Intrinsic molar volume

Solvatochromic parameters and intrinsic molar volume (Banerjee et al. 1990). 

It is, therefore, not surprising that there exists a definite relationship between Aand the enthalpy of vaporization, Av H, the former constituting a fraction between 0.2 and 0.3 of the latter, as is readily obtained from the data in Tables 3.1 and 3.9. The pressure dependence of the viscosity is also closely related to the free volume of the solvent. The fluidity (O = l/r ) is proportional to the ratio between the free and the occupied volume, the former, as mentioned above, being the difference between the actual molar volume and the intrinsic molar volume (Tables 3.1 and 3. 4) (Hildebrand 1978). In fact, the logarithm of the viscosity of liquids was found (Marcus 1998) to be described well for some 300 liquids by the empirical relationship ... 

RP-HPLC-k correlation, different stationary and mobile phases, Brodsky Ballschmiter 1988) 5.95 (calculated-solvatochromic parameters and intrinsic molar volume Vh Kamlet et al. 1988)... 

AV° — —160 + 12 cm mol is considered to be a consequence of the two contributions (1) the difference in the intrinsic molar volume of three tetramers and two hexamers and (2) the difference in the solvation contribution of these complexes. Since the calculations derived by Connolly s method revealed the possibility of either sign for the solvation effect, it could not be decided conclusively at that point which of the two contributions dominates in producing the remarkably large reaction volume observed. 

The openness of a liquid measures its free volume, which is the difference between its bulk molar volume and its intrinsic molar volume. The latter can be expressed as the van der Waals volume of its molecules per mole. A liquid cannot be compressed by an external pressure to have a lower molar volume. The van der Waals molar volume of water is Vydw = 12.4 cm mol at 25 °C. Another measure of the intrinsic volume of a liquid takes into account the exclusion volume adjacent to a given molecule, where another particle cannot penetrate because the crevices between the peripheral atoms are smaller than any atomic size. This is the McGowan intrinsic volume, which for water is Vx = 16.7 cm mol (Abraham and McGowan 1987). Both of these measures of the intrinsic molar volume of water are considerably smaller than its molar volume at 25 °C, V = 18.07cm moK (Marcus 1998)leaving some free volume. The fractions of free volume according to these two measures are (1 - Kdw/V) = 0.314 and (1 — Vx/10 = 0.076. The former is less relevant for the discussion of solutions, because it does not allow for the exclusion volume. 

A further measure of the sizes of ions, pertaining to ions in solution, is their intrinsic molar volumes, The molar volume of a bare unsolvated ion, 4jrNJ3)r, cannot represent the intrinsic volume of the ion in solution, because of the void spaces between the solvent molecules and the ion and among themselves. Mukerjee [52] proposed for aqueous alkali metal and halide ions at 25°C a factor of A = 1.213, producing ... 

An iterative calculation is required due to the mutual dependence of the field E(j) and the permittivity e (/) in each shell as discussed earlier (Eqs. 2.13 and 2.14). The resulting values for 25°C determined by Marcus [79-81] are shown in Table 2.10, but values for rounded temperatures from 0 to 200°C are also available. Note that discrepancies may exist between the ionic intrinsic molar volumes calculated from Kntr = dec listcd io TaWc 2.8, due to different modes of consideration... 

This theory is traceable in principle to that of McDevit and Long [31], the operative quantity of which is the difference between the intrinsic molar volume, V,.,. and the standard partial molar volume, V , of the electrolyte. According to Ref. 31 ... 

The validity of the simple relationship between viscosity for a liquid at atmospheric pressure and volume, rj = c/(v — w), where v is specific volume, w is a constant similar to the van der Waals b, and c is another constant, was demonstrated (Batschinski 1913) by linear plots of 1/rj versus v obtained for nonassociated liquids. This expression was later modified (Hildebrand 1971) to emphasize the dependence of fluidity on relative expansion from the intrinsic molar volume, Voo, where 1/ = 0... 

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