Perturbation Theory of the Heats of Mixing of Fused Salts

A theory of the thermodynamic properties of molten salts including the effects of short-range attractive interactions has been developed. The analysis builds upon the work of Reiss, Katz, and Kleppa who showed that many of the thermodynamic properties of molten salt mixtures could be understood in terms of a model ionic melt consisting of rigid impenetrable ions interacting with a long-range Coulomb potential. The RKK theory is inadequate for the description of recent experimental measurements of the heats of mixing of salts whose short-range attractive interactions are expected to be significant. Most of the molten salt data of Kleppa et al. have been fitted to the following equation for the heats of mixing: ΔHm=x1,x2(a+bx1)δ122+x1x2c, δ12=(λ2−λ1)/λ1,λ2,with xi the mole fraction of the ith component, a<0, b<0, and c>0. The major contribution to a arises from Coulomb interactions, and is well accounted for by the RKK analysis which, however, does not completely account for b and gives c=0. Using a perturbation analysis it is shown herein that the term c and part of b arise from short-range interactions between ions; the theoretical relationship deduced reproduces the observed composition dependence of the heat of mixing shown above. The qualitative deductions which can be made from the formal analysis are all in agreement with the available experimental data. It is also shown that there is a short-range potential contribution to the leading term (ax1x2) and explicit relationships for the coefficients a and b are obtained. A method of using the theorem of corresponding states to obtain information about the short-range coupling is suggested.