Ionic volume, partial molar

The revised HKF equation for the noneleclrostatic part of the ionic standard partial molar volume is ... 

Values of the ionic standard partial molar volumes of the hydrogen, alkali metal, alkaline earth metal, and anunonium cations and hydroxide, hahde, nitrate, perchlorate, and sulfate anions from 0 to 200°C at 25°C intervals have been reported by Marcus in Refs. 79-81. Conventional values V " for these ions (except CIO ) and also for HCOj" and HS are reported by Tanger and Helgeson [84] from 0 to 350°C at 25°C intervals. 

For Eq. (2) it is assumed that the volume of the micellar phase is proportional to the tenside concentration and that the partial molar volume v remains constant. (See Chapter 2.) A further prerequisite for the application of Eq. (2) is a constant ionic mobility of the micellar phase independent of the uptake of a solute (/x, . = const.). In contrast to HPLC, substances that have an infinitely high kP value, i.e., that are completely dissolved in the micellar phase, can be detected. In this case the sample molecule migrates with the mobility of the micelle. In the presence of several different micellar phases (coexistence of simple and mixed micelles), the calculation of kP is possible only when partial capacity factors are known (20). The determination of kP is then considerably more complicated. 

KP and v can, in contrast to kp, not be determined via the concentration gradient for binary and ternary mixed micelles, because for the calculation of the Nemstian distribution a constant CMC and an almost constant partial molar volume must be assumed. The calculation of aggregation constants of simple bile salt systems based on Eq. (4) yields similar results (Fig. 8b). Assuming the formation of several concurrent complexes, a brutto stability constant can be calculated. For each application of any tenside, suitable markers have to be found. The completeness of dissolution in the micellar phase is, among other parameters, dependent on the pH value and the ionic strength of the counterions. Therefore, the displacement method should be used, which is not dependent on the chemical solubilization properties of markers. For electrophoretic MACE studies, it is advantageous for the micellar constitution (structure of micelle, type of phase micellar or lamellar) to be known for the relevant range of concentrations (surfactant, lipids). 

Partial molar volumes of electrolytes may present an additional difficulty if the partial molar volumes of individual constituent ions are needed. The subject has been dealt with as part of a valuable discourse on metal ion solvation.158 For species in water and some other solvents, the reference point for calculation of other partial molar volumes of single ions is the partial molar volume of the solvated proton, although there have been different views on what this value should be.159 However, the variation in values is not large and the consequence of choice of value does not have a huge impact particularly for large ionic species. Theoretical models of partial molar volumes of hydrated ions have been developed in order that estimates of them can be calculated. 160-162... 

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... 

Several methods involve a study of the properties of solutions in equilibrium and are hence reasonably described as thermodynamic. These methods usually involve thermal measurements, as with the heat and entropy of solvation. Partial molar volume, compressibility, ionic activity, and dielectric measurements can make contributions to solvation studies and are in this group. 

Once partial molar volumes are broken down into the individual partial ionic voiumes (see Section 2.6.2), the information given by partiai moiar voiume measurements includes the net change in volume of the solvent that the ion causes upon entry and hence it provides information relevant to the general question of the structure near the ion, that is, its solvation. 

How Does One Obtain Individual Ionic Volume from the Partial Molar Volume of Electrolytes ... 

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.)...

Conway has suggested a method that seems to give results in agreement with those of a second entirely different method, the ionic vibration method (see later discussion). Conway found that plotting the partial molar volume of a series of electrolytes involving large cations (e.g., a tetraalkylammonium series) and a constant smaller... 

It is usually relatively easy to find the solvation-related property of an electrolyte (as, e.g., the heat of hydration, Section 2.5.2) or the partial molar volume (Section 2.6.2) of a salt in solution. However, experiments that reflect the properties oUndividual ions are difficult to devise, the only simple, direct one being the transport number of an ion (Section 2.10) and the associated individual ionic mobility (Section 2.10.1). 

Obtaining the individual properties of ions with solvation numbers from measurements of ionic vibration potentials and partial molar volumes is not necessary in the study of gas phase solvation (Section 2.13), where the individual heats of certain hydrated entities can be obtained from mass spectroscopy measurements. One injects a spray of the solution under study into a mass spectrometer and investigates the time of flight, thus leading to a determination of the total mass of individual ions and adherent water molecules. 

Observed molar conductivities were analyzed by assuming the ion association (ion-pair formation) between the complex ions and the counter ions in the same manner as described previously. The closest distances of approach of ions (a) in the Robinson-Stokes conductivity equation and in the Debye-HUckel equation were taken as 6.8 and 7.3 A for chlorides and perchlorates of the tris(phen) complexes 6.6 and 7.1 A for those of the tris(bpy) complex, respectively, using the effective ionic radii of the complex ions, shown in T le 1, and those of Cl (1.81 A) and C104 (2.30A). The values of ref were estimated from the ionic partial molar volumes (f i°°) by use of Glueckauf equation. > ... 

Table 1. Partial Molar Volume (Vj°°). Effective Ionic Radius (rjf), Stokes Radius (rs), and Temperature CoefScient of Walden Product (dln( A °°Tj ldT) at 25 ...

All the complex ions studied are regarded as hydrophobic stnicture-makers, since the dln( X °° 7] o)/d7 values are positive, similarly to the tetraalkylammonium ions.5 The hydrophobicity of the trivalent [Co(phen)3]3 ion is inferior to that of the divalent [Fe(phen)3]2+ ion since the dln( A °° Tt ldT value of the former complex is smaller than that of the latter complex. This suggests that the hydrophobic atmosphere around the complex ion is weakened with increasing ionic charge, correlated to the reduction of the partial molar volume (1, °°) which is explicable as the increase in the electrostriction by Glueckauf s equation. 

The effective ionic volume of an ion in solution, the partial molar volume, can be determined via a quantity that is directly obtainable. This is the apparent molar volume of a salt, defined by... 

Once partial-molar..volumes are broken down into the individual partial ionic... 

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