Mixing molar volume

Various properties indicate association dielectric behavior, solubility, heat of mixing, molar volume, viscosity, etc. 

This simple mo l contiimes to ignore the possibility of volume changes on mixing, so for simplicity the molar volumes and are taken as those of the pure components. It should come as no surprise that in... 

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. ... 

By adopting mixing rules similar to those given in Section II, Chueh showed that Eq. (55) can be used for calculating partial molar volumes in saturated liquid mixtures containing any number of components. Some results for binary systems are given in Figs. 7 and 8, which compare calculated partial molar volumes with those obtained from experimental data. 

Chao and Seader assume that the partial molar volumes are independent of composition this assumption is equivalent to saying that at constant temperature and pressure there is no volume change upon mixing the pure liquid components, be they real or hypothetical. The term on the right-hand side of Eq. (46) is assumed to be zero for all temperatures, pressures, and compositions. This assumption is very poor near critical conditions, and is undoubtedly the main reason for the poor performance of the Chao-Seader correlation in the critical region. 

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... 

V/1 is the molar volume of the solvent, ns and np the molar concentrations of the solvent and the polymer, respectively, and AGm the Gibbs free energy of mixing. Equation (26) reduces in the limit of infinite dilution to the well-known Van t Hoff equation... 

Figure 3.1 Mixing of nA moles of A and wg moles of B at constant p and T. The molar volumes of pure A and B are Fa and Fg. The partial molar volumes of A and B in the solution are VA and FB, respectively.

The volume of mixing for one mole of solution is termed the molar volume of mixing, A mixFm, and is derived by dividing eq. (3.14) by the total number of moles ( A + wb) in the system... 

The molar volume of mixing of two binary systems is shown in Figure 3.2. Pb-Sn shows positive deviation from the ideal behaviour at 1040 K [1] while the volume of mixing of Pb-Sb at 907 K is negative, with a minimum at Xpb 0.5 and asymmetric with respect to the composition [2],... 

So far we have considered mixtures of atoms or species of similar size and shape. Now we will consider a mixture of a polymeric solute and a solvent of monomers [7, 8], The ideal entropy of mixing used until now cannot possibly hold for this polymer solution, in which the solute molecule may be thousands or more times the size of the solvent. The long chain polymer may be considered to consist of r chain segments, each of which is equal in size to the solvent molecule. Therefore r is also equal to the ratio of the molar volumes of the solute and the solvent. The solute and the solvent can be distributed in a lattice where each lattice site can contain one solvent molecule. The coordination number of a lattice site is z. 

For many gaseous solutions, even if the gases are not ideal, the partial molar volumes of the components are equal to the molar volumes of the pure components at the same total pressure. The gases are said to obey Amagat s mle, and the volume change on mixing is zero. Under these conditions, the gaseous solution behaves ideally in the sense that it obeys the equation... 

For the titration of LDAO, solutions were made with their pH adjusted to 12 with NaOH and titrated with HCl. Binary mixtures of LDAO and SDS solutions were prepared by mixing different volumes of the surfactant solutions at equal molar concentration. 

If, however, site interactions of atoms on energetically equivalent sites are equal and the standard molar volumes of mixing components are not dissimilar (i.e., within 5 to 10% difference), equation 3.157 may be simplified and the activity of any component i in the mixture (a,) may be expressed in a generalized fashion as shown by Helgeson et al. (1978) ... 

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