Molten salts molar volume

In most cases, the formation of complexes in molten salts leads to an increase in the molar volume relative to the additive volume. This phenomenon is usually explained by an increase in bond covalency. Nevertheless, the nature of the initial components should be taken into account when analyzing deviations in property values, as was shown by Markov, Prisyagny and Volkov [314]. In particular, this rule applies absolutely when the system consists of pure ionic components. The presence of initial components with a significant share of covalent bonds leads to an S-shaped isotherm [314]. 

Figure 7. Isotherms of in various binary nitrates (Mi, M2)N03 as a function of molar volume. Mj = Na, A Mj =Li+ 0 Na+, n K, V Rb, 0 Cs, + Ag, x TF. (Reprinted from M. Chemla and I. Okada, Ionic Mobilities of Monovalent Cations in Molten Salt Mixtures, Electrochim. Acta 35 1761-1776, Fig. 7, Copyright 1990 with permission from Elsevier Science.)...

Molar volume of hypothetical molten salt, cm3/mol Contribution of gas, cation, and anion, respectively, to a salting-out coefficient... 

The formation of complex ions is an important problem for the study of the structure and properties of molten salts. Several physicochemical measurements give evidence of the presence of complex ions in melts. The most direct methods are the spectroscopic methods which obtain absorption, vibration and nuclear magnetic resonance spectra. Also, the formation of complex ions can be demonstrated, without establishing the quantitative formula of the complexes, by the variation of various physicochemical properties with the composition. These properties are electrical conductivity, viscosity, molecular refraction, diffusion and thermodynamic properties like molar volume, compressibility, heat of mixing, thermodynamic activity, surface tension. 

The reason for introducing Eqs. (6.58) and (6.61) is that in Eq. (6.56) for the two components equal molar volumes and equal surface areas per molecule were originally assumed. However, these two assumptions are not valid in molten salt mixtures as can be seen from the molar volume data. 

Table 1.10 shows the lattice energies, C/iatE, applicable at zero K, the molar cohesive energies of the molten salts, i.e., the products of the molar volumes Ve... 

Another method for the estimation of the intrinsic volumes of electrolytes, independent of values of the ionic radii, was proposed by Pedersen et al. [53], who employed the molar volume of the molten alkali metal halides, extrapolated to ambient temperatures, as a measure of their intrinsic volumes in aqueous solutions, but the extrapolation is quite long. A variant of this idea is to use the molar volumes of molten hydrated salts, proposed by Marcus [54], where the temperature extrapolation to 25°C is much shorter. It is then necessary to subtract the volume of the water of hydration, which is n times the molar volume of electrostricted water, 15.2 cm mok at 25°C [55], from the extrapolated molar volume of the undercooled molten hydrated salt containing n water molecules per formula unit of the salt. A cogent method, applicable to highly soluble salts, was proposed by Marcus [56]. The volumes considered, applied to aqueous solutions, are intrinsic, so they should be independent of the concentration c and to a certain extent also of the temperature T. The partial molar volume of an electrolyte, V c, T), describes the volume that it actually occupies in the solution and does not include the volume of the water. Therefore, a fairly short extrapolation of the hnear 25°C) from c = 3M to such high concentrations at which all of the solvent is as closely packed as possible (completely electrostricted) is equivalent to considering the electrolyte as an undercooled molten hydrated salt... 

Young and O Connell [140] introduced a characteristic temperature T = 0.4/ p i.e., a temperature that is inversely proportional to the isobaric expansibility p. The temperatures T for molten alkali metal halides, hydroxides and nitrates were listed. For the alkali metal halides T = (1.15 0.04)rm, but different ratios were obtained for the nitrates (1.56 0.11) and the two hydroxides tested (1.99 0.003). With a set of characteristic molar volumes V listed for these salts a universal expression over the range 0.5 < TIT <1.2 was obtained for the reduced molar volumes ... 

The derived cohesive energies at the corresponding temperature l.lTm are shown in Table 3.10. Included also in this table are the cohesive energy densities, ced, at the same temperature, using the molar volumes reported in Sect. 3.3.3 in Tables 3.13 and 3.14. Where no entries for ced are shown in Table 3.10 the reason is lack of density data for the molten salt. 

The constant volume molar heat capacity of molten salts, Cy, is not measured directly but is derived from Cp and requires volumetric data ... 

The molar volumes at 1.1 Tm of uni-univalent molten salts are related to the radii of the ions as... 

Table 3.13 The densities, pig-croT, the expansibilities, ctp/K, and the molar volumes, Wcm moP, of molten univalent metal salts at the corresponding temperatures from [214]...

The fluidity is the reciprocal of the viscosity, 0 = and for molten salts has been related by Marcus [256] to their molar volume V, as both vary with the temperature according to the Hildebrand and Lamoreaux [257] relationship. Fig. 3.6 ... 

The parameters B and Vq resulting from linear plots of 0 of molten salts against V are shown in Table 3.18 too. These parameters are independent of the temperature and the Vq values are in good agreement with those derived by Chhabra and Hunter [253] as seen in the Table. They correspond to the volume of the virtual molten salt that has no free volume, but in which the ions are free to rotate. Such a volume should be close to that of the crystalline salt at the melting point, but there are no accurate data for this quantity for comparison. Bockris and Richards [137] reported values of for alkali metal halides and nitrates, where vq is the incompressible volume per ion. These values for the salts, shown in italics in Table 3.18 are comparable with the Vq values reported there. The Vq values of molten salts are on the average 87 6 % of the molar volumes of the liquid salts at the corresponding temperature of l.lTm (Tables 3.13 and 3.14). 

Young and O Connell [140] presented a corresponding states correlation of alkali metal salt viscosities, from which a relationship with the molar volumes may be derived, which is, however, very much more complicated than Eq. (3.46). Janz et al. [258] subsequently extended this treatment to 1 2 and 2 1 molten salts. The resulting expressions are ... 

Fig. 3.6 The fluidities of some molten salts plotted against their molar volumes over a suitable temperature range, limited to that where the viscosity data are available LiF ( ), KF ( ), CaCl2 (A), Na2S04 (T), and CsNOs ( ) (From Marcus [256] by permission of the publisher (Elsevier))...

The conductance increases with the temperature, so that the minus sign before the activation energy for the conductance should be noted, contrary to the positive values of numerator of the exponent for the viscosity. The equivalent conductance of the molten salt, which is the product of the specific conductance with the molar volume of the molten salt, also follows an Arrhenius-type expression ... 

The conductivity of molten salts has been related to the existence of free volume in the melt [268] and it was argued that the Arrhenius activation energy Ba should be lower than the corresponding one for ion diffusion in the melt (see below), Bd as was in fact found. This would explain why the conductivity does not adhere to the Nemst-Einstein relation A = F D+ + D-)/RT for the diffusion or to Stokes law as mentioned above. The significant structure theory in this case [160] specifies that only the solid-like particles contribute to the conductivity. Their number per unit volume is where Fsd is the molar volume of the solid... 

Campbell AN, Williams DF (1964) The thermodynamics and conductances of molten salts and their mixtures. III. Densities, molar volumes, viscosities, and surface tensions of molten lithium chlorate, with small additions of water, and other substances. Can J Chem 42 1778-1787... 

The volumetric properties density, p, isobaric expansibility, p, and molar volume, V, of molten hydrated salts at the corresponding temperature T = TlTm, taken from [60], are shown in Table 5.5. 

The electrostriction volumes have been found to be proportional to the number of water molecules per formula unit Agi F = (3.3 0.3) for the 21 molten salt hydrates for which there are data, Fig. 5.1. Therefore, the molar volumes F and the densities of molten salt hydrates CpA, H20 at their corresponding... 

A different approach relates the fluidity of RTlLs to their molar volumes over a large temperature range, based on the Hildebrand-Lamoreaux expression [359], in analogy with its use for molten salts (Sect. 3.4) and many other fluids ... 

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