Volume change of mixing

For the volume change of mixing and the enthalpy change (heat) of mixing, which are direcdy measurable, AV = and AH =. ... 

In the original equation of van Laar, the effective molar volume was assumed to be independent of composition this assumption implies zero volume-change of mixing at constant temperature and pressure. While this assumption is a good one for solutions of ordinary liquids at low pressures, it is poor for high-pressure solutions of gases in liquids which expand (dilate) sharply as the critical composition is approached. The dilated van Laar model therefore assumes that... 

SOL.22.1. Prigogine and A. Bellemans, Application of the cell model to the statistical thermodynamics of solutions. Volume change of mixing in solutions of molecules slightly different in Size, J. Chem. Phys. 21, 561-562 (1953). 

A further method for the specification of the composition of a solution or mixture, related to the molar scale, is the volume fraction of the solute, ( ). This takes into account any change in the volume of the system that has taken place on the preparation of the solution-the volume (change) of mixing. Therefore for a solute I ... 

The ideal gas, consisting of molecules with zero volume that do not intera fulfills the conditions of solution ideality as a special case. When ideal gases mixed, there is no volume change of mixing, because the molar volume of mixture V B and the molar volumes of the pure species Vf are all equal to RT/... 

Thus the volume change of mixing A V and the enthalpy change of mixing AH found from the measured quantities AV and Q. Because of its association Q, AH is usually called the heat of mixing. 

We can calculate excess volumes (volume changes of mixing) for methanol(l)/water(2) system at 25°C from the volumetric data of Fig. 1 Equation (13.20) specializes to... 

The volume change of mixing is approximated on the basis of the assumption that it is only enthalpy dependent and the entropy contribution to the volume change of mixing is ignored. 

The behavior of binary hquid solutions is clearly displayed by plots of M, AM, and In y vs. Xi at constant T and P. The volume change of mixing (or excess volume) is the most easily measured of these quantities and is normally small. However, as illustrated by Fig. 4-1, it is subject to individualistic behavior, being sensitive to the effects of molecular size and shape and to differences in the nature and magnitude of intermolecular forces. 

For an ideal solution, the enthalpy and volume changes of mixing are zero. 

Lefebvre, K. K Lee, J. H., Balsara, N. P., et al. Relationship between internal energy and volume change of mixing in pressurized polymer blends. Macromol. 32, 5460-5462 (1999). 

At 298.15 K (25°C) and atmospheric pressure the volume change of mixing of binary liquid mixtures of species 1 and 2 is given by the equation ... 

Smith, B. D., et al., Critical Evaluation of Vapor-Liquid Equilibrium, Heat of Mixing, and Volume Change of Mixing Data, J. Phys. Chem. Ref. Data, v. 11, p. 941 (1982). 

The volume change of mixing (V = AV), the heat of mixing (H = AH), and the excess Gibbs energy G are experimentally accessible, AV and AH by direct measurement and G (or In Ji) indirectly by reduction of vapor/liquid equilibrium data. Knowledge of H and... 

Figure 2. Dependence of the corrected volume change of mixing sodium pectate with Cu + <0 > and with Ca + ( ) in 0.05 M aqueous NaC104. at 25 C. R is the ion-to-polymer repeating unit molar ratio.

Similarly, the excess volume ("volume change of mixing") is equal to the pressure derivative of g ... 

The z m 0 plane does not correspond to the average concentration (Q, + C,)l2 unless DAB is independent of composition. Duda and Vreatas6 have anelyzed the mose complex case of frea diffusion, where there is a volume change of mixing, and have shown that neglecting voiuma chenges may introduce significant errors in the diffusion coefficients calculated. 

The volume of the n-octanol-rich phase, assuming no volume change of mixing, is... 

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