Ionic conductivity, independent

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. 

This equation is valid for both strong and weak electrolytes, as a = 1 at the limiting dilution. The quantities A = zf- FU have the significance of ionic conductivities at infinite dilution. The Kohlrausch law of independent ionic conductivities holds for a solution containing an arbitrary number of ion species. At limiting dilution, all the ions conduct electric current independently the total conductivity of the solution is the sum of the contributions of the individual ions. 

When the limiting molar conductivities are to be obtained for a series of ions in a given solvent, the first step is to get the limiting molar conductivity of an ion by one of the above methods. Then, the limiting molar conductivities for other ions can be obtained sequentially by applying Kohlrausch s law of independent ionic migration (Section 5.8). 

If Kohlrausch s law of independent ionic migration is applicable to solutions of appreciable concentration, as well as to infinite dilution, as actually appears to be the case, the equivalent conductance of an electrolyte MA may be represented by an equation similar to the one on page 57, viz.. 

Note that, in contrast to electronic conduction, the ionic conductivity is Pq independent because the concentration of ionic defects is fixed extrinsi-cally. Such an independence of conductivity on partial pressure is usually taken to be strong evidence that a solid is indeed an ionic conductor. 

The A° values are not accessible to direct measurement, but they may be calculated from transport numbers. Kohlrausch s law of independent ionic conductivities states that at low electrolyte concentrations the conductivity is directly proportional to the sum of the n individual ion contributions, that is. 

A° values for other ions in the given solvent followed readily from the conductances of tetraethylammonium or picrate salts by application of Kohlrausch s rule of independent ionic migration. Ulich has summarised many of the earlier results some later examples of solvents to which this approach has been applied are ethylenedichloride (Pic"), HCN (Pic" and Bu4N ), dimethylacetamide (Bu4N+), and propanol, wopropanoF and butanoF ° (Hept4N and (/-Am)3BuN ). 

The ions conduct independently and are free for electrostatic interaction, which can be neglected for our purposes. Table 2 lists some equivalent ionic conductances. These are the currents in amperes that would flow if a potential difference of 1V were applied to a cell having two metallic plates, each 1 cm in area and placed 1 cm apart, with a solution between them that contained 1 g equiv of the ions in question in 1 cm. The unit of 2, therefore, is Q cm g-equiv. The reciprocal ohm, is commonly called the Siemens (S). The conductances of the dilute solutions used in 1C are commonly in the range of pS. 

Kohlrausch s law of independent ionic migration states that the molar conductivity at infinite dilution, A°, is given by the sum of the values for its ionic components, A + and. ... 

Both time- and voltage-dependent ionic conductances and voltage-independent ionic conductances are found in biological membranes. Two experimental methods have been developed in order to determine the relationship between the membrane potential and the ionic conductance these are the constant current or current clamp and the constant voltage or voltage clamp techniques. In the case of the current clamp, one applies a constant current step to the membrane and records the resulting membrane potential changes . 

Ionic conductors arise whenever there are mobile ions present. In electrolyte solutions, such ions are nonually fonued by the dissolution of an ionic solid. Provided the dissolution leads to the complete separation of the ionic components to fonu essentially independent anions and cations, the electrolyte is tenued strong. By contrast, weak electrolytes, such as organic carboxylic acids, are present mainly in the undissociated fonu in solution, with the total ionic concentration orders of magnitude lower than the fonual concentration of the solute. Ionic conductivity will be treated in some detail below, but we initially concentrate on the equilibrium stmcture of liquids and ionic solutions. 

Promotion, electrochemical promotion and metal-support interactions are three, at a first glance, independent phenomena which can affect catalyst activity and selectivity in a dramatic manner. In Chapter 5 we established the (functional) similarities and (operational) differences of promotion and electrochemical promotion. In this chapter we established again the functional similarities and only operational differences of electrochemical promotion and metal-support interactions on ionic and mixed conducting supports. It is therefore clear that promotion, electrochemical promotion and metal-support interactions on ion-conducting and mixed-conducting supports are three different facets of the same phenomenon. They are all three linked via the phenomenon of spillover-backspillover. And they are all three due to the same underlying cause The interaction of adsorbed reactants and intermediates with an effective double layer formed by promoting species at the metal/gas interface (Fig. 11.2). 

This same equation is, of course, also used to rationalise the general electronic behaviour of metals, semiconductors and insulators. The quantitative application of Eqn (2.1) is handicapped for ionic conductors by the great difficulty in obtaining independent estimates of c,- and u,-. Hall effect measurements can be used with electronic conductors to provide a means of separating c, and u,- but the Hall voltages associated with ionic conduction are at the nanovolt level and are generally too small to measure with any confidence. Furthermore, the validity of Hall measurements on hopping conductors is in doubt. 

There are two times to consider, therefore, in order to characterise ionic conduction. One is the actual time, tj, taken to jump between sites this is of the order of 10 -10 s and is largely independent of the material. The other time is the site residence time, which is the time (on average) between successful hops. The site residence times can vary enormously, from nanoseconds in the good solid electrolytes to geological times in the ionic insulators. Ion hopping rates, cOp, are defined as the inverse of the site residence times, i.e. 

The diffusivity is independent of the motion of any other species (e.g. electrons or holes) and is not influenced by internal electrical fields as in the case of chemical diffusion processes which require the simultaneous motion of electronic or other ionic species. The partial ionic conductivity of the mixed ionic and (predominantly) electronic conducting electrode is given by the product of the concentration and the diffusivity and may be related to the variations of the steady state and transient voltage ... 

Wagner s solution See Wagner s reagent. vag narz sa.Iu shan 1 Walden s rule phys chem A rule which states that the product of the viscosity and the equivalent ionic conductance at infinite dilution In electrolytic solutions is a constant, independent of the solvent It Is only approximately correct. wol-danz, rul ... 

---