NOTES
2663
Viscosity of Mixtures of Electrolyte Solutions’
The efflux time was measured to 0.1 sec with an electric timer. The over-all reproducibility and accuracy is
by Y. C. Wu2
=kO.l%.
Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830 (Receiued February 8, 1068)
Results and Discussion Viscosity measurements were made on solutions of LiCl, NaCl, and KCl and equimolar mixtures of LiC1NaCl and LiC1-KCl. I n addition, measurements were made on an NaCl-MgCl, mixture (88.06 mol % NaC1) having the Na : Mg ratio of sea water.O The results are shown in Table I.
The relative viscosity of binary electrolyte solutions is generally discussed in terms of the equation of Jones and Dole3
r/m
= 1
+ a 6 I + bI
(1)
where q is the viscosity of the solution, v0 is that of the solvent, and I is the ionic strength in molar concentration units. (This equation is most often written in terms of the molar concentration c rather than ionic strength. The form used here is more convenient in discussing mixtures and in comparison with other limiting laws. For 1: 1 electrolytes the two concentrations scales are the same.) The coefficient a has been identified as the slope of the limiting law of Falkenh a g e ~ ~The . ~ coefficient b has been shown to have the property of additivity5and has been discussed by several authorities on electrolyte solutions.6 Onsager and Fuoss’ developed equations for the ionic contribution to the viscosity of multicomponent systems, v*, which lead to a limiting law of the form
r* = 7 - T o = a ‘ d j
(2)
The limiting slopes in eq 1 and 2 are related by a’ =
am. I t has been suggested that the additivity rule for the b coefficient of eq 1 can be extended to multicomponent There appear to be no explicit tests of this rule. I n this communication, the viscosities of the systems LiC1-NaC1-R20, LiC1-KC1-H20, and NaC1-h!IgCl2H 2 0 a t 25” and in the concentration range 0.01 to 1 ionic strength are reported. These results are compared by means of eq 1 with the a coefficients of the Onsager-Fuoss theory and the b coefficients obtained from the additivity rule. Experimental Section Stock solutions of LiCl, NaCl, KC1, and P\/IgCl2were prepared from reagent grade chemicals which had been recrystallized and dried. The concentrations were verified by titration with AgN03. Dilutions and mixtures were made from these stock solutions. Viscosities were measured with Cannon-Ubbelohde semimicroviscometers with efflux times of about 400 sec. The kinetic energy correction for this type of viscometer* is very small and was neglected for the systems studied here. The relative viscosity was determined from the densities and efflux times; the viscosity of water a t 25” was taken as 0.8903 cP.‘jb The densities were measured with 5-ml pycnometers.
Table I : Viscosities (cP) at 25” LiC1-KCI
I
0.01 0.05 0.0625 0.10 0.125 0.25 0.50 1.00
KC1
0.8898 0.8900 0.8903 0.8883 0.8875
1:l
LiCl
0.8912 0.8944 0.8951 0.8976 0.8988 0.9078 0.9214 0.9540
0.8921 0.8978 0.8986 0.9045 0.9066 0.9246 0.9565 1.0250
LiC1-NaC1 1:l
NaCl
0.8918 0.8964
0.8915 0,8951
0.9017
0.8991
0.9400 0.9997
0,9294 0.9664
I
NaC1-MgC12 88.06 mol % NaCl
0.07034 0.1407 0.3517 0.7034 1.0551 1,4068
0.8978 0.9041 0.9240 0.9540 0.9934 1,0284
The Onsager-Fuoss theory’ provides a means of calculating the coefficient a’ of eq 2 and thus the limiting slope, a, of eq 1. The electrostatic contribution to the viscosity may be written as (ref 7, eq 3.7.2) (1) Research sponsored by The Office of Saline Water, U.S. Department of the Interior, under Union Carbide Corporation’s contract with the U. S. Atomic Energy Commission. (2) U. S. Department of Commerce, National Bureau of Standards, Washington, D. C. 20234. Dole, J . Am. Chem. SOC.,51, 2950 (1929). (3) G. Jones and IM. (4) H. Falkenhagen and M. Dole, Physik. Z., 30, 611 (1929); H. Falkenhagen, ibid., 32, 745 (1931); H. Falkenhagen and E. L. Vernon, Phil. Mag., 14, 537 (1932). (5) W. M. Cox and J. H. Wolfenden, Proc. Roy. SOC. (London), A145, 475 (1934); E.Asmus, 2.Naturforsch., 4a, 589 (1949); R.W. Gurney, “Ionic Processes in Solution,” McGraw-Hill Book Co., Inc., New York, N. Y., 1953; M. Kaminsky, Discussions Faraday SOC.,
24, 171 (1957). (6) (a) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958; (b) R. A. Robinson and R. H. Stokes, “Electro-
lyte Solutions,” 2nd ed revised, Butterworth and Co. Ltd., London, 1965; (c) R. H. Stokes and R. Mills, “Viscosity of Electrolytes and Related Properties,” Pergamon Press Inc., New York, N. Y . , 1965. (7) L. Onsager and R. M. Fuoss, J . Phys. Chem., 36, 2689 (1932). (8) M. R. Cannon, R. E. Manning, and J. D. Bell, Anal. Chem., 32,
355 (1960). (9) K. S. Spiegler, “Salt-Water Purification,” John Wiley and Sons, Inc., New York, N. Y., 1962.
’Volume 72,Number 7 July 1068
2664
NOTES 1" =
A'(P
- Qn)dj =a'dj
(3)
I
-
I
I
I
I
0.f5
where A' = 0.3622/Z(l/DT)'" 9
P =
CXiZi/Xd i
0.1
-
m
Qn = 4 [ R ]
n-0
bnS'"'
and xi is the ional fraction za the absolute value of the valence, and Xa the ionic equivalent conductance for ion i; D is the dielectric constant for the solvent, T is the absolute temperature, b, are the binomial coefficients, [RJ and 8'"' are matrices whose elements are functions of ionic fractions and ionic mobilities, n is the number of recursions, and A' = 0.00335 for aqueous solutions at 26" with the viscosity in poise units. Values for P , Q,, and a' calculated by eq 3 are given in Table I1 along with the resulting value of a for eq 1.
a
88.06 mol
P
Q8
a' X 106
a
0.01336 0.01641 0.01947 0.01800 0.01653 0.01665 0.01693
0,00000 0.00098 0.00143 0.00100 0.00049 0.00044 0.00032
4.47 5.17 6.03 5.68 5.37 5.43 5.56
0.00502 0,00580 0.00678 0.00638 0.00603 0.00610 0.00624
yo NaCl.
It can be seen from Table I1 that the P term is the main contribution to ?I*and that it is dependent on the mixing ratio. The Qn term is a small correction, but causes the limiting slope for mixtures to diverge from a linear combination of that of their components. It has been shown6 that the b coefficient of eq 1 for binary electrolyte solutions is an additive property of the constituent ions. It seemed reasonable that values of b for mixtures of electrolytes could be obtained from the values for the individual components; thus for a mixture of two electrolytes b =
+
(4) where YJ is the ionic strength fraction and bJ the linear coefficient of eq 1 for component J. Values of b for the pure salts and the mixtures are given in Table 111. In this table, values for the pure salts were obtained from the ionic valuesab and values for the mixtures were obtained from those for the pure salts combined according t o eq 4. Since most of the b coefficients in the literature are on the molar scale, it is necessary to divide these coefficients by a valence factor (1 for 1: 1 Y A ~ A
The Journal of Physical Chemistry
I
I
I
I
0
.2
04
.6
,8
Y B ~ B
I 1.0
fl Figure 1. Viscosities of pure salt solutions.
-
Table 11: Parameters of Eq 3
KCl LiC1-KC1 (1: 1) LiCl LiC1-NaCl (1 : 1) NaCl NaC1-MgClP MgClz
-,02
1 0
1
LICI-KCI
I
I
I
I
-
NOTES
2665
as plots of [(v/vo) - 11/47 vs. 4 j . The solid lines represent eq 1 with values of a from the OnsagerFuoss theory (Table 11) and values of b from the additivity rule (Table 111). The agreement between the calculated curves and the experimental points is satisfactory, at least up to I = 1.
Acknowledgment. The author expresses his indebtedness to Dr. E(. A. Kraus for his support, encouragement, and constructive criticism; his appreciation to Drs. J. S. Johnson, R. J. Raridon, and R. M. Rush for helpful discussion; and to Mr. J. Csurny for technical assistance. He also wishes to thank Professor H. L. Friedman of the State University of New York a t Stony Brook for his stimulating discussion and valuable suggestions.
Ion Exchange with a Two-Phase Glass
by R. H. Doremus General Electric Research and Deselopment Center, Schenectady, N e w York (Received November 27, 1967)
Many borosilicate glasses separate into two interconnected, amorphous phases. l p Z When the borate-rich phase is etched out, a porous glass of nearly pure silica (SiOJ results, which when heated collapses to a compact glass (Vycor) resembling fused silica. There is some evidence that commercial Pyrex glass, which is a sodium borosilicate glass containing more silica than the glasses from which Vycor is made, also separates into two continuous amorphous phases.2 However, no separation is observed in the electron microscope, nor can any phase be etched out from this glass, perhaps because the phase separation is on too fine a scale. In this work the exchange behavior of silver ions with Pyrex glass gives additional evidence that this glass contains two phases. Pieces of Pyrex glass (80% SiOz, 13% B203, 4.2% NazO, and 2% A1203, approximate composition in weight yo)tubing were placed in mixed sodium nitratesilver nitrate melts at 335" for several hours. Then layers of glass were etched off with 8% H F and were analyzed. Extrapolation of the profile of silver concentration to the glass surface gave the equilibrium concentration of silver that had exchanged with sodium ions in the glass. The exchange of silver ion in the melt with sodium ions in the glass can be represented by the equation Ag+(m)
+ Na+(g)
The exchange coefficient
=
Ag+(g)
+ Na+(m)
was calculated from the results. In eq 1, a is the thermodynamic activity of the nitrate in the melt, referred to a pure solution as the standard state as taken from the measurements of Laity,8and C is the concentration of an ion in the glass. The measured K values for Pyrex glass are given in Table I. Table I : Exchange of Silver Ions in a Sodium Nitrate Melt with Pyrex Glass Mole fraction of ailver nitrate in melt
0.398 0 310 0.153 0.0475 0 I0022 3 x 10-6
Exchange ooefficient, K
1.97 1.87 1.98 2.05 7 06 12.2
If the solution of ions in the glass is ideal, K should be constant with concentration. This constancy has been found for silver exchange with sodium ions in soda lime glass (15% Na20) and in fused silica (3 atomic ppm of sodium both of which contain one homogeneous phase. Therefore, if the Pyrex glass were a single phase containing uniform sodium borosilicate groups, one would expect a constant K for this exchange, since the density of exchanging groups is even less than in the soda lime glass. Thus the change in K a t lower silver concentrations, shown in Table I, is evidence that the glass separates into two different phases. A two-phase glass can be treated as a mixture of two ideal phases, each with its appropriate exchange coefficient K1 or Kz,invariant with ionic concentration, as defined in eq l. In terms of the ionic concentrations in the two phases, numbered 1 and 2, the experimentally measured distribution coefficient K is
I n terms of the coefficients K1 and K2 this measured K is K =
- Kz) + K2(? + Ki) + K1 + Nl(K2 - K1)
yNi(K1 T
(3)
in which N1 is the mole fraction of exchangeable ions in phase 1 (a constant for any given glass composition) and T is u N ~ / u A ~ the , ratio of activities in the melt. Consistent values of the parameters in eq 3 for the data in Table I are KI = 2.3 X lo2,Kz = 1.6, and N1 = 0.047. This treatment of ion exchange with two phases is formally equivalent to that with a single phase contain(1) M. E. Nordberg, J. Am. Ceramic Soc., 27, 299 (1944). (2) R. J. Charles, ibid., 47, 559 (1964). (3) R. W. Laity, J . Am. Chem. Soc., 7 9 , 1849 (1957). (4) R. H. Doremus, unpublished results.
Volume 78, Number 7 July 1068
