Volume, partial molal

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

COMPUTER PROJECT 3-4 The Partial Molal Volume of ZnCl2... 

Procedure. A study on the partial molal volume of ZnCl2 solutions gave the following data (Alberty, 1987)... 

Find the partial molal volume of ZnCl2 in these solutions at 0.5, 1.0, 1.5 and 2.0 molar concentrations. 

Table 31. Partial Molal Volume of Ion PAins at Infinite Dilution in Water at 25°C and 1 Atmosphere, and tiie Molal Volume in tiie Crystalline Solid, Both in Cm /Mole...

Fig. 57. Ion pairs in aqueous solution at 25°C. Partial molal volume at extreme dilution, plotted against the volume in the crystalline solid, both in cubic centimeters per mole.

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. 

E7.2 The following table gives the partial molal volumes at T = 298.15 K of ethyl acetate (1) and carbon tetrachloride (2) in solutions of the two. 

The value of is the difference in partial molal volume between the transition state and the initial state, but it can be approximated by the molar volume. Increasing pressure decreases the value of AV and if A V is negative the reaction rate is accelerated. This equation is not strictly obeyed above lOkbar. If the transition state of a reaction involves bond formation, concentration of charge, or ionization, a negative volume of activation often results. Cleavage of a bond, dispersal of charge, neutralization of the transition state and diffusion control lead to a positive volume of activation. Reactions for which rate enhancement is expected at high pressure include ... 

Interesting is a comparison of the volumes occupied by individual complexes in solution and in the solid state. The partial molal volumes can be obtained from precise measurements of the solution densities of the complexes as a function of concentration [177]. These values may be subsequently compared with the unit cell volumes per complex molecule derived from the crystal structure. For Fe[HB(pz)3]2, the apparent molal volume in tetrahydrofuran solution was determined as 340.9 em mol Taking into account that the complex in solution forms an equilibrium between 86% LS and 14% HS isomers and employing the volume difference between the two spin states AF° = 23.6 cm mol S the volume of the LS isomer was calculated as 337.6 cm mol This value agrees closely with the volume of 337.3 cm mol for the completely LS complex in solid Fe[HB(pz)3]2 [105]. 

It has been pointed out above that, at least for a number of suitable systems, the partial molal volume in solution and the volume occupied by a single molecule in the crystal are practically identical [177]. This finding provides additional support for the applicability of the theoretical models considered. In addition, the intermolecular contacts in the crystal should be similar to the solvation of the complexes in solution. 

For an ideal solution, the partial molal volumes equal the molar volumes of the pure liquid components. Denoting component the main components as 1 and the impurities as > 1, the volume becomes ... 

Vt partial molal volume of component / in the mixture p density of a mixture of components p, density of pure component i... 

The partial molar volume data of Table I on ammonia was calculated from density data in Landolt-Bornstein(57). The values of partial molal volume at infinite dilution can be expressed as ... 

Coefficient expressing the effect of concentration of gas on its activity coefficient, kg H20/mole Coefficient expressing the effect of change of partial molal volume of electrolyte (with temperature) on the salting-out coefficient, kg H20/cm3. Salt concentration, mol/2. 

The Krichevsky-Kasarnowsky equation takes into account both the temperature and pressure dependence of Henry s constant. The volume term in the equation is the partial molal volume of the gas in the liquid... 

When the Krichevsky-Kasarnowsky equation fails it may be because of either changing activity coefficient of the solute gas with composition, changing partial molal volume of the gas with pressure, or both. The Krichevsky-Ilinskaya equation takes into account the variation in the activity coefficient of the solute gas with mole fraction by means of a two-suffix Margules equation. 

The partial molal volumes of gases in water are needed to apply the Krichevsky-Kasarnowsky and the Krichevsky-Ilinskaya equations. A survey of the available experimentally measured partial molal volumes is given in Table VII. The results of Tiepel and Gubbins (2 ) seem especially reliable. The recent results of Popov and Drakin 26) usually appear to be much too high, possibly because of Popov and Drakin depended on literature solubility values for the concentration to be used in their calculation of the partial molal volume from the density data. 

The pressure-volume-temperature (PVT) properties of aqueous electrolyte and mixed electrolyte solutions are frequently needed to make practical engineering calculations. For example precise PVT properties of natural waters like seawater are required to determine the vertical stability, the circulation, and the mixing of waters in the oceans. Besides the practical interest, the PVT properties of aqueous electrolyte solutions can also yield information on the structure of solutions and the ionic interactions that occur in solution. The derived partial molal volumes of electrolytes yield information on ion-water and ion-ion interactions (1,2 ). The effect of pressure on chemical equilibria can also be derived from partial molal volume data (3). 

In kinetics, similar relationships apply, but the volume of activation AV can be determined only from the pressure dependence of the rate coefficient k, since the partial molal volumes V of transition states are not directly measurable. Conversely, however, equation 4 can yield values of V. ... 

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