Volume at infinite dilution

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

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 ... 

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) ). ... 

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. 

Note that the equations for estimating the pressure dependencies of 7 and aw (Eqs. 2.87 and 2.90) depend on the Pitzer equations (Eqs. 2.76, 2.80, and 2.81) but this is not the case for the pressure dependence of the equilibrium constants (Eq. 2.29) the latter equation is based entirely on partial molar volumes at infinite dilution, which are independent of concentration. Also, compared to the pressure-dependent equation for the equilibrium constant (Eq. 2.29), the pressure equations for activity coefficients (Eq. 2.87) and the activity of water (Eq. 2.90) do not contain compressibilities (K) because the database for these terms and the associated Pitzer parameters are lacking at present (Krumgalz et al. 1999). The consequences of truncating Eqs. 2.80 and 2.81 for ternary terms and Eqs. 2.87 and 2.90 for compressibilities will be discussed in Sect. 3.6 under limitations. 

The composition dependence of the total volume of a solution at constant temperature and pressure is expressed in terms of the partial molar volumes of the solute and the solvent. Since we are concerned with solvation properties, the quantities which we need to discuss are the partial molar volumes in infinite dilution of the solute so that solute-solute interactions make no contribution. In practice, partial molar volumes are obtained indirectly from precise density measurements. The partial molar volumes at infinite dilution of the amino acids are compiled in Table 2 [7]. It is apparent from these data that an approximately linear correlation exists between the partial molar volume and the number of carbon atoms in the backbone. The data indicate volume contributions from the polar head group (NH, COj) and from the CH2 group and to be about... 

The calculated correlation volumes and energetic parameters for the alcohol—water and hydrocarbon—water systems are hsted in Tables 4 and 5. The calculated volumes are compared with the sizes of clusters in several alcohol/water systems determined by small-angle X-ray scattering or light scattering " at low concentrations (Table 6). Table 6 shows that there is reasonable agreement between them and the calculated correlation volumes at infinite dilution. 

One can see from Tables 4 and 5 that the correlation volume at infinite dilution increases for both normal hydrocarbons and normal alcohols with the number of carbon atoms. A comparison between the two shows that they are several times larger for hydrocarbons than for the corresponding alcohols, but that the difference between them decreases as the number of carbon atoms increases (Figure 1). 

TABLE 6 Comparison between the Radius of the Correlation Volume at Infinite Dilution of Alcohol in ... 

Figure 1. Dependence of correlation volume at infinite dilution on the number of hydrocarbon atoms n. Hydrocarbon in water (A) and alcohol in water ( ).

Cooney, W. R. O Connell, J. P. Correlation of partial molar volumes at infinite dilution of salts in water. Chem. Eng. Commun. 1987, 56, 341-349. 

Several factors can affect this enhanced mass transfer. First, as Debenedetti and Reid ( pointed out, the very low kinematic viscosities in conjunction with very high buoyant forces serve to enhance natural convection at the same Reynolds number. This is accentuated by large density differences that can occur as naphthalene dissolves in the C02 It is possible to have very large, negative partial molar volumes (i.e., -2000 cc/mole) for a solute at conditions near the critical point (Eckert et al., (23)) which causes the fluid density to depend strongly on composition. At 35 0 and 100 atm, naphthalene s partial molar volume at infinite dilution is approximately -300 cc/mol. This can cause a significantly higher fluid... 

Thus, for the component A, we simply get the molar (or molecular) volume of pure A, whereas for component B, we get the partial molar volume at infinite dilution. 

This is a change in volume at infinite dilution when the solute and solvent are mixed to give the... 

Value of partial molar volume at infinite dilution. tValiie of pure-component molar volume. 

For very dilute mixtures of a gaseous solute(l) in water(2), experimental data show that, over wide temperature ranges, the partial molar volume at infinite dilution can be correlated by... 

The activity coefficient in (10.4.10) is to be evaluated at the system pressure, while the Poynting factor involves the partial molar volume at infinite dilution. Usually, we use (10.4.10) for some species and either (10.4.6) or (10.4.7) for the others. An expression exactly analogous to (10.4.10) can also be developed using the reference-solvent Henry s constant. 

FIGURE 8.11 Behavior of A 2,ex(SR) and p" (Ci2 - C°j) for an infinitely dilute CsBr aqueous solution as a function of the solvent density along three supercritical isotherms in comparison with experimental data. (Data from J. Sedlbauer, E. M. Yezdimer, and R. H. Wood, 1998, Partial Molar Volumes at Infinite Dilution in Aqueous Solutions of NaCl, LiCl, NaBr, and CsBr at Temperatures from 550 K to 725 K, Journal of Chemical Thermodynamics, 30, 3.) Vertical arrow indicates the estimated critical density of the model solvent... 

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