Transference number of an ion

A variety of organoboron polymer electrolytes were successfully prepared by hydroboration polymerization or dehydrocoupling polymerization. Investigations of the ion conductive properties of these polymers are summarized in Table 7. From this systematic study using defined organoboron polymers, it was clearly demonstrated that incorporation of organoboron anion receptors or lithium borate structures are fruitful approaches to improve the lithium transference number of an ion conductive matrix. 

Finally, the transference number of an ion in a binary salt solution is... 

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 transference number of an ion is not a simple property of the ion itself it depends on which other ions are present and on their relative concentrations. It is apparent that the sum of the transference numbers of all the ions in the solution must equal unity. 

The contribution to the total conductivity will come from all free ions according to their concentration, activity, charge, and mobility. The transference number of an ion species is its percentage contribution to the total conductivity. 

The transference number of an ion j depends on the mobilities of the other ions... 

For a completely dissociated electrolyte, the transference number of an ion is the number of faradays of electricity carried by the ion concerned across a reference plane, fixed with respect to the solvent, when one faraday of electricity passes across the plane [436]. 

The transport, or transference, number of an ion is defined as the proportion of the total current carried by that ion. The above method yields the total conductivity due to all ions present, i.e. cation and anion in the case of a simple dissolved salt. If the partial conductivity due to a single ion is required, a Faradaic electrode process must be devised, e.g. by using electrodes of the same metal as the cation. On application of a constant potential the current decays with time until a steady state is reached corresponding to the condition... 

The transference or transport number of an ion can be determined by (i) the analytical method (ii) the moving boundary method and (iii) the emf method. The first two methods will be dealt with here, but the third will figure in a later section. 

The limiting molar conductivity of an electrolyte (A°°) and the limiting transference numbers of the ions constituting the electrolyte are determined ex-... 

By measuring the fall in concentration of electrolyte in the vicinity of anode and cathode of an electrolytic cell, and at the same time determining the amount of material deposited on the cathode of the cell or of a coulometer in the circuit, it is possible to evaluate the transference numbers of the ions present in solution. Since the sum of and must be unity, it is not necessary to measure the concentration changes in both anode and cathode compartments, except for confirmatory purposes similarly, if the changes in both compartments are determined it is not strictly necessary to employ a coulometer in the circuit. It is, however, more accurate to evaluate the total amount of material deposited by the current by means of a coulometer than from the concentration changes. 

If it is required to determine the transference numbers of the ions constituting the electrolyte MA, e.g., potassium chloride, by the moving boundary method, it may be supposed that two other electrolytes, designated by M A and MA, e.g., lithium chloride and potassium acetate, each having an ion in common with the experimental solute MA, arc available to act as indicators.Imagine the solution of MA to be placed between the indicator solutions so as to form sharp boundaries at a and 5, as shown in Fig. 41 the anode is inserted in the. solution of M A and the cathode in that of MA. In order that the boundaries... 

When an electric current is passed through a solution of an electrolyte the various ions present carry different proportions of the current. These proportions are called the transference numbers of the ions. (In British publications they are usually referred to as transport numbers.) The relation between the transference number, of the positive ion of a binary electrolyte and the ion mobilities, u+ and u, of the electrolyte may be seen as follows From equation (8a)... 

The ion of the type Cdl+ is called an intermediate ion. The effect of this kind of ionization would be to increase the directly measured or apparent transference number of die constituent Cd++, since the complex ion we have postulated would carry iodine in the reverse direction to the normal motion of that ion and thus reduce the measured transference number of that ion. Another possibility, and the one which probably occurs in solutions of this salt, is the ionization of the polymerized salt in the form of complex ions, of which the following equations represent two of the many possibilities ... 

The molar conductivity of an electrolyte is the more generally useful quantity since the Kohlrausch law allows its limiting value to be resolved into those of its constituent ions. Comparison between different electrolytes with a common ion therefore allows the determination of an unknown molar conductivity. However, the quantity typically measured is the overall electrolytic conductivity. A way to apportion the conductivity (and hence mobility) to the individual ions of the electrolyte is required. Equation (20.1.2-11) shows that resolution of the molar conductivity into the terms arising from its constituent ions is possible if the transference number of the ion is found. Although this property and the methods developed to measure it may seem rather arcane, it has been of fundamental importance in the understanding of the conductivity and diffusion potentials developed within electrolyte solutions. Experimentally, a number of ways of measuring transference numbers have been developed these are summarised below. 

A 0.2 mol L"1 LiCl/THF solution possesses only very low conductivity of 1.6xl0"6 Scm"1. Addition of N(CH2 CH2NR2)3(R = CF3S02 short nomenclature M6R) yields an increase in conductivity by three orders of magnitude to 1.7 x 10 3 S cm"1. This approach is seemingly especially useful for battery electrolytes, because the transference number of the lithium ion is increased. Conceptually this approach is similar to the use of lith-... 

There are in principle two types of charge-transfer processes at ITIES, a single ion and a single electron transfer reaction. The first one can be described as the transfer of an ion Xf< with charge number z. ... 

To immobilize such anions as borate, organoboron polymers were reacted with aryllithium reagents.31,32 The reaction of alkylborane polymers with n-BuLi was examined first however, the ionic conductivity of the resulting material was very low. Moreover, complicated peaks were observed in the H-NMR spectrum. Conversely, selective lithium borate formation was observed in the nB-NMR spectrum when PhLi was employed (scheme 6). An ionic conductivity of 9.45 X 10 7Scm 1 was observed at 50°C. The observed ionic conductivity was relatively low because of the decreased number of carrier ions compared with dissolved salt systems. However, the lithium transference number of this polymer was markedly high (0.82 at 30°C). 

This value is discussed in terms of two-electron transfer when Zn + is reduced to free zinc on Pt(lll) surface with a true electron transfer number of = 2. Also, induced adsorption of OH ions takes place to give OHads in an oxidative process. 

Consider a zinc strip immersed in water. At equilibrium, a small number of Zn2+ ions will pass into solution per unit time, leaving twice as many electrons behind, while an equal number of Zn2+ ions already in the water will be redeposited as elemental zinc (reaction 16.1). The rate of this process, in terms of the electrons transferred per unit surface area of the metal, is the exchange current density io for equilibrium 16.1, as explained in Section 15.4 ... 

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