An Empirical Corresponding States Correlation of Densities and Transport Properties of 1-1 Alkali Metal Molten Salts Robert E. Young and John P. O'Connelll Department of Chemical Engineering, University of Florida, Gainesville, Flu. 31601
The temperature dependences of density, viscosity, thermal conductivity, ionic diffusivity, and specific conductivity of 1-1 alkali metal molten salts have been accurately correlated with corresponding states using reducing parameters from a convenient thermodynamic state. For systems where no data are available, approximate relations are given for the characteristic parameters. Rules for correlating properties of mixtures are also discussed.
T h e transport properties of fused salts are important physical design variables in many high-temperature thermal and chemical processes. Unfortunately, in addition to large experimental uncertainties, relatively little success has been achieved in predicting these properties for systems and conditions where data are not available, as discussed by Klemm (1964), Sundheim (1964), and White and Davis (1967). This paper describes a correlation of the temperature dependence of density, diffusivity, viscosity, thermal conductivity, and electrical conductivity of molten alkali metal halides, nitrates, and hydroxides, based on a phenomenological "law of corresponding states," which originated in the work done by White and Davis (1967)) Helfand and Rice (1960)) and McLaughlin (1961). The properties are reduced by characteristic values a t a convenient corresponding state described by Renon, et al. (1967), and the empirically determined reduced temperature dependence of reduced properties provides good agreement for all data available for molten alkali metal halides, nitrates, and hydroxides. Relationships between characteristic properties are developed for predictive use when no data are available. The extension of these results to mixed molten salts is also considered.
i, =
For systems a t the same number density interacting with conformable intermolecular potentials (characterized by a single energy parameter and a function of reduced distance), Donth (1966) has shown that the Helmholtz free energy of all substances can be expressed by an equation of state of the form
(4) Any convenient experimental value of f(p) may be chosen with p assigned as unity a t that temperature. Choosing f (f') to be 0.4 a t p = 1 in order to be within the liquid range of all salts considered, the values of T* shown in Table I were obtained and the comparison of data with eq 3 is shown in Figure 1. The triple point was explicitly avoided as the corresponding point since Guggenheim (1945) among others has indicated that the potentials are not likely to be conformable a t this state. I n fact, as Table I shows, T,/T* is not constant. However, as Figure 1 shows, the densities do follow the same reduced plot to a striking degree. (The data were taken from Janz, et al. (1968).) The line is !yell described by the equation
A(v/v*,T / T * ) p*v*where P*, v*, and T* are related to the potential parameters. This leads to a reduced equation of state of the form =
i,(T/T*, PIP*)
(2)
At low pressures, the pressure dependence of the density of saturated molten salts can be ignored and the equation is given in reduced variables as 1
To whom correspondence should be sent.
418
0.7458
+ 0.1084p + 0.1458p'
(5)
As a consequence of the above success, this phenomenological corresponding states theory was extended to transport properties such as viscosity, thermal conductivity, diffusivity, and specific electrical conductivity. The assumption was that a form like eq 3 is valid for reduced transport properties as well as thermodynamic properties. Data Treatment for 1-1 Molten Salts
A __-
U/V*
(3)
where ir = v/v* and p = T / T * . Under these conditions, then, the product of temperature and experimental expansivity is a universal function of reduced temperature.
i, =
Corresponding States Formulation
6(T)
Ind. Eng. Chem. Fundam., Vol. 10, No. 3, 1971
Since the available transport property data of many salts covers a limited temperature range, it was necessary to piece the curves together for data available in ranges of p from 0.9 to 1.0, 0.8 to 0.9, etc., to cover the entire range 0.5 to 1.2. By this smoothing process, the characteristic transport properties for all salts shown in Table I were obtained from data in Janz, et al. (1968), Zuca and Ionescu-Vasu (1967), Zuca and Oltcanu (1968), Lucks and Deem (1956), AIcDonald and Davis (1970)) Nurgulescu and Zuca (1965, 1966), and Klemm (1964). Figures 2-5 show the results. The equations describing the reduced curves are
Table 1. Empirically Determined Characteristic Parameters for 1-1 Molten Salts V*, XI+*, 10-5 D-*, 10-5 T*,
Salt
LiF NaF KF CsF LiCl NaCl KC1 RbCl CSCl LiBr KaBr KBr RbBr CsBr LiI NaI KI RbI CsI LiKo3 NaN03 KNOi RbN03 CSN03 XaOH KOH
rm/TY 0.812 0.925 0.976 0.873 0.713 0.957 1.003 0.985 0.911 0,624 0.922 0.991 0.962 0.919 0.621 0.855 0.961 0.929 0.873 0.508 0,642 0,673 0.662 0.775 0.503 0.504
crn3/mole
O K
1377 1355 1157 1094 1239 1121 1040 1003 1008 1319 1110 1017 991 989 1162 1093 997 983 1024 1038 908 906 890 886 1175 1256
15.41 22.14 30.70 43.43 31.47 38.17 48.73 54,10 62.46 39.47 45.37 56.15 61.78 70.13 49,24 57.88 68.97 75.16 85.78 46.23 51.02 61,lO 67.59 75.35 26.79 38.65
.
?Icp *,
...
... ... ... 0.639 1.183 1.180 1.289 1.022 0.477 1,132 1.191 1.384
... 0.669 0.985 1.469 1.204 1.283 0.686 0.839 0.927 1.178 1.287 0.526 0.314
17
=
+ 2.17/T
-2.11
- 0.06p8 0.5
