Partial molal volumes solvents

Let us now ask how this value could be used as a basis from which to measure the local disturbance of the water structure that will be caused by each ionic field. The electrostriction round each ion may lead to a local increase in the density of the solvent. As an example, let us first consider the following imaginary case let us suppose that in the neighborhood of each ion the density is such that 101 water molecules occupy the volume initially occupied by 100 molecules and that more distant molecules are not appreciably affected. In this case the local increase in density would exactly compensate for the 36.0 cm1 increment in volume per mole of KF. The volume of the solution would be the same as that of the initial pure solvent, and the partial molal volume of KF at infinite dilution would be zero. Moreover, if we had supposed that in the vicinity of each ion 101 molecules occupy rather less than the volume initially occupied by 100 molecules, the partial molal volume of the solute would in this case have a negative value. 

There is considerable interest in the nature of solute-solvent interactions in SCFs, and a variety of experimental and theoretical techniques have been brought to bear on the subject. Experimental work near the critical point often shows interesting anomalies. One of the groundbreaking studies found that partial molal volumes of infinitely dilute solutes become large and negative in the compressible region around the critical point... 

Let us first consider an integration of Equation IV. 13 appropriate for a liquid. We will make use of the observation that the partial molal volume of a species in a solution does not depend on the pressure to any significant extent. For a solvent this means that the liquid generally is essentially incompressible. If we integrate Equation IV.13 with respect to P at constant T, E, h, nh and rij with V independent of P, we obtain the following relations ... 

One of the diflSculties in applying the Born equation is that the effective radius of the ion is not known further, the calculations assume the dielectric constant of the solvent to be constant in the neighborhood of the ion. The treatment has been modified by Webb who allowed for the variation of dielectric constant and also for the work required to compress the solvent in the vicinity of the ion further, by expressing the effective ionic radius as a function of the partial molal volume of the ion, it was possible to derive values of the free energy of solvation without making any other assumptions concerning the effective ionic radius. 

Partial molal volumes of aqueous ionic species vary considerably with changes in pressure and temperature. The molar volume of an aqueous species can be split into a Coulombic and a non-Coulombic term. The non-Coulombic term consists of the intrinsic volume of the ion. The Coulombic term consists of the volume of solvation and the volume of collapse. The volume of solvation is related to the orientation of water dipoles around the aqueous species, and the volume of collapse is the component of the partial molal volume related to the collapse of the water structure in the vicinity of the aqueous species. The pressure and temperature dependence of the molar volume of aqueous species arises from a similar change in the electrostatic properties of the solvent... 

Helgeson and co-workers (10,11) have proposed an equation of state based on the electrostatic properties of the solvent that can be used to estimate standard partial molal volumes of uncomplexed ions at elevated temperatures and pressures. 

Standard Partial Molal Volumes of Electrolytes in Various Solvents at 25°C (ml mol"... 

In an attempt to correlate gross structure of solute-water with packing and stereochemistry, the partial molal volumes and isentropic partial molal compressibilities were measured for sugars, uronic acids, and some di- and trisaccharides in water at 25 C. Attempts to systematize the results were unsuccessful. In a different approach, the structural transitions at saturation temperature using Arrhenius plots of results obtained by conductance measurements on electrolyte-sucrose-water solution were determined. These transitions were postulated to be due to the ability of the sucrose to form intermolecular hydrogen bonds with the solvent, so that at saturation temperature it was considered to have entered the total structure of the solution. ... 

MiUero FJ (1971) Molal volumes of electrolytes. Chem Rev 71 147-176 Morris DFC (1968) Ionic radii and enthalpies of hydration of ions. Struct Bond 4 63-82 Morris DFC (1969) Ionic radii and enthalpies of hydration of ions. Struct Bond 6 157-159 Mukerjee P (1961) Ion-solvent interactions, I. Partial molal volumes of ions in aqueous solutions, II. Internal pressure and electrostriction of aqueous-solutions of electrolytes. J Phys Chem 65 740-746... 

The partial molal volume of solute 1 at Infinite dilution in solvent 2 can be calculated using the equation presented by Brelvi and O Connell ... 

Partial molal volumes are d( t( rminable from experiment by a variety of methods, the most commonly used one involving the computation of the apparent molal olume, pure solvent. The quantity

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They demonstrated that the RISM integral equation and MC methods gave comparable results and that the nearest CO molecules showed preferred orientations in certain positions parallel to the naphthalene molecular plane and to the long axis when above the plane but perpendicular to the plane whether abeam or ahead of the naphthalene. They also obtained the partial molal volume of naphthalene as a function of the density of solvent it is negative at low densities, owing to a number of COj molecules being attracted to naphthalene, increasing to reasonable positive values as density iuCTeases. 

Mukerjee, P. On ion-solvent interactions. Part I. Partial molal volumes of ions in aqueous solution. J. Phys. Chem. 65, 740 (1961). 

Mukerjee P (1961) Ion-solvent interactions. I. Partial molal volumes of ions in aqueous solutions. II. Internal pressure and electrostriction of aqueous solutions of electrolytes. J Phys Chem 65 740-744... 

In the event that the molar volumes of solute and solvent are not comparable, and the thermal agitation is not adequate to achieve maximum entropy of mixing, a nonideal entropy of mixing exists (Bustamante et al., 1989). Two equations that account for the nonideal entropy of mixing have been derived by considering the partial molal volurfiA,and the volume fraction, occupied by each solution component. The L rst was developed by Flory and Huggins (Hildebrand, 1949 Kertes, 1965) ... 

When Equations (6.28) and (6.31) are substituted into Equation (6.27) and the mole ratios are again expressed in terms of molalities, the partial molar volume of the solvent is given by... 

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