Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978 365
COMMUNICATIONS Absence of Outer Nonbonding Electrons in Methyl Groups Affects Solubility Parameters The strongly bonding electron pairs in methyl groups are accompanied by weak London force pair potentials. The solubility parameters of liquids with methyl groups should be altered accordingly. In addition, a new argument is presented regarding the strength of intermolecular interactions, which is based on the nature of localized molecular bonding orbitals and which explains the observed molecular behavior.
In a paper by Hildebrand and Dymond (1965) and reproduced in the book, “Regular Related Solutions”, by Hildebrand, Prausnitz, and Scott (1970), and here reproduced as Figure 1, the solubilities of iodine in different groups of liquids are plotted in terms of the members of the Regular Solution equation RT In ( a z S / x z = ) V,jJ12(6, - 61)2 (1) aZsis the activity coefficient of the solid solute referred to its undercooled liquid, 0.258 for iodine a t T = 298; x 2 is its mole fraction at T = 298; Vz is its extrapolated liquid volume, 58.5 cm3 mol-’; jJ1 is the molal volume fraction of the solvent, practically unity in these solutions; 62 and 6, are the solubility parameters of solute and solvent, usually calculated from the square root of the energy of vaporization divided by molal volume, (AEv/V)l/z. The points on line A are for solvents in which the solubility of iodine at 25 “C agrees closely with eq 1,with values of a1 = (aE1v/V1)1/2. They are, starting at the bottom, carbon disulfide, chloroform, titanium tetrachloride, cis-decalin, trans-decalin, carbon tetrachloride, cyclohexane, cyclopentane, silicon tetrachloride, CCl&F,, CCl2F.CC1F2,C4C13F7,c-C4C12F6.All of these solutions have the same violet color as the vapor of iodine. The solvents for the three points G are highly polar and the solutions are brown. The solvents F are aromatics which form brown complexes with iodine. The solvents B, C, D, E contain one to five methyl groups. The species in these groups are identified in Table I. The star at the extreme right denotes iodine in octamethyltetrasiloxane, C - ( S ~ O ) ~ ( C H ~These ) , . points are all displaced from line A, although the solutions are violet in color, and the partial molal entropy of iodine in each is “regular”, Shinoda and Hildebrand (1957). In the references cited in the introductory paragraph (Hildebrand and Dymond, 1965; Hildebrand et al., 1970) we suggested, without any theory, that the anomaly is connected with failure of the geometrical mean in (6, - 6’), = €jZ2 + 612 - 26&, where a16, = [(AEl/V1)(aE2/V2)]1/2. That was not a useful surmise, because it could not be independently evaluated. I show in this communication that the molal energy of vaporization of a liquid divided by its molal volume yields a parameter suitable only for mixtures of liquids which both contain methyl groups, but not for other mixtures. London (1930) explained the nature of “van der Waals” forces, which are purely physical forces between neutral molecules, as resulting from a quantum perturbation of the electrons in outer orbitals of neighboring molecules. But the molecules of hydrogen, methane, and methyl 0019-7874/78/1017-0365$01.00/0
Table Ia
AE,~/ VI
line
solvent
loox,
6,
B B B B C C D D E
cyclohexane methylcyclohexane ethylcyclohexane dimethylcyclohexane n-heptane n-pentane 2,3-dimethylbutane 2,2-dimethylbutane 2,2,34rimethylbutane (triptane) 2,2,4-trimethylpentane (isooctane) octamethylcyclotetrasiloxane
0.918 0.920 1.036 0.931 0.619 0.595 0.561 0.469 0.621
8.2 8.3 8.4 8.3 1.9 1.9 1.7 8.0
8.2 8.1 8.0 7.8 1.4 1.1 7.0 6.1 1.0
0.592
7.9
6.8
0.813
8.2
6.4
E
*
1.7
lOOx, is the solubility of iodine in mole percent a t 25 “ C . Two values for the solubility parameters for liquids whose molecules contain methyl group are (1)6 1, calculated from solvent power for iodine and ( 2 ) calculated from cohesion, as measured by (AE,V/V,)”2,where is molal energy of vaporization.
groups contain no outer, valence electrons, only those in tightly held electron pair bonds between carbon atoms and protons. The ionization potential of methane is extraordinarily high, 13.0 eV; hence its electrons cannot contribute strongly to London forces. Figure 2 shows second virial coefficients of gases plotted against temperature taken from the book by Dymond and Smith (1969). One sees that attractions between molecules of methane are much weaker than those between molecules of CF4 and that molecules of neopentane, with four methyl groups, are weaker than those of n-pentane, with two methyl groups. Table I gives values of (aElv/V1)1/2for the methylcontaining liquids of Figure 1,whose points are off line A. In order to place the points for these liquids on line A, their solubility parameters must have the values in the column headed 6’. Fortunately, these values, derived from their solvent power for iodine, agree with those for other substances. The strongly divergent point for c-(SiO)4(CH,), was placed by its value of ( U l v / V l ) 1 / 2= 6.4, which would suggest that its mixture with c-C6F11CFS,parameter 6.1, would be nearly ideal, whereas for the two liquid layers we calculated 6’ - 8.2 (Shinoda and Iiiiciebrand, 1957), the same value as that yielded by the solubility of iodine. In the book by Hildebrand et al. (19701, p 179, there is a plot, Figure 10.8, which shows that values of (UIv/ Vl)’/2 for i-C8H18and n-C7H16must be increased by the same amount for SnI, as for I,. 0 1978 American Chemical Society
366 Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978 '
I
'01
'
'
'
'
0 0 0
O L L C - - - ~ L - . . . L - - I 0 0 2 0 4 0 6 0 8 I O 1 2 I 4 16
I 8 20
S I -(E:/Vl)1'2
Figure 3. Ftelation of 61- AE branched chain alkanes, in accord with experimental observations. The argument presented here does not only apply to C-H bonds, but to all situations in which H is bonded to atoms with higher electron density in similar bonding conditions (Si, say). As to C-F and other bonds involving "nonbonding" valence shell electrons, the situation is more complicated in general, and in particular with respect to intermolecular forces between molecules containing such bonds and nonbonding electrons. Literature Cited Dymond, J. H., Smith, E. B., "The Virial Coefficients of Gases",Oxford Universlty Press, London, 1969. Hlldebrand,J. H.. Dyrnond, J. H., Roc. NaN. Acad. Sci. USA, 54, 1001 (1965). Hildebrand, J. H., hausnitz,J. M., Scott, R. L., "Regular and Related Solutions," Van Nostrand-Reinhoid, New York, N.Y., 1970. Jolley, J. E., Hildebrand, J. H., J . Pbys. Chem., 81, 791 (1957). London, F., 2. Phys. Cbem., B11, 222 (1930). Shinoda, K., Hildebrand, J. H., J . Phys. Cbern., 81, 791 (1957).
Department o f Chemistry University o f California Berkeley, California 94720
Joel H. Hildebrand
Received for review March 13, 1978 Accepted July 7 , 1978
