SEVERAL SOLUTIONS O F NON-POLAR SUBSTANCES J. H. HILDEBRAND Department of Chemistry, University o j Calijornia, Berkeley, C a l i j m i a Received October 4, 1988 I. T B E SYSTEM IODINE-CARBON TETRACHLORIDE THROUGH A RANGE OF 161°C.
The large deviations from Raoult's law shown by solutions of iodine with carbon tetrachloride, and their dependence upon differences in internal pressure rather than upon changes in molecular species, have made this system one of the most interesting examples of a non-ideal solution, and it has been dealt with in several previous papers (6, 7). In the most recent of these the course of the solubility curve for the range 0" to 50°C. was made the basis for predicting the existence of two liquid phases above the melting point of iodine. This proved to be true, with a consolute temperature of 16I0C., well within the limit of accuracy of the prediction. It has seemed desirable to determine a few points within the long interval between 50' and 130"C.,so as to have a better record of the temperature dependence. As part of this program, direct determinations of the heat of fusion of iodine and the heat capacities of both solid and liquid have been carried out in this laboratory by K. J. Frederick (3). This has lent more confidence to our calculations of the ideal solubility of the solid iodine. Iodine from Kahlbaum and carbon tetrachloride from the Eastman Kodak Company were used without further purification than drying the latter with calcium chloride. The proper amounts were put into a simple Pyrex glass apparatus consisting of a horizontal, cylindrical mixing compartment, with two side bulbs attached to the vertical stem. The charge in the main compartment was frozen in liquid air, and the apparatus was evacuated and sealed. The apparatus was placed in a thermostat and rocked so that the liquid surged vigorously back and forth. When it was judged that equilibrium had been reached, the apparatus was tilted so as to pour solution into one of the side bulbs. The great density of iodine, together with the fact that the excess solid mats together, made it unlikely that any solid particles would be carried over. The apparatus was then cooled, and the bulb was sealed off and weighed. The bulb was opened 1 Presented at the Symposium on Intermolecular Action, held at Brown University, Providence, Rhode Island, December 27-29, 1938, under the auspices of the Division of Physical and Inorganic Chemistry of the American Chemical Society. 109
110
J. H. HILDEBRAND
and its iodine content determined by titration with thiosulfate. The glass was weighed and the carbon tetrachloride was determined by difference. Table 1 gives the results of four determinations. These correlated so well with each other and with the data for the same system a t high and a t low temperatures that they are sufficiently accurate for our purpose. Table 2 shows the correlation of all the data for this system, including the solubility of solid iodine from 0" to 100°C. and of liquid iodine from TABLE 1 Solubility of iodine i n carbon tetrachloride
t
I
IODINE
TEFERATURE
IODINE
'C.
weight per cent
mols per cent
80.2 97.0 99.5 99.9
11.53
7.35 13.56 14.59 14.71
--Loa
N:
22.00 22.16
I
I
LOG N;
VI
"(17,
V1
-LOQ Nt
D
2.379 1.940 1.798 1.556 1.134 0.868 0.836 0.833 0.347 0.306 0.260 0.167
5.82 5.61 5.60 5.40 5.18 4.91 4.90 4.88 4.43 4.38 4.18 4.28
__
'C.
0 25 35 50
80.2 97.0 99.5 99.9 150 154 158 161
94.4 97.5 98.8 100.7 104.8 107.0 107.5 107.5 116 117 118 118.5
0.790 0.582 0.503 0.394 0.193 0.093 0.078 0.075 0.086 0.099 0.119 0.167
58.5 59.6 60.1 60.8 62.2 65.4 65.5 65.5 66.0 66.2 66.4 66.5
0.998 0.993 0.990 0.984 0.954 0.912 0.906 0.905 0.686 0.648 0.594 0.462
0.282 0.316 0.361 0.462
-
150' to 161OC. This is done by calculating the parameter D in t h e equation (7) RT In (%/N')
= VZ?
0'
This becomes RT In
(N;/N')
=
~~(33: - ~;2)D2
for two liquid phases below the critical solution temperature and 1.985T6(N1Vl f N I V ~ )=~
~V:V~NIN~D'
SEVERAL SOLUTIONS OF NOS-POLAR SUBSTANCES
111
a t that point. Here N is mole fraction, a is activity referred to the pure liquid as standard, v is molal volume, 3 is volume fraction, i.e.,
vi = NIVI/(NIVI-k N2V2) Subscripts refer to the components, and N~ and N: in the second equation refer to the mole fractions of iodine in the two liquid phases in equilibrium. The value of a? for the solid iodine is calculated by aid of the equation: TWl
R In aa = R In N: = -
(H'
-
H*)d(l/T)
where E@is the heat content of the pure solid and HO that of the liquid, T, is the melting point, and N: the ideal solubility. HO - H' is the heat of fusion a t the meIting point, but this varies with temperature depending
:L 0
20 4 0 Temperature, 60 80 1 0 0'C.IM 140 160
FIG.1. Plot of D against temperature for iodine in carbon tetrachloride
on the difference in heat capacity of the solid and liquid forms. The data previously referred to have been used for the present purpose. However, in view of the peculiar form found for the dependence of the heat content of solid iodine with temperature, it was thought preferable to plot the data for HO and H* against 1/T, assume that "Ivaries linearly with T below the melting point as it seems to do above, and integrate graphically between l/Tmand 1/T. This process yielded the values of -log N: given in table 2. In the portion of the table referring to liquid iodine, log N: is replaced by log N;, referring to the second liquid phase. The last column gives the values of D calculated from all the data, and these are plotted against temperature in figure 1. That the points show so little variation from the smooth line through them is evidence of the very satisfactory correlation of the data, all the more remarkable in that i t includes a range of 161°C. and both solid-liquid and liquid-liquid systems; that the line is straight is indeed surprising, since the effect of clustering near the critical point is ignored in the derivation of the equation.
112
J. H. HILDEBRAND 11. OSMIUM TETROXIDE SOLUTIONS WITH CARBON TEmACHLORIDE
An interesting paper has recently been published by Anderson and Yost (I), giving properties of osmium tetroxide in carbon tetrachloride solutions. They show that the distribution ratio of the tetroxide between carbon tetrachloride and water varies with the concentration, and that the vapor pressure of carbon tetrachloride from its solutions with the tetroxide does not follow Raoult’s law but agrees rather well with the assumption of an equilibrium between Os04 and (OSO4)a. These authors mention the other possible explanation of the fact that this solution is not ideal, Le., that the molecular field strengths or internal pressures of these two substances are sufficiently different to cause departure from Raoult’s law without the presence of any definite polymer of either species. Polymerization in solution is contraindicated by the evidence that even in the pure liquid state osmium tetroxide behaves as a normal liquid. The vapor pressure has been measured by Ruff and Tschirch (12), by von Wartenberg (16), and by Ogawa (11). Plotted in the usual way, log TABLE 3 Data f o r the system osmium tetrozide-carbon tetrachloride
1
3.13 2.84 2.81
Mean.. , . . . . . . , . . . . . , , . . . . , . , , , . . . . . , . , . . , . . , , . . . , . . . . . . . . . . . . . . . /
2.93
0.395 0.599 0.693
1
5.39
0.686 0.540 0.470
! ~
1
1.133 1.344 1.530
1
0.278 0.47P 0.574
p against 1/T, the values agree rather well, those of Ogawa appearing most consistent, and give a molal heat of vaporization of about 9040 cal. at the boiling point (130°C.)’ corresponding to a Trouton quotient of 22.4. This test and the more rigid test by the aid of the “Hildebrand rule” (9) indicate a normal liquid. This conclusion is further confirmed by surface tension measurements by Ogawa. I shall next show that the extent of the departure of the solutions of the tetroxide in carbon tetrachloride from Raoult’s law is approximately what could have been predicted from the difference in their internal pressures as measured by the energy of vaporization per cubic centimeter, AE/v. Actually we use the square root of this quotient. For carbon tetrachloride a t 25°C. this is 8.54 (cal. per cubic centimeter)*. The vapor pressures of the osmium tetroxide just cited give AH = 9800, extrapolated to 25OC., and AE = 9200 at the same temperature. The liquid densities observed by Ogawa give a molal volume of 58.0 cc. extrapolated to 25°C. from the melting point (4OoC.),hence (AE/v)+ = 12.60. Let us now obtain a value by using the vapor pressure data of Anderson and Yost for the solution
SEVERAL SOLUTIONS OF NON-POLAR SUBSTANCES
113
in connection with the approximation formula, equation 1. We designate al as the activity of carbon tetrachloride, which we may set equal to its partial vapor pressure, p l , divided by its saturation pressure, 11.46 cm. a t 25OC.;N~as its mole fraction in solution; v1 as its molal volume a t 25OC., 97.1 cc.; and 3 2 as the volume fraction of the osmium tetroxide in solution. Table 3 gives the values for those solutions sufficiently concentrated in the tetroxide to show deviations from Raoult’s law. If we add the mean value of D to the value of (AE/v)~for carbon tetrachloride, 8.54, we obtain 11.5, which we may compare with the value 12.6 for osmium tetroxide obtained above from its energy of vaporization. The agreement is sufficiently good, in view of the extrapolations and approximations involved, to indicate the adequacy of this explanation for the departure of these solutions from Raoult’s law. III. SOLUTIONS OF HEXANE WITH HEXADECANE~
Guggenheim (5), a t the Symposium on Intermolecular Forces held by the Faraday Society in 1936, raised the interesting question of the validity of Raoult’s law for solutions of components of equal molecular field strength but unequal volumes. I n a subsequent publication (8) I discussed this problem with particular reference to solutions of normal paraffins, in which a parallel arrangement of molecules might be assumed, and reached the conclusion that the number of different configurations possible in such solutions corresponded to an entropy of transfer of component 2 from pure liquid to solution of - R In NZ. This is the same as for a solution of molecules of the same size, in which case, as in a solid solution with a fixed crystal lattice, the entropy is that of an ideal solution. More recently Fowler and Rushbrooke (2) have made a searching application of statistical theory to the case of two components, the molecules of one of which occupy one point each in a lattice, while the molecules of the other occupy two with all possible orientations permitted. The result was “that mere change of size is sufficient to cause deviations from linearity; . . . . though definite, the deviation is unexpectedly small for so large a change of size.” Several factors involved, however, could not be estimated with any precision, so that the authors did not claim that the deviation had been established with certainty. In my paper (8) I was able to cite only very limited experimental evidence, consisting of data on solutions of diphenyl and benzene, butane and heptane, and dicetyl in propane, butane, and heptane. In the case I wish to acknowledge my indebtedness t o Mr. John M. Sweny for assistance in this investigation. We hope to present later more numerous and more precise results, in order to detect any deviations of the type deduced by Fowler and Ruahbrooke. f
114
J. H. HILDEBRAND
of dicetyl, the uncertainty regarding the ideal solubility limited the argument to the equality of solubility in butane and heptane and the inference that this is the ideal solubility. This equality has since been extended by Sayer (13) to several other normal paraffin solvents,-hexane, octane, decane, and dodecane. It has seemed worth while to seek a direct experimental check of this interesting matter. For this a system likely to conform as closely as possible to the model of'parallel arranged molecules assumed in my previous paper was desired. This indicated the choice of one component with a melting point not far below the temperature of the experiment. Normal may be assumed to retain in the liquid a t hexadecane, melting a t 16"C., 25OC. much of the parallel arrangement of molecules which it undoubtedly possesses in the solid form. For the other component hexane was selected, which has a vapor pressure of 149 mm. a t 25OC., a convenient magnitude to measure by simple means. The vapor pressure of hexadecane at 25OC. TABLE 4 Activity of hezane in solutions with hezadecane at 86°C. MOLE FRACTION NI
1
PI
149.7 0.708
0.648 0.626
1
I
VAPORPREBBURE
99.6 92.7
1 j
1 .Ooo 0.709 0.665 0.619
M e a n . ... . .. . . ... .. . . .. . . . . . , , . . . . . . . . . . .. .. . . . . . . . . . . . . .
A~IVITT COEQFICIEM alINI
1.001 1.025 0.989
.I
1.005
is negligible. A small stock of each component in very pure form was available, hence it was necessary to use an appropriate method. The method used years ago in investigating the vapor pressure of amalgams (10) was selected. The solution was confined in a U-tube sealed a t one end; the other end was connected to a hydrogen-filled system provided with a manometer whose pressure could be varied to balance the vapor pressure in the closed limb. Escape of hexane vapor up the long limb was prevented by a condenser cooled by solid carbon dioxide. Partial results are reported here on account of their pertinence to this symposium. Further and more precise results are to be sought. Table 4 gives a brief summary of the measurements thus far obtained. Each pressure recorded represents the mean of a number of observations. The activity coefficients in the last column differ from unity only by an amount within the experimental error, indicating that this system obeys Raoult's law rather closely, in spite of the fact that the length of the molecule of the one component is 2.7 times that of the other.
SEVERAL SOLUTIONS O F NON-POLAR SUBSTANCES
115
IV. TELLURIUM TETRACHLORIDE AND IODINE3
I n the table of internal pressures of liquids a t 25°C. given in the monograph on solubility (7), iodine and tellurium tetrachloride have identical values and, if no disturbing factors were present, should give ideal solutions with each other. This can not be tested directly, as neither substance can be supercooled in the liquid state to this temperature, and the data in the table are of use only for predicting their solubilities in substances which are liquid a t ordinary temperatures. If we turn to temperatures above the melting point of iodine, where an experimental check is possible, we obtain values for their internal pressures which are still not far apart. Iodine melts a t 113.4"C., and at 140OC. its molal heat of vaporization, calculated from the vapor pressure table in the International Critical Tables, is 10,620 cal. The molal volume of liquid iodine a t this temperature is 65.2 cc., hence the energy of vaporization per cubic centimeter, AE/v, is 156.4 cal. The corresponding values for tellurium tetrachloride, calculated from the data of Simons (14), are AH = 18,400 cal.; v = 100 cc. (extrapolated); AE/V = 175.8 cal. per cubic centimeter. The deviation from Raoult's law, in terms of the approximate equation frequently used for this purpose, is determined by the parameter,
In this case D2 = 0.61, which corresponds to only a moderate departure from ideality. However, tellurium tetrachloride is a substance whose molecular field may be rather different in type as well as in strength from tetrachlorides of the elements from carbon to tin. Its melting and boiling points are 225" and 390"C., respectively, while the corresponding points for stannic chloride, for example, are -30" and 113°C. It has an electric conductivity in the liquid state a t 236°C. of 0.115 mhos, according to Vogt and Biltz (15). The application of the "Hildebrand rule" (9) to the vapor pressure curve reveals an entropy of vaporization of 30.6 units a t a concentration of vapor of 0.00507 mole per liter, a t which normal liquids show an entropy of vaporization of only 27.4. We have undertaken, accordingly, to learn whether or not tellurium chloride gives regular and approximately ideal solutions with iodine. Knowing, as we now do, the heat of fusion and specific heats of tellurium tebrachloride from the measurements of Frederick and Hildebrand (4), it is possible to use the freezing point-composition diagram for our purpose. This was determined by means of cooling curves with solutions sealed in Pyrex tubes provided with central wells for the insertion of a calibrated 8 It is our intention to study this system more thoroughly. I am indebted to Mr. D. J. Turner for the nieasurements reported here.
116
J. H. HILDEBRAND
copper-"advance" thermocouple. The iodine was of high purity and was resublimed once. The tellurium tetrachloride was redistilled. Table 5 gives the points determined. They are plotted in fizure 2 along with the ideal curves calculated from the heats of fusion. It is evident that the actual points are far from the ideal curves, indicating that the TABLE 5 The system iodine-tellurium tetrachloride T X L L W U Y TIFBACELOBIDII
I
I
mde per cent
"0.
0 0.88 (2.0) 2.82 3.81 6.62 13.98 21.78 32.83
113.4 111.9 110.0 111.8 113.0 117.0 125.5 129 .O 134 .O
SOLID PEME
I, I: Eutectic TeCI4 Tech Tech TeCI4 TeC14 Tech
FIQ.2. Freezing point-composition diagram for iodine-tellurium tetrachloride two components are actually very different. It is to be noted that the lowering of the freezing point of iodine is much greater than ideal, as it would be if the tellurium chloride were ionized, also that the flattening of the right-hand branch corresponds to an approach to immiscibility. This evidence is in line with the observation of S i o n s that tellurium tetrachloride has a negligible solubility in carbon tetrachloride at 100°C. Al-
SEVERAL SOLUTIONS OF NON-POLAR SUBSTANCES
117
though the low internal pressure of this solvent indicates only a small solvent power for this solute, if the solution is regular, this alone would not suffice to make it too small for observation. SUMMARY
1. New determinations of the solubility of iodine in carbon tetrachloride in the region 80' to 100OC. bridge the gap heretofore existing between data for the solid from 0 ' to 50°C. and for the liquid from 150' to 161"C., the critical solution temperature. The trend with temperature of the parameter in the solubility equation which expreeaes the deviation from ideal behavior is quite uniform and shows no effect ascribable to clustering near the critical solution temperature. 2. Data for the vapor pressure of carbon tetrachloride in solution with osmium tetroxide are analyzed. It is shown that the deviation from Raoult's law is approximately of the amount predictable from the internal pressure difference of the components. 3. Preliminary figures for the vapor pressure of n-hexane from solutions with n-hexadecane indicate that, as predicted by theory, these solutions obey Raoult's law within the limit of error, in spite of the ratio of 2.7 for the lengths of the two species of molecule. 4. Freezing point data for the system iodine-tellurium tetrachloride show that, in spite of approximately equal internal pressures in the liquid state, these solutions are far from ideal, owing, probably, to a more or less salt-like character of the tellurium tetrachloride, giving a molecular field different in kind from that of iodine. REFERENCES (1) ANDERSON, LEROYH., AND YOST,DONM.: J. Am. Chem. SOC. 60, 1822 (1938). (2) FOWLER, R.A., AND RUSHBROOKE, G. S.: Trans. Faraday SOC. 33, 1272 (1937). K.J., AND HILDEBRAND, J. H.: J. Am. Chem. SOC.60, 1436 (1938). (3) FREDERICK, K.J., AND HILDEBRAND, J. H.: J. Am. Chem. SOC.60, 2522 (1938). (4) FREDERICK, (5) GUQGENHEIM, E.A.: Trans. Faraday SOC.33, 151 (1937). J. H., AND JENKS, C. W.: J. Am. Chem. SOC.42, 2180 (1920). (6) (a) HILDEBRAND, (b) NEQISHI,G. R., DONALLY, L. H., AND HILDEBRAND, J. H.: J. Am. Chem. SOC.66, 4793 (1933). (c) HILDEBRAND, J. H.: J. Am. Chem. SOC.67, 866 (1935). (d) HILDEBRAND, J. H.: J. Am. Chem. SOC.69, 2083 (1937). (7) HILDEBRAND, J. H. : Solubility of Non-electrolytes. Reinhold Publishing Corporation, New York (1936). (8) HILDEBRAND, J. H.: J. Am. Chem. SOC.69, 794 (1937). (9) HILDEBRAND, J. H.:J. Am. Chem. SOO.87, 970 (1915). (10) HILDEBRAND, J. H.: Trans. Am. Electrochem. SOC.22, 319 (1912). (11) OGAWA, E.: Bull. Chem. SOC.Japan 6, 302 (1931). (12) RUFF,O.,AND TSCHIRCH, F. W.: Ber. 46, 929 (1913). W.F.: J. Am. Chem. SOC.60, 827 (1938). (13) SAYER, (14) SIMONS,J. H.: J. Am. Chem. SOC.62, 3488 (1930). (15) VOGT,A., AND BILTZ,w.: 2. anorg. allgem. Chem. 188, 277 (1924). (16) VON WARTENBERQ,H.:Ann. 440,97 (1924).
