Specific volume Molecules

Starting at condition A with the ethane in the liquid phase, and assuming isothermal depletion, then as the pressure is reduced so the specific volume increases as the molecules move further apart. The relationship between pressure and volume is governed by the compressibility of the liquid ethane. 

As the temperature is decreased, free-volume is lost. If the molecular shape or cross-linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled further, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. 

Regarding Case 1, it is known that the rotator phases of -paraffins are three dimensionally ordered solids with molecules in aW-trans conformation, their specific volumes, Vh, and specific entropies, Sh, are closer to corresponding values and for the orthorhombic phases than they are to those for the melt and Sm In contrast,... 

Carbon monoxide (CO) is a colorless and odorless gas molecule. This inorganic compound, at standard temperature and pressure, is chemically stable with low solubility in water but high solubility in alcohol and benzene. Incomplete oxidation of carbon in combustion is the major source of environmental production of CO. When it burns, CO yields a violet flame. The specific gravity of CO is 0.96716 with a boiling point of -190°C and a solidification point of-207°C. The specific volume of CO is 13.8 cu ft/lb (70°F). 

Combination of the Perrin function, p often referred as the frictional ratio due to shape with the frictional ratio (f/fo) enables the degree of expansion of the molecule (vh/ w ) to be estimated, where Vh, (cw / g) is the volume of the swollen molecule (Polysaccharide or protein + associated solvent) per unit mass of polysaccharide and v is the partial specific volume (essentially the anhydrous molecule) ... 

A gas condenses to a liquid if it is cooled sufficiently. Condensation occurs when the average kinetic energy of motion of molecules falls below the value needed for the molecules to move about independently. Thus, the molecules in a liquid are confined to a specific volume by intermolecular forces of attraction. Although they cannot readily escape, liquid molecules remain free to move about within the liquid phase, hi this behavior, liquid molecules behave like the molecules of a gas. The large-scale consequences of the molecular-level properties are apparent. Like gases, liquids are fluid, so they flow easily from place to place. Unlike gases, however, liquids are compact, so they cannot expand or contract significantly. 

In a liquid, intermolecular forces are strong enough to confine the molecules to a specific volume, but they are not strong enough to keep molecules from moving from place to place within the liquid. The relative freedom of motion of liquid molecules leads to three liquid properties arising from intermolecular forces surface tension, capillary action, and viscosity. ... 

H. Durschlag, Specific Volumes of Biological Macromolecules and Some other Molecules of Biological Interest, in ... 

V being the (partial) specific volume of the polymer and m=xV/v the mass of a polymer molecule. The sign and magnitude of the total free energy change AF for a given distance a depends, through J, on or on — exactly as we have pointed out previously... 

A third and slightly older method available is the UNITY package from Tripos Inc. This also relies on the user to identify pharmacophore features and spatial arrangement. When multiple compounds and biological activity is known, this can be used to focus on a limited number of features or to exclude specific volume from the molecule. The compounds in the database are then compared to the query... 

The view that the clay surface perturbs water molecules at distances well in excess of 10 A has been largely based on measurements of thermodynamic properties of the adsorbed water as a function of the water content of the clay-water mixture. There is an extensive literature on this subject which has been summarized by Low (6.). The properties examined are, among others, the apparent specific heat capacity, the partial specific volume, and the apparent specific expansibility (6.). These measurements were made on samples prepared by mixing predetermined amounts of water and smectite to achieve the desired number of adsorbed water layers. The number of water layers adsorbed on the clay is derived from the amount of water added to the clay and the surface area of the clay. 

The radius of the peptide molecule can be calculated from the molecular mass, Avogadro number, and the partial specific volume. 

The distance between chemically bound atoms in many molecules is shorter than the sum of the radii of the same atoms when free, and the specific volume of the compound may be actually smaller than the total covolume of its gaseous products. If, as seems plausible, the drastic compression within the detonation front ruptures chemical bonds, many atoms suddenly expand, exerting forces like those by which solids resist compression. Such forces could result in a spike pressure much higher than the peak pressure of the non-reactive shock front, exert a brisant effect on the surroundings, and expedite the progress of the detonation wave. This view accords with observations of cases in which... 

Cj) Caldirola Paterson Equation of State. Dunkle (Ref 10, p 183), stated that Cook (Ref 2c) found by working backward from experimental detonation rates to Corresponding values of covolume, that for all expls at very high pressures the Covolume is a function of the specific volume only. At these pressures all molecules have the same covolume per unit weight the dependence of a(T,v) on temperature is exceedingly small. The equation of state can be written pV = nRT +a(v)p... 

This revision to the ideal gas law accounted for the specific volume of gas molecules and assumed a force between these molecules which are now known as van der Waals forces. With this law, the existence of... 

Here Vi and v are the partial specific volumes of the polymer (/ = 2,4) and the solvent, respectively M is the molar weight of the solvent and Xu and 724 are the Flory-Huggins interaction parameters, quantifying the energy of interaction between unlike lattice-based polymer segments (%24) or between polymer segments and solvent molecules (%u). 

The volume of tabular information necessary to record in detail the thermodynamic data for the paraffin hydrocarbons and their mixtures, as was done for steam, is excessive. It appears hopeful that graphical generalizations typified by the work of Edmister (19) will prove adequate for the less rigorous requirements of design, whereas the Benedict equation of state (4) may be employed where precision is necessary. However, the effective application of this equation of state to compounds containing more than four carbon atoms per molecule still awaits the evaluation of the constants. After the composition and specific volume have been established for a particular state, the solution of equations of state to establish enthalpy and entropy is a straightforward process. 

EXAMPLE 3.3 Excluded Volume of Bovine Serum Albumin from Osmotic Pressure Measurements. A plot of 7r/c versus c for an aqueous solution of the bovine serum albumin molecule at 25°C and pH = 5.37 is shown in Figure 3.6. The molecule is known to be nearly spherical and uncharged at this pH. Evaluate the molecular weight and the excluded volume of this protein from the intercept and slope of this line, 0.268 torr (g kg-1)-1 and 1.37 10 3 torr kg2 g 2, respectively. From the particle mass and volume, estimate the partial specific volume of the solute in solution. The specific volume of the unsolvated protein is about 0.75 cm3 g 1 does the solute appear to be solvated ... 

T. E. Thorpe s formula for the specific volume i> at the temp. 0 is u=l +00009158960 +0 0000008329602 +0 00000000275O03. The vapour density is that theoretically required for IC1 with oxygen 32, the value for IC1 is 162 38 at 120°, the vapour density is 1606, and at 512°. 156 4. Conclusions as to the degree of dissociation at different temp, cannot be derived from the vapour density determinations since it proceeds without changing the number of molecules—2ICI—>I2+C12- Iodine trichloride vapour is almost completely dissociated into the monochloride and chlorine. K. Beck s value for the viscosity is 7 029 at 15°, 5 069 at 28 4°—benzene at 5° unity. 

---