Reference molecular volume

F = Function of the molecular volume of the solute. Correlations for this parameter are given in Figure 7 as a function of the parameter (j), which is an empirical constant that depends on the solvent characteristics. As points of reference for water, (j) = 1.0 for methanol, (j) = 0.82 and for benzene, (j) = 0.70. The two-film theory is convenient for describing gas-liquid mass transfer where the pollutant solute is considered to be continuously diffusing through the gas and liquid films. 

Va = 26.7 for NHg from Table 9-44 (molecular volume) Note The value of Va is from Ref. 63. Molecular volume values vary between references. 

Figure 5.2 Correlation of the hardnesses of the Group IV elements, and the associated isoelectronic III-V compounds, with their bond moduli. Room temperature data. For the elements, the molecular volumes refer to the diatoms C-C, Si-Si, Ge-Ge, and Sn-Sn.

A more direct link with molecular volumes holds for alkali halides, because the lattice energy (IT) is inversely proportional to interatomic distance or the cube root of molecular volume (MV). The latter has been approximated by a logarithmic function which gives a superior data fit. Plots of AH against log(MV) are linear for alkali halides 37a). Presumably, U and AH can be equated because AH M, ) is a constant in a series, and AH (halide )) is approximately constant when the anion is referred to the dihalogen as the standard state. 

FIGURE 21. Correlation of molecular polarizabilities oc with molecular volumes V for a number of hydrocarbons including cyclopropane. Data from Reference 180... 

Figure 1.1 A plot of relaxation times versus molecular volume for a series of closely related alcohols demonstrating the overall validity of the Debye equation. The outlying point refers to benzyl alcohol (see text for further discussion).

Chemical information can be expressed in a number of ways. Chemical descriptors are commonly used in QSAR. There are thousands of chemical descriptors possibly used in QSAR. Indeed, programs such as DRAGON and CODESSA, just to name a couple, can calculate thousands of parameters [7, 8]. Chemical descriptors have different complexities. Some of them do not require any information on the structure, such as molecular weight. Others refer to the bidimensional structure, such as the number of double bonds. While some others require tridimensional information, such as molecular volume. Chemical descriptors can be geometrical, topological, quantum-mechanical, electrostatical, etc. There are a few books describing chemical descriptors [7, 8],... 

Here vp is the molecular volume of the polymer and the superscripts M and El refer to the mixing and elastic contributions, respectively. 

For hydrogen, 1 gram is produced by 96487 As, corresponding to a volume of half the molecular volume (=22.4 litres, referring to a temperature of 273 K... 

It is a logical requirement that equations of state approach the ideal gas equation at the limit of low pressures. As the pressure decreases, the volume increases so that at very low pressures a/V P and V. If these terms are dropped from the van der Waals equation, it reduces to the ideal gas form. The terms and b account for intermolecular forces and molecular volume. The parameters a and b are called the attraction and repulsion parameters, respectively. The parameter b is also referred to as the effective molecular volume. 

We now proceed to explain in detail how the molecular constants enumerated in the preceding section can be determined experimentally. There is first the molecular volume, the determination of which, when neutral molecules are in question, can be effected by the methods of the kinetic theory of gases, already referred to in Chapter I (viscosity, free path, diffusion and direct measurement by molecular rays). The following table shows some molecular diameters so determined, in Angstroms ... 

As a product of mental elaboration, rather than of direct sensory perception, shape is a concept that eludes simple quantification. Even the picture of intersecting atomic spheres is very complicated, and some numerical indices describing molecular shape need to be constructed. Cseif [8] is the ratio of molecular volume to that of the molecular box of Figure 12.3 it is called the self-packing coefficient and is equal to unity for a brick-shaped object and is very small for a branched object. Some ratios of moments of inertia can be taken, and compared with the same ratios for reference objects. For example [3] ... 

The picture arrived at after exhaustive research with luminous bacteria, and eventually discussed at length with reference to many other types of biological processes, involved molecular volume changes of activation in the enzyme reaction and volume changes of reaction in the reversible denaturation of the protein moiety. Continued research concerning the... 

For the hydrogen atom, for example, the electron density is negligible at a distance beyond about 1.2 x 10" m (1.2 A or 0.12 nm) from the nucleus. The atom can therefore be regarded as a sphere with this radius. This radius is referred to as the van der Waals radius, after the Dutch physicist J. D. van der Waals (1837-1923) who related such radii and the corresponding atomic and molecular volumes to the pressure-volume behavior of gases. 

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