Partial molar volume ionic solutes

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. 

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. 

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. 

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... 

Marcus Y (2008) On the relation between thermodynamic, transport and structural properties of electrolyte solutions Russ. J Electrochem 44 16-27 Marcus Y (2008a) Properties of individual ions in solution. In Bostrelli DV (ed) Solution chemistry research progress. Nova Science pubhshers, Inc., Hauppauge, 51-68 Marcus Y (2009) The standard partial molar volumes of ions in solution, part 4. Ionic volumes in water at 0-100 °C. J Phys Chem B 113 10285-10291 Marcus Y (2009a) The effects of ions on the structure of water structure-breaking and—making. Chem Rev 109 1346-1370... 

Marcus Y (2012a) The standard partial molar volumes of ions in solution. Part 5. Ionic volumes in water at 125-200 °C. J. Phys. Chem. B 117 http //dx.doi/10.1021/jp212518t Marcus Y (2012b) Are ionic Stokes radii of any use J. Solution Chem in the press Marcus Y, Hefter G (1999) On the pressure and electric field dependencies of the relative permittivity of liquids. J Sol Chem 28 575-591 Marcus Y, Hefter G (2006) Ion pairing. Chem Rev 106 4585-4621... 

The unusual mole fraction scale for the solution, with 5 x(H+,aq) = -68.2 J mol was used for the calculation of values of Astmc5 for the alkali metal and halide ions as well as Ag+ and CIO4 (Abraham et al. 1982). However, the choices of the value of 5 (H+, aq) and the mole fraction scale caused K+ to appear as a strue-ture making ion. This unacceptable result is corrected by adjustment to the molar scale with 5° (H+, aq) = - 22.2 J mol. Linear correlations of Astmc5 with the viscosity coefficients and with the NMR coefficients (Sect. 3.1.3) and also with the ionic partial molar volumes or their electrostricted volumes were noted by Abraham et al. (1982). 

Tabulated are single-ion entropies of about 110 diatomic and polyatomic ions in water Gibbs energies, enthalpies, and entropies of hydration of monatomic ions at 25 C partial molar volumes of about 120 common ions at 25 C ionic partial molar heat capacities of ions Gibbs energies of transfer of inorganic electrolytes from HjO to 020 and calorimetrically determined enthalpies of solution of salts in H2O and 020. 

For the illustrated drugs (solute), Kp is about 10 for pro-pranolole and nearly 0 for chloramphenicol and ibuprofen the partial molar volume v of the micelle has been calculated as 0.021 mmol at a pH of 7.4. Note that for salicylic acid only a slight change of the ionic mobility is visible due to its very similar mobility compared to that of the micelle itself (Figure 3). 

Another method for the estimation of the intrinsic volumes of electrolytes, independent of values of the ionic radii, was proposed by Pedersen et al. [53], who employed the molar volume of the molten alkali metal halides, extrapolated to ambient temperatures, as a measure of their intrinsic volumes in aqueous solutions, but the extrapolation is quite long. A variant of this idea is to use the molar volumes of molten hydrated salts, proposed by Marcus [54], where the temperature extrapolation to 25°C is much shorter. It is then necessary to subtract the volume of the water of hydration, which is n times the molar volume of electrostricted water, 15.2 cm mok at 25°C [55], from the extrapolated molar volume of the undercooled molten hydrated salt containing n water molecules per formula unit of the salt. A cogent method, applicable to highly soluble salts, was proposed by Marcus [56]. The volumes considered, applied to aqueous solutions, are intrinsic, so they should be independent of the concentration c and to a certain extent also of the temperature T. The partial molar volume of an electrolyte, V c, T), describes the volume that it actually occupies in the solution and does not include the volume of the water. Therefore, a fairly short extrapolation of the hnear 25°C) from c = 3M to such high concentrations at which all of the solvent is as closely packed as possible (completely electrostricted) is equivalent to considering the electrolyte as an undercooled molten hydrated salt... 

As mentioned earlier, the actual volume to be assigned to an ion in the solution at infinite dilution is its standard partial molar volume V". It may be negative, in particular for small highly charged ions, because the electrostriction (volume diminution), 1/,", such ions cause in the water surrounding the ion may be numerically larger than the intrinsic volume of the ion, [80], Ionic intrinsic volumes that are independent of the concentration are discussed in Section 2.2 and are shown for... 

Concentrations will be expressed as mole fraction of a component or species /, x = nj/E nj as molality, mole per mass of solvent, mol kg or molarity, mole per volume of solution. The concentration scale will depend on the properties of the solutes (i.e., ionic, polar, nonpolar, etc.). Pressure, p, and the gas phase partial pressure of species i, / , will be expressed in bars (approximately equal to atmospheres). 

A single homogeneous phase such as an aqueous salt (say NaCl) solution has a large number of properties, such as temperature, density, NaCl molality, refractive index, heat capacity, absorption spectra, vapor pressure, conductivity, partial molar entropy of water, partial molar enthalpy of NaCl, ionization constant, osmotic coefficient, ionic strength, and so on. We know however that these properties are not all independent of one another. Most chemists know instinctively that a solution of NaCl in water will have all its properties fixed if temperature, pressure, and salt concentration are fixed. In other words, there are apparently three independent variables for this two-component system, or three variables which must be fixed before all variables are fixed. Furthermore, there seems to be no fundamental reason for singling out temperature, pressure, and salt concentration from the dozens of properties available, it s just more convenient any three would do. In saying this we have made the usual assumption that properties means intensive variables, or that the size of the system is irrelevant. If extensive variables are included, one extra variable is needed to fix all variables. This could be the system volume, or any other extensive parameter. 

One important solute is water, which is completely miscible in imidazolium salts with short alkyl side chains and hydrophilic anions such as d, but is only partially miscible with ionic liquids with longer side chains and less hydrophilic anions. Extraction into an aqueous phase is important for product recovery from an ionic liquid medium. Hanke and Lynden-BeU [143] used simulation to investigate thermodynamic properties and local structure in mixtures of water with [MMIM]Q and [MMIM][PF6] liquids. They found that the excess energy of solvation was negative for the chloride and positive for the [PF ]" liquid, as shown in Fig. 4.2-12. There is a similar difference in the molar volumes of mixing shown in Fig. 4.2-13. This is consistent with the perception of the [PFe]" anion as being more hydrophobic than the chloride anion. 

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