ION CONDUCTANCES I N WATER-METHANOL
MIXTURES’
L. G . LONGSWORTH AND D. A. MAcINNES dockejellsr Institute for Medical Research, New York, New York Received October 17. 1858 INTRODUCTION
It is a part of the program of this laboratory to study thermodynamic and other properties of electrolytes in non-aqueous solvents by the methods (12) that we have already used for aqueous solutions. These methods included E.M.F. measurements of cells with transference, conductances, and measurements of transference numbers by means of moving boundaries. It has been found, however, that the extension of the last-mentioned method to non-aqueous solvents introduces a number of difficulties. For example, most non-aqueous solutions have lower conductances than the corresponding aqueous solutions, with the result that boundary disturbances due to thermal convection are more serious in these solvents than in water. It seemed desirable, therefore, to test the moving-boundary method in water-methanol mixtures where the transition from aqueous to non-aqueous solvents could be made gradually. Using “autogenic” boundaries, a cadmium anode and narrow tubes, we were able to obtain satisfactory cation boundaries with sodium and lithium chlorides in solvents having a methanol mole fraction of 0.8 or less. The boundaries in pure methanol, however, were distorted and did not give reproducible values. This difficulty has not yet been overcome. The data obtained in the aqueous methanol solutions are reported below. The viscosities of water-methanol mixtures were also determined, since the existing viscosity data are insufficient for correlation with the observed ion conductances. EXPERIMENTAL
The methanol used in this research was a synthetic product which was refluxed and distilled from anhydrous copper sulfate. The specific conductance and density of the distillate were 1.1 X IO-’ mhos and 0.78657 g. per cubic centimeter at 25”C., respectively. Accepting 0.78653 (10) as 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. 239
240
L. G. LONGSWORTH AND D. A . MACINNES
the density of pure methbnol, our sample contained 0.024 mole per cent of water, which was taken into account in coniputing the mole fractions of the various mixtures prepared from this material. The densities of the solvents and solutions were measured to about 0.002 per cent in the pycnometer described in connection with our transference measurements in mixtures of light and heavy water (11). The values for the water-methanol mixtures agreed satisfactorily with those of Gibson (9) throughout the entire range of composition. The apparatus and methods used in the transference number determinations were similar to those used for aqueous solutions of lanthanum chloride and have been fully described (13, 14). TABLE
1
Transference and conductance measurements of solutions o,f sodium and lithium chlorides i n water-methanol mixtures at d6'C.
O.oo00 0.1015 0.2022 0.4020 0.6027 0.8007
0.06ooo 0.05006 0.04998 0.05062 0.05002 0 .ON08
1
0.3876 0.4049 62.20
0.4475
53.12 55.78
Lithium chloride
O.oo00
0.05000
0.1006 0.2008 0.4027 0.8020 0,8024
0.05130 0.05146 0.05177 0.05019 0.05054
0.3211 0.3242 0.3292 0.3412 0.3601 0.3804
100.14 67.85 54 03 46 24 46.52 49.75
241
ION CONDUCTANCES IN WATER-METHANOL
displacement of the boundary and the quantity of electricity passed. The boundaries were not distorted. The transference numbers were found to be independent of the current density used and of the diameter of the tube in which the boundaries were observed. The equivalent conductances, A, of all solutions used in transference experiments were measured on the bridge described by Shedlovsky (16) and are recorded in the last column of table 1. The corrections which would be necessary in order to redyce these values to a concentration of exactly 0.05 normal are small enough not to affect any of the conclusions of this paper. The conductivity cell, with truncated cone electrodes, had a constant of 7.6353 on the basis of 0.012856 for 0.1 demal potassium chloride a t 25OC. The viscosity measurements were made with the aid of a quartz viscometer of the type described by Washburn and Williams (20). The instrument was filled with the aid of a filtering weight buret especially designed for the purpose. A working volume of approximately 50 ml. was used, the exact value being determined from the weight of liquid drawn from the buret. Correction of the time of efflux for water to the actual volume was made with the aid of the experimentally determined relation efflux time for HzO = 363.07
+ 0.468 (working volume
- 50)
The viscometer constants, which are necessary in making the kinetic energy correction, are as follows: length of capillary, 17.4 cm.; diameter of capillary, 0.0540 cm.; average head, 20.1 cm.; efflux volume, 9.50 ml. A special design of the viscometer support provided a rapid and convenient method for. obtaining a reproducible position of the instrument in the thermostat. The viscometer was permanently mounted in a brass frame provided with three hardened steel pins as shown a t a, b, and c in figure 1. These pins were the points of contact between the frame and the rigid supporting arm, A. Pin a rests in a conical hole in the hardened steel block a', b in a v-shaped groove in b', and c presses against a polished steel disc c'. With this arrangement the viscometer automatically comes to rest in the thermostat in a definite position. The time of efflux was measured with a counter reading directly to 0.01 sec. and driven through a clutch by a synchronous motor. Efflux times for successive fillings exhibited an average deviation from the mean of 0.02 per cent. The results of the viscosity measurements are recorded in table 2. In this table the mole fractions of the mixtures are given in the first column and their densities in column 2. Owing to the magnitude and uncertainty of the kinetic energy correction we have reported in the third column of the table the values of the ratio, td/t&, in which d denotes density and t the
242
L. 0. LONGSWORTH AND D. A. MACINNES
time of efflux, the subscripts referring to water. In applying the correction to this ratio a value of 1.12 for rn in the general viscosity equation (3) was used. The relative viscosities, corrected for kinetic energy but not for surface tension, are recorded in the last column of table 2. A short extrapolation gives a value of 9/90 = 0.6050 for pure methanol. This may be compared with the value 0.6056, also uncorrected for surface ten-
Viscosit NCH,OH
0.0509
0.1014 0.2015 0.4020 0.6027 0.7954 0.8945 0.9992
p . 0
4'
0.98196 0.96946 0.94708 0.90243 0.85997 0.82242 0.80461
0.78666
~
td Cod0
-
1.2520 1 ,4779 1 .7437 1.6567 1.2913 0.9310 0.7830 0.6091
1.2556 1.4842 1 .7529 1.6654 1.2966 0.9325 0.7623 0.6060
1)
70
sion, obtained by Jones and Fornwalt (10) in a viscometer similar to ours. The discrepancy between the two values probably arises from differences in the computation of the kinetic energy correction. DISCUSSION OF RESULTS
From the data of table 1 the conductances of the ion constituents, A = TA, have been computed and the results are given in table 3. In
243
ION CONDUCTANCES I N WATER-METHANOL
correlating ion conductances with the viscosity of the solvent it is desirable to use the limiting conductances, XO, thereby eliminating the effects of ion-ion interaction. Since the three ions listed in table 3 were found to behave similarly in mater-methanol mixtures, we have selected the lithium ion as example in the following discussion. Approximate values of XO for this ion in each of the mixtures have been computed and are given in the last column of the table. These computations were made with the aid of the assumption that 1/X varies linearly with and has the theoretical slope (17). Sufficient data are available to test the validity of this extrapolation in water and in methanol. The tests indicate that values of XO computed in this manner are not in error by more than about 1 per cent, the error being greatest in the water-rich mixtures. In figure 2 curve A shows the variation of ha for the lithium ion with the mole fraction of methanol. Curve B indicates the corresponding variation of the viscosity of the solvent. It will be observed that whereas curve TABLE 3 Ion conductances i n water-methanol miztures at W C .
0.0 0.1 0.2 0.4 0.6 0.8
43.04 31.21 26.01 23.02 23.43 24.96
I1 1
I
32.15 22.m 17.79 15.78 16 75 18.92
~
1
68.01 45.87 36.19 30.45 29.69 30.82
67.99 45.85 36.24 30.46 29.77 30.82
1 I
39.3 27.2 22.4 20.9 23.7 28.9
244
L. G. LONGSWORTH AND D. A. MACINNES
It is not surprising, therefore, that the Walden rule is not applicable to these ion-solvent complexes, since the customary methods of testing the rule, Le., variation of the viscosity by changes of temperature, pressure, solvent, etc., are almost certainly accompanied by changes in this complex. Additional evidence for an increase in the size of the lithium ion-solvent complex with increasing mole fraction of methanol may be obtained from a consideration of the apparent molal volume of lithium chloride in solution. Thus the salt has an apparent volume of 17.0 ml. in water (8) and -3.8 ml. in methanol (19),whereas the molal volume in the crystal is 20.5 ml. The contraction occurring on solution in water has been explained (2) as due to orientation of water dipoles about the ions, the solvent molecules
Mole fmction of methanol
FIG.2. Ion conductance-viscosity relations in water-methanol mixtures. Curve A, limiting conductances, XO, of the lithium ion. Curve B, relative viscosities, 9 -, of
9 product. Curve D, a plot the solvent mixtures. Curve C, a plot of the io.-
70
?O
of the ho(;JP'*'
product.
of the ion-water complex being more closely packed, presumably, than in normal water. The still greater contraction observed in methanol suggests that the ion-methanol complex is larger than the ion-water complex. I n the A! - N~H,OH curves for each of the three ions studied, a slight 70
maximum occurs in the water-rich mixtures, being more pronounced for the sodium ion than for the lithium and chloride ions. In terms of the hypothesis discussed in the preceding paragraphs this would indicate a slight decrease in the size of the ion-solvent complex compared with its value in water. It is in this region of solvent composition that the com-
ION CONDUCTANCES I N WATER-METHAXOL
24 5
ponents exhibit the largest deviations from Raoult’s law, indicating considerable interaction. I t does not seem improbable that this dipole-dipole interaction occurs at the expense of the ion-dipole interaction, thereby reducing alightly the size of the ion-water complex. Empirically, the maximum in curve C of figure 2 disappears if the viscosity is raised to a fractional power. Thus X O
(:>”
86
is very nearly linear \!ith the mole frac-
tion as shown by curve I). This is also true for the data on the chloride and sodium ions. Though frequently used, no theoretical justification of these fractional exponents has been advanced.
Additivity of ion conductances i n water-methanol mixtures As indicated in columns 4 and 5 of table 3, the agreement between the chloride-ion conductances of the two alkali chlorides furnishes striking evidence of the equal ionization of these two salts in a given water-methanol mixture. These salts are completely dissociated in water, and it seems reasonable to assume that they are also complefely dissociated in the water-methanol mixtures. This assumption is obviously the simplest explanation of the observed additivity of ion conductances. It is also in agreement with modern theories of ionic solutions. For example, Fuoss and Kraus (7), in their extension of the Bjerrum concept (4) of ion association, point out that in a solvent of a given dielectric constant ions above a certain critical size cannot form pairs. This size, a, “the Bjerrum distance,” is given by the relation a=-
e’
2DkT
in which the symbols have their usual significance. For water a t 25OC. a = 3.5 A., while for a water-methanol mixture of N C H ~ O=H0.8 and a dielectric constant of 37.7 (I), a = 7.4 A. Thus, in terms of this theory the sums of the radii of the solvated anion and cation must be at least 3.5 A. in water and 7.4 A. in the mixture for which NCH,OH = 0.8 if no ion pairs are to be formed. Brown and MacInnes (6) obtained 4.45 A. as the distance of closest approach for the ions of sodium chloride in water from an application of the Debye-Huckel equation to their activity measurements. Similar meavurements are not available for water-methanol mixtures, but if we can assume that the product is a measure of the size of the ion-solvent complex a tentative value of a for sodium chloride in the mixture for which NCH,OH = 0.8 may be computed from the relation
246
L. 0. LONQBWORTH AND D. A. MACINNEB
The value thus computed is 7.77 b. This is somewhat larger than the critical size of 7.4 b.,which is necessary if no ion pairs are to be formed. Consequently our conclusion that sodium and lithium chlorides are completely dissociated in water-methanol mixtures is in apparent agreement with the theories of Bjerrum and of Fuoss and Kraus. SUMMARY
Transference and conductance measurements of 0.05 normal solutions of sodium and lithium chlorides in water-methanol mixtures have been made, together with determinations of viscosity. The product of the equivalent ion conductance and the viscosity deviates greatly from Walden’s rule and indicates increasing size of the ion-solvent complex with increasing methanol concentration. I n a given solvent the chloride-ion conductances of the two salts are very nearly equal. This is in accord with the assumption of the complete diasociation of sodium and lithium chlorides in these solvenb. REFERENCES (1) B K E R ~ G.: ~ F ,J. Am. Chem. Soc. 64, 4125 (1932). R. H.: J. Chem. Phys. 1, 515 (1933). (2) BERNAL,J. D., AND FOWLER, E. C.: Fluidity and Plasticity. McGraw-Hill Book Co., Inc., New (3) BINGHAM, York (1922). (4) BJERBUM,N.: Kgl. Danske Videnskab. Selskab. 7, No. 9, 2 (1926). (5) BORN,M.: Z. Physik 1, 221 (1920). (6) BROWN, A. S., AND MACINNES, D. A.: J. Am. Chem. Soc. 67, 1356 (1935). (7) Fnoss, R. M., AND KRAUS,C. A.: J. Am. Chem. Soc. 66, 1019 (1933). (8) GEFFCKEN, W.: Z. physik. Chem. A166, 1 (1931). (9) GIBSON,R. E.: 3. Am. Chem. SOC.67, 1551 (1935). (10) JONES, G., AND FORNWALT, H. J.: J. Am. Chem. SOC.Bo, 1683 (1938). L. G., AND MACINNEB, D. A,: J. Am. Chem. SOC.69,1666 (1937). (11) LONQSWORTH, D. A.: Science 88, 23 (1937). (12) MACINNES, D. A., AND LONGSWORTH, L. G.: Chem. Rev. 11, 171 (1932). (13) ~MACINNES, D. A., AND LONGSWORTH, L. G.: J. Am. Chem. SOC.,forthcoming (14) MACINNES,
publication.
SCHMICK, H.: Z. Physik 24, 56 (1924). SHEDLOVBKY, T.: J. Am. Chem. sot. 62, 1793 (1930). SHEDLOVSKY, T.: J. Franklin Inst. H 6 , 739 (1938). ULICH,H.: Fortschr. Chem. Physik physik. Chem. 18, 567 (1926). VOSBURGH, W. C., CONNELL, L. C., AND BUTLER,J. A. V.: J. Chem. SOC. 1985, 933. (20) WASHBURN, E. W., AND WILLIAMS, G. Y.: J. Am. Chem. SOC.36,737 (1913).
(15) (16) (17) (18) (19)
