Coefficients, molar virial

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)... 

TABLE 1.3-1 Expressions for the Partial Molar Virial Coefficients B, and... 

The ELBT program on the CD-ROM permits the correlation of isothermal VLE data of homogeneous binary systems with equations derived from the Redlich-Kister expansion. Vapor-phase imperfection and the variation of the Gibbs energy of the pure liquid components are accounted for through the second molar virial coefficients By and the molar volumes V° under saturation pressures (Chap. 3.5.5). The correlated total vapor pressure P and... 

The tables in this volume refer to four physical quantities P - pressure, T - temperature, xj - mole fraction of component 1 in liquid phase, and y - mole fraction of component 1 in vapor phase. The pure component liquid molar volumes F, and the second molar virial coefficients By are auxiliary quantities used in calculating (f - the... 

The pure component vapor pressures, PI and P2, are displayed if present in the SELF file, i.e. if reported in the original publication Otherwise they must be entered to proceed with the correlation. The values of the second molar virial coefficients, Bll, B2 2, and B12, and of the liquid molar volumes, VI and V2, are not mandatory. The units of all the auxiliary values may be selected in advance (Fig. 3.11). 

Vapor pressure of pure component 1 Vapor pressure of pure component 2 Second molar virial coefficient of component Second molar virial coefficient of component Second molar cross virial coefficient Molar volume of pure liquid component 1 Molar volume of pure liquid component 2... 

Extensive tables and equations are given in ref. 1 for viscosity, surface tension, thermal conductivity, molar density, vapor pressure, and second virial coefficient as functions of temperature. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

D 4th virial coefficient. cmVmoP cmVmoP V Molar or unit-mass volume mVmol ttVlb mol... 

V is the molar volume of the solvent and pp the density of the polymer. For polydisperse polymers A2 is a more complex average, which shall not be discussed here in detail [7]. For good solvents and high concentrations, the influence of the 3rd virial coefficient A3 cannot be ignored, and n/c versus c sometimes does not lead to a linear plot. In these cases, a linearization can frequently be obtained with the approximation A3 = A (M)n/A by plotting [12,13]... 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

Note that the constants in Equation (2.4) are distinguishable from those in Equation (2.3) because they lack the prime symbol. For both Equations (2.3) and (2.4), the terms in brackets represents the molar compressibility Z. Table 2.5 lists a few virial coefficients. 

B and C are second and third virial coefficients. The partial molar free energy of the vapor phase neglecting higher order terms is thus... 

A more careful analysis taking into account vapor nonideality through the second virial coefficient and the isotope effect on condensed phase molar volume yields Equation 5.16... 

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