Intrinsic volume

The intrinsic volume of activation was estimated to correspond to the molar volume difference between cyclohexene and cyclohexane, adding the molar volume difference between ethane and ethene to account for... 

Compressing a gas brings the particles into close proximity, thereby increasing the probability of interparticle collisions, and magnifying the number of interactions. At this point, we need to consider two physicochemical effects that operate in opposing directions. Firstly, interparticle interactions are usually attractive, encouraging the particles to get closer, with the result that the gas has a smaller molar volume than expected. Secondly, since the particles have their own intrinsic volume, the molar volume of a gas is described not only by the separations between particles but also by the particles themselves. We need to account for these two factors when we describe the physical properties of a real gas. 

Similarly to equation 13.2, the intrinsic volume change can be expressed in terms of measurable quantities, according to equation 13.11 ... 

Here, V refers to the molar volume of the nonelectrolyte, V and Vs° are the intrinsic3 and apparent molar volume of the salt, respectively, and /3 is the isothermic compressibility coefficient of the solution. Although this equation is strictly valid in the limit of Vi - 0 and ca - 0, it works quite satisfactorily for small nonpolar solutes. The equation shows that the effect is greatest for nonelectrolytes of large molar volume Vi, and for salts that cause the largest electrostriction, Vs - Vs°. A difficulty with this expression is that it is not always easy to evaluate the intrinsic volume of a salt (the mere volume, without... 

Intrinsic volume is the hypothetical molar volume of the liquid salt at the temperature in question. 

A simplihed approach to the description of AV starts from the statement made by Hamann [270] that the partial molar volume of any dissolved species in solution is the sum of the intrinsic volume of the species, corresponding to its van der Waals radius (intrinsic contribution), and of the contribution due to interaction with the solvent and with the other dissolved species (environmental... 

The intrinsic volume of a mole of the solvent molecules as they are in the liquid solvent should be a temperature- and pressure-independent quantity. 

It is approximately the difference between its molar and intrinsic volumes... 

The molar volume Vi should strictly be taken as the partial molar volume which is normally unknown or the intrinsic volume of the solute species, rather than its molar volume when pure, or as a hypothetical supercooled liquid when the neat solute is a solid at the working temperature. 

The intrinsic volume of a liquid can be estimated if it is assumed to be characterized by the vanishing of the internal pressure Pj10. In this case... 

In studying processes of accumulation of the Frenkel defects, one uses three different types of simple models the box, continuum, and discrete (lattice) models. In the simplest, box model, which was proposed first in [22], one studies the accumulation of complementary particles in boxes having a certain capacity, with walls impenetrable for diffusion of particles among the boxes. The continuum model treats respectively a continuous medium the intrinsic volume of similar defects at any point of the space is not bounded. In the model of a discrete medium a single cell (e.g., crystalline lattice site) cannot contain more than one defect (v or i). 

A quite different approach to the molecular size of solvents is the estimation of its molecular surface area and volume from the van der Waals radii of the constituent atoms and the manner and geometry of their mutual bonding (Bondi 1964). The necessary calculations are quite involved, and the values shown in Table 3.4 have been taken from a single source (DIPPR 1997), in order to be consistent. The reported molar van der Waals surface areas, Ayiw, are in 104 m2 mol 1 and the molar van der Waals volumes, Fvdw, are in cm3 mol 1, the latter in order to be comparable with the molar volumes (in Table 3.1) and the intrinsic volumes, defined below, also reported in Table 3.4. 

For various purposes it is necessary to know the intrinsic volume of a mole of the solvent molecules as they are in the liquid solvent, which should be a temperature- and pressure-independent quantity, since only the amount of void space is taken to increase on thermal expansion and decrease on compression. The van der Waals volume is one measure of the intrinsic volume, but several ways of its calculation lead to somewhat different results. In particular, this calculated volume should depend on the conformation of the molecules in the liquid, whether extended or folded, and if the latter, to what average shape. This problem can be circumvented by the calculation of Vx (McGowan 1978, 1984 Abraham and McGowan 1987), that depends additively and solely on the numbers N and kinds i of atoms constituting the solvent and the number of bonds between these atoms, NbOBds. The following values of F,./cm3 mol 1 have been assigned to the atoms to be found in the solvents in our List ... 

A drawback of the resulting intrinsic volume is that it does not distinguish between isomers, not only geometrical ones, such as 1,1-dichloro- and 1,2- dichloroethane, both having Vx = 63.5 cm3 mol 1, but also structural ones, such as 1-butanol and diethyl ether, both having Vx = 73.1 cm3 mol1. The Vx values, shown in Table 3. 4, are nearly proportional to the van der Waals intrinsic... 

The openness of the solvent depends on its so-called free volume, that can be approximated by the difference between its molar and intrinsic volumes ... 

The latter can be taken as either Vx, or Evdw, or VL, related by Eqs. (3.19), (3.20), and (3.21), respectively, to the constitution of the solvents. It is obvious that the free volumes defined according to these choices of the intrinsic volume are not the same, and caution must be exercised when this notion is applied to concrete problems. The fluidity O = l/r of solvents depends on the free volume O = B[(V - V0)/V0J, according to (Hildebrand 1978), where B is a temperature-independent constant and V0 is the occupied volume, that may be equated with the intrinsic volume, see also Eq. (3.33). As mentioned in Chapter 3, the compressibilities of solvents appear to depend mainly on their free volumes, according to Eq. (3.8), so that there exists a relationship between the compressibilities of solvents and their fluidities (Marcus 1998). Two non-linear curves result from plots of log O v s kt, one for non-associated liquids and the... 

The intrinsic viscosity [rj is attributed to an overall hydrodynamic volume of the solute. The values of [rj for the above disaccharides are close to each other but that for trehalose is slightly larger [11]. Partial molar volume V is the sum of the intrinsic volume V)nt of the solute and the volume contribution Psoiute—solvent due to solute-solvent interactions... 

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