Liquid density method

The COSTALD (Corresponding states liquid density) method was originally developed for calculating the densities of liquefied gases its use has become generally widespread. 

Liquid densities can be calculated according two types of methods, both based on the principle of corresponding states. 

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. 

Molecular volumes are usually computed by a nonquantum mechanical method, which integrates the area inside a van der Waals or Connolly surface of some sort. Alternatively, molecular volume can be determined by choosing an isosurface of the electron density and determining the volume inside of that surface. Thus, one could find the isosurface that contains a certain percentage of the electron density. These properties are important due to their relationship to certain applications, such as determining whether a molecule will fit in the active site of an enzyme, predicting liquid densities, and determining the cavity size for solvation calculations. 

Liquid Density Prediction Methods for the prediction of pure saturated hydrocarbons and nonhydrocarbon organics, compressed hydrocarbon hquids, and defined and undefined hydrocarbon mixtures were evaluated. Only the most accurate and convenient methods are included here. 

An analytical method for the prediction of compressed liquid densities was proposed by Thomson et al. " The method requires the saturated liquid density at the temperature of interest, the critical temperature, the critical pressure, an acentric factor (preferably the one optimized for vapor pressure data), and the vapor pressure at the temperature of interest. All properties not known experimentally maybe estimated. Errors range from about 1 percent for hydrocarbons to 2 percent for nonhydrocarbons. 

Mathews and Rawlings (1998) successfully applied model-based control using solids hold-up and liquid density measurements to control the filtrability of a photochemical product. Togkalidou etal. (2001) report results of a factorial design approach to investigate relative effects of operating conditions on the filtration resistance of slurry produced in a semi-continuous batch crystallizer using various empirical chemometric methods. This method is proposed as an alternative approach to the development of first principle mathematical models of crystallization for application to non-ideal crystals shapes such as needles found in many pharmaceutical crystals. 

Ionic liquid System Cation Anion(s) Temperature, (X Conduc- tivity (k), mS cm Conduc- tivity method Viscosity (n), cP Viscosity method Density (p), gcm Density method Molar conductivity fAJ, cm iT mor Walden product (An) Ref. 

The vapour density can be neglected when it is small compared with the liquid density. The parachor can be calculated using the group contributions given in Table 8.7. The method is illustrated in Example 8.13. 

The study of liquids near solid surfaces using microscopic (atomistic-based) descriptions of liquid molecules is relatively new. Given a potential energy function for the interaction between liquid molecules and between the liquid molecules and the solid surface, the integral equation for the liquid density profile and the liquid molecules orientation can be solved approximately, or the molecular dynamics method can be used to calculate these and many other structural and dynamic properties. In applying these methods to water near a metal surface, care must be taken to include additional features that are unique to this system (see later discussion). 

Semisolid samples. As with liquid samples, methods (B) and (C) are the best choices for this type of sample. The specific choice will depend on fhe rheological properties (viscosity, density, air retention) of the particular preparation. These samples are best measured in the transflectance mode. Liquid and semisolid samples may contain a mixture of solvents of disparate volatility which may evaporate separately during the measurement process. Differences in solvent volatility can alter the sample matrix and lead to errors in the determination which are best avoided by using a set of calibration samples spanning an expanded range of solvent proportions. ... 

Eq. (1) is valid for a particle settling without the interference of other particles, i.e., for diluted systems. The particle settling velocity decreases as particle concentration increases. This phenomenon is known as hindered settling. Several equations can be found in the literature to account for this phenomenon, but a simple method to calculate the hindered settling velocity is to use Eq. (1) replacing the liquid density and viscosity by the apparent density and viscosity of the suspension [24]. 

Solvents used here for a general liquid-liquid extraction method were selected from Snyders solvent selectivity triangle. As extraction liquids have to be composed of mixtures of three solvents which may enter into maximum interaction with the analyte, three solvents had to be selected that represent a wide variety of selective interactions. In addition, the solvents should be sufficiently polar to ensure quantitative extraction. Besides selectivity and polarity requirements, the solvents should also meet a few other criteria, mainly for practical reasons they should not be miscible with water, have low boiling points (for relatively fast evaporation procedures) and have densities sufficiently different from the density of water, for pure solvents as well as for selected binary or ternary mixtures of solvents. 

Recently, Rebelo and coworkers [172] presented a method to estimate the critical temperatures of some ILs based on fhe temperature dependence of fheir surface tension and liquid densities. The molar enfhalpies of vaporization of a series of commonly used ILs were also determined for fhe firsf fime. The molar enfhalpies of vaporization of [C Cilm][Tf2N] ILs in fhe function of the alkyl chain length have been presented [214]. The critical properties (T(, P(, Vf), the normal boiling temperatures, and the acentric factors of 50 ILs were determined as well for fhe firsf fime [215]. 

This method will be evaluated for the same example problem detailed in A5.3.3 above. Additional data are that 1 at the maximum accumulated pressure of 2.6 bara, the latent heat is 920 kJ/kg, vfg is 0.3523, G is 2633 kg/m2s and the liquid density is 937 kg/m3. Further data required are the void fraction in the reactor at the relief pressure, aR, and the void fraction at disengagement, aD... 

As an example, let us estimate the diffusivity of benzene in air. According to Table 18.3, the molar volume of benzene calculated from liquid density (89 cm3mol 1) and from the component method by Fuller et al. (90.8 cm3mor1) yield similar results. Incorporating these estimates into Eq. 18-44 yields ... 

Estimate the molar volume Vt of dichlorodifluoromethane CC12F2 (also called freon-12 or CFC-12) (a) from its liquid density and (b) with the element contribution method by Fuller (Table 18.2). 

For comparison, in Table 18.3 we have also listed the molar volume of TCE calculated from its liquid density, Mt/ p/L = 90.2 cm3mol-1, and from the method proposed by Abraham and McGowan (1987) given in Box 5.1 (71.6 cm3mor ). The molecular radius is approximated assuming the molecules are spherical (see Eq. 18-40) ... 

An analytical method for applying Polanyi s theory at temperatures near the critical temperature of the adsorbate is described. The procedure involves the Cohen-Kisarov equation for the characteristic curve as well as extrapolated values from the physical properties of the liquid. This method was adequate for adsorption on various molecular sieves. The range of temperature, where this method is valid, is discussed. The Dubinin-Rad/ush-kevich equation was a limiting case of the Cohen-Kisarov s equation. From the value of the integral molar entropy of adsorption, the adsorbed phase appears to have less freedom than the compressed phase of same density. 

Peneloux et al. [35] have introduced a clever method of improving the saturated liquid molar volume predictions of a cubic equation of state, by translating the calculated volumes without efffecting the prediction of phase equilibrium. The volume-translation parameter is chosen to give the correct saturated liquid volume at some temperature, usually at a reduced temperature Tr = T/Tc = 0.7, which is near the normal boiling point. It is possible to improve the liquid density predictions further by making the translation parameter temperature dependent. 

The calculation of liquid density at pressures above the bubble point is a two-step procedure. First, the density at the bubble point must be computed using one of the methods previously described. Then this density must be adjusted to take into account the compression due to the increase in pressure from bubble-point pressure to the pressure of interest. 

The analogy just mentioned with the BBGKI set of equations being quite prominent still needs more detailed specification. To cut off an infinite hierarchy of coupled equations for many-particle densities, methods developed in the statistical theory of dense gases and liquids could be good candidates to be applied. However, one has to take into account that a number of the... 

ISO 1183-1 2004. Methods for determining the density of non-cellular plastics - Part 1 Immersion method, liquid pyknometer method and titration method. 

Method of Grain Grain has proposed a method to estimate the liquid density from normal boiling point data using the following equation [2] ... 

In the second edition of this volume, special attention has been paid lo improving the accuracy of the estimation techniques used for liquid heat capacity, vapor and liquid viscosity. and vapor thermal conductivity. Improved methods of extending data on liquid density and thermal conductivity have been used m this edition New experimental data has also been included. Particular attention has been paid to include new data on aqueous solution and pressure effects on physical properties... 

C to WC for DK.K and from I0T to M>C for MIBK. The dcitMlics of (hose three compounds have been estimated from - X0°f to their vnlical temperature by the method proposed by l.ydersen, Ciieenkorn. and llougen.1 When com-pared with 10 experimental values, the average error was 0 4% I he liquid densities of aqueous acetone solutions from... 

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