Estimation from molar volume

Kamiya et al. [33] studied diffusion of seven hydrocarbons (w-butane, wobutane, 1-butene, cw-2-butene, fran -2-butene, isobutylene, 1,3-butadiene) in two rubbery polymers 1,2-polybutadiene and ethylene-vinyl acetate copolymer. The observed diffusion coefficients were compared with the sizes of diffusing molecules, estimated from molar volumes of liquid hydrocarbons, and shown to decrease regularly with increasing molecular size (see Figure 9.6) ... 

Values of the molecular radii were estimated from molar volumes. .. Bondi (1968). All pX values were adjusted for the solvent and concentration effects using Bie appropriate form of the Debye Huckel equation. Thermodynamic values for dissociation constants of barbituric acid and several derivatives were determined in solvents containing 0-50% ethyl alcohol in water... 

Estimate the molar volume, Vh of TrCB from its density and molar mass given in Appendix C (see also Eq. 3-18) ... 

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). 

A, the estimated dielectric constant is 63.5 from Eq. (35), and EA = 8.3 x 103 esu-cm 2. The estimated electrostrictional molar volume change (0.144 x 18) is 0.26 cm3-mole 1. This is in good agreement with the estimates of Desnoyers, Verrall, and Conway 8 for this field strength. The effect of the term (-Pu,iA.AA/2).dV on the interaction energy of interaction up to dielectric saturation is small, but not negligible. 

For the passive transport mechanism (Fig. 1, Path 2b), there is a linear dependence for permeability on diffusivity and the partition coefficient between aqueous and membrane compartments [Eq. (1)]. Diffusivity, which can be calculated from molar volume, generally varies within 1 order of magnitude, while partitioning can range over many orders of magnitude. Hence, for molecules with passive transport as the dominant pathway, determination of the partition coefficient can be a useful estimate of permeability. 

The estimated partial molar volumes are shown in Rgures 5.8 and 5.9 (data for water and IL solutes, respectively). In Figure 5.8, the absolute deviation of the partial molar volume of water from the molar volume of pure water at each studied temperature is shown as a function of concentration for the set of isotherms studied... 

FIGURE 3 shows the new linear plots of log CL versus chlorine number and FIGURE 4 the same data as a function of molar vol ume. The slopes of the three group regressions are similar but not identical. It is possible to estimate solubility from molar volume from these plots with a probable accuracy of plus or minus a factor of 10 down to 10" mol m and a factor of 100 at 10 mohrn". Frequently, reported data contain considerable error. Plots such as FIGURE 4 help to identify such data. 

Indication of an 7d mechanism for substitution reactions of [Co(NH3)5X] + ions and an associative interchange (7a) mechanism for [Cr(NH3)6X] ions comes from studies of these systems at high pressures. These workers prefer to use a volume profile diagram (Figure 2) which involves comparison of the experimentally estimated partial molar volumes of the reactant [M(NH3)sX] + ions and the calculated... 

S.Values for the Poynting effect can be determined from available or estimated liquid molar volume data. 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

The volume of the micellar pseudophase can be estimated from the molar volume of the micellised surfactant V-moiji ... 

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

Tyn-Calus This correlation requires data in the form of molar volumes and parachors = ViCp (a property which, over moderate temperature ranges, is nearly constant), measured at the same temperature (not necessarily the temperature of interest). The parachors for the components may also be evaluated at different temperatures from each other. Quale has compiled values of fj for many chemicals. Group contribution methods are available for estimation purposes (Reid et al.). The following suggestions were made by Reid et al. The correlation is constrained to cases in which fig < 30 cP. If the solute is water or if the solute is an organic acid and the solvent is not water or a short-chain alcohol, dimerization of the solute A should be assumed for purposes of estimating its volume and parachor. For example, the appropriate values for water as solute at 25°C are = 37.4 cmVmol and yn = 105.2 cm g Vs mol. Finally, if the solute is nonpolar, the solvent volume and parachor should be multiplied by 8 Ig. 

Thus, p can be estimated from the observed pressure and the ideal pressure calculated from the molar volume and the ideal gas equation. Klotz and Rosenburg3 report that the error in using equation (6.23) to calculate p is less than 1% for O2 up to a pressure of 10 MPa. For CO2 (g) the error is 1% at 2.5 MPa and 4% at 5 MPa. 

Use the estimates of molar constant-volume heat capacities given in the text (as multiples of R) to estimate the change in reaction enthalpy of N2(g) + 3 H,(g) —> 2 NH.(g) when the temperature is increased from 300. K to 500. K. Ignore the vibrational contributions to heat capacity. Is the reaction more or less exothermic at the higher temperature ... 

This chapter presents new information about the physical properties of humic acid fractions from the Okefenokee Swamp, Georgia. Specialized techniques of fluorescence depolarization spectroscopy and phase-shift fluorometry allow the nondestructive determination of molar volume and shape in aqueous solutions. The techniques also provide sufficient data to make a reliable estimate of the number of different fluorophores in the molecule their respective excitation and emission spectra, and their phase-resolved emission spectra. These measurements are possible even in instances where two fluorophores have nearly identical emission specta. The general theoretical background of each method is presented first, followed by the specific results of our measurements. Parts of the theoretical treatment of depolarization and phase-shift fluorometry given here are more fully expanded upon in (5,9-ll). Recent work and reviews of these techniques are given by Warner and McGown (72). 

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