NOTES
2532
of temperature. Further, it is consistent with Sherwood’s analysis of second-virial coefficient datag which shows that when experimental data are reduced with the square-well potential, the reduced well width for methane is 1.60, whereas that for tetrafluoromethane is 1.48. Acknowledgmenl. The authors are grateful to the National Science Foundation for financial support and to J. H. Hildebrand and R. L. Scott for helpful discussions. (9) A. E. Sherwood and J . M . Prausnitz, J . Chem. Phys., 41, 429 (1964).
ruptions in regularity for AHt” of ions between the various nonaqueous solvents. Unfortunately the scarcity of data precluded a definite conclusion. Similar trend reversals for apparent molal heat contents of ions in aqueous solution have been observed by Lindenbaum.’ For both cations and anions the interruption occurs between the largest simple ion and the smallest complex ion. The results are explained in, terms of water structure promotion by the large complex ions. Viscosities of electrolytic solutions have long been used as an indication of the amount of structure within a solution.2r10-12 The relative viscosity of an electrolytic solution is given by the well-known Jones-Dole equation13 in which 77 and 70 are the viscosities of the
Some Observations on the Viscosity Coefficients
of Ions in Various Solvents
by Cecil M. Criss* and Martin J. Rlastroianni Department of Chemistry, Unirersity of M i a m i , Coral Gables, Florida $3184 (Received A’ouember IS, 1970) Publication costs assisted by the National Science Foundation
Much has been written concerning the effect of the simple alkali metal, halide, and tetraalkylammonium ions on the thermal and transport properties of aqueous solutions.’-* The effects are generally ascribed to the ability of the various ions to increase or decrease the structure of water over that of the pure solvent. The general argument is that small simple ions such as lithium are structure makers while large simple ions such as cesium are structure breakers. On the other hand the tetraalliylammonium salts follow the reverse pattern from the simple ions, and this is usually explained in terms of the special hydrophobic interactions of the hydrocarbon groups with mater to increase its “ice-like” s t r u ~ t u r e . ~Presumably these effects will be observed only in solvents having a high degree of initial structure and capable of being structured still further through hydrophobic interactions. Because of this water has been considered anomalous in this respect. The effect should not be observed for solvents exhibiting only a small amount of structure. Wu and Friedman5 and Friedman6 have examined the heats of transfer of several ions between water and propylene carbonate as a function of ionic radius and observed that AH*” decreases as r increases for the simple ions, but the trend reverses for the tetraalkylammonium ions. Since it is expected that propylene carbonate is nonstructured and is therefore an ideal solvent, this reversal in trend is ascribed entirely t o the specific interactions with water. On the other hand, Bhatnagar and Crissg examined AHt” for several alkali metal and tetraalkylammonium iodides in various solvents and in some cases observed interThe Journal of Physical Chemistry, V o l . 76, No. 16, 1971
solution and pure solvent respectively, A , and B, are empirical constants, and c is the concentration. A , can be calculated the ore tic all^^^^^^^ and is associated with ion-ion interactions, while B,, the ion-solvent parameter, cannot presently be calcuIated satisfactorily on an a priori basis. However, this parameter can be evaluated experimentally, and when it is divided into its ionic components to obtain B, (ion) it provides a very useful tool for indicating the degree of structure in solution. A survey of the literature has produced B, coeficients for a number of electrolytes containing both simple and complex ions, in the solvents water, methanol, and acetonitrile.8~10,’6-’sThe validity of eq 1 for the nonaqueous solutions indicates that, for the (1) H . S. Frank and W. Wen, Discuss. Faraday
SOC., 24, 133 (1957).
(2) M . Kaminsky, ibid., 24, 171 (1957). (3) Th. Ackerman, ibid., 24, 180 (1957).
(4) H. Rbterians, F. Schreiner, U. Sage, and Th. Ackerman, J . Phus. Chem., 73, 986 (1969). (5) Y. C. Wu and H. L. Friedman, ibid., 70, 501 (1966). (6) H. L. Friedman, ibid., 71, 1723 (1967). (7) S. Lindenbaum, ibid., 74, 3027 (1970). (8) R . L. Kay, T . Vituccio, C. Zawoyski, and D. F.Evans, ibid., 70, 2336 (1966). (9) 0. N. Bhatnagar and C. M. Criss, ibid., 73, 174 (1969). (10) R. W. Gurney, “Ionic Processes in Solution,” McGraw-Hill, Kew York, N. Y., 1953. (11) R. H . Stokes and R . Mills, “Viscosity of Electrolytes and Related Properties,” in “The International Encyclopedia of Physical Chemistry and Chemical Physics,” E. A . Guggenheim, J. E . Mayer, and F. C. Tompkins, Ed., Pergamon Press, New York, N. Y . , 1965. (12) E. R. Nightingale, Jr., “Chemical Physics of Ionic Solutions,” B. E. Conivay and R. G. Barradas, Ed., Wlley, New York, N. Y., 1966, Chapter 7. (13) G. Jones and M . Dole, J . A m e r . Chem. Soc., 51, 2950 (1929). (14) H Falkenhagen and M. Dole, Z.Phys. Chem., Abt. R , 6, 159
(1929).
(15) H. Falkenhagen and E. L. Vernon, Phys. Z.,30, 140 (1932). (16) G. Jones and H. J. Fornwalt, J . A m e r . Chem. Soe., 57, 2041 (1935) (17) D. F. Tuan and R. M. Fuoss, J. Phys. Chem., 67, 1343 (1963). (18) R. P. T. Tomkins, E. Andalaft, and G. J. Janz, Trans. Faraday SOC.,65, 1906 (1969).
2533
NOTES Table I: B, (ion) Coefficients in Various Solvents a t 25” ----B,
(ion)
Radius, Ion
Li
+
Na +
2J - 0. 4s g. a - 0.2 Y
- 0.0
Kf Rb +
cs
+
NH4+ Me4N+ Et4N + Pr4N + BuaN c1Br+
- -0.2
I-
Pic BPha-
4
1
-0.2
1
2
3
4
5
6
r (‘A)
Figure 1. Variation of B, (ion) coefficients with radius of ion: cations, solid curves; anions, dashed curves; theoretical value, broken curve; open circles, aqueous solutions; solid circles, methanolic solutions; squares, acetonitrile solutions.
concentrations over which B, was evaluated, no dissociation was occurring and therefore ion-pair formation is probably not significant. Furthermore, for acetonitrile B, (ion) has been shown to be approximately additive.l’ The B, (ion) data along with the radii of the various ions are summarized in Table I. For the solvents, water and methanol, the division of B, into its ionic components is on the basis that B, (I
