Liquids, calculation from density

Table 2 shows that the parachors of pure ionic liquids calculated from density and surface tension data and the parachors estimated by the group contribution method agree very well [122]. Similarly, the molar refraction Rm,est was estimated and used to determine the refractive index R est by (2) (Lorentz-Lorenz equation), which is also compared to Ri,exp in Table 2 [123] ... 

The hydrogen content of petroleum fuels can be calculated from density with the following formula, with an accuracy of about 1 percent for petroleum liquids that contain no sulfur, water, or ash ... 

Porosity calculations from density measurements have also been applied to granulations prepared using different processes. The method of granulation, such as the type of adjuvant used [64] or the amount of granulation liquid [74], was found to change the bulk density and porosity of the material. Consequently, the compression and flow properties of the materials were also different. 

Values of molar volumes can be calculated from densities measured for the liquid salt, or can be calculated as for hypothetical subcooled liquid at 298.15 K using the group contribution method [47]. As expected, the molar volumes of 1,3-dialkylimidazolium salts and quaternary ammonium salts increase progressively as the length of alkyl chain of the substituent increases. Some molar volumes values at 298.15 K are listed in Table 1.3. 

Figure 7.17 Left Fluctuating density in a liquid phase near a solid surface, relative to the bulk density p0. The first maximum occurs at the hard-sphere contact distance from the surface, at r = a the molecular diameter. Right Pair potentials for two molecules in the liquid calculated from p(r) - p0exp[-w/kT]...

To calculate micelle size and diffusion coefficient, the viscosity and refractive index of the continuous phase must be known (equations 2 to 4). It was assumed that the fluid viscosity and refractive index were equal to those of the pure fluid (xenon or alkane) at the same temperature and pressure. We believe this approximation is valid since most of the dissolved AOT is associated with the micelles, thus the monomeric AOT concentration in the continuous phase is very small. The density of supercritical ethane at various pressures was obtained from interpolated values (2B.). Refractive indices were calculated from density values for ethane, propane and pentane using a semi-empirical Lorentz-Lorenz type relationship (25.) Viscosities of propane and ethane were calculated from the fluid density via an empirical relationship (30). Supercritical xenon densities were interpolated from tabulated values (21.) The Lorentz-Lorenz function (22) was used to calculate the xenon refractive indices. Viscosities of supercritical xenon (22)r liquid pentane, heptane, decane (21) r hexane and octane (22.) were obtained from previously determined values. 

Batchinski observed that zero-shear viscosity ( jo) of low-molecular-weight liquids at different T and P changes with the density, p rjooup [Batchinski, 1913]. Later, Doolittle correlated In rjo with redefined free volume, (po, also calculated from density [Doolittle, 1951a,b, 1952, 1954 Doolittle and Doolittle, 1957] ... 

Density, p, is defined as the mass per unit volume at constant temperature and pressure, so the unit for density is kg/ rri. Density for ILs decreases with temperature in their liquid range and increases with pressure, both linearly (Gardas et al., 2007 Rilo et al., 2010c). The reciprocal value of density is the specific volume, which is usually refered as the molar volume, Vm, calculated from density and the molar mass value, M,... 

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

Fig. Ill-13. (a) Plots of molecular density versus distance normal to the interface a is molecular diameter. Upper plot a dielectric liquid. Lower plot as calculated for liquid mercury. (From Ref. 122.) (b) Equilibrium density profiles for atoms A and B in a rare-gas-like mixmre for which o,bb/ o,aa = 0.4 and q,ab is given by Eq. III-56. Atoms A and B have the same a (of Eq. m-46) and the same molecular weight of SO g/mol the solution mole fraction is jcb = 0.047. Note the strong adsorption of B at the interface. [Reprinted with permission from D. J. Lee, M. M. Telo de Gama, and K. E. Gubbins, J. Phys. Chem., 89, 1514 (1985) (Ref. 88). Copyright 1985, American Chemical Society.]...

In the next section we discuss linear hydrodynamics and its role in understanding the inelastic light scattering experiments from liquids, by calculating the density-density correlation fiinction,. Spp. 

The molecular area, calculated from the density of the supercooled liquid at 77 K is a ,(Kr) = 15-2 A, but Beebe found it necessary to adopt the higher value 19-5 A to bring the krypton-based area into line with the area of Harkins reference sample of anatase. ... 

Here df, is the mean separation of nearest neighbours in the bulk liquid, and is calculable from the liquid density. Substitution of Tq = 2y/r (cf. Equation (3.58)) gives the further relation... 

For any ultrasound of frequency v, the longitudinal wavelength 7i at the surface can be calculated from Equation 19.1, in which a is the surface tension of the liquid and p is the density of the liquid. 

In order to ensure thermodynamic consistency, in almost all cases these properties are calculated from Tr. and the vapor pressure and liquid density correlation coefficients listed in those tables. This means that there will be slight differences between the values listed here and those in the DIPPR tables. Most of the differences are less than 1%, and almost all the rest are less than the estimated accuracy of the quantity in question. 

Calculated from values of pressure, volume (or density), and temperature in Vasserman, Kazavchinsldi, and Rabinovich, Thetmophysical Fropetties of Air and Air Components, Moscow, Naiika, 1966, and NBS-NSF Trans. TT 70-50095, 1971 and Vasserman and Rabinovich, Thetmophysical Fropetiies of Liquid Air and Its Components, Moscow, 1968, and NBS-NSF Trans. 69-55092, 1970. 

Tlic density (p) of a substance is tlic ratio of its mass to its volume and may be expressed in units of pounds per cubic foot (Ib/ft ) or kilograms per cubic meter (kg/nv ). For solids, density can be determined easily by placing a known mass of the substance in a liquid and measuring tlie displaced volume. The density of a liquid can be measured by weighing a known volume of the liquid in a gradmitcd cylinder. For gases, tlie ideal gas law (to be discussed in Section 4.6) can be used to calculate tlie density from tlie temperature, pressure, and molecular weight of tlie gas. 

This value is also taken as the mean density of the fluid in the downcomer which means that for safe design the clear liquid back-up, calculated from equation 11.91, should not exceed half the plate spacing lt, to avoid flooding. 

We apply Archimides Principle to measure a sample s density by a technique known as densimetry. We weigh the sample twice, once when suspended in air and again while suspended in a liquid of known density. We calculate its density from Eq. 7,6,... 

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