Molar volume determination

Shim, J.-J., and K. P. Johnston. 1991. Phase equilibria, partial molar enthalpies, and partial molar volumes determined by supercritical fluid chromatography. J. Phys. Chem. 95 353-360. 

The change in coordination number is reflected in the absolute partial molar volumes, determined in aqueous LnCh solutions (Fig. 4.6). The calculated absolute partial molar volumes using the semi-empirical model of Swaddle [20, 21] agree well with [Ln(H20)g] + at the beginning and with [Ln(H20)8] at the end of the Ln series. 

In this section the experimental liquid phase compositions and liquid molar volumes determined for the P-diketone/C02 systems studied will be presented coupled with the modeling results using the Peng-Robinson EOS with van der Waals-1 mixing rules. Table II lists the estimated critical constants, Tc and Pc, and the acentric factor, co, needed for modeling these systems. 

As predicted by Eq. (33), an increase in the modifier molar mass, Le. increase in Zm, shifts the phase separation region to lower conversions (there is a decrease in peril.)- Figure 12 shows binodal curves calculated for an epoxy-diamine system, modified by three butadiene-acrylonitrile copolymers of different number-average molar mass [72]. These curves were calculated in a similar way as the curves shown in Fig. 11, Le. both components were regarded as mono-disperse with a molar volume determined by the number-average molar mass (constant for the butadiene-acrylonitrile copolymer and variable with conversion for the epoxy-diamine system). The interaction parameter for each particular system was fitted by making the predicted binodal curves to pass through the experimental points (< >mo> Pep)-... 

Example 9.2 Listed in Table 9.1 are data for the upper critical solution temperature of six polystyrene (PS)-in-dioctylphthalate (DOP) solutions as a function of molecular weight [10]. Also given is the corresponding ratio of molar volumes. Determine the temperature dependence of the interaction parameter. 

Standard-state fugacities at zero pressure are evaluated using the Equation (A-2) for both condensable and noncondensable components. The Rackett Equation (B-2) is evaluated to determine the liquid molar volumes as a function of temperature. Standard-state fugacities at system temperature and pressure are given by the product of the standard-state fugacity at zero pressure and the Poynting correction shown in Equation (4-1). Double precision is advisable. 

Samples can be removed for analysis, phase volumes can be measured to determine mixture composition and molar volumes (70), and phase boundaries can be measured. Many different configurations of view cells have been proposed. Some are capable of pressures ia excess of 100 MPa (14,500 psi). The cell coateats may be viewed safely through the sapphire wiadow by use of a mirror, video camera, or borescope. 

For predic ting diffiisivities in binary polar or associating liquid systems at liign solute dilution, the method of Wilke and Chang " defined in Eq. (2-156) can be utilized. The Tyn and Cains equation (2-152) can be used to determine the molar volume of the solute at the normal boihng point. Errors average 20 percent, with occasional errors of 35 percent. The method is not considered to be accurate above a solute concentration of 5 mole percent. 

The concept of equilibrium is central in thermodynamics, for associated with the condition of internal eqmlibrium is the concept of. state. A system has an identifiable, reproducible state when 1 its propei ties, such as temperature T, pressure P, and molar volume are fixed. The concepts oi state a.ndpropeity are again coupled. One can equally well say that the properties of a system are fixed by its state. Although the properties T, P, and V may be detected with measuring instruments, the existence of the primitive thermodynamic properties (see Postulates I and 3 following) is recognized much more indirectly. The number of properties for wdiich values must be specified in order to fix the state of a system depends on the nature of the system and is ultimately determined from experience. 

Temperature, pressure, and composition are thermodynamic coordinates representing conditions imposed upon or exhibited by the system, andtne functional dependence of the thermodynamic properties on these conditions is determined by experiment. This is quite direct for molar or specific volume which can be measured, and leads immediately to the conclusion that there exists an equation of. state relating molar volume to temperature, pressure, and composition for any particular homogeneous PVT system. The equation of state is a primaiy tool in apphcations of thermodyuamics. 

Consider Ni exposed to Oj/HjO vapour mixtures. Possible oxidation products are NiO and Ni (OH)2, but the large molar volume of Ni (OH)2, (24 cm compared with that of Ni, 6.6 cm ) means that the hydroxide is not likely to form as a continuous film. From thermodynamic data, Ni (OH)2 is the stable species in pure water vapour, and in all Oj/HjO vapour mixtures in which O2 is present in measurable quantities, and certainly if the partial pressure of O2 is greater than the dissociation pressure of NiO. But the actual reaction product is determined by kinetics, not by thermodynamics, and because the mechanism of hydroxide formation is more complex than oxide formation, Ni (OH)2 is only expected to form in the later stages of the oxidation at the NiO/gas interface. As it does so, cation vacancies are formed in the oxide according to... 

Deterioration of electrode performance due to corrosion of electrode components is a critical problem. The susceptibility of MHt electrodes to corrosion is essentially determined by two factors surface passivation due to the presence of surface oxides or hydroxides, and the molar volume of hydrogen, VH, in the hydride phase. As pointed out by Willems and Buschow [40], VH is important since it governs alloy expansion and contraction during the charge-discharge cycle. Large volume changes... 

Plot an appropriate volume unit vs. mole fraction of acetic acid. Determine the partial molar volumes of water and acetic acid at X2 = 0, 1, and several intermediate compositions (at least three). Plot V and V2 as a function of. Y2. 

In the case of solutions, lnF] would be determined from equation (6.85) using the partial molar volume of the solvent, V, in the solution, rather than the molar volume of the pure solvent. 

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). 

It has been stated above that the difference of partial molar volumes of the LS and HS isomers AK° can be obtained from the relaxation amplitude A of ultrasonic absorption. An independent method for the determination of AE° is based on the pressure dependence of the equilibrium constant. The pressure derivative of being determined by ... 

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