J. Phys. Chem. 1981, 85, 3151-3152
3151
Viscosities of Binary Molten Nitrate Mixtures J. D. Pandey’ and Alec D. M. David Department of Chemlstty, University of Alkhabad, Al&habad-.?ll 002, Ind& (Received:&nary 21, 1981; In Flnal Form: June 3, 1981)
The viscosities and excess viscosities of binary molten nitrate mixtures have been evaluated with respect to both temperature and composition. The theoretical values were obtained by using AG values from Flory’s statistical theory. The agreement between experimental and theoretical values was found to be satisfactory.
Introduction For a number of years, systems of molten salts have been a subject of extensive research. Their behavior in various media, thermodynamic properties, and industrial applications have held the interest of many workers around the globe. One of the many liquid-state treatments applied to the study of molten salts is Flory’s statistical theory., Formerly it was applied to study the surface tension of pure molten salts,2but it appears from the literature that application of the theory to study the viscous flow in molten salts remains an unexplored possibility. In the present work the viscosities of binary molten nitrate mixtures were studied and Flory’s theory was applied to calculate the free energy of mixing the reduced and characteristicparameters of both pure and binary systems. Recent theories3* have emphasized the importance of the free-volume difference between the two components constituting the mixtures. The diverse contribution arising from the free-volume difference may be understood in the following way. The more volatile compound is condensed in the presence of the denser one or its free volume is diminished. As a result, there is a negative contribution to the heats of mixing and the entropy of mixing. It would be interesting to investigate whether measurements of viscosities combined with free-volume theories could give some information on the importance of free-volume terms in viscosities of mixtures. Bloomfield and Dewan7have used the calculated free energy of mixing as an approximation to the free energy of activation. They have shown on systems with relatively small differences in free volume that there is a good agreement between calculated and experimental excess viscosities. It have seemed worthwhile to us to study the viscosity of binary molten nitrate mixtures mainly because of the symmetrical shape of the ions and because of a small free-volume difference between the components constituting the mixtures, both factors being essential to describe the good agreement between the calculated and experimental values of viscosities. The temperature-dependant values of density from which the thermal expansion coefficient values were evaluated, the isothermal compressibility values, and the experimental values of viscosity were obtained from the literature.&1° (1) (a) Flory, P. J. J. Am. Chem. SOC. 1965, 87, 1833. (b) Abe, A,; Flory, P. J. Ibid. 1965,87, 1838. (2) Pandey, J. D.; Chaturvedi, B. R.; Pandey, R. P. J. Phys. Chem., submitted. (3) Prigogine, I.; Bellemans, A.; Mathot, V. “The Molecular Theory of Solution”; North-Holland Publishing Co.: Amsterdam and Interscience: New York, 1957. (4) Patterson, D.; Delmas, G. Discuss. Faraday SOC. 1970, 49, 98. (6) Patterson, D.; Delmas, G.; Somcysky, T. J.Polym. Sci. 1962,57, 79. (6) Flory, P. J.; Orwoll, R. A,; Vrij, V. A. J . Am. Chem. SOC. 1964,86, 3515. (7) Bloomfield, V.; Dewan, R. J. Phys. Chem. 1971, 75, 3113.
0022-365418112085-3151$01.25/0
Theoretical Section Theories relate the viscosities of liquids to either the activation energy required for the molecule to overcome the attractive forces or the probability of an existing empty site near a molecule. Macedo and Litowitz’l advocate a combination of the above-mentionedpossibilities. Similar assumptions are made for binary mixtures. Furthermore, a bridge can be formed to the thermodynamic function of mixing by assuming a simple relationship between solution activation energy AG’, the pureliquid activation energies AG*, and AG*2, and the excess free energy of mixing AGMM.12 AG = xlAG*l + X ~ A G -’ ~AGM (1) For pure components i the viscosities are related to the solution activation energy AG*i and may be expressed as qi = A exp[AGli/RT + (Vi - l)-l] (2) where 6 is the reduced volume of the pure component i. When logs are taken, eq 2 may be expressed as In qi = In A + AGli/RT + (Vi - l)-l (3) Equation 3 may be applied to the solution and the pure components to obtain excess viscosity which may be expressed as A In q = In qmir - (xl In q1 + x 2 In 72) (4) If eq 1 and 2 are applied to eq 4, the activation energies are eliminated and A In q is related to the free energy of mixing by A h q = -AGM/RT
1 X1 x2 +6-1 - 6,-1 - v2-1 (5)
From eq 4 and 5 In
qmix =
-AGM/RT
1 X1 x2 +- -- -+ v - 1 v,-1 v2-1
X I In vl + x2 In q2 (6) where 6 is the reduced volume of the mixture and q1 and q2 are the viscosities of the pure components 1 and 2, respectively. The reduced and characteristic parameters 6 and V*, respectively, are calculated according to Flory’s theory. For the pure components Vi is obtained from the values of the thermal expansion coefficient (ai):
(7)
v* =
v/v
(8)
(8) Murgulescu, I. G.; Zuca, S. Electrochim. Acta 1966,11, 1381. (9) Murgulescu, I. G.; Zuca, S. Electrochim. Acta 1969,14, 519. London, Ser. A. 1967, (10) Bockris, J.; Richards, N. E. Proc. R. SOC. 241,44. (11) Macedo, P. B.; Litowitz, T. A. J. Chem. Phys. 1965, 31, 1164. (12) Jambon, C.; Delmas, G. Can. J. Chem. 1977,55, 1360.
0 1981 American Chemical Society
5152
TABLE 11: Calculated and Experimental Values of Viscosity and Excess Viscosity for (Li-K)NO, System
TABLE I: Calculated and Experimental Values of Viscosity and Excess Vtscosity for (Li-Na)NO, System 10-'qx- 10-'qx-
lo-%,-
Aq-
Aq-
(calcd), (exptl), (calcd), (exptl), P P P P
T,K
3c
623
0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2
2.43 2.29 2.00 1.11 2.03 1.93 1.69 1.77
2.83 2.65 2.49 2.43 2.51 2.36 2.2 2.16
673
0.8 0.6 0.4 0.2
1.83 1.77 1.57 1.67
2.17 2.03 1.93 1.89
698
0.8 0.6 0.4 0.2
1.69 1.65 1.56 1.53
1.99 1.86 1.77 1.71
648
-
648
0.799 0.797 0.73 0.797
0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2
1.87 1.79 1.78 1.99 1.68 1.56 1.52 1.70
2.34 2.21 2.12 2.15 2.12 1.96 1.89 1.93
0.72 0.70 0.72 0.82 0.74 0.72 0.70 0.80
0.90 0.875 0.85 0.89 0.92 0.87 0.87 0.91
0.81 0.83 0.77 0.85 0.82 0.85 0.77 0.86
0.96 0.94 0.93 0.96 0.97 0.95 0.95 0.96
698
0.8 0.6 0.4 0.2
1.57 1.44 1.39 1.56
1.94 1.80 1.75 1.76
0.74 0.71 0.70 0.82
0.93 0.89 0.89 0.92
673
TABLE 111: Calculated and Experimental Values of Viscosity and Excess Viscosity for (Na-K)NO, System 10-'n..-
where pni, is the isothermal compressibilitiesof component i. The value of the free energy of mixing is obtained as follows: G-I, = .,P1*Vl*[ + 3p1ln p1v3- 1 +
(41
(+ +) (i+)+ 3p2ln (m)] p2w1
+
~l~l*vl*ezxlz (11) v1
where 8 is the site fraction and Xlz is the interaction parameter. The reduced volume of the mixture was obtained from the following expression: = V,/(X,*V,* XZV,*) (12)
v
An
0.96 0.94 0.93 0.90 0.99 0.97 0.94 0.97
0.82 0.82 0.75 0.83
-
An-
x
The characteristic pressure is evaluated from the following expression: pi* = (ai/PT(i))TP (10)
[.,
lo%,-
(calcd3, (expto, (calcd), (exptl), P P P P
T, K
The recuced temperature is obtained from values of reduced V:
1.1
Pandey and David
The Journal of Physical Chemlstty, Vol. 85, No. 27, lQ8l
+
where V, is the molar volume of the mixture.
Results and Discussion The experimental viscosity values which were used for comparison with the calculated values were determined by Sternberg and Zuca8vBin the temperature range 300-500 "C by the improved damped oscillating sphere method. The damping oscillations were automatically recorded by means of a photodyne which resulted in a higher precision of the logarithmic decrement (
