Viscosity coefficients molar volume

In liquids, predictive methods for diffusivity are typically semiempirical, relating the diffusivity of a solute at infinite dilution to the solvent viscosity, the molar volumes of the components, and sometimes other quantities [15]. For finite concentrations, the manner in which the diffusion coefficients pass from one infinite-dilution limit to the other is sometimes complex, and the models that exist [15] typically have a parameter that must be fitted to data. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Diffiusion Coefficient. The method of Reference 237 has been recommended for many low pressure binary gases (238). Other methods use solvent and solute parachors to calculate diffusion coefficients of dissolved organic gases in Hquid solvents (239,240). Molar volume and viscosity are also required and may be estimated by the methods previously discussed. Caution should be exercised because errors are multiphcative by these methods. 

The Stokes-Einstein equation predicts that DfxITa is independent of the solvent however, for real solutions, it has long been known that the product of limiting interdiffusion coefficient for solutes and the solvent viscosity decreases with increasing solute molar volume [401]. Based upon a large number of experimental results, Wilke and Chang [437] proposed a semiempirical equation,... 

Equations (18) and (19) show that the diffusion coefficient is inversely proportional to both solvent viscosity and the molar volume of the hydrodynamic... 

Generally, diffusion coefficients strongly depend on viscosities and densities as well as molar volumes. The surface tension represents another important factor in calculations of mixture properties and mass transport correlations. Thus, possibly accurate determination methods are required. 

The physical property monitors of ASPEN provide very complete flexibility in computing physical properties. Quite often a user may need to compute a property in one area of a process with high accuracy, which is expensive in computer time, and then compromise the accuracy in another area, in order to save computer time. In ASPEN, the user can do this by specifying the method or "property route", as it is called. The property route is the detailed specification of how to calculate one of the ten major properties for a given vapor, liquid, or solid phase of a pure component or mixture. Properties that can be calculated are enthalpy, entropy, free energy, molar volume, equilibrium ratio, fugacity coefficient, viscosity, thermal conductivity, diffusion coefficient, and thermal conductivity. 

Partial molar entropies of ions can, for example, be calculated assuming S (H+) = 0. Alternatively, because K+ and Cl ions are isoelectronic and have similar radii, the ionic properties of these ions in solution can be equated, e.g. analysis of B-viscosity coefficients (Gurney, 1953). In other cases, a particular theoretical treatment which relates solvation parameters to ionic radii indicates how the subdivision could be made. For example, the Bom equation requires that AGf (ion) be proportional to the reciprocal of the ionic radius (Friedman and Krishnan, 1973b). However, this approach involves new problems associated with the definition of ionic radius (Stem and Amis, 1959). In another approach to this problem, the properties of a series of salts in solution are plotted in such a way that the value for a common ion is obtained as the intercept. For example, when the partial molar volumes of some alkylammonium iodides, V (R4N+I ) in water (Millero, 1971) are plotted against the relative molecular mass of the cation, M+, the intercept at M + = 0 is equated to Ve (I-) (Conway et al., 1966). This procedure has been used to... 

Another advance in the concepts of liquid-phase diffusion was provided by Hildebrand [Science, 174, 490 (1971)] who adapted a theory of viscosity to self-diffusivity. He postulated that DAA = B(V-V )/V , where DAA is the self-diffusion coefficient, V is the molar volume, and V is the molar volume at which fluidity is zero (i.e., the molar volume of the solid phase at the melting temperature). The difference (V -V ) can be thought of as the free volume, which increases with temperature and B is a proportionality constant. 

From Wilke-Chang correlation, D°AB=7.4xlO 8(tMB) TAlBVA - , where D°AB/cm l is mutual diffusion coefficient of solute A in solvent B, Mb /g-mok is molecular weight of solvent B, tib /cp is viscosity of solvent B, Va /cm3-mol is molar volume of solute A at its nomial boiling temperature, and is association factor of solvent B. 

From Eqs. 5.8a to 5.16, it is clear that the diffusion coefficient is a function of two parameters, the solvent viscosity and the solute molar volume, both of which depend on the pressiue. Thus, we can write... 

Probably the most systematic and complete study on the influence of temperature on water transfer has been performed on mammalian red cells [10,20,28]. The dependence on temperature of both the tracer diffusional permeability coefficient (cotho) 3 nd the hydraulic conductivity (Lp) of water in human and dog red-cell membranes have been studied. The apparent activation energies calculated from these results for both processes are given in Table 2. The values for the apparent activation energies for water self-diffusion and for water transport in a lipid bilayer are also included in the table. For dog red cells, the value of 4.9 kcal/mol is not significantly different from that of 4.6-4.8 kcal/mol for the apparent activation energy of the water diffusion coefficient ( >,) in free solution. Furthermore, it can be shown that the product L — THOV )rt, where is the partial molar volume of water and the viscosity of water remains virtually independent of temperature for dog, hut not for the human red-cell membrane [20]. The similarity of the transmembrane diffusion with bulk water diffusion and the invariance of the... 

As we can see, the calculation of the coefficient of diffusion of the solution s component accordingly to Eq. (73) needs the knowledge, first of all, the coeffieient of the viscosity of the presented component and its partial-molar volume. 

Here, >i is the volume fraction of the solvent in the swollen polymer, Oxx is the stress developed within the polymer, Dn is the mutual diffusion coefficient, % is the polymer-solvent interaction parameter, Vi is the molar volume of the solvent, T is the temperature, E is the modulus of die polymer and T is the viscosity of the polymer. Equation (1) is valid in the region between x s R and x = S. 

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