186
M. L. MILLERAND M. DORAN
evaluated graphically from two plots, one of h/m versus m and one of h/rn'/*ver.sus m'/l BS jn equations l a and lb. The values of y so computed and of 4 are summarized in Table 11.
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Discussion of Results The behavior of these salts in highly concentrated solutions is an extension of their behavior a t low concentrations and shows nothing unexpected.
CONCENTRATED SALT SOLUTIONS. 11. VISCOSITY AND DENSITY OF SODIUM THIOCYANATE, SODIUM PERCHLORATE AND SODIUM IODIDE BY M. L. MILLERAND M. DORAN Contribution from the Stamford Laboratories, Research Diwision, American Cganamid Company, Stamford, Conn. Received April #Q, 1Q66
Viscosities of solutions of NaSCN, NaCIO, and NaI from low Concentrations up to saturation (or above) have been measured at 0, 30 and 50". Usin absolute rate theory, free energies, entropies and heats of activation of viscous flow have been calculated at 30". These v i u e s have been interpreted to mean that at high concentration the three salts studied take on quasi-crystalline short range local order. This interpretation is supported by computation of excess partial molal entropies.
'
4
I. Introduction Theoretical treatments of aqueous salt solutions have been confined to the dilute or moderately dilute region (not over 4 N ) . The range 6 N or above is largely an uncharted wilderness containing few experimental outposts. It seems reasonable to expect that a valid theoretical treatment, when it comes, may well stem from a theory of molten salt behavior rather than from a theory of the infinitely dilute solution. With this in mind, we should look for evidence, in the properties of very concentrated aqueous electrolyte solution of the beginning of short range local order. I n the very concentrated ranges, we should also expect to find that ion size plays a predominant role in determining solution properties. Some evidence for the existence of a t least short range local order in concentrated salt solutions has already been found in studies of (a) density,'B2 and (b) vapor pressure.* Since 1936, there have been a number of attempts to use the quasi-crystalline concept as a basis for a theory of the liquid state. (See reference 4 and references quoted therein.) Although somewhat declining in favor as applied to pure liqu i d ~ the , ~ concept of quasi-crystalline local order has much more to recommend it in the field of highly concentrated salt solutions (see Duttra6). Eyring and associates' have used, with much success, the concept of quasi-crystalline structure in correlating the properties of pure liquids. Their methods are available for use in the study of concentrated aqueous salt solutions. In this work, we have measured the viscosity of sodium thiocyanate. sodium perchlorate and sodium iodide solutions a t 0, 30 and 50" from zero (1) H. 8. Harned and B. B. Owen, "The Physical Chemistry of Electrolyte Solutions,'' 1st Ed., Reinhold Publ. Corp.. New York. N. Y.. 1943, p. 259. (2) A. F. Scott, THISJOURNAL, S6, 3379 (1931). (3) R. H. Stokes and R. A . Robinson, J . Am. Chem. Soc., 7 0 , 1870 (1948). (4) J . 9. Rowlinson and C. F. Curtiss. J . Cham. Phys., 19, 1519 (1951). (6) J. H. Hildebrand, Disc.Faraday Soc., 16, 9 (1953). (6) M. Duttra, Proc. Nall. Znsl. Sci. India, 19, 183 (1953). (7) 8. Gladstone, K. J. Laidler and H. Eyring, "The Theory of Rate Processes," McGraw-Hill Book Co., New York, N. Y., 1941, 1st Edition.
per cent. to near (or sometimes above) saturation. Although there is a large amount of viscosity data in the literature, there is very little on aqueous solutions above 5 N and even less in this concentrated range a t two or more temperatures. Among 1-1 salts only ammonium nitrate and silver nitrate, measured by Campbell and Kartzmark" and Campbell, Gray and Kartzmarkg at 25, 35 and 95' and the data on lithium chloride in "The International Critical Tables" meet the above requirements.
II. Experimental Preparation of Solutions.-The source of the salts and the preparation and assay of solutions was the same as in previous work on vapor pressure.10 Measurement of Viscosity.-Viscosity measurements were made using conventional techniques. Timing was by an electric timer registering to 0.1 second. Two viscometers, an Ostwald and a Cannon-Fenske type, were used. T o guard aga.inst instrument error and to be sure that shear effects were not entering a t higher concentrations, several of the more concentrated solutions were measured in both viscometers. For a measurement, 5 =I=0.15 ml. was introduced into a viscometer and the amount weighed. The exact volume at the temperature of measurement was calculated from the density. Use of a weighed amount of solution was necessary to ensure sufficient precision. Because the volume, especially a t high concentrations, wag rarely accurately 5 ml., it was corrected to 5.00 ml. by a calibration curve prepared for each viscometer. The correction for a difference of 0.15 ml. never amounted to more than 0.8% of the flow time. Viscometers were calibrated to correct for turbulent flow and drainage using water, and 20 and 40% sucrosell solutions as standards. Sucrose solutions were prepared by weight and their concentrations checked by measurement of the index of refraction. Viscosity values for sucrose solutions were taken from the work of Bingham and Jackson.I2 The calibration equation was assumed to be of the form q / d = At - B / t where t is the flow time, d is density and 7 is absolute viscosity in centipoise. (8) A. N. Campbell and E. M. Kartzmark, Can. J . Chem., 30, 128 (1952). (9) A. N. Campbell, A. P. Gray and E. M. Kartzmark, ibid., 81, 617 (1955). (10) M. L. Miller and C. L. Sheridan, THIS JOVRNAL,60, 184 (1956). (11) Glycerol solutions, commonly recommended as calibrating liquids, proved too hygroscopic. (12) E. C. Bingham and R. F. Jackson, Bull. Bur. Slda., 14, 59 (1918-19).
VISCOSITY AND DENSITY OF CONCENTRATED SALTSOLUTIONS
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187
Temperature Control.-The temperature at 0" was maintained by a well-stirred ice-bath. At 29.87' a thermostat regulated to 29.87 f 0.02', as measured by a platinum resistance thermometer calibrated at the National Bureau of Standards, was used. The temperature of the 50' bath was measured on a mercury thermometer also calibrated at the National Bureau of Standards. Density Measurements.-Density values over the wide concentration and temperature range needed in this work are available for sodium iodide only.13J4 They had to be determined for sodium perchloratel6 and sodium thiocysnate. Densities were measured with both 10- and 25-ml. pycnometers using standard procedures. They are precise to f0.0005 density unit. This is more than adequate for the purpose at hand.
111. Results The densities of sodium thiocyanate and sodium perchlorate are represented by the Masson equation as shown below For NaSCN to nearly saturation at 0'
d = 0.9999 29.87" d = 0.9957 50.1' d = 0.9880
+ 0.04823N - 0.003472N'/r
u = 0.0004
+ 0.04137N - 0.001600Na/z
u = 0.0005
+ 0.03857N - 0.000861Na/2
u = 0.0005
An alternative equation at 50.1' is d = 0.9880
+ 0.03778N - 0.0002084N'
u = 0.0002
For NaC104 through and including 60% solution, a t 0"
+
d = 0.9999 0.08749N - 0.00422Nah u = 0.0007 29.87' d = 0.9957 f 0.07919N - 0.00185N8/* u = 0.00056 49.3' d = 0.9884 0:07558N - 0.000883N8/z u 0.00036
+
N equals moles per liter at the temperature designated and u is the average difference between observed and calculated densities. The observed viscosities are shown in Fig. 1 and in Tables I, I1 and III.* Concentrations are expressed as moles per 1000 g. of solvent and viscosities as relative viscosities, Le. Flow time of soh. (cor.) Flow time of water (cor.)
Density of soh. Density of water
It will be observed that at low and moderate concentrations, the relative viscosity, as is common with aqueous salt solutions is greater at 50" than at 0". This means that the temperature coefficient of viscosity is less for the solution than for water. At 5-6 N the relative viscosity curves for sodium thiocyanate, shown in Fig. 1, cross each other and fan out. Thereafter, the relative viscosity at 0' is greater than at 50". The relative viscosity-concentration curves for sodium perchlorate and sodium iodide behave in much the same way. With sodium perchlorate, the relative viscosity-concentration curves a t different temperatures (not shown) cross each (13) W. Geffcken, 2. physik. Chem., BI, 81 (1929). (14) (a) A. F. Scott and E. J. Durham, T H r s JOURNAL, 34, 1424 (1930); (b) A. F. Scott and W. R. Fraeier, ibid., 31, 459 (1927). (15) The densities of Wirth and Collier (H.E. Wirth and F. N. Collier, Jr., J . Am. Chem. Soc., 78, 5292 (1950)) cover only the range 0 to approximately 6 N at 25O. * Tables I, I1 and I11 referred to in this paper may be obtained b y ordering Document No. 4773, from the American Documentation Institute, Library of Congrese, Washington 25, D . C.,remitting in advance by check or money order $1.25 for microfilm or 81.25 for photoprint.
4 6 8 10 Normality. Fig. l.-Relative viscosity of NaSCN solutions as a function of normality: 0, 0"; 0,29.87'; a, 50.1. 0
2
other at 5-6 N . With sodium iodide this crossover is at 7-8 N . Examination of data in the literature shows that with lithium chloride the relative viscosity-concentration curves at different temperatures remain very close together from 8-11 N and do not fan out appreciably until around 13 N.I6 The measurements of Campbell and Kartzmark, and Campbell, Gray and K a r t ~ m a r kon~ ~two ~ nitrates show that at saturation at 25 to 35" the relative viscosity-concentration curves of silver nitrate at different temperatures are approaching each other while those of ammonium nitrate are far apart.
IV. Discussion Eyring7 points out that since viscous flow can be thought of as a process in which a molecule jumps from a position which it is occupying into a hole, it can be treated as a rate process. Therefore, the absolute rate theory can be used to interpret viscosity (on pure liquids) and to compute free energies and entropies of activation for viscous flow. Similarly, we can, in a purely formal way, regard a solution of 1 N (or 2 N , 3 N , etc.) NaSCN as a single entity and compute over-all energies and entropies of activation for its viscous flow. For unassociated liquids, the plots of In q (where q is absolute viscosity) versus l/T give straight lines from whose slope the energy of activation for viscous flow AE can be calculated, i.e.
*
For associated liquids, the plots of In q versus 1/T are not linear, i.e., A E f varies with temperature. I n Fig. 2 In 7 has been plotted against 1/T for sodium thiocyanate solutions at 0, l, 2. . . . . 10 N . Values for the viscosity at even normalities at each (16) Because the data on lithium chloride are rather fragmentary at high concentrations, supplementary measurements have been made OD the viscosity of the 18 molal solution ( I 3 N at 30') at three temperatures. The results are shown below: Temp., OC. 0 29.87 49.3 Relative viecosity 18.9 14 4 13.1
M. L. MILLERAND M. DORAN
188
temperature were obtained by interpolation in large plots of the type of Fig. 1. From the slopes read off the curves in Fig. 2 (and similar plots for sodium perchlorate and sodium iodide) values of AE* have been obtained.
tion of some sort of short range local order in the solution before flow can take place.l8 TABLE IV FREE ENERGY, ENTROPY AND HEAT OF ACTIVATION OF VISCOUS FLOW Salt
Water NaSCN
NaCIOI
NaI I
I
I
I
3.0
3.3 3.6 1/T X 108. Fig. 2.-Temperature dependence of the viscosity of NaSCN solutions.
Values of the free energy of activation for viscous flow, AF*, have been computed from the equationla
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LiCl
Moles per liter of soh,
N
0 2 3 4 5 6 7 8 9 10 2 3 4 ‘ 5 6 7 8 9 9.5 2 3 4 5 6
7 8 10.75 13
kg. cal.
AF$.
AH$, kg. cal.
As$,
2.17 2.27 2.36 2.46 2.58 2.72 2.88 3.08 3.30 3.55 2.26 2.34 2.45 2.59 2.78 2.97 3.19 3.45 3.59 2.22 2.28 2.35 2.46 2.59 2.75 2.92 3.38 3.72
3.89 3.63 3.70 3.70 3.93 4.12 4.44 4.78 5.70 8.18 3.54 3.67 3.67 3.71 4.00 4.68 5.25 8.70 9.85 3.40 3.55 3.55 3.65 3.90 4.32 4.42 4.68 8.50
5.7 4.5 4.4 4.1 4.5 4.6 5.2 5.6 7.9 15.3 4.2 4.4 4.0 3.7 4.0 5.6 6.8 17.3 20.7 3.9 4.2 4.0 3.9 4.3 5.2 5.0 4.3 15.7
e.u.
AF* = R T l n f i
hL If order has to be destroyed before flow can take Here V is the molal volume of the moving unit, h place in these highly concentrated solutions, this is Planck’s constant and Lis Avogadro’s number. V means order is present in them. If the concentration a t which the viscosity conwas computed from the density as an averagevalue for the solution as a whole, assuming complete centration curves cross each other is thought of as marking the concentration where this local orderionization.‘? Assuming that the measured AEf is identical ing becomes significant, we can conclude that the with AH*, the heat of activation of viscous flow, larger the anion (C101- > SCN- > I-) the lower the entropy of activation, AS*, can be computed the concentration a t which this order begins to manifest itself. With nitrates there is no evidence from the relationship for this sort of order and with lithium chloride it AF* = AH* - TA8* does not appear until around 11to 12 N . The values of AE*, AF* and AS* for the three Although the viscosity behavior of the concensalts under investigation are summarized in Table trated salt solutions studied here can be interpreted TV. as evidence for the existence of some sort of order, Examination of the figures in this table brings viscosity furnishes no clue as to whether this is orout some interesting relationships. In water dering of the ions, analogous to molten salts, or there is a small entropy of activation of viscous ordering of the water, as in hydration. flow, due t o the necessity of breaking hydrogen The sign of the partial molal entropy of the conbonds,? which is decreased by adding salt. With stituents of the solution, calculated by the method NaSCN, NaClOI, and to a lesser extent with NaI (18) Such order is not to be thought of aa, in gny sense, crystalline the entropy of activation of viscous flow starts t o order. If the environmont of any ion is observed over a long period rise around 6 N and increases rapidly with concen- of time, a high degree of looal order in the arrangement of its neighbors tration. This entropy of activation can be visual- would be observed and might extend over many ionic diameters but would not extend throughout the entire system as in a crystal. This ized as resulting from the necessity for the disrup- order would be characterized by an alternate Iayering of plus and (17) If the number of moles of water in one liter of solution equals B and the number of mol= of sodium ion plua moles of thiocyanate ion equala 2 N,then V = 1000/(B 2 N).
+
minus charges in the neighborhood of any positive ion and a corresponding alternate layering of minus and plus charges in the neighborhood of any negative ion.
ELECTRICAL CONDUCTANCE OF CONCENTRATED SALTSOLUTIONS
Feb., 1956
189
.
1 -VrO -8
I 0
I
2 4 6 8 10 12 Moles/l. at 30" (25" for LiCI). Fig. 3.-Excess partial molal entropy of water in concentrated salt solutions.
of Frank and Robinson,'g helps to decide between these two possibilities. To calculate the partial molal entropy of the constituents of the solutions, vapor pressures and heats of dilution are needed a t high concentrations. Such data are available for sodium thiocyanate, sodium iodide10~20 and lithium chloride.20 For sodium perchlorate the vapor pressures are available'O but not the heats of dilution. Following Frank and Robinson, the excess partial molal entropy of water AS1*, and of salt, ASz*, in solutions of sodium thiocyanate, sodium iodide and lithium chloride up to concentrations near saturation have been computed. These values for AS2* are plotted in Fig. 4. From this plot we see that for concentrated sodium thiocyanate solutions (19) H. 8. Frank and A. L. Robinson, J . Chem. Phya., 8 , 933 (1 940). (20) F. D. Rosaini, D. D. Wagman, W. H. Evans, 5. Levine and I. Joffe, "Selected Values of Chemical Thermodynamic Properties," U. 8. Dept. of Commerce, National Bureau of Standards, 1952.
0
2 4 6 8 10 12 Moles/l. at 30" (25" for LiC1). Fig. 4.-Excess partial molal entropy of salts in concentrated solutions.
AS2+ is negative, indicating more order of the solute in concentrated solution than in the infinitely dilute reference solution. Sodium iodide behaves like sodium thiocyanate but to a lesser degree. This is consistent with its viscosity behavior. In contrast to these two salts, solutions of lithium chloride show a positive ASz* and a negative AS1*. At 11 N . where the viscosity behavior began to show up some arrangement in the solution, the A&* for water in the lithium chloride solution is rapidly becoming very negative. The little order in lithium chloride solutions at high concentrations is, therefore, associated with the solvent (hydrated lithium ion) while the more pronounced order in sodium perchlorate, sodium thiocyanate and sodium iodide solutions is associated for the most part with the solute. Acknowledgment.-The authors are indebted to G . Yates for carrying out many of the density and viscosity measurements reported here.
CONCENTRATED SALT SOLUTIONS. 111. ELECTRICAL CONDUCTANCE OF SOLUTIONS OF SODIUM THIOCYANATE, SODIUM IODIDE AND SODIUM PERCHLORATE BY M. L. MILLER Contribution from the Stamford Laboralories, Research Division, American Cyanamid Company, Stamford, Conn. Received April IO, 1066
The electrical conductance of solutions of sodium thiocyanate, sodium perchlorate and sodium iodide has been measured at 0, 30 and 50" from 1 N to saturation. A t higher concentrations, the conductances of all three salts (all sodium salts appear to be a roaching a common limit. This suggests that as the concentration increases more and more of the current is being carrieigy the sodium ions. Comparison of the energy of activation for conductance with the energy of activation of viscous flow is consistent with this view.
I. Introduction Preceding papers in this series's2 have reported measurements of the viscosity, density and vapor pressure of aqueous solutions of sodium thiocyanate, sodium perchlorate and sodium iodide from 1 N to saturation at 0, 30 and 50". The present paper deals with the electrical conductivity over the same concentration and temperature range. Although there is a very large amount of conductance data in the literature, there are very (1) M. L. Miller and C. L. Sheridan, THIEJOURNAL,80, 184 (1956). (2) M. L. Miller and M. Doran, ibid., 60, 186 (1956).
few measurements on aqueous 1-1 salt solutions in the region above 8 N and fewer still at these high concentrations a t two or more temperatures. There are the measurements of Campbell and Kartsmarka and Campbell, Gray and Kartzmark4 a t 25, 35 and 95" on silver nitrate and ammonium nitrate and some data on lithium chloride in "International Critical Tables." (3) A. N. Campbell and E. M. Kartzmark. Canadian J . Clem., SO, 128 (1952). (4) A. N. Campbell, A. P. Gray and E. M. Kartzmark. iWd.. 81, 617 (1953).
