Molten 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]. 

Okada et al. found that the internal mobilities of LT in molten alkali nitrates are well expressed as a function of molar volume, independent of the kind of the second cation. This finding leads to a general empirical equation ... 

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.)...

Figure 12. Isotherms of M-n compared with in various binary nitrates as a function of molar volume. (Reprinted from I. Okada and P.-H. Chou, Anomalous Behavior of Internal Mobilities for Ag(I) and T1(I) Ions in Molten Nitrates, J. Electrochem. Soc. 144(4) 1333, 1997, Fig. 13. Reproduced by permission of the Electrochemical Society, Inc.)...

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

The Clausius-Clapeyron equation describes the univariant equilibrium between crystal and melt in the P-Tfield. Because molar volumes and molar entropies of molten phases are generally greater than their crystalline counterparts, the two terms and AFfusion both positive and we almost invariably observe an... 

Like heat capacity, the molar volume of chemically complex silicate melts may also be obtained through a linear combination of the molar volumes of molten oxide components—i.e.,... 

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 details of sample preparation, molar volume measurement, and X-ray diffraction analyses have been reported in the preliminary works on molten CeClj and ErCl,. CeClj is known to be hexagonal with a bimolecular unit, in which each Ce atom is surrounded by nine Cl atoms. On the other hand, ErCl, forms a monoclinic crystal, the unit cell of which contains four molecules. The number of the nearest Cl atom around Er atom is six. As shown in Fig. 1, the first peak centered at 0.28 to 0.29nm appeared sharply in the correlation function G(r) for molten CeCl, and the broad peak existed in the range of 0.46 to 0.6nm upon which the shoulder-like peak overlapped in the neighborhood of 0.4nm. According to the ionic radius list by Shannon, the first peak was assignable to the Ce-Cl pair since the ionic radii of Ce (VI) and Cr(VI) were 0.101 and 0.181 nm, respectively, and the... 

The density of the melts of the molten system KF-K2M0O4-B2O3 was measured by Chrenkova et al. (1994). For the concentration dependence of the molar volume in the investigated ternary system at the temperature of 827°C, the following equation was obtained... 

For the partial molar volume of K2NbFy in the infinitely diluted solution in NaF we obtain the value yK2NbFy = 126.02cm. mol This value is again lower than the molar volume of the pure KyNbFy. Remembering the physical reason of the partial molar volume it can be concluded that the small volume contraction upon addition of KyNbFy into molten LiF and NaF indicates the formation of the [NbFg] complex anion in both systems, since its volume would be smaller than the sum of the volumes of F and [NbFy] anions. 

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. 

The densities of molten KCI-YCI3 mixtures of various compositions were reported to show a linear dependence upon temperature, and the positive departure of molar volume from additive values was interpreted in terms of a more open structure in the mixture than in the pure compound. The nature of the interaction between yttrium and potassium chlorides was discussed. 

In the case of molten polymers, oligomers or solvents characterized by highly extended linear backbones, the proposed expression is the same but Ey corresponds to the so-called unit of flow energy, i.e. the energy needed to move the proper segment of the chain in the viscous flow (Van Krevelen, 1976). The same concept is applied also to Fs, which becomes the molar volume of the segment . 

We observe that, for a given polymerization degree, the partial volume is higher in cyclohexane than in benzene. The origin of this difference is not known exactly. It may be related to two different facts (a) the molar volume of cyclohexane is larger than the molar volume of benzene (b) benzene is a better solvent of polystyrene than cyclohexane. Incidentally, we may also note, in connection with these facts, that the partial volume of a chain attains its highest value when it is in the molten state. 

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... 

Shirao K, Fujii Y, Tominaga J et al (2002) Electronic polarizabilities of Sr " " and Ba " " estimated from refractive indexes and molar volumes of molten StCL and BaQ2. J Alloys Comp 339 309-316... 

Vieillard P (1987) A new set of values for Pauling s ionic radii. Acta Cryst B43 513-517 Iwadate Y, Fukushima K (1995) Electronic polarizability of a fluoride ion estimated by refractive indexes and molar volumes of molten eutectic LiF-NaF-KF. 1 Chem Phys 103 6300-6302... 

Fig. 8. Excess molar volume (cm mot ) of the molten Fig. 9. Excess molar volume (cm mot ) of the molten system KF-KCl KBF.t at the temperature of system KF-KCl-K2TiFfi at the temperature of hoOK. HOOK.

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... 

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