Molar volume, calculation

The elution volumes for n-hydrocarbons show a straight line relationship vs the logarithms of their molar volumes. Molar volumes, calculated from the densities of compounds other than n-hydrocarbons, must be modified to have the elution volumes of these compounds conform to the same calibration line (elution volume vs log molar volume) as that for the n-hydrocarbons. W. W. Schulz (1 ) related the elution behavior of branched alkanes in the range of Cy-C] ] to the average numbers of gauche arrangements (Zg) which the molecule can assume. 

It has been shown 8) that VT, the molar volume calculated from Traube s rule 4), VM, the molar volume of Exner 3), and the parachor,5) P all give significant correlation with the equation... 

Fig. 15-1. Vatues of molar volume calculated with a two-constant equation of state.

Many modifications of the original Redlich/Kwohg equation that appear in the literature are intended for special-purpose applications. The SRJt equation, developed for vapor/liquid equilibrium calculations, is designed specifically to yield reasonable vapor pressures for pure fluids. Thus, there is no assurance that molar volumes calculated by the SRK equation are more accurate than values given by the original Redlich/Kwong equation. 

Figure 48 shows a plot of molar volumes calculated according to the relation V = where M is the molecular weight of the oxide and n its molar fraction. 

Table 5.2. "Experimental" values [2] of the solubility parameter (8) deduced indirectly from various types of experiments, and predicted values ( i and 82, respectively) computed by combining ECOhl and Ec0ii2 with molar volumes calculated by using equations 3.13 and 3.14. The units for the solubility parameter are (J/cc)0-5. 

Figure 2 Electrostatic and neutral contributions to the standard molar Gibbs energy of transfer of univalent cations from water to solvents having two different molar volumes, calculated from the single-layer electrostatic model. Calculations are valid for 25 C and assume a hypothetical constant solvent dielectric constant equal to 10. Solid lines correspond to the electrostatic term [from Eqs. (5)...

Physical and Thermodynamic Properties of Pure Chemicals Data Compilation This comprehensive data base is designed primarily for the chemical engineer and, consequently, includes many thermodynamic quantities such as enthalpies and free energies of formation, standard entropies, and so on. Molar volume calculated from density, and van der Waal s surface, and volume are also cited. Supplementary updates are published periodically. 

Figure 6.3. Equilibrium swelling vs. plasticizer molar volume calculated from Eq. [6.4] at =10 mol/m and Huggins parameter, 0.5 (2), and 0.8 (3).

Here, is the number density of solvent sites a. Unfortunately, HFEs calculated using the GF free energy functional have only a qualitative agreement with experiment. The error in hydration free energies calculated by the GF functional in 3D RISM is strongly correlated with the partial molar volume calculated by 3D RISM [67, 94, 104]. The 3D RISM/UC free energy functional developed from this observation is a linear combination of the 07 , the dimensionless partial molar contribution, pV, and a bias correction, b (intercept) [104] ... 

Molar volume, calculated from the molecular weight (MW) and the liquid density at the boiling point. 

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... 

The x-axis, molar volume, is a logarithmic scale. For reference, at 1 atm the vapor/liquid region spans from 0.09 liter/mol (liquid molar volume) to 22.4 liter/mol (vapor molar volume). A point within the two-phase region corresponds to the average molar volume, calculated as... 

Table 7.19 - The Behaviour of Standard Compounds in Gel Permeation Chromatography Molar Volumes Calculated... 

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