CONDUCTIVITY OF CONCENTRATED ELECTROLYTE SYSTEMS
447
sidered to be in the trans form, are very nearly the same. The value of the cis form is very much smaller. In this case all that can be said is that, since dy/dt is a measure of the entropy of the surface, the interfacial tension coefficient of the cis isomer with water is lower than that of the trans isomer. It is of further interest to note that the work of cohesion and work of adhesion tend to approach each other in the caw of decane and octane, as seen in table 6. The difference is very nearly equal to that between the values found and those calculated by Antonoff's rule. The exact significance of this is difficult to explain until reliable values of the actual solubilities of these hydrocarbons and water are known. SUMMARY
1. The interfacial tensions of several cyclic and normal paraffins against water have been measured between 20" and 70°C. by the differential bubble pressure methods. 2. The interfacial tensions appear to be a linear function of temperature over the range investigated. 3. The interfacial temperature coefficients of the trans forms show a marked difference from that of the cis form of decahydronaphthalene. 4. Antonoff's rule is closely obeyed by octane and decane, for which the difference between the work of cohesion and that of adhesion approaches zero. REFERENCES (1) GUEST,W.,AND LEWIS,W.: Proc. Roy. SOC. (London) A170, 501 (1939). (2) HARKINS, W.D . , AND HUMPHREY, E. C.: J. Am. Chem. SOC. 38, 228 (1916). E.:Trans. Faraday SOC.99, 229 (1943). (3) HUTCHINSON, (4) MATHEWS, J. B.: Trans. Faraday SOC.36,1113 (1939). (5) SEYER,W.F . , AND DAVENPORT, C. H . : J. Am. Chem. SOC. 63, 2425 (1941). (6)SUGDEN, S.:J. Chem. SOC. 191,858 (1922).
T H E CONDUCTIVITY OF CONCENTRATED ELECTROLYTE SYSTEMS AS A FUNCTION OF TEMPERATURE AND CONCENTRATION' L. R. DAWSON, G . R . LEADER,
AND
H. K. ZIMMERMAN, JR.
Department of Chemistry, University of Kentucky, Leringlon, Kentucky Received April 10, 1060
Despite its continuing importance and use in a variety of industrial applications, the study of the physical behavior of concentrated systems of electrolytes appears to have received relatively little attention. Certainly it can be said that, although the conductance behavior of dilute electrolytes in various solvents 1 This paper is baaed on research performed for the U.S. Army Signal Corps, Fort Monmouth, Xew Jersey, under Contracts W36-039-sc-32265and W36-039-sc-38184.
448
L. R. DAWSON, G. R . LEADER, AND H. K. ZIMMERMAN, JR.
is comparatively well understood at this time (cf. reference 3 and other papers of that series), the problem of the conductivity of concentrated electrolytes remains largely in the realm of uncharted territory. A few attempts to explore this question have met with some measure of success (1, 4),but neither volume of data nor development of theory has as yet given any clear picture of the situation. Herein are presented the results of a number of measurements on the conducting properties of several 1-1 electrolytes in the solvents water and dimethylformamide. Because of the obscurity which at present overhangs the theory of concentrated systems of electrolytes, it will not be possible to present any quantitative interpretation of the results. However, it will be possible to observe certain general trends which may be of value in the elucidation of the problem as more experimental material accumulates. EXPERIMENTAL
Because the systems investigated contained relatively large concentrations of solutes, extreme sensitivity was not required in the apparatus used for measuring the conductivities. Therefore, the measurements were made using an ordinary Wheatstone bridge, with a stable oscillator as current source and a headphone detector to determine the null point. Measurements were made in a calibrated Washburn cell of the medium resistance type. Temperature control to 3 precision of 0.5"C. over the range 20" to -5OOC. was obtained, using a manually operated thermostat which consisted of dry ice and acetone contained in a 1-gallon Dewar flask. Again because the high concentrations employed made it useless to seek extremely high sensitivities, the water used as solvent was purified only by double distillation and used without further treatment. Lithium methanesulfonate was prepared by adding lithium hydroxide to methanesulfonic acid to the neutral point (as indicated by a pH of 7). The acid which was used contained approximately 1 per cent of sulfuric acid by weight, so that the methanesulfonate-ion concentrations given are about 2 per cent higher than the actual values. Similarly lithium sulfamate was prepared by adding lithium hydroxide to a weighed quantity of sulfamir acid until a pH of 7 was reached. Dimethylformamide supplied by the du Pont company was used after purification by fractional distillation under vacuum. The ammonium thiocyanate and ammonium bromide were of C.P. grade, while the guanidine nitrate was of Eastman Kodak practical grade. RE8ULTS AND DISCUESION
The specific conductivities of concentrated aqueous solutions of lithium sulfamate and of lithium methanesulfonate are shown in figures 1 and 2, respeotively. I n figures 3, 4, and 5 we show, respectively, the specific conductivities of anhydrous solutions of ammonium thiocyanate, ammonium bromide, and guanidine nitrate in dimethylformamide.
449
CONDUCTIVITY OF CONCENTRATED ELECTROLYTE SYSTEMS
A word concerning the manner of presentation of these data is in order. The figures aa given constitute contour maps of a “surface” of specific conductance as a function of both temperature and concentration of salt. The experimentally
0 -
4.03 -10-
-
*
0
e.19
0-
2.64* 30I “SUPERSATUPATED SOLUTION
I I
I
I
1
3
2
MOLES OF SOLUTE PER
3.01
5
4
T H O W D GRAMS OF SOLVENT
FIQ.1. Contour map of the specific conductance of aqueous lithium sulfamate solutions aa a function of temperature and solute concentration. Numbered contours indicate conductance X I@. oc.
I
I
I
I
I
I
I
‘361
I
‘3.52
I
I
‘3.26 / ‘3010
‘2.47 ‘2.45 2.37 ‘2.23-------____-_/
\ \
-20
‘1.64
1
0
I
‘1.59
I I I I I I 2 3 4 MOLES OF SOLUTE PER THOUSAND GRAMS OF SOLVENT 1
I
I
-
1
5
FIQ. 2. Contour map of the specific conductance of aqueow lithium rnethanesulfonate solutions as a function of temperature and solute concentration. Numbered contours indicate conductance X W.
determined points are given explicitly, and the contour lines indicate the topographical characteristics of the surface .aa obtained by interpolation. There is thus available a graphic means of obtaining at a glance the overall conducting characteristics of the system. The usual isotherm at any given temperature
450
L. R. DAWSON, G. R. LEADER, AND
n.
K. ZIMMERMAN, JR.
'c.
22-
0 -
18
0
16
-10-
174
----14 -
3
-
-40
2 1
5.61'
-50 0.0
02 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 MOLES OF SOLUTE PER THOUSAND GRAMS OF SOLVENT
3.34
2.0
FIG.3. Contour map of the specific conductance of solutions of ammonium thiocyanate in dimethylformamide as a function of temperature and solute concentration. Numbered contours indicate conductance X 108. 20
IO
* C. 0 -10
-20 -30 -40
-50 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.2 0.4 MOLES OF SOLUTE PER THOUSAND GRAMS OF SOLVENT FIG.4. Contour map of the specific conductance of solutiona of ammonium bromide io dimethylformamide aa a function of temperature and solute concentration. Numbered contours indicate conductance X lo*.
CONDUCTIVITY OF CONCENTRATED ELECTROLYTE SYSTEMS
45 1
may be obtained aa a horizontal cross-section, or profile, of the contour surface, while, similarly, the temperature dependence of the conductivity at any given concentration may be found from the vertical profile a t that point. In addition to these graphical advantages, the maps retain all the advantages of tabular presentation, since all the experimental data are given. Furthermore, if inconsistencies in the data exist, they become apparent immediately, because under such circumstances the contour lines are no longer systematic curves but become erratic and poorly defined. From these contour mappings, certain interesting qualitative conclusions may be drawn. For example, in figures 1 and 2, the measurements of conductivity have been carried down to temperatures which are within only a few degrees of the freezing points of the various systems in question. It may be wen that in these cases the conductance at these low temperatures rapidly becomes virtually independent of the concentration. For instance, in the case of lithium sulfamate, the conductivity at - 10”to 0°C. becomes practically constant for concentrations above about 2.5 molal, and as the temperature is raised the lower concentration limit of this region of constancy rises progressively to higher and higher concentrations, until at about 0°C. it has reached about 3.75 molal; at still higher temperatures it disappears entirely. In fact, at 20”C., one finds that the isotherm appears to have a small maximum of specific conductance in the neighborhood of about 4 molal. Some of these same features are also noted in figure 2 for lithium methanesulfonate. There one sees once again the tendency toward the flat isotherm a t the higher concentrations, the isotherm being this time in the vicinity of -20°C. because of the fact that at the higher concentrations these solutions have freezing points between -20” and -25°C. At the higher temperatures (e.g., 20°C.) the isotherm definitely possesses a maximum. In addition to these characteristics which the two aqueous systems have in common, it may be noted that in the case of the lithium methanesulfonate the conductivity rises very slowly with incroasing temperature at concentrations below 0.5 molal. Continuing the topographical concept, therefore, it appears from these two systems that the overall conductivity of these systems consists of a “hill” whose summit is located at some as yet undetermined combination of high temperature and concentration, and which falls off to a sort of “valley” or “plain” at very low temperatures or concentrations. On the basis of this view, one might predict that, as the concentration is lowered and the temperature raised, the contour lines should bend back upon themselves, thereby reflecting a maximum in the curves of conductivity as a function of temperature a t any given low concentration. Indeed, examination of figures 3 and 5 indicates an excellent likelihood that such is actually the case for both ammonium thiocyanate and guanidine nitrate in the solvent dimethylformamide. A similar feature appears to be incipient in figure 4, for ammonium bromide in dimethylformamide; however, at present data are not available for the lower concentrations in sufficient quantity to confirm this conclusively. With respect to the other rharacteristics of figures 3 and 4, it appears that
L. R. DAWSON, G. R. LEADER, AND n. K. ZIMMERMAN, JR.
452
the shift to a system of lower freezing point (dimethylformamide) has essentially removed the region in which the conductance is independent of concentration; Le., the contours in these figures represent a region higher on the side of the
-I 0
SUPERSATURATED
MOLES OF SOLUTE
PER THOUSAND
SOLUTION
GRAMS OF SOLVENT
FIG.5. Contour map of the specific conductance of solutions of guanidine nitrate in dimethylformsmide 88 a function of temperature and solute concentration. Numbered contours indicate conductance X 10’.
TABLE 1 Density of aqueous solutions of lithium suljamate as a function of tanpaature and wncentration
Wld
0.822
1.66 2.43 3.43 4.73
6./d
8.M.
1.w.
I./d.
1.049 1.089 1.123 1.168 1.230
1.052 1.092 1.126 1.171 1.233
1.053 1.094 1.128 1.172 1.235
1.054. 1.173 1.236
Supercooled solution.
postulated “hill.” The system ammonium bromiddimethyl fonnamide shows, in addition, a small irregularity in the slope of this “hill” in the region of 0.8 molal and temperatures below about -40°C. This, to preserve the topographical analogy, might be termed a “shoulder” in the “hill.” Why it should occur under these conditions is not at all apparent.
453
CONDUCTIVITY O F CONCENTRATED ELECTROLYTE SYSTEMS
The map given in figure 5 for guanidine nitrate in dimethylfomamide is only fragmentary, because the solubility of this salt is low, particularly at the lower temperatures. Insofar as the data permit of conclusions, however, this system bears out the observations recorded for the other four. Furthermore, the condition of the contours bending back upon themselves at the low concentrations is particularly marked in this case, even to the extent that below about 0.3 molal
TABLE 2 Viscosity of aqueous solutions of lithium sulfamate a8 a function of temperature and concentration YISCOLUTY, IN CENTIPOILILS, AT T t H P I M T Q R E S 0 "
S O L m EONCLNTMTION
10.C.
20.C
0%
-10.C.
WWd l
CP.
CP.
CP.
CP.
0.822 1.66 2.43 3.43 4.73
1.181 1.290 1.600 1.946 2.628
1.543 1.747 2.177 2.610 3.448
2.040 2.359 2.773 3.346 4.101
3.748 4.508
8OLUTl W N U N TRATION
20.C
1O.C.
0,9952 0.9999 1.002 1.027 1.036 1.056 1.069 1.088 1.113 1.135 1.157 1.172
0.9997 1.002 1.005 1.029 1.038 1.058 1.071 1.090 1,115 1 A37 1.161 1.175
O.C.
-1O.C.
-1S.C.
1.121 1.143 1.167 1.183
1.145 1.169 1.187 (-ZO'C.)
WWld
0.023
0.062 0.124 0.560 0.755 1.211 1.536 2.018 2.714 3.361 4.094 4.614
0.9992 1.002 1.006 1.030 1.039 1.059 1.074 1.092 1.118 1.140 1.164 1.179
the conductivity seems to be very nearly temperature-independent between 0" and 20°C. In the cmes of the aqueous solutions densities and viscosities were determined also a t temperatures and concentrations chosen to coincide with those a t which the recorded conductivities were measured. Tables 1 and 2, respectively, show the densities and viscosities of the lithium sulfamate solutions, while tables 3 and 4, respectively, show the densities and viscosities of the lithium methanesulfonate solutions.
454
L. R DAWBON, 0. R LEADER, AND H. K. ZIMMERMAN, JR.
The densities were determined only incidentally in the course of measuring the viscosities. It was hoped that these viscosity measurements might shed some light upon the conductance behavior of these systems (see reference 4 and work there cited) which has been noted above. However, it will be observed that, although the conductance isotherms at the lowest temperatures become virtually constant at the high concentrations of solute, the viscosities rise in a normal manner. Hence it must be concluded that, a t least under these circumstances, the conductivity is not controlled by viscosity. In the case of the aqueous lithium methanesulfonate the data are not conclusive, but it appears that at the low temperatures and high concentrations there is a maximum in the isotherm. It is possible that a part of this effect may be due to the influence of viscosity. TABLE 4 Viscositv of aqueous solutions of lithium methaneeulfonate as a function of temperature and concentration VISCOSITY, IN CEmImIsEs, AT TEMPERATURES GIVEN
SOLUTE CONCLNTPATION
O'C.
--Io*c.
-1S'C.
mold
0.023 0.062 0.124 0.560 0.755 1.211 1.536 2.018 2.714 3.361 4.094 4.614
1.040 1.169 1.218 1.236 1.284 1.459
1.375 1.484 1.636 1.705 1.663 1.902
1.751 1.830 1,902 2.147 2.242 2.253 2.616 2.815 3.552
, ~
1 ,
4.76
However, the magnitude of the change observed makes it seem unlikely that viscosity is the only, or even the principal, factor. From the evidence a t hand it would seem that the occurrence of the maximum in the isotherm a t high concentrations should be attributed most likely to the effects of ion-association and solvation. Theoretical equipment for the treatment of this problem in the case of very concentrated solutions such as those at hand is entirely inadequate. The method of Fuoss and Kraus (2) is applicable only to relatively dilute systems and cannot be used here. It is hoped, however, that continued study of such highly concentrated solutions, together with the accumulation of more data relative to them, will lead to the development of an adequate interpretation of these complex electrolyte systems. SUMMARY
Specific conductances have been measured for concentrated aqueous solutions of lithium sulfamate and lithium methanesulfonate up to about 5 molal and
VISCOSITY OF SUSPENSIOSS O F SPHERES
455
from 20°C. down to the vicinity of the freezing point. Similar data are presented for dimethylformamide solutions of guanidine nitrate between 20" and -50°C. up to the limit of solubility of this salt. Also, conductance measurements have been made over this temperature range for dimethylformamide solutions of ammonium thiocyanate from 0.2 to 2.0 molal and of ammonium bromide from about 0.2 to 1.6 molar The data are presented in the form of contour maps which show specific conductivity as a function of temperature and concentration simultaneously. By means of these maps general conclusions may be drawn concerning the changes in conductance which occur over a broad range of conditions. Density and viscosity data are presented for the two aqueous systems also. These data indicate that the conductivity is not controlled entirely by the viscosity of these systems. Various phases of the experimental work reported herein were performed by Messrs. Michael Golben, William M. Keely, Albert Tockman, Curtis H. Ward, and Forrest V. Williams, while employed as research assistants on Contracts W36-039-sc-32265 and W36-039-sc-38184 with the U. S. Army Signal Corps, Fort Monmouth, New Jersey. The authors gratefully acknowledge the valuable contributions of each of these men. REFERENCES (1) (2) (3) (4)
EDELSON, D., AND Fuoss, R . M . : J. Am. Chem. SOC.73, 335-10 (1950). Fuoss, R . M., AND KRAUS,C. A . : J. Am. Chem. SOC.66, 476-88 (1933). PICKERINQ, H. L., AND KRAUS,C . A . : J. Am. Chem. SOC.71, 32M-93 (1949). STRONG, L. E., AND KRAUS,C. A.: J. Am. Chem. SOC.72, 166-71 (1950).
T H E VISCOSITY OF SUSPENSIONS OF SPHERES. I1
THEEFFECT OF SPHEREDIAMETER JAMES V. ROBIXSOS The Mead Corporation, Chillicothe, Ohio
Received April 14, 1060 INTRODUCTION
The present paper demonstrates the effect of the size of small glass spheres upon the viscosity of their suspensions, employing for the analysis of the results an equation derived and demonstrated previously (4). The demonstrations to be made are that a decrease in the size of the spheres increases their relative volume, measured indirectly by viscosity and directly in a packed sediment, and that the increase in relative volume is caused by interaction of the spheres with the suspension medium.
