Molal volumes

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. 

T = absolute temperature, °K Vc = critical molal volume, cc/gmole 12 subscripts indicating components 1 and 2, respectively... 

It is a common practice to evaluate the molal volume ( V) of an ideal gas at a set of reference conditions known as the standard state. If the standard state is chosen to be... 

The intensive variable for volume (V) can be either the specific volume ( V, volume/mass) or the specific molal volume ( V volume/mole). 

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. 

Let Fig. 58a represent a molecule in the pure solvent, with four nearest neighbors and let Fig. 585 represent the simple substitution of a solute particle for the central molecule. The displaced molecule is to be put on the surface of the liquid. In water, if there were no other disturbance of the liquid, this would lead to the value 18 cm3/mole for the solute. Next let Fig. 58c represent the si lua-tion where the number of nearest neighbors has been increased by unity. In this case no solvent molecule has to be placed on the surface of the liquid and if there were no other disturbance of the surrounding liquid, the observed molal volume for the solute would clearly be zero. 

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. 

Major determinants of membrane fluidity may be grouped within two categories [53] (1) intrinsic determinants, i.e., those quantifying the membrane composition and phase behavior, and (2) extrinsic determinants, i.e., environmental factors (Table 1). In general, any manipulation that induces an increase in the molal volume of the lipids, e.g., increase in temperature or increase in the fraction of unsaturated acyl chains, will lead to an increase in membrane fluidity. In addition, several intrinsic and extrinsic factors presented in Table 1 determine the temperature at which the lipid molecules undergo a transition from the gel state to liquid crystalline state, a transition associated with a large increase in bilayer fluidity. 

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... 

If Type I adsorption behavior is obeyed, a plot of PA/v versus PA should be linear with slope l/vm. Once the volume corresponding to a mono-layer has been determined, it can be converted to the number of molecules adsorbed by dividing by the molal volume at the reference conditions and multiplying by Avogadro s number (N0). When this number of molecules is multiplied in turn by the area covered per adsorbed molecule (a), the total surface area of the catalyst (S) is obtained. Thus,... 

If the gas behaves ideally the volumetric flow rate at the reactor inlet is given by the product of the molal flow rate [(500/146) lb moles/hr] and the molal volume at the pressure and temperature in question. The latter may be calculated by correcting the standard molal volume (359 ft3/lb mole) for variations in temperature and pressure between the reactor inlet and standard conditions. Hence... 

Changes in the linear velocity arise from variations in the molal volume of the reacting fluid. Hence... 

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