Infinite dilution partial molar volume

Figure 7 Measured infinite dilution partial molar volume of naphthalene in supercritical ethylene at 12°C (Ziger et al., 1986).

Fig. 2.15. Plot of infinite-dilution partial molar volumes of homologous R4N chlorides in water against the cation molecular weight allowing extrapolation to obtain (Reprinted from B. E. Conway, Ionic Hydration in Chemistry and Biophysics, Elsevier, New York, 1981.)...

Figure 1. Infinite dilution partial molar volume of naphthalene in SCF ethylene at 285 K. (Reprinted from ref. 12.1986 American Chemical Society.)...

There have been a number of modeling efforts that employ the concept of clustering in supercritical fluid solutions. Debenedetti (22) has used a fluctuation analysis to estimate what might be described as a cluster size or aggregation number from the solute infinite dilution partial molar volumes. These calculations indicate the possible formation of very large clusters in the region of highest solvent compressibility, which is near the critical point. Recently, Lee and coworkers have calculated pair correlation functions of solutes in supercritical fluid solutions ( ). Their results are also consistent with the cluster theory. 

McGuigan, D. B., and P. A. Monson. 1990. Analysis of infinite dilution partial molar volumes using a distribution function theory. 7. Fluid Phase Equil. 57 227-247. 

FIGURE 9.3 Variations of Krichevskii function, for various small solutes in water (a) for high solvent densities, (b) for lower densities. Symbols for data, lines for Equation 9.25. (Reprinted with permission from J. P. O Connell, A. V. Sharygin, and R. H. Wood, 1996, Infinite Dilution Partial Molar Volumes of Aqueous Solutes over Wide Ranges of Conditions, Industrial and Engineering Chemistry Research, 35, 2808. With permission from ACS Publishing.)... 

These analytically integrable expressions are included in the evaluations for and for (Sedlbauer, O Connell, and Wood 2000). Figure 9.8 shows results for this model for aqueous NaCl with data for infinite dilution partial molar volumes... 

Maloney and Prausnitz (29) used high-pressure, gas-liquid chromatography to measure Henry s constants and infinite-dilution partial molar volumes of ethylene in liquid polyethylene. 

The volume fhKtion of penetrant is related easily to penetrant sorption concentratron it tire paniai muiai volume of the penetrant can be approximated by its molar volume as a hypothetical liquid. Values of the infinite dilution partial molar volume of various gases in a series of low-molecular-weight liquids are shown in Table 20.4-4. Since rubbery polymers are essentially high-motecular-weight liquids, the average values shown in the table for the various penetrants would be reasonable estimates of the partial molar volume in polymeric media also. 

O Connell, J. P. Sharygin, A. V. Wood, R. H. (1996) Infinitely Dilution Partial Molar Volumes of Aqueous Solutes over Wide Ranges of Conditions, Industrial Engineering Chemistry Research 35, 2808-2812... 

Infinite-dilution partial molar volumes for CO2 in various low molecular weight hquids (Table 6) are insensitive to the type of medium and decrease only shghtly as interactions between the medium and CO2 increase. This approximation may be somewhat inappropriate for highly supercritical gases such as nitrogen or methane, but for CO2 near ambient temperature it appears valid. The average of the CO2 partial molar volumes in the organic liquids is approximately 46 cm /mol. The value for CO2 in silicone rubber determined from analysis of... 

The experimental quantities reported in the study publication are indicated in the 10th column density (d) differential density (solution density minus water density) (dd) solution molar volume (V) solution specific volume (Vs) apparent molar volume (Vf) solute infinite dilution partial molar volume (Vo), excess volume (Ve), volume of mixing (Vm), compressibility factor (Z), virial coefficients (B, C, D, E), and soimd velocity (sv). 

Plyasunov, A. V., J. P. O Connell, and R. H. Wood. 2000. Infinite dilution partial molar properties of aqueous solutions of nonelectrolytes. I. Equations for partial molar volumes at infinite dilution and standard thermodynamic functions of hydration of volatile nonelectrolytes over wide ranges of conditions. Geochimica et Cosmochimica Acta. 64,495. 

VSTR is useful for estimating partial molar volumes at infinite dilution but is not used here because of Equation (4-17)... 

FIg. 6. Partial molar volumes of gaseous solutes at infinite dilution in expanded solvents. 

Figure 5.3 shows V and V2 for the (benzene + cyclohexane) system as a function of mole fraction, obtained in this manner.3 Shown on the graph are Fm, i and F, 2, the partial molar volumes (which are the molar volumes) of the pure benzene and pure cyclohexane. The opposite ends of the curves gives Vf and Vf, the partial molar volumes in an infinitely dilute solution. We note that... 

Two additional data points with 15 to 35 C temperature intervals were obtained from data of Yasunishi and Yoshida(34). Partial molar volumes of salts of infinite dilution were obtained from a compilation by Millero.(47) Results are presented in Figure 10. (Note that the salts are listed there in the order of increasing difference in partial molar volume.) The correlation is surprisingly good, with the constant c equal to —0.0056 kg H20/cm3. 

The partial molar volume data of Table I on ammonia was calculated from density data in Landolt-Bornstein(57). The values of partial molal volume at infinite dilution can be expressed as ... 

Lattice energy of crystalline salt, k cal/mol Partial molar volume of molecular specie at infinite dilution, cm3/mol... 

Partial molar volumes at infinite dilution were adopted from the correlation of Brelvi and O Connell (20). (In the pressure range regarded here (p 100 atm) Poynting corrections are very small and can be neglected for all electrolytes as well as for water (eqs. E1, E2) ). ... 

As seen from Eq. (130) an activity coefficient may deviate significantly from unity at higher salt concentrations. The activity coefficient can therefore also be used as a measure of the deviation of the salt solution from a thermodynamically ideal solution. If the chemical potential of a solute in a (pressure-dependent) standard state of infinite dilution is /x°, we find the standard partial molar volume from... 

Thus, the partial molar volume is constant along the Henry s-law line and equal to the standard partial molar volume. The only real solution along the Henry s-law line is the infinitely dilute solution, so... 

The excess molar volumes of 10-40 mol % methanol/C02 mixtures at 26°C as a function of pressure has been determined. The excess molar volumes varied with composition and pressure significant interaction between CO2 and methanol was noted from the observed excess molar volumes. To better characterize the interaction and its effect on analyte solubility, the partial molar volume of naphthalene at infinite dilution in liquid 10 and 40 mol % methanol/C02 mixtures was determined. The variation of the partial molar volume at infinite dilution with pressure correlated well with isothermal compressibility of the methanol/C02 mixtures (Souvignet and Olesik, 1995). 

The partial molar volumes at infinite dilution of the amides show a consistent volume decrease for the amides on transfer into the aqueous phase, which becomes greater with increasing size of the substituents and amounts to about 2.5 cc. per mole per pair of methylenic groups in the case of the acetamide series. This value may be compared with that found in the alcohol series (6), where a more negative value of about 2.5 cc. per mole per methylenic group is found, and also to similar de-... 

Special classes of apparatus are used for the determination of particular thermodynamic properties, such as activity coefficients at infinite dilution, Henry s constants, or partial molar volumes at infinite dilution [105,106]. These data, together with a thermodynamic model, can be used for the calculation of the compositions of the coexisting phases at equilibrium, and for that reason - in this context - these methods are considered as indirect methods of measurement. 

Bj2 - vi )/RT, v = the partial molar volume of the sample at infinite dilution in the stationary (liquid) phase, (1) refers to the sample, (2) to the carrier gas, (3) to the stationary liquid, and is a function of the column inlet and outlet pressures, and pQ. 

In equations (18.91) and (18.92), C° 2 and V are the partial molar heat capacity and partial molar volume of the surfactant in the infinitely dilute solution (standard state values). 

In Equations (10.43) and (10.44) Vf represents the partial molar volume of the component in the infinitely dilute solution, which is also the partial molar volume of the component in the standard state. The right-hand side of Equation (10.44) contains only quantities that can be determined experimentally, and thus A/j. [T, P, x] can be determined. However, just as in the previous case, the pressure is a function of the mole fraction. Therefore, if we require values of A/tf at some arbitrary constant pressure, the correction expressed in Equation (10.34) must be made with the substitution of Vf for... 

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