Ionic Molar Mobility

The solution species were characterised in terms of ionic molar mobility, diffusivity, mobility, and hydrated ion radius prior to speciation. Equilibrium pH of the backffound solution was estimated as a function of gas type and operatingpressure. 

The ionic molar mobility (Perry and Chilton (1973)) is defined as... 

T Time period [s] [Pg.371]

In the development of the theory of ionic conductance it has been shown that the viscosity of the solvent is an important parameter determining ionic mobility. Initially, conductivity data were only available in water so that attention was focused on the effects of ionic size, structure, and charge in determining mobility and its concentration dependence. More recently, data have become available in a wide variety of non-aqueous solvents [11, 12], that is, in media with a wide range of permittivities and viscosities. On the basis of these data one may examine in more detail the role of solvent viscosity in determining the transport properties of single ions. Values of the limiting ionic molar conductance for selected monovalent cations and anions are summarized in tables 6.4 and 6.5, respectively. 

The ionic mobility, transport number and ionic molar conductivity are all linked. The velocity with which an ion migrates is proportional to the drop in potential over the region in which the ion migrates. Put otherwise, the velocity of migration is proportional to the electric field. 

This method for determining transport numbers is the preferred method since it is inherently more accurate than the Hittorf method. Even more important is the fact that the transport numbers can be found over a range of concentrations. This, in turn, means that ionic mobilities and individual ionic molar conductivities can also be found over a range of concentrations. 

The terms in the mobility can be expressed in terms of the ionic molar conductivities, since kj = ZjFuj see Section 11.17, and so multiplying throughout by ZjF gives ... 

The mobilities of ions at infinite dilution, Mi , are directly proportional to the limiting ionic molar conductivities ... 

The rates of movement of ions in an electric field are expressed by their mobilities Mj, measuring their speed at unit field. The mobilities at infinite dilution, m", are directly proportional to the limiting ionic molar conductivities ... 

Conductivities k of electrolytes are related to molar conductivities A, ion conductivities A, and ionic mobilities w(- by Eq. (57)... 

Figure 7. Isotherms of in various binary nitrates (Mi, M2)N03 as a function of molar volume. Mj = Na, A Mj =Li+ 0 Na+, n K, V Rb, 0 Cs, + Ag, x TF. (Reprinted from M. Chemla and I. Okada, Ionic Mobilities of Monovalent Cations in Molten Salt Mixtures, Electrochim. Acta 35 1761-1776, Fig. 7, Copyright 1990 with permission from Elsevier Science.)...

In the classical theory of conductivity of electrolyte solutions, independent ionic migration is assumed. However, in real solutions the mobilities Uj and molar conductivities Xj of the individual ions depend on the total solution concentration, a situation which, for instance, is reflected in Kohhausch s square-root law. The values of said quantities also depend on the identities of the other ions. All these observations point to an influence of ion-ion interaction on the migration of the ions in solution. 

Table 8.2 lists the conductivities, transport numbers and molar conductivities of the electrolyte A = olc, and ions Xj = t+A for a number of melts as weU as for 0.1 M KCl solution. Melt conductivities are high, but the ionic mobilities are much lower in ionic liquids than in aqueous solutions the high concentrations of the ions evidently give rise to difficulties in their mutual displacement. 

The electrophoretic mobility of an ion is inversely related to the ionic strength of the buffer rather than to its molar concentration. The ionic strength (ytt) of a buffer is half the sum of the product of the molar concentration and the valency squared for all the ions present in the solution. The factor of a half is necessary because only half of the total ions present in the buffer carry an opposite charge to the colloid and are capable of modifying its charge ... 

The value for k will normally decrease as the concentration of the solution decreases but the value for A will increase because of the increased dissociation of molecules in dilute solutions. A value for the molar conductance at infinite dilution (A,)) can be determined by plotting the calculated values for A against the molar concentration of the solution used and determining the plateau value for A. From such investigations it is possible to determine the ionic mobilities of ions (Table 4.3) and calculate the molar conductance of an... 

Such a chemical approach which links ionic conductivity with thermodynamic characteristics of the dissociating species was initially proposed by Ravaine and Souquet (1977). Since it simply extends to glasses the theory of electrolytic dissociation proposed a century ago by Arrhenius for liquid ionic solutions, this approach is currently called the weak electrolyte theory. The weak electrolyte approach allows, for a glass in which the ionic conductivity is mainly dominated by an MY salt, a simple relationship between the cationic conductivity a+, the electrical mobility u+ of the charge carrier, the dissociation constant and the thermodynamic activity of the salt with a partial molar free energy AG y with respect to an arbitrary reference state ... 

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. 

Example 3.7 Use molar ionic conductivity data in Table 3-1 to calculate the mobility and diffusivity of Na+, Cl and NaCl at infinite dilution and 298.15 K. 

Note e = electron charge NA = Avogadro s number z, = charge of ion of type Mt = molar concentration of ions in the bulk e = dielectric constant of the medium 4 = energy of attraction A = Hamaker constant d = distance between the surfaces 4 = energy of repulsion = ionic concentration (in number/volume) T0 1 17 = viscosity of the liquid u = electrophoretic mobility... 

---