Determination of the Transference Number

The electrolyte is sandwiched between two electrodes which have different but precisely known chemical potentials for the electroactive species. Since no overall current is allowed to pass the external electric circuit (i.e., =0), integration of Eq. 

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Table II. Test of "Adjusting Effect. Result of Interrupting Current in Determination of the Transference Number of the Chloride Ion in 0.01 Normal NaCl...

Table III. The Influence of the Volume Correction in the Determination of the Transference Number of Potassium Chloride...

If possible, electrodes blocking for the least conducting species should be used in this kind of experiment, as it gives the highest accuracy in the determination of the transference numbers. 

It is particularly important to note that [ /TO)] is a function of the transfer number B. This dependence as determined by Emmons is shown in Fig. 6.18. 

To this end, io c.c. of the oil are boiled for an hour with an equal volume of acetic anhydride and 2 grams of dry sodium acetate in a flask fitted with a ground-in, upright condenser. When cold, the liquid is diluted with water, heated for about half an hour on a water-bath and then transferred to a separating funnel. The acetylated oil is separated from the aqueous liquid, washed with water or sodium chloride solution until it is neutral and dried by means of anhydrous sodium sulphate. 2 grams of this acetylated oil are then employed for the determination of the saponification number as described above (p. 279). 

The -> concentration cells are used only for determination of -> transport (transference) numbers, - activity, and -> activity coefficients of electrolytes and other quantities. Their practical application is limited by the -> selfdischarge due to the spontaneous diffusion process. In concentration cells no chemical reactions occur, a physical process (the equalization of activities by diffusion) causes the potential difference and supplies the energy. 

The chains of the produced polymer are lengthened by combination, but not by disproportionation. This affects the molecular mass distribution but the differences are not very large, differing by a factor of 2 at most. Due to the inaccuracies in molecular mass determinations, it is almost impossible to make estimates of the relation between termination and disproportionation from the distributions. Even labelling of the initiator and determination of the average number of its fragments in a macromolecule (one for disproportionation and two for combination) is usually unsafe because of transfer. 

One of the challenges faced during the transfer of HPLC methods is to ensure that samples used in the transfer are from identical batches of materials. Associated with this challenge is the determination of the appropriate number of... 

Concerning heat transfer,and the determination of the Nusselt number, the Gnielinski correlation valid for Re > 2300 is the most general [17] ... 

Heat transfer in micrombes with viscous dissipation is investigated by Tung and Bayazitoglu [15]. The temperature jump, is ignored in the calculation of the temperature distribution, but taken into account in determination of the Nusselt number. 

Tschapek et al. [68, 69] proposed a method to determine the position of the PZC of oxides and related materials in the presence of KCl based on the pH dependence of the transference number of cation k+ in a plug or paste. KCl was chosen because the K and Cf ions are nearly equitrasferent. i.e. another salt or salt mixtue with fcation 0-5 could be used as well. The transference number is determined from the potential of the following cell ... 

The procedure to be described is a determination of a transference number by the Hittorf1 method. The solution can be arbitrarily divided into three portions, as shown in the diagram, called respectively the anode, middle, and cathode portions. On passing a current the anode portion will become more concentrated, and the cathode portion more dilute. The middle portion will retain its original concentration. After the electrolysis the separate portions may be drawn off one after... 

The failure of Walden s rule to hold except as an approximation indicates that the ions are not sufficiently large when compared with those of the solvent medium for Stokes Law to be valid, or that the radii of the ions (r+ and r ) vary from solvent to solvent, or that, possibly, the deviations are due to both these causes. It is known, from the determinations of true transference numbers described in Chapter 4 and from other evidence, that ions are hydrated in aqueous solution, and it is probable that they are solvated in other media. It is unlikely, therefore, that the radii of the ions would remain constant-in different solvents so that the failure of Walden s rule to be more than an approximation is not surprising. 

Use of cells with and without transference in determination of the transport numbers of large ions... 

Equation 2.18 effectively incorporates the retardation effects into the mobility determination for high concentration solutions. As an example, for aqueous solution at room temperature T = 298K), using D = 78.56 and t] = 0.008948, the variation of the mobility of the positive ion with concentration in 1,1 valency electrolytes of HCl, KNO3, and NaCl are plotted in Figure 2.5 according to Equation 2.18. The variation of the transference numbers of the cations with the concentration are also plotted to discern its effect on the mobility of each ion. As observed, the square root model represents the reduction of the mobility of each ion with increasing concentration, where the reduction appear to be mostly dependent on A. ... 

R 671 H. -c. Zhang, X. -p. Xuan, J. -j. Wang and H. -q. Wang, Progress on the Determination of Ionic Transference Numbers in Polymer Electrolytes , Dianyuan Jishu, 2003,27, 54... 

Graphical methods for the determination of the required number of theoretical stages discussed so far, are easy to use and are of practical importance for first approximations for separation processes of binary mixtures, or for systems with inert carrier mixtures and a single component to be transferred. If several components are transferred between the phases in contact, the number of separation stages can only be calculated with the aid of a computer graphical methods can only be partially applied. 

Fig. 2-66. Nomogram for the determination of the diameter, number of transfer elements and related shaft area for a cross-flow tray of type KSG-S (see Table 2-19) of Montz GmbH.

The required packing height Z for mass and heat transfer between counterflow phases may be calculated in two different ways as discussed in Chapter 1.9.2. After determination of the desired number of theoretical separation stages N, by numerical or graphical means, and the separation efficiency experimentally under conditions close to the operating conditions and suitable for scale up, the packing height is... 

This section would not be complete without mention of the complementary indirect m.b. method. Here the concentration of the adjusted Kohlrausch solution behind the boundary is measured the transference number of the following ion-constituent can then be calculated from the Kohlrausch equation and a knowledge of the transference number of the leading ion-constituent. 6.S. Hartley and his co-coworkers (21) were the first to develop this approach which has proved valuable for determining transference numbers of very slow ion-constituents such as cetyltrimethylammonium (6 1) and other surfactant species and, quite recently, of cadmium in dilute aqueous CdCl solutions (62.). ... 

He was a well-known scientist (see e.g., the invitation from the Nobel Prize Committee for nomination). He elaborated a method for the determination of the hydration number of ions by measuring the transference numbers of the ions in the presence of indifferent (organic) compounds of different concentrations (Fig. 12.5). At that time, it was the most accurate measurement of the hydration number as pointed out by Nemst in his book [5],... 

For classical microporous membranes and 1 1 salts (z+ =z =1 and C+=C ), the relative magnitude of the transference numbers for the positive and negative ions is determined by the ratio of their mobility ... 

In order to determine the packed height it is necessary to obtain a value of the overall number of transfer units methods for doing this are available for binary systems in any standard text covering distillation (73) and, in a more complex way, for multicomponent systems (81). However, it is simpler to calculate the number of required theoretical stages and make the conversion ... 

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