Volume molar fraction

Abstract An approach based on the theory of mixtures with the concept of molar volume fractions and on the basic principles of continuum mechanics and macroscopic thermodynamics is introduced to model soil freezing of solute saturated soil. 

Keywords Soil, salinity, frost phenomenon, molar volume fractions... 

It was thus postulated that the liquid phase mole fraction X3 of the solid solute in the ternary system is proportional to the partial molar volume fraction (PMVF) of the solvent in the binary solution. In other words, the solvent capacity of the C02-diluted solution is due to the solvent s contribution to the molar volume of the solution. This new term, PMVF, defined as [(1 — Xi)v2/v], is thus a characteristic parameter depicting the solvent capacity of the binary (C02-diluted) solvent mixture for the solid solute, and it varies between 0 and 1. Figure 24 shows that the PMVF of the solvent decreases with increasing CO2 mole fraction, as does the solvent capacity for the solid solute (57). The retention of solid molecules in the liquid phase is primarily attributed to the capacity of the partially surrounded solvent molecule to retain its affinity for the solute molecules. In other words, the number of solid molecules that can be accommodated in the vicinity of the solvent molecules in the C02-diluted solution phase is attributed to the relative strength of the clustered solvent molecules, which are only partially available for the solid solute molecules. 

Mukhopadhyay M, Dalvi SV. Solid solubility prediction from partial molar volume fraction of solvent in antisolvent-solvent mixture. Proceedings of Super Green-2002, 1st International S5mposium on Supercritical Fluid Technology for Energy and Environmental Applications, Suwon, Korea, Nov. 3-6, 2002. 

In the general model the state variables are chosen to be the molar volume fractions intrinsic densities a. and strains 6k f-j of the components, and the common temperature T [Kj. The indicator function taking care of the restriction for the molar volume fractions is... 

The molar volume characteristics, V, for petroleum fractions and hydrocarbons can be obtained from the known density at temperature T ... 

V, = molar volume of component i Xj, = volume fraction of component i Xj = mole fraction of component i l = conductivity of the component i in the liquid state A, = conductivity of the mixture in the liquid state... 

An equation algebraically equivalent to Eq. XI-4 results if instead of site adsorption the surface region is regarded as an interfacial solution phase, much as in the treatment in Section III-7C. The condition is now that the (constant) volume of the interfacial solution is i = V + JV2V2, where V and Vi are the molar volumes of the solvent and solute, respectively. If the activities of the two components in the interfacial phase are replaced by the volume fractions, the result is... 

As in osmotic pressure experiments, polymer concentations are usually expressed in mass volume units rather than in the volume fraction units indicated by the Einstein equation. For dilute solutions, however, Eq. (8.100) shows that

partial molar volume of the polymer in solution, and M is the molecular weight of the polymer. Substituting this relationship for (pin Eq. (9.9)gives... 

Xi j = mole fraction of component or / in the liquid mixture V I = liquid molar volume of pure component or / at temperature T, mVkmol... 

If the volume fraction of methanol in the original mixture was (a), then the volume fraction of water would be (1-a). The molar volume of a substance is the ratio of the molecular weight to the density and thus the molar concentration of methanol and... 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

Mixture densities of Uie binary mixtures require a knowledge of volume fraction for each component. The component molar volume is ... 

The volume fractions and mole fractions become identical in ideal gas mixtures at fixed conditions of pressure and temperature. In an isolated, nonreactive system, the molar composition does not vary with temperature. 

In order to draw the property - composition diagram, coordinates are usually chosen so that the ideal system values correspond with the additive law regarding concentration [313]. It is known, for instance, that in an ideal system, molar volume changes additively with the concentration, and is expressed in molar fractions or molar percentages, whereas specific volume changes linearly with the concentration, and is expressed in mass fractions or mass percentages. 

Figure 5.3 shows V and V2 for the (benzene + cyclohexane) system as a function of mole fraction, obtained in this manner.3 Shown on the graph are Fm, i and F, 2, the partial molar volumes (which are the molar volumes) of the pure benzene and pure cyclohexane. The opposite ends of the curves gives Vf and Vf, the partial molar volumes in an infinitely dilute solution. We note that... 

Plot an appropriate volume unit vs. mole fraction of acetic acid. Determine the partial molar volumes of water and acetic acid at X2 = 0, 1, and several intermediate compositions (at least three). Plot V and V2 as a function of. Y2. 

This is done by assuming that the number of segments per molecule is proportional to the molar volume of the molecule (v). Volume fraction in a sol vent/polymer solution is therefore represented by... 

There is an unfortunate consequence of replacing segment fraction by volume fraction. For given composition (weight or mole fraction), volume fraction is temperature dependent because molar volume is temperature dependent. 

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