1838
G. BERTOZZI AND G. SOLDANI
Surface Tension of Molten Salts: Solutions of the Alkaline Earth Halides in the Alkali Halides
by G. Bertozzi and G. Soldani Chemistry Department, High Temperature Chemistry, Euratom, C.C.R., I s p r a , Italy (Received November 22, 1965)
Surface tension isotherms a t 850” are reported as a function of the composition for 12 binary systems of alkali metal halides with alkali earth metal halides. Deviations from linearity of the isotherms are shown to be proportional to the size-charge parameter [(r++/2 - r+)/(di &)I2.
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Introduction I n previous papers,1,2 we have reported measurements of the surface tension of binary systems of uniunivalent molten salts and the shape of the surface tension isotherms as a function of the composition of the mixture was considered. Although in general this property is not a linear function of the composition (not even in ideal mixtures) , nevertheless we were led to consider as significant the deviations from linearity, because our treatment refers to deviations from linearity of the coulombic energy of an array of mixed ions, as is shown later. Moreover, the deviations from linearity of the ideal surface tension isotherms (as calculated from Guggenheim’s equation) are in general negligible in comparison with the observed effect. Finally, the Guggenheim treatment for ideal mixtures3 requires that the molecular surface areas of the two components be equal, which condition is not fulfilled in our case. The deviations of the isotherms from linearity were shown to be related to the difference of the ionic radii of the two cations, if the anion is common. I n the case of alkali metal salts, the simple relationship A j = -KD
radii of the cation and the anion (the Goldschmidt values4were used). If the two salts have the same anion, the difference dl - d2 is equal to rl - r2 (rl and r2 being the cation radii), so that the parameter D can be written
D = [(ri
- 4/(& + ddI2
(3)
The choice of this parameter relies upon a calculation initially proposed by FOrlandj5s6in which it is shown that the electrostatic energy associated to an ion triplet A+B-C+ is not a linear function of the energies of the triplets A+B-A+ (pure salt A+B-) and C+B-C+ (pure salt C+B-). A negative deviation takes place, due to the change of the repulsion of the cations
(4)
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Since ( l / d l ) (l/d2) is nearly constant in comparison with D , eq 4 has the form A€
=
(3
-KID
I n the present work, our investigation is extended to mixtures of molten salts of alkali metals with salts of alkaline earth metals in order to notice the effect on the
(1) ~~
was shown to hold, where A j is the maximum deviation of the surface tension isotherm from linearity, and
D
=
[(di - dz)/(di
+ &)I2
(2)
dl and dz are the cation-anion distances for salts 1 and 2, respectively, and were calculated as the sum of the T h s Journal of Physical Chemistry
(1) G. Bertozzi and G. Sternheim, J . P h ~ s Chem., . 68, 2908 (1964). (2) G. Bertosai, ibid., 69, 2606 (1965).
(3) E. A. Guggenheim, “Mixtures,” Oxford University Press, London, 1952. (4) C. J. Smithells, “Metals Reference Book,” Butterworth and Co. Ltd., London, 1962, Table 29. (5) T. Forland, J . Phys. Chem., 59, 152 (1955). (6) T. Forland, Norge Tek. Vitenskapsakad-Ser., 2, No. 4 (1957).
SURFACE TENSION OF MOLTEN SALTS
1839
surface tension isotherms of mixing cations with different charges. The aim is to derive experimentally the modified form of the parameter D, which should be a function of charge as well as of ionic size.
1
A ,'her
Experimental Details and Results The Wilhelmy slide method previously described' was again used; the results were reproducible within 0.5%. The surface tension of the following binary systems was measured in a range of about 100" above the melting point: (a) barium chloride alkali metal chlorides; (b) barium bromide alkali metal bromides; (c) strontium chloride alkali metal chlorides. The surface tension of all mixtures always shows a linear dependence on temperature, with a temperature coefficient of 0.06-0.08 dyne/cm deg. For each system the surface tension isotherms as a function of the molar composition at 850" are reported in Figures 1-3. The surface tensions of BaC& and SrClz were calculated at 850" by extrapolating below the melting point.
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a
0
w
7s HdrK
100
e
Figure 2. Surface tension isotherms at 850" for the systems BaBr2 alkali bromides.
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Discussion We have already pointed out that the shape of the surface tension isotherms does not depend on the difference between the surface tension of the two pure components.' This statement is again confirmed in the present work. It is apparent"from Figures 1-3 that the surface tension isotherms of the systems
1
4T
Figure 3. Surface tension isotherms a t 850" for the systems SrC12 alkali chlorides.
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I 0
I
I
2s
50
1
1
75 Hd.W
Figure 1. Surface tension isotherms a t 850" for the systems BaClz alkali chlorides.
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I
m
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BaClz NaCI, BaBrz NaBr, and SrC1, NaCl deviate only slightly from linearity, although the surface tension of the alkaline earth metal halides is 50% higher than that of the corresponding sodium salts. It seems reasonable to suppose that, in the case of mixtures of molten salts with common anion, the shape Volume 70,Number 6 June 1968
1840
G. BERTOZZI AND G. SOLDANI
of the surface tension isotherms (ie., their deviations from linearity) is essentially a function of the difference in size and charge of the two cations. Kleppa and Hersch7>*found the following empirical expression for the heats of solution of calcium nitrate in the alkali nitrates AH
=
A - B[
(?- r+)/($
+ dz)]’
(6)
where r++ and r+ are the ionic radii of the divalent and monovalent cation, respectively. The parameter which appears in eq 6 is clearly a “size-charge parameter,” as differences in size and charge of the ions are likewise taken into account; it can be generalized as
where rl and r2 are the radii of the cations carrying charges z1 and 21, respectively. When X I = z2 = 1, eq 7 reduces to (3). Thus, we were led to investigate our surface tension isotherms by relat’ing the deviations from linearity to a parameter similar to that of eq 7 ; this corresponds to the assumption that the divalent cation having radius r++ can be considered as a monovalent one, the radius of which is r + + / 2 . I n such a manner, the (‘size-chargeparameter” becomes
where dl
=
d2 = r+
(r++/2)
+ r-
+ r- and
(r- being the anionic radius)
The Journal of Physical Chembtry
D -
Figure 4. Maximum deviations of surface tension isotherms from linearity as a function of the parameter D of eq 8: a, BaCh alkali chlorides; A, BrtBrz alkali bromides; €3,SrCh alkali chlorides.
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I n Figure 4 the maximum deviations of the surface tension isotherms from linearity are plotted against the parameter D, as written in eq 8. It is apparent that all three groups of systems show a linear dependence on this parameter. The curves have similar slopes. However, the straight lines do not pass through the origin, so that the relationship between A j and the size-charge parameter is expressed by Aj = A
- KD
(9)
The term A expresses the deviation from linearity which would be expected for any mixture where the radius of the divalent cation is exactly twice that of the monovalent one. (7) 0. J. Kleppa and L. S. Hersch, Discitssions Faraday SOC.,32, 99 (1961). (8) 0. J. Kleppa, J. Phys. Chem., 66, 1668 (1962).
