylcyclohexane and perfluoromet,hylcyclohexane. MOL fraction solubilities at 30" in CeHllCHs and CJ?&Fs, respectively, are helium 1.68 X 7.85 'X neon 2.34 X 11.5 X lO-',.argon 18.3 X,lO-: 43.4. X krypton 55.6 X 80.8 X lo-' and xenon 218 X 161 X 10-4. Heats of solution and entropies of solution are less in the fluorocarbon than the hydrocarbon for a given gas but both fit the Butler-Barclay plot within experimental error. Gas solubility parameters calculated from the Hildebrand equation using the experimental solubilities and assuming the gas partial molar volume equal to the critical volume are helium 3.2, neon 1.8, argon 5.5,krypton 6.6 and xenon 7.5.
The solubility of helium, neon, argon, krypton (1) Presented before the Division of Physical a n d Inorganic Chemistry, 127th National Meeting of the American Chemical Society, Cinoinnati. Ohio, April, 1955.
and xenon has been determined at a total pressure of one atmosphere and temperatures of about 16, methylcyclohexane and 30 and 430 in the perfluoromethylcyclohexane.
90
62 -4
-8
- 12 ai
M
8
2
-16
d
d
P
u
0
h -20
a
51
13
8 -24
-28
-32 -15
-9 -6 -3 0 3 Heat of soln., kcal. /mole. Fig. 1.-Heat of solution us. entropy of solution, 25". The gases in: 0, methylcyclohexane; 0 , perfluoromethylcyclohexane; O, benzene; a, cyclohexane; 0,dodecane, a), isooctane; 0 , hexane. Heats and entropies of condensation: 0,the seven points to left are the pure solvents at one atmosphere and 25", the five points to the right are the rare gases a t their normal boiling points. The straight line A S = -12.75 0.00124 AH is from Frank (ref. 8).
-12
+
Experimental The solubility apparatus and procedure have been described before.2 Excepting xenon, the gases are the same used previously. The pure xenon was a gift of the Linde Air Products Co. Purification of Solvents.-Methylcyclohexane, Eastman Kodak white label was dried over sodium a;d distilled; corrected b.p. 100.95-100.97", lit.3b.p. 100.93 Perfluoromethylcyclohexane, du Pont FCS-326, shaken with coned. HzS04, washed, dried over Drierite and distilled, b. .75.95 to 76.05' a t 753 mm., lit.4 b.p. 78.14" at 760 mm. %he density of the fluorocarbon at the three temperatures was determined by direct weighing of 250 mi. of the material in a previously calibrated 250-ml. volumetric flask. The densities along with the other physical properties of both fluorocarbons and hydrocarbons are compared in Table I.
TABLE I1 SOLUBILITY OF HELIUM,NEON, ARGON, KRYPTON AND XENONIN METHYLCYCLOHEXANE AND PERFLUOROMETHYLCYCLOHEXANE
.
Gas
Helium
T%mp., C.
Mole fr. soly. ratio, FluoroSolubility carbon Molefraction X IO4 HydroOstwald X 102 C7H14 C7F14 C7Hl4 C7FI4 carbon
-
16.0 2.72 8.65 1.46 7.05 4 . 8 30.0 3.25 9.91 1.68 7.85 4 . 7 43.1 4.10 10.6 2.07 8.23 4 . 0 Neon 16.0 3.95 13.2 2.11 10.8 5.1 30.0 4.54 14.6 2.34 11.5 4.9 TABLE I 43.1 5.62 15.7 2.82 12.2 4 . 3 SOMEPHYSICAL PROPERTIES OF METHYLCYCLOHEXANE AND 16.0 34.9 57.0 18.6 46.2 2 . 5 PERFLUOROMETHYLCYCLOHEXANEArgon" 18.3 43.4 2 . 4 30.0 35.4 55.0 Density, Heat of vaporization, Solubility Temp., g./ml. cal./mole parameter 43.1 35.5 55.3 17.9 42.7 2 . 4 C7HI4 C7FI4 C7Hl4 C7FI4 C7FI4 C7Fl4 Krypton 16.0 115 112 61.4 90.6 1 . 5 16.0 0.7729 1.811 30.0 107.8 102.7 55.6 80.8 1 . 5 30.0 .7607 1.774 8458 7830 7.8 6.0 43.1 99.9 101 50.2 77.7 1 . 6 43.1 .7497 1.739 Xenon 16.0 480 233 250 186 0.74 (2) H. L. Clever, R. Battino, J. H. Saylor and P. M. Gross, THIS 30.0 430 206 218 161 .74 JOURNAL, 61, 1078 (1957). 43.1 373 187 185 143 .77 (3) F. D. Rossini, et al., "Selected Values of Properties of Hydroa L. W. Reeves and J. H. Hildebrand, J. Am. Chem. SOC., carbons," National Bureau of Standards, Circular C461, 1947. 79, 1313 (1957), report argon solubilities in the same sol(4) D. N. Glew and L. W. Reeves, THISJOURNAL, 60, 615 (1956). vents. Our solubilities in methylcyclohexane agree quite (5) R. D. Fowler, J. M. Hamilton, Jr., J. 5. Kasper, C. E. Weber, well but our values in perfluoromethylcyclohexane are about W. B. Burford, 111, and H. C. Anderson, Ind. Eng. Chem., 39, 375 (1947). 2 yolower.
SOLTJBILITY OF RAREGASESIN METHYLCYCLOHEXANE
Jan., 1958
Results and Discussion The solubilities corrected to one atmosphere gas pressure by Henry’s law are given in Table I1 in units of Ostwald coefficient and mole fraction. Heats and Entropies of Solution.-The temperature dependence of the solubility has been used to calculate heats and entropies of transferring one mole of the gas from the gas phase at one atmosphere t o the hypothetical unit mole fraction solution6 a t 25”. The heats are smaller and the entropies less negative for transfer to the perfluoromethylcyclohexane than to the methylcyclohexane and other hydrocarbon solvents. However values for both solvents fit the Butler-Barclay’ plot given by Frank*as A 8 = -12.75
+ 0.00124AH
Figure 1 shows the A S against AH plot for the five rare gases in methylcyclohexane and perfluoromethylcyclohexane as well as the values for benzene, cyclohexane, n-hexane and isooctane measured previously.2 Values of AH and AS of condensation from one atmosphere at 25’ for the pure solvents fit the same line, but are considerably more negative. One cannot estimate AH and A S of condensation of the rare gases at 25’ but values at the normal b.p.’s are included in Fig. 1. and fall in the same general region. Solubility and Solvent Surface Tension.-The Uhlig equation9 predicts a linear relationship between solvent surface tension and the logarithm of the Ostwald coefficient. Using slopes and intercepts representing the average behavior in 13 hydrocarbons,2 calculated Ostwald coefficients in methylcyclohexane and perfluoromethylcyclohexane, respectively, are in error for helium -3.7, -36; neon -1.0, -36; argon -7.7, -2.8; krypton -15, +37; xenon -10, 157%. The large errors in the calculated solubilities in the fluorocarbon are probably due to its “super” nonassociated nature as a liquid. The Eotvos constant for perfluoromethylcyclohexane calculated from surface tension, density and critical temperature reported by Fowler, et U Z . , ~ is 2.77. Normal liquids have a value of about 2.2 while associated liquids have a smaller value. The Hildebrand Equation.-Gjaldbaek and Hildebrand‘O developed the equation VZ + 0.434 1 - - + -log Xz = -log Xtl + log -
+
91
and VZmolar volumes of solvent and liquefied solute gas, respectively, and 81 and 82 solubility parameters of solvent and solute gas, respectively. The experimental solubilities, the methylcyclohexane and perfluoromethylcyclohexane molar volumes and solubility parameters were substituted in the equation; the ideal solubility was eliminated and the result solved for the rare gas solubility parameter to give 385.3 XZhydrocarbon + 6.45 62 = VZ log 1’528 XZfluorocarbon The gas solubility parameters were calculated using gas molar volumes corresponding to (1) the volume of the liquefied gas a t its normal b.p., (2) the gas critical volume and (3) van der Waals b. Of the three calculations only the one using V2 corresponding to the critical volume resulted in positive values of the solubility parameter for all five gases (Table 111). Excepting helium the calculated solubility parameters are smaller than the corresponding values at the normal b.p. as expected.’l For helium V O= 32, the molar volume at the gas b.p.; a2 = 0.6 and X 2 = 0.00139 is as good a set of values and more compatible with the solubility parameter a t the gas b.p.
1
{
TABLE I11 CALCULATED VALUES OF SOLUBILITY PARAMETER AND IDEAL SOLUBILITY Gas
Solubility parameter at normal b.p.
Critical vol. cm.*/mole
Calcd. solubility parameter
Calcd. ideal mole fraction solubility
Helium Neon Argon Krypton Xenon
0.5 4.9 7.0 7.5 8.0
57.7 41.7 75.3 92.1 113.7
3.2 1.8 5.5 6.6 7.5
0.00139 .00180 .00314 .00659
.0220
The above value for helium and the values from Table I11 for the other gases were used to calculate the mole fraction solubilities in the thirteen hydrocarbons previously reported.2 The mean percentage error and average deviations are Helium
Neon
Argon
Kwpton
All 13 solvents ‘13f 9 1 3 & 7 8 1 4 6 1 3 6, 7, 8 carbon solvents 16 f 10 12 f 9 9 i 5 5 f 3 9, 10, 12, 14 carbon solvents 6f 4 1 6 f 2 5 f 1 7 f l
3
The values of 8 2 , Va and X z from Table 111 reproduce the experimental solubilities quite well and are a decided improvement over previously suggested values for the 9, 10, 12 and 14 carbon solfor gas solubilities where x2 is the mole fraction vents. solubility, xZithe ideal mole fraction solubility, V1 It is interesting that the ratio of mole fraction solubilities (Table 11) goes through a maximum at (6) H. S. Frank and M. W. Evans, J . Chem. Phya., 18, 507 (1945). (7) I. M. Barclay and J. A. V. Butler, Trans. Faraday Soc., 34, 1445 neon. It seems significant that the critical vol(1938). umes, volumes at the gas b.p. and van der Waals b (8) H. 8. Frank, J. Chem. Phys., 13, 493 (1945). all go through a minimum at neon. JOURNAL, 41, 1215 (1937). (9) H. H. Uhlig, THIS Vl
(
(10) J. Chr. Gjaldbaek and J. H. Hildebrand, J. A m . Chem. Soc., 71, 3147 (1949).
(11) J. H. Hildebrand and R. L. Scott, “Solubility of Nonelectrolytes,” 3rd ed., Reinhold Publ. Corp., New York, N. Y.,1950, p. 433
