Activity coefficient from cell with transference

ACTIVITY COEFFICIENT FROM CELL WITH TRANSFERENCE 

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. 

In the same table are given values of the cation transport number taken from the measurements of Longsworth (J. Amer. Chem. Soc. 1932, 54, 2741). 

By subtraction we obtain the e.m.f. E of cells in which the molalities m and m of the two electrode solutions are equal to pairs of successive values of m in table 1. For such a cell we have the relation 

By meeuis of formula (1) we obtain values of A log my and by subtracting A log m we obtain values of A log y. We define a quantity y (compare problem 81) by 

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ACTIVITY COEFFICIENTS FROM CELLS WITH TRANSFERENCE... 

Activity Coefficients from Cells With Transference.—In order to set up a cell without transference it is necessary to have electrodes reversible with respect to each of the ions of the electrolyte this is not always possible or convenient, and hence the use of cells with transference, which require electrodes reversible with respect to one ion only, has obvious advantages. In order that such cells may be employed for the purpose of determining activity coefficients, however, it is necessary to have accurate transference number data for the electrolyte being studied. Such data have become available in recent years, and in the method described below it will be assumed that the transference numbers are known over a range of concentrations. ... 

Table IV. Activity Coefficients of Calcium Chloride from Cells with Transference at 25°...

For solutions dilute enough for equation (29) to be applicable, the plot of log (///o) + -4 Vc against [a — log (///o)]Vc should be a straight line with intercept equal to a. The value of a, which is required for the purpose of this plot, is obtained by a short series of approximations. Once a, which is equal to — log /o, is known, it is possible to derive log / for any solution from the values of log ///o obtained previously. The activity coefficient of the electrolyte can thus be evaluated from the e.m.f. s of cells with transference, provided the required transference number information is available. 

Determination of Transference Numbers.—Since activity coefficients can be derived from e.m.f. measurements if transference numbers are known, it is apparent that the procedure could be reversed so as to make it possible to calculate transference numbers from e.m.f. data. The method employed is based on measurements of cells containing the same electrolyte, with and without transference. The e.m.f. of a concentration cell without transference E) is given by equation (11), and if the intermediate electrodes are removed so as to form a concentration cell with transference, the e.m.f., represented by Et, is now determined by equation (25), provided the transference numbers may be taken as constant within the range of concentrations in the cells. It follows, therefore, on dividing equation (25) by (11), that... 

The computation involved in obtaining activity coefficients from data on the potentials of concentration cells with transference is as follows. According to equation (19) the potential of a cell with transference of the type, for instance, of (10) or (11) is the integral of... 

The computation of activity coefficients from A log j values will be illustrated for hydrochloric acid since in that case direct comparison can be made with the results of measurements on concentration cells without transference of the type described in Chapter 6. The relevant data are given in Table II and are from the work of Shedlovsky and Maclnnes.18 The emf data in the second column were obtained from a cell of the type illustrated in Fig. 4. The transference numbers in the third column were interpolated from the measurements of Longs-worth given in Table IV of Chapter 4. The A log f values in the fourth column were computed as described in the last paragraph. 

Values at other temperatures are given in Table V, Knowing Eq it is evidently possible to compute the activity coefficients, 7, of hydrochloric acid at the molality, m, from the potential E of the cell of equation (11). Such activity coefficients, as a matter of fact, agree very closely with those obtained from concentration cells with transference. This is indicated indirectly by Fig. 5, Chapter 8. 

Precise values of the activity coefficients of aqueous ammonium chloride solutions at 25 °C, determined from e.m.f. measurements of cells with transference, have been reported for the concentration range 0—0.2moll. The results show no anomalous behaviour with respect to the Debye-Hiickel limiting law. An interpretation of excess thermodynamic functions of potassium and ammonium chloride solutions has been made in terms of ionic influences on solvent structure. ... 

Nernst s equations were soon adopted by other workers although they often multiplied the ratio of concentrations by the ratio of molar conductances to allow for incomplete dissociation (even for strong electrolytes). Only in 1920 did Macinnes and Beattie (1 ) replace concentrations by activities and use the emf equation in its proper differential form. A more general equation in terms of ion-constituent transference numbers and applicable also to electrodes reversible to a complex ion was later derived by the present author (H). In 1935 Brown and Macinnes (92) initiated the converse procedure of calculating activity coefficients from the accurate m.b. transference numbers then available and the emfs of cells with transference, an approach that required only one type of reversible electrode. 

This equation provides a means of determining the transference number of the negative ions from measurement of the emf of the cell with the conditions that all of the assumptions made in obtaining the equation are valid and that the values of the mean activity coefficients in the solutions are known. An equation can be derived by use of the same methods for the case in which the solutions contain several solutes. When the electrodes are reversible with respect to the M+ ion, the equation is... 

Fig. 20. Largest Liapunov exponent versus heat transfer coefficient for gas-phase coupling K for the NO/CO reaction modeled on a catalyst wafer. The wafer is composed of 100 cells with 10 randomly distributed active cells as shown on the grid. The numbers pointing at various regions indicate the onset of particular periodicities chaos is observed for 0.15 < i < 18. (From Ref. 232.)...

It is worth noting that the remarkable effect described for the carbon support porosity on the metal utilization factor and hence on the specific electrocat-alytic activity in methanol electrooxidation was only observed when the catalysts were incorporated in ME As and measured in a single cell. The measurements performed for thin catalytic layers in a conventional electrochemical cell with liquid electrolyte provided similar specific catalytic activities for Pt-Ru/C samples with similar metal dispersions but different BET surface areas of carbon supports [223]. The conclusions drawn from measurements performed in liquid electrolytes are thus not always directly transferable to PEM fuel cells, where catalytic particles are in contact with a solid electrolyte. Discrepancies between the measurements performed with liquid and solid electrolytes may arise from (1) different utilization factors (higher utilization factors are usually expected in the former case), (2) different solubilities and diffusion coefficients, and (3) different electrode structures. Thus, to access the influence of carbon support porosity... 

The model of Lebedev assumes that the chemical reaction of A and B begins only when they are in some active volume, v, given by 7X3 where X is the permanent crystal lattice parameter and 7 is a coefficient which depends on the nature of the matrix and which usually differs little from unity. Initially, no more than one particle is located in the cell. The particles can transfer from one cell to another with an average frequency, km, so that the diffusion coefficient Def = km /6X2. Particles appearing in the active volume, v, are in thermal equilibrium with the surrounding medium for a period l/ftm during which the probability of reaction is proportional to k, the rate coefficient of the unimolecular conversion (A. . . B) - AB. The probability of the reaction occurring in the cell is... 

Probably the most systematic and complete study on the influence of temperature on water transfer has been performed on mammalian red cells [10,20,28]. The dependence on temperature of both the tracer diffusional permeability coefficient (cotho) 3 nd the hydraulic conductivity (Lp) of water in human and dog red-cell membranes have been studied. The apparent activation energies calculated from these results for both processes are given in Table 2. The values for the apparent activation energies for water self-diffusion and for water transport in a lipid bilayer are also included in the table. For dog red cells, the value of 4.9 kcal/mol is not significantly different from that of 4.6-4.8 kcal/mol for the apparent activation energy of the water diffusion coefficient ( >,) in free solution. Furthermore, it can be shown that the product L — THOV )rt, where is the partial molar volume of water and the viscosity of water remains virtually independent of temperature for dog, hut not for the human red-cell membrane [20]. The similarity of the transmembrane diffusion with bulk water diffusion and the invariance of the... 

ABSTRACT Voltammetric and thermoelectrochemical (TEC) transfer function measurements have been carried out to study the eleetrodeposition of silver from nitric and tartaric solutions. For an isothermal cell, the observed increase of the limiting current is due to the diffusion coefficient increase and to the mass transport boundary layer decrease when bath temperature increases. In a non-isothermal cell, through the use of sine wave temperature modulation, the TEC transfer function measurements show a typical mass transport responses and typical adsorption relaxation in middle frequency domain. The experimental data are in good accordance with previously developed model and permit to determine the diffusion activation energy and the densification coefficients of silver ions in this media. 

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