Partial Molar Volumes of Ions in Solution

PARTIAL MOLAR VOLUMES OF IONS IN SOLUTION 2.6.1. Definition 

The molar volume of a pure substance can be obtained from density measurements, i.e., p = (molecular weight)/(molar volume). The volume contributed to a solution by the addition of 1 mole of an ion is, however, more difficult to determine. In fact, it has to be measured indirectly. This is because, upon entry into a solvent, the 

The effective ionic voiume of an ion in soiution, the partiai moiar voiume, can be determined via a quantity that is directly obtainable. This is the apparent moiar voiume of a salt, V 2 defined by 

if the volume of the solvent were not affected by the presence of the ion, V- would indeed be the volume occupied by 2 moles of ions. However, the complicating fact is that the solvent volume is no longer, per mole of solvent the molar volume of the solvent is affected by the presence of the ion, and so V 2 is called the apparent molar volume of the ion of the salt. Obviously, as when 2 0, the 

This equation tells one that the density of the solution that gives for a series of concentrations gives the partial molar volume t/ at any value of n - Knowing from and / , Eq. (2.7) can be used to obtain as a function of n - Extrapolation of Vto /ij = 0 gives the partial molar volume of the electrolyte at infinite dilution, V (i.e., free of interionic effects). 

---

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... 

Marcus Y (2012) The standard partial molar volumes of ions in solution. Part 5. Irmic volumes in water at 125 to 200°C. J Phys Chem B 116 7232-7239... 

Ellis, A.J. McFadden, I.M. "Partial Molar Volumes of Ions in Hydrothermal Solutions," Geochem. Cosmochim. Acta, 1972, 36, 413-26. 

Rb, and Cs. The heats of hydration of these ions vary in the same order. Thus it seems that the deviations from the limiting law are related to the intensity of the interaction energy between the dissolved ions and the solvent. A similar conclusion is suggested by Stewart s f observation that the variation of the partial molar volume of ions with concentration is closely linked with the change of the structure of water in the same solutions, as revealed by X-ray studies. Unfortunately there are no satisfactory quantitative theories to account for these complex phenomena. 

Similar cases of specific interactions have been found also for the partial molar volumes of electrolytes (ions) in mixed solvents. The reports concerning the partial molar volumes of electrolytes in mixed solvents generally do no pertain to dilute solutions of the cosolvent, but on the contrary, most such studies cover the entire composition range. The curves tend to be very asymmetric in the solvent composition and changes in direction are often encountered, as shown, for example, in Figure 6.1 for some electrolytes in aqueous DMSO according to Letellier et al. [30]. In a few cases were very dilute solutions were studied, so that pair-interaction parameters could be... 

These equilibrium reactions occur with large decreases in both volume and entropy. Volume changes range from —80 to —300 cm /mol depending on the solute and pressure. These volume changes, A V, are associated with the electrostriction of the solvent around the product anion, Fei(ion), and, to some extent, with a contribution of the partial molar volume of the electron, V(e). Thus ... 

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... 

The question of coordination in aqueous solutions is not as clear as in solid state. Sped-ding s work [53] on the partial molar volumes of aquo ions of lanthanides and the irregular trends of these quantities in the lanthanides has been taken as evidence for change in coordination number in the lanthanide series [54]. The change in coordination from 9 to 8 in the lanthanide series has been confirmed by X-ray and neutron diffraction studies of LnCb solutions [55], The coordination numbers of lanthanides determined in aqueous solutions by various techniques along with the coordination numbers obtained are given below ... 

The transport of water by the ions was first measured by Washburn. Using the Hittorf method, a reference substance such as sugar or urea is added to the solution. Presumably the reference substance does not move in the field, and the transport of the solvent can be calculated from the analysis of the solution in the three compartments. If a value is assumed f or the number of water molecules attached to one ion, a value f or the number attached to the other ion can be calculated. Presently other methods for evaluation of hydration numbers are preferred—from measurements of the partial molar volume of the salt in the solution, for example. The different methods are internally consistent but often do not agree well with each other. It is generally assumed that the negative ions are not hydrated. Then the hydration numbers are, approximately Li", 6 Na", 4 K", 2 Rb", 1. 

The partial molar volume is a thermodynamic quantity that plays an essential role in the analysis of pressure effects on chemical reactions, reaction rate as well as chemical equilibrium in solution. In the field of biophysics, the pressure-induced denaturation of protein molecules has continuously been investigated since an egg white gel was observed under the pressure of 7000 atmospheres [60]. The partial molar volume is a key quantity in analyzing such pressure effects on protein conformations When the pressure in increased, a change of the protein conformation is promoted in the direction that the partial molar volume reduces. A considerable amount of experimental work has been devoted to measuring the partial molar volume of a variety of solutes in many different solvents. However, analysis and interpretation of the experimental data are in many cases based on drastically simplified models of solution or on speculations without physical ground, even for the simplest solutes such as alkali-halide ions in aqueous solution. Matters become more serious when protein molecules featuring complicated conformations are considered. 

The standard partial molar volume of an ion in aqueous solution, Vf, is the actual volume to be assigned to the ion in the solution (at infinite dilution). It is the sum of its intrinsic volume, Tnntr", and the electrostriction that the ion has caused in the water around it, yieiec , the latter being a negative quantity. The volume of a bare unhydrated ion, A%Np,l i)r, cannot represent its intrinsic volume and must be enlarged to account for the void spaces between the water molecules and the ion and among themselves in order to represent the intrinsic volume of the ion in the solution. A factor of A = 1.213 was proposed by Mukerjee (1961) for the alkali metal and the halide ions, producing ... 

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. 

---