Measurement of transport numbers

It is very important to be able to measure transport numbers over a range of concentrations as this is the only way to determine the dependence of individual molar ionic conductivities as a function of concentration. If this can be done, then it means that observed molar conductivities for any electrolyte at given concentrations can be split up into the contributions from the ions of the electrolyte. 

if A and f+ are known, then A+ can be found. From this. A- is found since A = xA+ + yA-, and likewise the dependence of A+ and /l on concentration can be found. 

There are two main methods for determining transport numbers, both of which were developed early in the study of conductance. They are the Hittorf method and the moving boundary method. The emf method has been described in Section 9.21. 

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The measurement of transport numbers by the above electrochemical methods entails a significant amount of experimental effort to generate high-quality data. In addition, the methods do not appear applicable to many of the newer non-haloalu-minate ionic liquid systems. An interesting alternative to the above method utilizes the NMR-generated self-diffusion coefficient data discussed above. If both the cation (Dr+) and anion (Dx ) self-diffusion coefficients are measured, then both the cation (tR+) and anion (tx ) transport numbers can be determined by using the following Equations (3.6-6) and (3.6-7) [41, 44] ... 

The metals, and to a lesser extent Ca, Sr, Ba, Eu, and Yb, are soluble in liquid ammonia and certain other solvents, giving solutions that are blue when dilute. These solutions conduct electricity electrolytically and measurements of transport numbers suggest that the main current carrier, which has an extraordinarily high mobility, is the solvated electron. Solvated electrons are also formed in aqueous or other polar media by photolysis, radiolysis with ionizing radiations such as X rays, electrolysis, and probably some chemical reactions. The high reactivity of the electron and its short lifetime (in 0.75 M HC104, 6 x 10"11 s in neutral water, tm ca. 10-4 s) make detection of such low concentrations difficult. Electrons can also be trapped in ionic lattices or in frozen water or alcohol when irradiated and again blue colors are observed. In very pure liquid ammonia, the lifetime of the... 

Measurement of Transport Numbers in Liquid Electrolytes.. . . 5.6.13. Radiotracer Method of Calculating Transport Numbers in... 

Fig. 32.—Tubandt s method for measurement of transport numbers of ions in a-Agl.

To determine activity coefficients of NaCl in aqueous solution at 25 C from e.m.f. measurements of cells with transference and measurements of transport numbers. 

Ratios of the activity coefficients of sodium chloride in aqueous solutions of various concentrations at 15 °C, 25 °C, and 35 °Chave been determined by Janz and Gordon (J. Amer. Chem. Soc. 1943, 65, 218) by combining measurements of e.m.f. of concentration cells with independent measurements of transport number. Their data can be fitted by the formula (compare problems 81 and 86)... 

A proper interpretation of EMF measurements of transport numbers should take into account the polarization of electrodes in the case of ionic transport [43]. This can be obtained from impedance spectra. 

Measurement of Transport Numbers In Aqueous Solutions of Electrolytes Russian Chemical Reviews (Uspekhi Khimii) 89 (1966)... 

The Tubandt method is a direct approach to the measurement of transport number according to Faraday s law. It is particularly applicable to network polymers," which can be arranged as a stack of discs placed in electrical series between two electrodes made of the same metal as the cation. For each Faraday of charge passed, the disc next to the positive electrode gains t /xm moles of salt which can be determined by weighing (or some other analysis) provided the disc can be separated from the stack at the end of the experiment. 

The empirical phase of the development of solid electrolyte fuel cells was overcome only after many general advances in research on solids. These included development of X-ray structure analysis, new knowledge on the ion conduction of solids from the measurements of transport numbers by Tubandt (first detection of unipolar conduction by anions), the establishment of the theory of disorder in solids by Frenkel, Schottky, Wagner and Jost, and the development of isotope methods for the investigation of diffusion processes in solids. 

By the mid-1980s, measurements of transport numbers were showing that the anion was, at least, carrying a current equal to the cation and, in many measurements, a current greater than that carried by the cation. This observation made the original conductivity model inadequate. Molecular models have now been developed that describe motion of the ions based on oscillations of the polymer strands. And the free volume model for conductivity has been adopted from polymer chemistry. 

It is unclear at this time whether this difference is due to the different anions present in the non-haloaluminate ionic liquids or due to differences in the two types of transport number measurements. The apparent greater importance of the cation to the movement of charge demonstrated by the transport numbers (Table 3.6-7) is consistent with the observations made from the diffusion and conductivity data above. Indeed, these data taken in total may indicate that the cation tends to be the majority charge carrier for all ionic liquids, especially the allcylimidazoliums. However, a greater quantity of transport number measurements, performed on a wider variety of ionic liquids, will be needed to ascertain whether this is indeed the case. 

For a fully dissociated salt, all techniques should give the same values of transport number, t. Transference number measurements are appropriate for electrolytes containing associated species and any technique within one of the three groups will give a similar response, but values of 7] across the groups may vary. 

There is difficulty in defining the absolute mobilities of the constituent ions in a molten salt, since it does not contain fixed particles that could serve as a coordinate reference. Experimental means for measuring external transport numbers or external mobilities are scarce, although the zone electromigration method (layer method) and the improved Hittorf method may be used. In addition, external mobilities in molten salts cannot be easily calculated, even from molecular dynamics simulation. 

During electrolysis there is no change in composition of an individual melt close to the electrode surfaces only its quantity (volume) will change. The resulting void space is filled again by flow of the entire liquid melt mass. This flow replaces the diffusional transport of ions customarily associated with aqueous solutions. This has particular consequences for the method used to measure ionic transport numbers ... 

Fig. 2.10 Schematic design of a cell for the determination of transport numbers from measurements of the concentration decrease in electrode compartments (Hittorf s method)...

If the cation is more hydrated, then W is a positive number if the anion is more hydrated, then W is a negative number and water is transported to the anode. Transport numbers calculated from measured concentration changes involving transport of water by solvated ions are sometimes called Hittorf (/, ) numbers those corrected for the transport of water are called true transport numbers (f,). These two types of transport numbers are related by... 

With high dilutions P. Walden found the increase with dilution is very small and finally decreases, showing that the salt is completely hydrolyzed. W. Hittorf measured the transport numbers of the ions of the sodium salt. 

The VMATs are also among the very few vesicular neurotransmitter transporters whose turnover number is known. At 29° C, they transport —5 molecules of serotonin per second and up to 20 molecules of dopamine (Peter et al., 1994). Since synaptic vesicles contain 5 to 20,000 molecules of transmitter and can recycle within at least 20 seconds (Ryan and Smith, 1995 Rizzoli et al., 2003), this rate has important implications for quantal size. At 5 molecules/second, the vesicle would contain only 100 molecules of transmitter after 20 seconds—if there were only one transporter per vesicle. Recent estimates suggest several transporters per vesicle (Takamori et al., 2006), but these might still not suffice to fill a rapidly cycling vesicle with monoamine unless the turnover was substantially higher at 37° C, where it is more difficult to measure transport accurately due to increased membrane leakiness. Indeed, the ability to determine the turnover of VMATs has been enabled by the availability of ligands to quantify the transporter and hence provide a denominator for measurements of transport. 

The chemiosmotic model requires that flow of electrons through the electron-transport chain leads to extrusion of protons from the mitochondrion, thus generating the proton electrochemical-potential gradient. Measurements of the number of H+ ions extruded per O atom reduced by complex IV of the electron-transport chain (the H+/0 ratio) are experimentally important because the ratio can be used to test the validity of mechanistic models of proton translocation (Sec. 14.6). 

Can one explain this importance of the slag Measurements of conductance as a function of temperature and of transport number indicate that the slag is an ionic conductor (liquid electrolyte). In the metal-slag interface, one has the classic situation (Fig. 5.81) of a metal (i.e., iron) in contact with an electrolyte (i.e., the molten oxide electrolyte, slag), with all the attendant possibilities of corrosion of the metal. Corrosion of metals is usually a wasteful process, but here the current-balancing partial electrodic reactions that make up a corrosion situation are indeed the very factors that control the equilibrium of various components (e.g., S ) between slag and metal and hence the properties of the metal, which depend greatly on its trace impurities. For example,... 

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