IRREGULAR SOLUTIONS OF IODINE
605
Irregular S o h tions of Iodine
by Kozo Shinoda and Joel H. Hildebrand Department of Chemistry, University of California, Berkeley, California
(Received October 3, 1964)
The solubility of iodine at 25” has been determined in a series of solvents selected as tests of certain types of irregular behavior. Mole per cents of iodine at 25’ are as follows: cyclopentane, 0.773; cis-decalin, 1.540; trans-decalin, 1.451; methylcyclohexane, 0.920; truns-l,2-dimethylcyclohexaneJ 0.937 ; toluene, 6.256 ; 17%-xylene,8.201 ; methylene chloride, 1.524; n-hexadecane, 1.450. In the last two cases, measurements were made over a range of temperatures giving for R(b In xz/b In T ) 20.4 in CHzC12 and 20.65 in n-C16H34. Points for cyclopentane and the two decalins fall on a line for regular solutions in a plot of log xz us. (& - 61)2, the solubility parameters. Solvents containing methyl groups diverge in the direction indicating that the well-known failure of niany saturated hydrocarbons to agree with solubility parameter theory is attributable mainly to methyl groups, with solvent-solute attraction less than that of a geometric mean. These divergences do not involve irregular entropy. A solubility parameter for CHzC12calculated from its energy of vaporization, (AE”/v)”’, is larger than the value calculated from its solvent power because of its dipole moment.
I iraoka and I ik,,rand’ recently published a plot of the solubility of iodine as the logarithm of its mole fraction us. the square of the difference between the solubility parameters of iodine and solvent. This constitutes a test of the equation2
where a28 is the activity of solid iodine with respect to its supercooled liquid (0.256 at 2 5 O ) , vz the molal volume of its supercooled liquid (58.5 cc.), x2 the iiiole fraction of iodine at saturation, 41 the voluine fraction of the solvent, aZ the solubility parameter of iodine (14.1), and 61 that of the solvent. The plot in ref: 1 showed points for violet solutions in 15 solvents that fall closely on the line of the equation, with xz values spread over a 300-fold range. Figure 1 in the present paper includes these points. The original plot showed two groups of solutions whose points diverge from the line, one consisting of solutions in benzene, p-xylene, and mesitylene, the other, of solutions in n-heptane, Z,Z-dimethylbutane, and 2,2,4-trimethylpentaneJ “isooctane.” This research was undertaken, first, to add toluene and inxylene to the first group, the electron donor-acceptor nature of which is now well known, but especially to
seek an explanation of the divergence of the second group although it is violet in color. It has not been at all clear whether this irregularity should be attributed to failure of the term in eq. 1 for entropy, - R ln 5 2 , or to failure of the one for enthalpy, V ~ + I ~ ( &- 61)~.
Experimental M’ateyials. Toluene, m-xylene, cyclopentane, and methylcyclohexane were Matheson Coleman and Bell Spectroquality reagents. Methylene dichloride was Eastman Organic Chemicals Spectrograde materials; trans-lJ2-dimethylcyclohexanewas ;\latheson Coleinan and Bell Pure grade. These were fractionally distilled shortly before use. n-Hexadecane from HuinphreyWilkinson was obtained through the kindness of Dr. Sawyer of Shell Development Co. It was passed through silica gel and distilled. Vapor phase chromatography showed about 2% of tetradecaiie and 4% of pentadecane but no other impurities. cis- and trunsdecahydronaphthalene were I< and I< Laboratories, TIE., Pure grade materials. The apparatus and procedure were those in earlier s t u d i e ~ . ~ (1) H. Hiraoka and J. H. Hildebrand, J P h y s Chem 67, 916 (1963). (2) J. H. Hildebrand and R. L Scott, “liegular Solutions.” PrenticeHall, New Tork. N. T I1962, p 102 ~
Volume 69, 2Vumber 2
Februarg 1966
606
KBzd SHINODA A N D JOEL H. HILDEBRAND
The solubility parameters of all but three liquids are from ref. 2, p. 171. The missing ones were calculated from boiling points by the empirical equation given in ref. 2, p. 168: AHV2g8= -2950 23.7Tb 0.020, Tb2. The figures are given in Table 111.
+
+
Table lIIQ Tb
AH'w
&-Decalin 194.5 12,510 trans-Decalin 185.8 12,150 trans-1,2-Dimethylcyclohexane 123.2 9,585 a
\ -40L-L
Zb
I
I 40 (14.1
- 6,/ ?
I
I
J
I
80
60
Figure 1. Irregular solubility of iodine in solvents whose molecules contain a-electrons, methyl groups, and dipoles. The solvents corresponding to the unlabeled open circle points may be identified, if desired, from Figure 1 in ref. 1.
Results Table I gives the results for the solvents n-CleH, and CH2C12. These were determined over a range of temperature sufficient to give values for the temperature coefficient. Table I :
Solubility of Iodine in Mole yo,100x2 R-
n-CIe.Ha4 1, "C. 18 100.~~~1 CH1CI2 t , "C. 15 100.~c2 1
91 20 47 25 06 30 05 167 1 233 1 450 1 722 01 19 90 25 00 088 1 283 1 524
d In zz dln T
20 65 20 4
Table I1 : Solubility of Iodine a t 25",100r2, and Solubility Parameter of Solvent, 61 Solvent
lOOZ1
Cyclopeni ane czs-llecalin trans-Decalin Methylryclohexane trans- 1,2-Ihmethylcyclohexane Tolriene nz-X)ivlene Jtethylene chloride n-Hexadecmie
0 773 1 540 1 451 0 920 0 937 6.256 8,201 1.524 1 450
Thr Joiirnal of Physical Chemistry
61
81 88 86 7 8 79 8.9 8.8 9.8 8.0
v
6
153.2 8 . 8 155.0 8.6 145.3 7.9
Units: cal. and cc.
Seyer and Mann4 have published data for the vapor pressures of the decalins from room temperatures to boiling points, but the plot of log P us. 1 / T gives lines curving in ways that are incredible; therefore, we calculated from the boiling points.
Discussion We invite attention, first, to the addition of toluene and m-xylene to the aromatic solvents heretofore used; see Figure 1. The solubility of iodine in benzene is larger than the regular solution value corresponding to its solubility parameter, 9.15, which is close to that of chloroform. Solubility increases in order in the series, benzene, toluene, the xylenes, and mesitylene, given in the order of increasing basic donor strength in decreasing ionization potential. The more important results of this study concern the solubility of iodine in the group of saturated hydrocarbons-straight, branched chain, and cyclic. We were struck long ago by the fact that cyclohexane behaves normally, whereas n-heptane and isooctane do not. The magnitudes of solubility parameters that would conform to empirical solvent parameters for iodine exceed the values derived from their energies of vaporization, ( A E I " / V I ) " ~ , by 0.6 for n-heptane and 1.0 for isooctane. We see in Figure 1 that three additional cyclic compounds, cyclopentane and cis- and trans-decahydronaphthalene, conform as does cyclohexane. On the other hand, n-hexadecane is off the regular line by about the same amount as n-heptane. Further, the departure from the line of the two branched paraffins is nearly double that of the two normal paraffins. These correlations suggest that it is the methyl groups that are responsible for the irregular behavior. We see (3) D. N. Glew and J. H. Hildebrand, J . Phys. Chem., 60,616 (1956). (4) W. F. Seyer and C. W. Mann, J . A m . Chem. Soc., 6 7 , 328 (1945).
IRREGULAR SOLCTIOW OF IODIXE
607
that the introduction of one or two methyl groups into cyclohexane makes them, likewise, poorer solvents for iodine (see Figure 1). I t remains to be determined whether the departures from the regular solution line in Figure 1 are to be attributed to entropy or to enthalpy. In order to reveal the entropy, me have added points for the new data to a plot of R ( b In x2/d hi T ) 8 Sus. t - R ln z2, a plot devised for this purpose by Hildebrand and G l e ~ .This ~ plot does not involve solubility parameters. The entropy of solution at saturation is 1s2
-
S2'
=
R(d I n xz/b In T ) 8 , t ( bIn az/d In
~
2
(2)~
)
The factor, ( b In a 2 / bIn z-JT,which is "Henry's law" factor, is so nearly unity that it can be ignored without affecting the argument. Walltley and Hildebrand,6 by measuring the partial vapor pressure of iodine over its solutions, found it to be 0.86 in CS2 and 0.98 in CCI,. I t is necessarily still closer to unity in all solvents in which iodine is less soluble than in CCI,. The fact that certain points which depart strongly from the normal line in Figure 1 fall on the line in Figure 2 has already been noted in the cases of solutions in n-heptane, isooctane, 2,2-dimethylbutane, and octaiiiethylcyclotetrasiloxane. This indicates that any factor of a purely physical nature, such as expansion, which causes the entropy to depart from the ideal -- R In x2,is offset by a corresponding change in enthalpy, a relation pointed out long ago by Scatchard.' This is not the case where departures are the result of chemical coniplexing, as seen by the points in Figure 2 for the aromatics. I t is significant that an eiiipirical increase in the solubility parameter of isooctane from 6.85, the value of (AE1"/~1)1'2, to 7.85 would correct its solvent power for iodine and also its partial molal volume* at high dilution in CC1, and CS2. We iiiust conclude, therefore, that solubility parameters do not give a correct measure of attractive forces between iodine and methyl groups. The term (62
--
61)2
=
AEIV v1
~
AEZV +- 2(v2
v1
is twice the difference bet'ween an arithmetic and a geometric mean. The geometric mean is clearly t'oo large to represent accurately the attraction between molecules of iodine and those of a molecule containing groups methy]. groups' do cause serious departures, as shown by the conformity of solutions in cyclopentane, cyclohexane, and the two The divergence begirls with the introduction of inethyl groups into cyclohexane.
14
1
The point in Figure 2 for n-Cl6H34 falls below the line by 0.8 cal. deg.-', an amount that is almost trivial and which may be explained by relative departures froin unity of the Henry's law factor, ( b In az/d ln Q ) ~ , in eq. 2. An expression for it may be obtained by differentiating eq. l9 to give
(3)
If this is applied to this solution and its near neighbors, we get the following values for this factor: TiCl,, 0.940; ~C16H34, 0.983; CCl,, 0.936; cYClO-CgH12, 0.967. With these corrections, the points for each solution fall on the same line, shown dotted in the figure. The solution in CH2C12is interesting in that it is the first one found to give a point below the line in Figure 1. This prompted us to plot points for l,l-C2H4C12 and 1,2-C2H4C12,using the measurenients by Benesi and Hildebrand1O made in 1948. They had not previously been included in this kind of plot because they cqoniplex weakly with iodine, as seen in the plot by Hildebrand and Glew and in the shift they cause i n the wave length of the visible peak of iodine reported by Ralltley, Glew, and Hildebrand. Coinplexiiig alone would ( 5 ) J. H. Hildebrand and D. N. Glew, J . P h y s . Chem., 6 0 , 618 (1956); see ref. 2, p. 120, Figure 3. (6) J. Walkley and J. H. Hildebrand, i b i d . , 63, 1174 (1959).
(7) G . Scatchard, Trans. Faraday SOC.,33, 160 (1937). (8) See r e f , 2, pp. l l o , 123, (9) See ref. 5 and also K . Shinoda and J , H. Hildebrand, J . Phys. Chem., 61, 789 (1957). (10) H. A. Benesi and J. H. Hildebrand, J . Am. Chcm. Soc., 7 0 , 3978
(1948). (11) J. Walkley, D. N.Glew, and J , H . Hildehrand, J . Chem. P h y s . , 3 3 , 621 (1960):
v o l u m e 69, S u m h e r 2
Febrirary 1.966
D. N. BHATTACHARYYA, C. L. LEE, J. SMID,AND M. SZWARC
608
be expected to raise the points for these solutions above the line in Figure 1. The fact that instead they fall below, as does CH2C1,, would seem to be related to the considerable polarity of these three liquids, raising their energies of vaporization without correspondingly enhancing their solvent power for iodine. I n other words, (AE~”/v1)’”is too large for an effective solubility parameter. A comparison of the dielectric constants, e , and the dipole moments, g, of these anomalous solvents with those of conforming solvents, CHCI3and Cla,is seen in Table IV.
Table 1V:
lo’*@
Ilielectric Constants and Dipole Moments
CCli
CHClJ
CHGh
2 24 0
4 81 1 02
9 08 1 54
1 2-C~HiC12
10 4 1 20
l,l-C?H,Cl? 10 0 2 06
Acknowledgment. This work was supported by the Atomic Energy Commission, for which we express our appreciation.
Studies of Ions and Ion Pairs in Tetrahydrofuran Solution. Alkali Metal Salts of Tetraphenylboride
by D. N. Bhattacharyya, C. L. Lee, J. Smid, and M. Szwarc Department of Chemistry. State University College of Forestry, Syracuse Cnibersity, Syracuse. S e w I’orh (Received September 99,1964)
15210
The conductance of tetraphenylborides of Li+, Na+, K+, Csf, Bu&+, and (isoan~yl)~BuN + in T H F was investigated at 25” in the concentration range lop6 to 2 X lop4 M . Fuoss plots gave straight lines from which the limiting conductances and the ionic dissociation constants were calculated. The liiiiiting conductances of the cations in T H F were obtained by assuniing Ao+((isoamyl)3BuX) = Ao-(BPhA). The lowest value of &+ was obtained for Li+, showing the high degree of solvation of this intrinsically small ion, and the largest A. was found for Cs+, which apparently is not solvated. These findings corroborate with the data for Kdls. The Li+ and S a + salts are the most dissociated, whereas Kdlsof the Cs+ salt is about one-fiftieth as large as that of Na+. In spite of their bulkiness, the tetraalkylaiiinioniuni salts are less dissociated than the Na+ or Li+ salts, indicating lack of solvation of these ammonium ions.
Kinetic studies of anionic polymerization of styrene in tetrahydrofuran revealed that the free polystyryl ions W S - , as well as the respective ion pairs, “S-, IT+, participate in the propagation.’I2 Further investigations of these problems required determination of the limiting conductance, Ao+, of alkali cations in
T h e Journal of Physical Chemistry
Preparation and Purification of A l k a l i Tetraphenylborides. The sodium salt, NaBPh4, was acquired from Fisher (99.7%) and it was recrystallized three times from aqueous acetone (3 parts of acetone by voluine to 1 part of water). The absence of other alkalis in the
