Molar volumes, polarizability

The solvent triangle classification method of Snyder Is the most cosDBon approach to solvent characterization used by chromatographers (510,517). The solvent polarity index, P, and solvent selectivity factors, X), which characterize the relative importemce of orientation and proton donor/acceptor interactions to the total polarity, were based on Rohrscbneider s compilation of experimental gas-liquid distribution constants for a number of test solutes in 75 common, volatile solvents. Snyder chose the solutes nitromethane, ethanol and dloxane as probes for a solvent s capacity for orientation, proton acceptor and proton donor capacity, respectively. The influence of solute molecular size, solute/solvent dispersion interactions, and solute/solvent induction interactions as a result of solvent polarizability were subtracted from the experimental distribution constants first multiplying the experimental distribution constant by the solvent molar volume and thm referencing this quantity to the value calculated for a hypothetical n-alkane with a molar volume identical to the test solute. Each value was then corrected empirically to give a value of zero for the polar distribution constant of the test solutes for saturated hydrocarbon solvents. These residual, values were supposed to arise from inductive and... 

While Onsager s formula has been widely used, there have also been numerous efforts to improve and generalize it. An obvious matter for concern is the cavity. The results are very sensitive to its size, since Eqs. (33) and (35) contain the radius raised to the third power. Within the spherical approximation, the radius can be obtained from the molar volume, as determined by some empirical means, for example from the density, the molar refraction, polarizability, gas viscosity, etc.90 However the volumes obtained by such methods can differ considerably. The shape of the cavity is also an important issue. Ideally, it should be that of the molecule, and the latter should completely fill the cavity. Even if the second condition is not satisfied, as by a point dipole, at least the shape of the cavity should be more realistic most molecules are not well represented by spheres. There was accordingly, already some time ago, considerable interest in progressing to more suitable cavities, such as spheroids91 92 and ellipsoids,93 using appropriate coordinate systems. Such shapes... 

Isotope Effects on Dipole Moments, Polarizability, NMR Shielding, and Molar Volume... 

Abstract Although the electronic structure and the electrical properties of molecules in first approximation are independent of isotope substitution, small differences do exist. These are usually due to the isotopic differences which occur on vibrational averaging. Vibrational amplitude effects are important when considering isotope effects on dipole moments, polarizability, NMR chemical shifts, molar volumes, and fine structure in electron spin resonance, all properties which must be averaged over vibrational motion. 

Using Equation 12.12 one obtains (AA/A — Av /v 2) = (Aao/ao). We see that precise refractive index differences measured over a reasonable range of wavelengths allow the recovery of the polarizability isotope effect (i.e. the isotope effect on the electric field induced dipole moment), provided the molar volume and its isotope effect are available. 

Van Hook, W. A. and Wolfsberg, M., Comments on H/D isotope effects on polarizabilities. Correlation with virial coefficient, molar volume and electronic second moment isotope effects. Z Naturforsch. 49A, 563 (1994)... 

Abraham et at. [2], [3], [4] Solubility, excess molar refraction, polarizability, hydrogen-bond acidity/basicity, and McGowan volume... 

The polarizability is related to the molar volume, hence, to the third power of the linear dimension of the solute or the solvent. Hence, the product of the polarizabilities depends on the sixth power of the distance between the centers of the interacting molecules. Consequently, these tendencies balance each other. For large molecules (e.g., metal chelates, liquid hydrocarbons), it is bet-... 

A number of useful properties of the Group 1 elements (alkali metals) are given in Table 8. They include ionization potentials and electron affinities Pauling, Allred-Rochow and Allen electronegativities ionic, covalent and van der Waals radii v steric parameters and polarizabilities. It should be noted that the ionic radii, ri, are a linear function of the molar volumes, Vm, and the a values. If they are used as parameters, they cannot distinguish between polarizability and ionic size. 

Dielectric polarization is the polarized condition in a dielectric resulting from an applied AC or DC field. The polarizability is the electric dipole moment per unit volume induced by an applied field or unit effective intensity. The molar polarizability is a measure of the polarizability per molar volume thus it is related to the polarizability of the individual molecules or polymer repeat unit. 

Molar volume and those quantities linearly related to it are proportional to polarizability. 

Polak and Sundahl used the Clausius-Mossoti equation to combine molar volume and polarizability to obtain values of dielectric constant. 

The refractive index, nD, defined as the ratio of light speed at the sodium D-line in a vacuum to that in the medium, is used in obtaining the polarizability, a, of solvent molecules. The relationship between a and nD is given by a = (3Vm/ 4 rNA)( D-l)/(wD + 2), where NA is the Avogadro constant and Vm is the molar volume.4 Solvent molecules with high a-values tend to interact easily with one another or with other polarizable solute particles by dispersion forces.5 ... 

Although it is possible to correlate solute solubility to different physical properties, such as molar volume, polarity, polarizability, and chain length, the most frequently used property is the... 

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