1285
PROPERTIES OF NaN03, NaC104, AND NaCNS IN SOLUTION
Electrical Conductance, Diffusion, Viscosity, and Density of Sodium Nitrate, Sodium Perchlorate, and Sodium Thiocyanate in Concentrated Aqueous Solutions
by G. J. Janz, B. G. Oliver, G. R. Lakshminarayanan, and G. E. Mayer Rensselaer Polytechnic Institute, Department o j Chemistry, Troy, New York
18181 (Received October 14, 1969)
The properties of NaN03, NaC104, and NaCNS in concentrated aqueous solutions have been investigated at 25” by the techniques of electrical conductance, diffusion (Stokes’ diaphragm technique), viscosity, and density, and the comparison of these with those of NaCl (as model electrolyte) is reported. In addition to the analytical characterization, the data are examined as an indication of ion-ion and solvation type interactions, and structural transitions in very concentrated salt solutions.
Introduction While the use of electrical conductance, diffusion, and viscosity measurements to study the nature of the kinetic species in salt solutions has long been recognized, relatively little work on the conductance and viscosity of concentrated electrolytes has been done, and precise diffusion coefficients of electrolytes in such concentrated solutions are virtually nonexistent. The present communication reports the accurate and precise characterization of these properties, and, as well, the densities, for a series of 1: 1 salts, T\’ah’O3, T\TaC1O4,and NaCiSS, and the comparison of these data with those of KaC1 (as model electrolyte), Application of the WishawStokes conductance and the Hartley-Crank diffusion equations is examined; in addition, empirical equations for the analytical characterization of these salt solutions are developed. The use of electrical conductance and diffusion as criteria for structiiral changes in very concentrated solutions is examined.
Experimental Results Doubly-distilled water was obtained from a two stage still composed of a Stokes forestill (Model 171-E, F. J. Stokes Co.) and a Corning all-glass final still (Model AG-2, Fisher Scientific Co.). The specific conductance of water prepared in this way was 1-3 X mho. Sodium nitrate (analytical grade) was recrystallized twice from double-distilled water, sodium perchlorate (analytical grade) was recrystallized twice from nbutyl alcohol, and sodium thiocyanate (analytical grade) was recrystallized twice from double-distilled water and twice from ethanol. All the salts were dried in a vacuum oven at 110” and stored over ;\/Ig(C104)2. The conductance measurements were made with a Jones bridge (L & N) with accessories. Correction for polarization effects at the bright platinum electrodes was made by extrapolation to infinite frequency, and all measurements were corrected for the conductance of the solvent.
Densities were determined to an accuracy of 0.02% using a 25-ml pycnometer (Fisher Scientific Company, Weld Type). Viscosity measurements were made with Ostwald viscometers (Cannon Fenske design, Fisher Scientific Co.) which were calibrated with conductivity water and benzene. The stirred diaphragm diffusion cell has been deso it is sufficient to remark on a scribed el~ewherel-~ few salient features. Each half-cell capacity was about 50 ml, while the diaphragm (Gallenkamp, 76 X 14; average pore size 15 p ) had a volume of about 0.5 ml. The stirrers were made of soft iron wire sealed in glass. The changes of density and viscosity of the solutions were sufficiently great to require several changes of the stirrers. The diaphragm was flushed with several liters of degassed water prior to cell filling. The initial concentrations for the solutions in upper and lower compartments of the cell were selected so that differential diffusion coefficients could be obtained directly from the relation --
D
=
1 -1n-
ICt
c1
-
cs
- c4
c2
Here c1 and c3 are the concentrations in the lower compartment at time t = 0 and t = t , respectively, c2 and c4 are the corresponding concentrations in the upper compartment, and IC is the cell constant. To establish the tolerance limits for c1 and c2 in this differential technique, a series of exploratory measurements was required. It was found empirically that concentration differences between the two solutions up to 0.2 mol/l. gave identical diffusion coefficients (within the limits of error) for the (1) R . H. Stokes, J. Amer. Chem. Soc., 7 2 , 763 (1950). (2) G. J. Jans and G. E. Mayer, “Diffusion of Electrolytes: Principles and Practice of the Diaphragm Diffusion Technique,” Research and Development Progress Report No. 196, United States Department of the Interior (1966). (3) R. Mills and L. A. Woolf, “The Diaphragm Cell.” Diffusion Research Unit 67-1, The Australian National University, Canberra (1967).
Volume 74, Number 6 March 19, 1970
G.J. JANZ, B.G.OLIVER, G.It. LAKSHMINARAYANAN, A N D G.E.MAYER
1286
Table I : Equations for the Equivalent Conductances, Diffusion Coefficients, Relative Viscosities, and Densities of Aqueous NaN03, Tu’aClO4, and NaCNS Solutions a t 25’ Standarda deviation
Beat equation
+
A = 83.921 - 8 . 4 6 7 9 ~ 0 39726~’- 18 663 log (c 0.001)
NaNOI
+
I
I
x 10-4 + 1.3761 -t 0.001) 11/90 = 0.9998 + 4.0273 X 10-2c + 2:2289 X 10% 11/11Q = 1.3143 + 3.5343 X 10-8cs D = 1.4320 - 8.0034 X lo-%
0.171
0.1-7.3 M (18)
0.007
0.05-7.2 1M (10)
0.002 0.019 0.0005 0.105,
0.1-4.0 4.0-7.8 0.1-7.8 0.1-9.1
0.007
0.06-12 0 M (10)
0 004 0.017 0.0007 0.253
0.5-4.0 4.0-9.1 0.1-9.1 0.1-9.2
0,010
0.05-9.8 M (13)
0.003
0.1-4.0 M (8)
0.028 0.0004
4.0-10.6 M (6) 0.1-10.6 M (20)
(c2
+ 5.3742 X 10-k - 4.2901 X 10-4c2 8 . 3 9 5 9 ~+ 2.1777 X - 5.7838 + 0.001) + 5.3804 X 1 0 3 - 6.1248 X 1 0 - 8 ~ +2 7.3565 x 1.7635 X 10-4c8 (c + 0.001) 2.8739 X 10-2ln (c + 0:OOl) 9/70 = 1 0148 + 3.2564 X 10-zcz + 1.9846 X 7/vo = 1.1540 + 6.0861 X P = 0,99834 + 7.6913 X 10% - 3.9159 X 10-4ca A = 86.952 - 7 . 4 0 8 6 ~- 4.9473 In (c + 0.001) + 5.9554 x 10-4e~ D = 1.3171 + 0 . 2 0 0 8 1 ~- 3.4266 X 1 0 - 2 ~+ 2 2.8700 X 1.6157 X 10-%a (c2 + 0.001) 0.16349 log (c -+ 0.001) 1 1 h o = 1.0354 + 3.0071 X 10-2c2 + 1.7947 X 10-2 In (c + 0.001) 7/70 = 1.2151 + 5.2020 X 10-8ca + 1.2599 X lOW4eC P = 0.99784 + 3.9762 X 10% - 3.5933 x lo-4c2 P = 0.99844 A = 85.455 In (c D = 1.4040
NaClOl
Concentration range and number of data points
M M M M
(11) (8) (18) (16)
I
’
NaCNS
di(X,-
I
M (8) M (5) M(16)
M (19)
-
a Standard deviation is defined as X,)z/n p , where X,is the experimental value a t a particular concentration, X,the calculated value from the least squares equation a t the same concentration, n the number of experimental data points, p the number of coefficients in the least-squares equation.
same average concentration. I n all subsequent work the maximum concentration difference (0.2 M ) was used in order to aid the accuracy in the ultimate analyses. Initial concentrations for the lower compartment, CI, were calculated by the characteristic cell equation c1
=
c3
+ (c4 - cdf
(2)
+
where f is the cell factor. This is defined as (V” V ) / ( V ’ V ) and can be calculated from the volumes of the diaphragm cell compartments (corrected for stirrer volumes) V’ and V”, and the pore volume of the diaphragm, V . The compartment and diaphragm volumes could be determined by direct weight calibrations with water to an accuracy of hO.001 ml because of the use of l0/20 teflon-lined capillary bore plugs on the cell. The diaphragm cell constant, k , is defined by the expression
+
IC=-A 1
(-V‘+ - ;’,)
where A is the total effective cross-sectional area for the The Journal of Physical Chemistry
pores, and 1, an average length. With prolonged use, the wear of the diaphragm leads to an increase in IC over a period of time. In the present study, this effect was investigated, and t,he variation was found to be related to the cell lifetime, L, (hr) by
A _ -- 2.9694 X lO-5L 1
+ 6.60605
(4)
AIL rather than k is used since the former is characteristic of the diaphragm only. For these periodic calibration experiments, aqueous KC1 data4-e were used in the conventional manner. The compositions of all the solutions used in the diffusion measurements were analyzed conductometrically. The thermostats for the above measurements were controlled at 25.00 h 0.003’. I n Table I are the concentration-dependent equations for the electrical conductance A, viscosity V / ~ O ,diffusion D , and density p ; these were calculated from the (4) R. H.Stokes, J . Amer. Chem. Soc., 7 3 , 3527 (1951). (5) L. S. Gosting, ibid., 72, 4418 (1950). (6) H.9 . Harned and R. L. Nuttall,ibid., 71, 1460 (1949)
PROPERTIES OF NaNOa, NaC104, AND NaCNS
IN
1287
SOLUTION
Table I1 : Equivalent Conductance, Diffusion Coefficients, and Relative Viscosities of Aqueous NaC1, NaNOa, NaC104, and NaCNS Solutions at 26” 0,
_-_-
A, mhos-----
-
-------D
cmPge~-l------,
mol/l.
NaCl
NaNOa
NaC104
NaCNS
NaCl
NaNOs
NaClOd
NaCNS
0.1 0.5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
106.74 93.62 85.76 74.71 65.57 57.23 49.46
...
97.55 86.67 79.54 68.71 59.30 50.49 42.03 33.88 26.12 19.17 14.23
1.437 1.393 1.352 1.272 1.192 1.112 1.032 0.952 0.872
...
97.88 85.26 77.07 64.83 54.50 45.25 36.89 29.42 22.90 17.41 13.06
1.484 1.474 1.483 1.514 1.544 1.584
*..
101.66 85.39 75.84 62.95 53.19 45.17 38.47 32.89 28.34
1.475 1.449 1.452 1.469 1.483 1.493 1.496 1.493 1.485 1.473 1.458
1.474 1.457 1.485 1.545 1.577 1.577 1.552 1.519 1.460 1.410 1.371
...
...
...
*..
... ... ... ...
, ,.
..,
preceding experimental observations7 and with the computer facility at Rensselaer, using double precision Fortran IV programming. The number of experimental data points and the precisions of the leastsquares data analysis are also given for reference. A comparision of these properties as log hq/q0 vs. concentration (on a log scale), and D vs. the square root of concentration, is shown in Figures 1 and 2, respectively, and numerical values a t rounded concentrations are shown in Table 11.
Discussion From the experimental densities and those from reference 8, the apparent molal volumes were calculated. The concentration dependence of &. for the electrolytes can be represented with a precision of 0.3% by equations XaC1 KaN03 NaC104 NaCNS
+ 2.172dF 27.710 + 2.495dF (bv = 42.737 + 2.1042/F = 38.962 + 1.8702/F cy = +v
&C
=
16.364
(5)
(6)
(7) (8)
Thus the order of apparent molal volumes is Clod- > > NO3- > C1-. This trend is the same as that reported by Padovagfor limiting partial molar volumes. The above equations have the same form as those used by Massonlo to represent the apparent molal volumes of various aqueous electrolytes. While this equation is theoretically significant as a limiting law,ll it is empirical when used a t higher concentrations. An aim in the present work was to investigate the changes in the transport properties of sodium salts for which the anions varied from C1- to CNS-. From Table I1 it is evident that the conductance of XaC1 at a fixed concentration is higher than the conductance of the other electrolytes in the series. This correlates with a trend in the apparent molal volumes, although it does not necessarily follow that the higher conductance is solely due to the smaller volume requirements for the C1- ion in this series. The results for NaN03, NaC104,
CKS-
----
~/‘10------------
NaCl
NaNOs
1.010 1.046 1.096 1.219 1.379 1.580 1.858
1.004 1.026 1.062 1.169 1.321 1.518 1.756 2.078 2.527
... ... ... ...
... ...
NaClOi
NaCNS
...
...
1.023 1.047 1.145 1.308 1.554 1.944 2.549 3.459 4.862 7.199
1.031 1.065 1.168 1.326 1.555 1.884 2.390 3.138 4.254 6.028
and NaCYS fall more closely together. This proximity may be accounted for, in part, by cancellation of a number of effects such as ionic volume, viscosity, and ion-pair formation, e.g., NaC104 has a larger apparent molal volume than NaCYS but a smaller relative viscosity. An examination of Figure 1 (log Aq/qo us. log c) gives some indication of the magnitude of the above effects. Figure 2 shows that changing the anion has anoticeable effect on the diffusion coefficient of sodium salts. The diffusion data for the sodium salts of the monatomic anions are uniformly above those of the sodium salts with polyatomic anions. Intuitively this seems to correlate with lower mobilities expected of the polyatomic anions because of lowered symmetry, and larger spatial requirements. However, the driving force for diffusion is the gradient of chemical potential in the solutions, and a more correct representation of the mobility of the ions is gained if the diffusion coefficient is divided by d(1n f.t)/d(ln m), the thermodynamic driving force. When such a procedure is carried out the “corrected” diffusion data give a series of curves of similar forms, and clustered more closely than the corresponding “uncorrected” diffusion data. There is, then, little doubt that the observed disparity between diffusion coefficient curves can be ascribed, in large part, to activity coefficient differences. Samoilov12 has stated that the structure of concentrated solutions resembles the crystal hydrates, if (7) For detailed tables (111-IX) supplementary to this article order Document 00750 from National Auxiliary Publication Service, c/o CCM Information Sciences, Inc., 909 3rd Ave., New York, N. Y., 10022. A copy may be secured by citing the document number and by remitting $1.00 for microfiche or 83.00 for photocopies. Advance payment is required. Make checks or money orders payable to: ASIS-NAPS. (8) International Critical Tables, Vol. 111, p 79, 1926. (9) J. Padova, J. Chem. Phys., 39, 1552 (1963). (10) H. 8 . Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” Reinhold Publishing Corp., New York, N. Y., 1958. (11) B. B. Owen and S. R. Brinkley, Jr., Ann. N . Y . Acad. Sci., 51, 753 (1949). Volume 74, Number 6 March IOt 1970
1288
G. J. JANZ, B. G, OLIVER,G. R. LAKSHMINARAYANAN, AND G. E. MAYER
Y 2.01
1
\
I
and
I
(i)
F(D) = 1
\
+ 0.036m
p,
-
- h’)
(10)
where F(D) is defined by
(11) 1.9
The two parameters, h and h’, are the hydration numbers introduced by Hartley and Crank, and Wishaw and Stokes, and may be gained from a graphical analysis of F ( D ) and F(D)r/so os. m, respectively. The other parameters have their conventional ~ignificance,’~
&
2
< -0
CI,
I
I .9
I
La
C (moles / I) Figure 1. Log Ar/qo us. c (log scale) for aqueous NaC1, NaNOs, NaC104, and NaCNS solutions a t 25’.
such are formed by the solute-solvent pair. Some support for this has been advanced by Mathieu and Lounsbury13 in the studies of the vibrational spectroscopy of aqueous metallic nitrates; the results could be interpreted qualitatively if it was assumed that the ions approached a distribution characteristic of crystal hydrate at high concentrations (ie., near saturation). Similarly, K l ~ t s c h k ohas ~ ~ interpreted the maxima exhibited by specific conductance curves in salt-water systems as clue to a probable transition of solution structure. The current investigation shows that, in addition to specific conductance maxima, the systems studied show a sharp minimum in log h v / v o vs. log c curves (Figure 1) and a definite break a t high concentration in the mobility ratio, Dcorr/A,vs. c curves. The preceding two observations may be additional indicators for transition of solution structure from that of water to that of crystal hydrate. To gain information on the hydration interactions in these solutions, the Hartley-Crank diffusion equationl6 (as extended to electrolytes by Wishaw and StokesI6) has been applied to the diffusion data. The two equations, respectively, may be written
F(0) = 1
+ 0.036m (DI;o,o -- h )
T h e Journal of Physical Chemistru
(9)
2.0
ILO
JC (moles/
3.0
1)
Figure 2. Diffusion coefficient us. the square root of concentration for aqueous NaC1, NaN08, NaC104, and NaCNS solutions a t 25’.
and need not be defined here. The values of h and h’ gained in this manner, and which represent the experimental results with an average deviation of about 1% below 1.0 M , are: NaCl,17 h = 3.5, h’ = 1.1; NaN08, h = 1.4, h’ = -0.3; NaC104,h = 2.8, h’ = 1.3; NaCNS, h = 4.3, h’ = 2.6. The values of the hydration numbers calculated from the viscosity-corrected and (12) 0. Y. Samoilov, “Structure of Aqueous Electrolyte Solutions and the Hydration of Ions,” Translated from Russian by D. J. G. Ives, London, 1965; Consultants Bureau Publishers, New York., N. Y. (13) J. P. .Mathieu and 53, Lounsbury, Discussions Faraday Soc., 9, 196 (1950). (14) M. A. Klotschko, Dokl. Akad. N a u k SSSR, 82, 261 (1952). (15) G. S . Hartley and J. Crank, Trans. Faraday Soc., 45, 801 (1949). (16) B. F. Wishaw and R. H. Stokes, J . Amer. Chem. Soc., 76, 2065 (1954). (17) R. A. Robinson and R. H . Stokes, “Electrolyte Solutions,” 2nd ed, rev, Butterworths and Co. Ltd., London, 1968.
PROPERTIES OF NaNOa, NaC104, AND NaCNS IN SOLUTION the uncorrected Wishaw-Stokes equations (eq 10 and 9, respectively) differ considerably. Because the change of the bulk viscosity resulting from the addition of ions is not necessarily a fair measure of the change in the frictional resistance experienced by the ions, the true hydration number probably lies in between these two ~ a 1 u e s . l ~Hydration numbers calculated from activity datal8 (NaCI, 3.5; NaN03, 0.5; NaC104, 2.1; NaCNS, 2.6) reinforce this viewpoint. The large change in the hydration number with changing anion is somewhat surprising, but can be rationalized on the basis of structure making and breaking effects of the anions. The larger the hydrophobic structure breaking effect of the anion the smaller will be the hydration number of the salt. On this basis, keeping in mind that these hydration numbers were calculated by fitting the observed diffusion data to a semiempirical expression, it is possible to arrange the anions according to their structure-breaking effect: NOa- > C104- > C1- > CNS-. This is to be compared with the sequence advanced from infrared Le., C104- > NOS- > studies by Choppin and Buijs>lB C1- > CNS-. The two are basically in agreement, the sequence being the same with the exception of Clodand NO3-. An evaluation of the semiempiricsl Wishaw-Stokes conductance equation'e
1289
associated while NaCl and NaCNS are essentially unassociated for the concentration range investigated. The free volume-entropy interpretationz5vz6 for concentrated electrolytes leads to an expression for the conductance and fluidity A, 6
=
A exp [ - k / ( N o - N ) ]
(13)
It is found that the present data may be expressed by this equation ( f1%) over the entire concentration range; No is not constant for A and 4 but the values found are, respectively: n'aNO3, NoA = 46, No$ = 29; NaC104, NoA= 32, No" = 19; NaCNS, Non = 23, No4 = 20. The aqueous quasi-lattice mode1z7p28 is essentially one of competing association and hydration equilibria and is similar to the B.E.T. adsorption modelzsfirst advanced by Stokes and Robinson'* in the extension of the Debye-Huckel theory to concentrated solutions. Recent successes in applying such models to activity30 and diffusion31would seem to indicate this area warrants further attention. Acknowledgtnents. This research was supported by the Office of Saline Water, U. S. Department of the Interior, Washington, D. C.
(18) R . H. Stokes and R. A. Robinson, J. Amer. Chem. Soc., 70, 1870 (1948). (19) G. R. Choppin and K. Buijs, J. Chem. Phys., 39, 2042 (1963). (20) A. N. Campbell and W. G. Paterson, Can. J. Chem., 36, 1004 (1958). (21) A. N. Campbell and E. M. Kartzmark, ibid., 33, 887 (1955). (22) G. J. Jane and M. J. Tait, ibid., 45, 1101 (1967). (23) E. Andalaft, R. P. T . Tomkins, and G. J. Jana, Can. J. Chem., 46, 2959 (1968). (24) W. M. Latimer, J. Chem. Phys., 23, 90 (1955). is of interest in view of its moderate success in other (25) C. A. Angell, J. Phys. Chem., 70, 3988 (1966). concentrated aqueous systems.16~z0J1The equation (26) C. A. Angell, J. Chem. Phys., 46, 4673 (1967). represents the conductance of NaC1, NaiY03, NaC104, (27) J. Braunstein, J. Phys. Chem., 71, 3402 (1967). and NaCNS with average deviations of about 0.5% (28) J. Braunstein in "Ionic Interactions: Dilute Solutions to Molten Salts," S. Petrucci, Ed., Academic Press, New York, N. Y., up to concentrations of 3 Mousing the a parameter 1969, Chapter 4. values 5.5, 3.3, 4.1, and 5.7 A, respectively., If the (29) S. Brunauer, P. H. Emmett, and E. Teller, J. Amer. Chem. Soc., 60, 309 (1938). Wishaw-Stokes equation for associated electrolytes is ~ A. N. Campbell and B. G. Oliver, Can. J. Chem., 47, 2671 used together with values for a the p r e d i ~ t e d ~ ~ +(30) (1969). from ion-cavity considerations and crystallographic (31) G. J. Janz, G. R. Lakshminarayanan, and M. P. Klotskin, radii, it is found that NaN03 and NaC104 are partially J . Phys. Chem., 70, 2562 (1966).
Volume 74, Number B
March 19, 1970
