True transference numbers

On determining experimentally the number of moles of water transported and correcting Hittorf s transference numbers <+ accordingly, we obtain the true transference numbers (<+)ttue- Both values valid for cations of some electrolytes at 25 °C and in 1.3 N - solution are indicated in the following table ... 

The interaction of ions with solvent molecules suggests a more detailed picture in which during electrolysis the cations are transporting nj+ solvent molecules into the cathode compartment and the anions nj solvent molecules out of that region into the opposite direction. The residual molecules of the solvent, which remain unaffected by the ion movement, are regarded as free , n = ni+, ni are total solvation numbers of the ions which differ from those in Chapter III. The transference numbers t[ referred to the free solvent (index ) are called true transference numbers The diffusion current density referred to the velocity v j of the free solvent results from Eq. (51) ... 

True and Apparent Transference Numbers.—The fundamental assumption of the Hittorf method for evaluating transference numbers from concentration changes is that the water remains stationary. There is ample evidence, however, that ions are solvated in solution and hence they carry water molecules with them in their migration through the electrolyte this will result in concentration changes which affect the measured or apparent transference number. Suppose that each cation and anion has associated with it and w- molecules of water, respectively let T+ and be the true transference numbers, i.e., the actual fraction of current carried by cations and anions, respectively. For the passage of one faraday of electricity the cations will carry w T+ moles of water in one direction and the anions will transport W-T- moles in the opposite direction there will consequently be a resultant transfer of... 

It may be noted that the values obtained by the moving boundary method, like those given by the Hittorf method, are the so-called apparent transference numbers (p. 114), because the transport of water by the ions will affect the volume through which the boundary moves. It is the practice, however, to record observed transference numbers without applying any correction, since much uncertainty is attached to the determination of the transport of water during the passage of current. Further, in connection with the study of certain types of voltaic cell, it is the apparent" rather than the true" transference number that is involved (cf. p. 202). 

The so-called true transference numbers are considered on page 91. 

True Transference Numbers and Ionic Hydration. In addition to ionic complexes arising from association and partial dissociation of the solute in solutions of electrolytes there is also the possibility of solvation, that is to say, complex formation between the solute and the solvent. With aqueous solutions it is called hydration. There is much experimental evidence showing that electrolytes are hydrated in aqueous solutions.40 One of the most important types of this evidence will be outlined below. 

The use of the method just outlined for determining the amount of hydration involves the assumptions (a) that the reference substance does not move under an impressed emf, and (b) that it does not form compounds with the solute. The first assumption is capable of experimental test, and Buchboclc made the validity of the second appear extremely probable since he found the same true transference number using various amounts of reference substance. 

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. 

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. 

Nn/Nu,)x equiv. The apparent transference number of the cation will thus be smaller than the true value by this amount that is,... 

In exactly the same way it may be shown that the water transported by the ions will cause a decrease of concentration in the cathode compartment hence the transference number will be larger than the true value, viz.,... 

If the net amount of water (x) transported were known, it would thus be possible to evaluate the true and apparent transference numbers from the results obtained by the Hittorf method. 

A solution, 100 g. of which contained 2.9359 g. of sodium chloride and 0.58599 g. urea, was electrolyzed with a silver anode and a silver chloride cathode after the passage of current which resulted in the deposition of 4.5025 g. of silver in a coulometer, Taylor and Sawyer [/. Chem. Soc. 2095 (1929)] found 141.984 g. of anode solution to contain 3.2871 g. sodium chloride and 0.84277 g. urea, whereas 57.712 g. of cathode solution contained 2.5775 g. sodium chloride and 0.32872 g. urea. Calculate the true and apparent transference numbers of the ions of sodium chloride in the experimental solution. 

Let s consider 4, within the above-mentioned ranges of temperatures and pressures. The true ionic transference number based on [10] can be expressed according to the following equation ... 

The conclusion is legitimate, provided that the true transport numbers really alter with concentration This, however, has been called in question in view of the newer results obtained by means of the reference substance method of determining transference numbers... 

Transference numbers obtained by a method which is uninfluenced by the movement of water of hydration have been called true 41 transference numbers. The first attempt to obtain such numbers was made by Nernst and associates.42 Successful measurements in this field have been carried out by Buchbock43 and much more extensively by Washburn.44 The procedure employed was essentially that of a Hittorf measurement. However, a second solute (usually a carbohydrate, such as sucrose or raffinose) is added to the aqueous solution, and, instead of referring the changes of salt concentration to the water, as in the computations for Hittorf transference numbers, the changes, both of salt and of water, are referred to the added solute. The apparatus used by Washburn has already been described. It is evident that if the added "reference substance is uninfluenced by the passage of the... 

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. 

Table VIII. "True and Hittorf Cation Transference Numbers and Transference of Water for a Series of Chlorides, at 1.3 Normal...

In this simplified treatment, we assume that the transference numbers are essentially the same in the bulk solution and in the diffusion layer near an electrode. This will be true when the concentrations of ions in the solution are high, so that only small fractional changes in local concentration are caused by the electrolytic generation or removal of ions. This condition is met in most experiments. If the electrolysis significantly perturbs the ionic concentrations in the diffusion layer compared to those in the bulk solution, the values clearly will differ, as shown by equation 4.2.10 (12). 

The authors [32] took into account the axial dispersion in both phases through the number of overall transfer units (NTUs), which consists both of the number of true transfer units determined by the interfacial transfer rate and the number of dispersion units. The column was divided into sections in which temperatures and thermal properties of both phases were approximately constant. 

Roes and van Swaaij [35] described the adsorption process with the model of interphase mass transfer (the number of true transfer units, and axially dispersed plug flow ... 

The boundary conditions were represented by Danckwerts equations [40]. The authors used the experimental results for axial dispersion from their previous investigations [29,30]. The differential equations were solved using several well-known approximations, which relate the number of overall transfer units with the number of true transfer units, as well as with the axial dispersion and with the extraction factor. 

Lastly, it was assumed that the details of the screw geometry do not affect the heat transfer to the barrel this is not completely true. The number of flights, the flight clearance, the flight helix angle, and the flight width all affect the heat transfer from the polymer melt to the barrel. If we want to study the effect of these parameters in detail we have to use a more complicated, numerical analysis. 

If Equation 9 is true then the transference number measured by the Hittorf or the m.b. method should be identical to that obtained from the emfs of cells with transport (111). Moreover, the sensitivity of this test increases with increasing electrolyte concentration. During the 1970s three transference studies with concentrated solutions were undertaken to test the equation ... 

Table 1.2 Transference numbers in sulfuric acid and potassium hydroxide at room temperature. For diluted solutions of sulfuric acid given in Ref. 10, but also true for concentrations used in batteries. For potassium hydroxide true for a wide concentration range given in Ref. 11. 

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