Transference number definition

It is well known that the flow of either the positive or the negative ions, or of both, is responsible for the electric conduction process through the body of the solution of an electrolyte. Let the fraction of the current carried by each ion in a given electrolyte be considered. For this purpose, the transference numbers mentioned in the previous section are introduced according to the definitions... 

Based on the Sherwood number definition and the solutions for a range of inlet velocities, evaluate the surface mass transfer (kg/m2 s) of gallium to the surface. Assume that only gallium remains on the surface and that methyl groups desorb back to the gas,... 

Since the fraction of electrons and holes, although very small, depends on the (local) oxygen potential and since the mobility of the electronic defects is far larger than that of the ionic defects, the electronic conductivity may, by continuously changing the oxygen potential, eventually exceed the ionic conductivity. By definition, the transference number is t-loa = erion/(crion + crei)> which explicitly yields... 

These equations can be expressed in terms of the chemical potentials of the salts when the usual definition of the chemical potentials of strong electrolytes is used. The transference numbers may be a function of x as well as the molality. Arguments which are not thermodynamic must be used to evaluate the integrals in such cases (see Kirkwood and Oppenheim [33]). One special type of cell to which either Equation (12.112) or Equation (12.113) applies is one in which a strong electrolyte is present in both solutions at concentrations that are large with respect to the concentrations of the other solutes. Such a cell, based on that represented in Equation (12.97), is... 

And substitution into Equation 3.50 leads to a phenomenological definition of the mass transfer number ... 

Although there are many definitions of the mass transfer number, they are mostly generated for specific conditions such as droplet burning or boundary layer burning. All retain the same physical concept, which is the capability of the flame to self-sustain by generating more fuel. If B > 1, then the flame will produce more fuel than that necessary to sustain burning. 

The use of equation (30) gives a mean transference number of the electrolyte within the range of concentrations from Ci to C2, but this is of little value because of the variation of transference numbers with concentration a modified treatment, to give the results at a series of definite concentrations, may, however, be employed. If the concentrations of the solutions are c and c + dc, the e.m.f. of the cell with transference is given by the general form of equation (22) as... 

If the right-hand side is constant, for cells with transference containing different chlorides at definite concentrations, it may be concluded that the approximate equation (36) gives a satisfactory measure of the liquid junction potential between two solutions of the same electrolyte. The results in Table XLV provide support for the reliability of this equation, within certain limits the transference numbers employed are the mean values for the two solutions, the individual figures not differing greatly in the range of concentrations involved. 

Type of Boundary and Liquid Junction Potential.—When the two solutions forming the junction contain different electrolytes, the structure of the boundary, and hence the concentrations of the ions at different points, will depend on the method used for bringing the solutions together. It is evident that the transference number of each ionic species, and to some extent its activity, will be greatly dependent on the nature of the boundary hence the liquid junction potential may vary with the type of junction employed. If the electrolyte is the same in both solutions, however, the potential should be independent of the manner in which the junction is formed. In these circumstances the solution at any point in the boundary layer will consist of only one electrolyte at a definite concentration hence each ionic species should have a definite transference number and activity. When carrying out the integration... 

This term is somewhat unfortunate since it implies that the Hittorf transference numbers are false. The latter are, however, the values used in thermodynamic relations, and are measures of a perfectly definite, though somewhat complex, process. The term true in this connection is, however, of too general usage to make a change advisable. 

Chapter 13 includes a short introduction to the theory of nonequilibrium thermodynamics. A discussion of frames of reference in the definition of transport coefficients is given and a systematic theory of diffusion is presented. Fluctuations in electrolyte solutions are analyzed, and the parameters measured in electrophoretic light-scattering experiments are related to conductance and to the transference numbers—quantities usually measured in conventional electrochemistry. 

The transference number of an ion is defined as the fraction of the current carried by that ion. By Eq. (31.29) the conductivity of a solution containing any number of electrolytes is K = CiXi, then by definition the transference number of the fcth ion is... 

The frame of reference used in the definition of transference numbers in solution, and therefore in their determination, is an imaginary plane fixed with respect to the solvent as a whole (sect. 5.8). Yet some solvent molecules must be solvating and travelling along with the ions while other molecules of solvent remain relatively unaffected by the passage of current and could be regarded as free . This concept has already been referred to in sect. 5.10.1. Were it possible to set up a plane stationary with respect to the free part of the solvent only, one would be able... 

The definition of transference numbers, Eqs. (52), entails for 1, 1 electrolytes the relationships... 

Solid ionic conductors that can be used in electrochemical cells as an electrolyte are called solid electrolytes. In such compotmds only one ion is mobile (see entry. Solid State Electrochemistry, Electrochemistry Using Solid Electrolytes). Generally, any conductor with a high ionic transference number can serve as an electrolyte. Often, the definition after Patterson is used who described solids with a transference number > 0.99 as solid electrolytes [1]. The transference number is not a fixed value. It depends on the temperature and the partial pressure of the gas involved in the chemical reaction with the mobile ion. Therefore, all solids are more or less conductors with a mixed ionic and electronic conductivity, so-called mixed conductors. For the application in sensors and fuel cells, only a window concerning temperature and partial pressure is suitable. This is also called as electrolytic domain. The phenomenon that solids exhibit a high ionic conductivity is also designed as fast ion transport. 

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