Transference numbers in mixtures

Transference Numbers in Mixtures.—Relatively little work has been done on the transference numbers of ions in mixtures, although both Hittorf and moving boundary methods have been employed. In the former case, it follows from equation (3) that the transference number of any ion in a mixture is equal to the number of equivalents of that ion migrating from the appropriate compartment divided by the total number of equivalents deposited in a coulometer. It is possible, therefore, to derive the required transference numbers by analysis of the anode and cathode compartments before and after electrolysis. 

The Transference Numbers of Ion Constituents in Mixtures of Electrolytes. The moving boundary method can in certain cases be used to determine the transference numbers of the ion constituents in mixtures of electrolytes. The method used by Longsworth 32 for determining the transference numbers in mixtures of hydrochloric acid and potassium chloride is as follows. 

With the series of transference numbers for mixtures of HCl and KC1 already referred to and conduct-ance values for the same solutions, values of An for the various mixtures were obtained by Langs worth. These were found to vary linearly with the mixing fraction, and could be extrapolated without error to yidd A iarK .. . the equivalent conductance of vanishingly small amounts of hydrogen Ion in... 

Ionic transference numbers in liquid mixtures of NH3 and HF containing 80.85 wt % HF have been measured at room temperature the results for NH4... 

Ratkje, S.K., Rajabu, H. and p0rland, T. (1993) Transference coefficients and transference numbers in salt mixtures relevant for the aluminium electrolysis. Electrochim. Acta, 38, 415-423. 

A benzene-toluene mixture is to be separated in a tower packed with 1-in. fieri saddles. The feed is 55.2 mol% (liquid feed, saturated), and an overhead of 90 mol% benzene, and bottoms of not more than 24 mol% benzene is desired. Using the data of Ref. 51 plotted in Figure 9-98, determine the number of transfer units in the rectifying and stripping sections using a reflux ratio (reflux to product, L/B) = 1.35. 

Chemiluminescence also occurs during electrolysis of mixtures of DPACI2 99 and rubrene or perylene In the case of rubrene the chemiluminescence matches the fluorescence of the latter at the reduction potential of rubrene radical anion formation ( — 1.4 V) at —1.9 V, the reduction potential of DPA radical anion, a mixed emission is observed consisting of rubrene and DPA fluorescence. Similar results were obtained with the dibromide 100 and DPA and/or rubrene. An energy-transfer mechanism from excited DPA to rubrene could not be detected under the reaction conditions (see also 154>). There seems to be no explanation yet as to why, in mixtures of halides like DPACI2 and aromatic hydrocarbons, electrogenerated chemiluminescence always stems from that hydrocarbon which is most easily reduced. A great number of aryl and alkyl halides is reported to exhibit this type of rather efficient chemiluminescence 155>. 

The standard ruthenium arene and CATHy catalysts are insoluble in water, but are nevertheless stable in the presence of water. Reactions in the I PA system can be carried out in mixtures of isopropanol and water the net effect is a lower rate due to dilution of the hydrogen donor. The use of formate salts in water, with CATHy or other transfer hydrogenation catalysts dissolved in a second immiscible phase was shown to work well with a number of substrates and in some cases to improved reaction rates [34]. The use of water as reaction solvent will be discussed in more detail in Section 35.5. 

In aqueous solution the exchange process H20 + D20 2HD0 occurs very rapidly via proton transfer. Consequently, in H20—D20 mixtures the rare earth has an average number of O—H bonds in its solvation sphere, the number being proportional to the H20/D20 ratio. The major quenching of a rare-earth ion in solution is due to the hydrogen vibrations about it and is proportional to the number of these bonds. 

Mikami has carried out a number of investigations aimed at elucidating mechanistic aspects of this Si-atom transfer process. In particular, when the aldol addition reaction was conducted with a 1 1 mixture of enoxysilanes 60 and 62, differentiated by the nature of the 0-alkyl and 0-silyl moieties, only the adducts of intramolecular silyl-group transfer 63 and 64 are obtained (Scheme 8B2.6). This observation in addition to results obtained with substituted enol silanes have led Mikami to postulate a silatropic ene-like mechanism involving a cyclic, closed transition-state structure organized around the silyl group (Scheme 8B2.6). 

Another classification involves the number of phases in the reaction system. This classification influences the number and importance of mass and energy transfer processes in the design. Consider a stirred mixture of two liquid reactants A and B, and a catalyst consisting of small particles of a solid added to increase the reaction rate. A mass transfer resistance occurs between the bulk liquid and the surface of the catalyst particles. This is because the small particles tend to move with the liquid. Consequently, there is a layer of stagnant fluid that surrounds each particle. This results in reactants A and B transferring through this layer by diffusion in order to reach the catalyst surface. The diffusion resistance gives a difference in concentration between... 

Example 10.5 Diffusion cell and transference numbers The diffusion cell shown in Figure 10.2 has NaCl mixtures in the two chambers with concentrations c1A = lOOmmol/L and c1B = lOmmol/L. The mobilities of Na+ and Cl- ions are different and their ratio yields their transference numbers b+lb = t+/t = 0.39/0.61 (NaCl). The transference number t for an ion is the fraction of the total electric current carried by the ion when the mixture is subjected to an electric potential gradient. For monovalent ions, we have t+lt = 1. Estimate the diffusion potential of the cell at steady-state conditions at 298 K. Assume that activity coefficients are equal in the two reservoirs (Garby and Larsen, 1995). 

The reduced transference numbers and are the Washburn numbers W2 and Wi introduced by Agar In his discussion the movement of a neutral solute is treated with respect to the solvent. Later on, Feakins used Washburn numbers to explain the solvent transport in mixtures of two solvent components when the solvent mole fraction is varied between 0 and 1. 

With the mean molar velocity v of the solvent mixture as reference velocity the reduced transference number of the non-aqueous component is equal to A, as shown in Eq. (97). 

Cell (D) has been used several times to determine the solvent transference number A of the sparingly soluble salt Ag2S04 in the binary solvent mixtures acetonitrile-water l, dimethylsulphoxide-water and dimethylsulphoxide-methanol In Fig. 3 the solvent transference number of Ag2S04 is plotted versus Xdmso =... 

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