Transference number potentials

As the cell is discharged, Zn2+ ions are produced at the anode while Cu2+ ions are used up at the cathode. To maintain electrical neutrality, SO4- ions must migrate through the porous membrane,dd which serves to keep the two solutions from mixing. The result of this migration is a potential difference across the membrane. This junction potential works in opposition to the cell voltage E and affects the value obtained. Junction potentials are usually small, and in some cases, corrections can be made to E if the transference numbers of the ions are known as a function of concentration.ee It is difficult to accurately make these corrections, and, if possible, cells with transference should be avoided when using cell measurements to obtain thermodynamic data. 

Initially, a small current, called residual current, flows and continues till the decomposition potential of reducible ionic species is reached. A further increase in applied potential increases the current linearly and reaches to a maximum value called limiting current. Three factors effect the current that during the electrolysis are (i) migration or an electrical effect which depends upon the charge and transference number of the electroactive species, (ii) diffusion of all charged and uncharged species in solution between the... 

On the basis of the combined weight of the above results, we believe that bifunctional electrocatalytic properties may be operative for both MOR and ORR on the AuPt bimetallic nanoparticle catalysts depending on the nature of the electrolyte. For ORR in acidic electrolyte, the approaching of both the reduction potential and the electron transfer number for the bimetallic catalyst with less than 25%Pt to those for pure Pt catalyst is indicative of a synergistic effect of Au and Pt in the catalyst. For MOR in alkaline electrol)he, the similarity of both the oxidation potential and the current density for the bimetallic catalyst with less than 25%Pt to those for pure Pt catalyst is suggestive of the operation of bifunctional mechanism. Such a bifunctional mechanism may involve the following reactions ... 

The extent of ion permselectivity displayed by a membrane can be expressed quantitatively by the transference numbers [88] for cations (t+) and anions (t ) within the membrane. Transference numbers can be determined potentiometrically by using a concentration cell [88], in which the membrane to be evaluated separates two electrolyte solutions that contain the same salt but at different concentrations. For a 1 1 salt, the membrane potential (E ,) is given by... 

In fact, at the pzc, the membrane should show the liquid junction potential [88] based on the transference numbers of the ions in the bulk solution. 

The potential use of polymeric ion-exchange membranes in the next generation single-ion secondary lithium polymer batteries was shown by Sachan et al 84,85 Conductivities exceeding 10 S/cm with transference numbers of unity were achieved for Nafion converted to the Li+ salt form. 

Numbers given in the body of this table indicate the references in which measured solubilities and derived transfer chemical potentials are reported an asterisk indicates that the transfer chemical potentials have been used in Initial state-transition state analyses of reactivity trends for base hydrolysis. tsb = (89) with X = H or Me. (75 ) = (75) with quinolyl in place of pyridyl. Bcage = (78) with X = F or OBu (also analogues with Ph, Ph in place of Me, Me and X = OBu", and with -CH2CH2CH2CH2- in place of Me, Me (i.e., cyclohexyl moieties) and X = F). 

Zn UPD on Pt Underpotential deposition of zinc was observed on Pt(l 11) in alkaline solution as a sharp cyclic voltammetric (CV) peak, in contrast to the behavior on polycrystalline Pt, when several broad UPD peaks were observed [193]. The changes of the peak potential with concentration of Zn02 were equal to 60 mV/log [Zn02 ] and led to the apparent electron transfer number ria = 1. 

Equations (4.94) and (4.95) provide examples of the fundamental equations which describe the electronic conduction in ionic solids. Figure 4-2 shows the electronic transference number tel as a function of the chemical potential of component X. 

Equation (8.14) demonstrates once more that the cation flux caused by the oxygen potential gradient consists of two terms 1) the well known diffusional term, and 2) a drift term which is induced by the vacancy flux and weighted by the cation transference number. We note the equivalence of the formulations which led to Eqns. (8.2) and (8.14). Since vb = jv - Vm, we may express the drift term by the shift velocity vb of the crystal. Let us finally point out that this segregation and demixing effect is purely kinetic. Its magnitude depends on ft = bB/bA, the cation mobility ratio. It is in no way related to the thermodynamic stability (AC 0, AG go) of the component oxides AO and BO. This will become even clearer in the next section when we discuss the kinetic decomposition of stoichiometric compounds. 

Since the fraction of electrons and holes, although very small, depends on the (local) oxygen potential and since the mobility of the electronic defects is far larger than that of the ionic defects, the electronic conductivity may, by continuously changing the oxygen potential, eventually exceed the ionic conductivity. By definition, the transference number is t-loa = erion/(crion + crei)> which explicitly yields... 

Equation (15.5) shows that for very high and very low A>2(/ o2) the transference number of the ions vanishes. From Eqn. (15.4), we read that ( E/dp oJ is zero if / (= 1 - /<.]) vanishes. This means that stabilized zirconia cannot be uied as a solid electrolyte in the ranges of oxygen potential where po>P and Pq2galvanic cells or in fuel cells. For p >Pot>P < the oxide is said to be in its electrolytic domain (Fig. 15-12). 

For the calculation of membrane phenomena as diffusion through membranes, membrane potentials, electrical resistance, transference numbers during electrodialysis, concentration profiles in the membrane under different circumstances, the flux equations have to be solved with the appropriate boundary-conditions. 

For the calculation of the membrane potential EM with the aid of (39), the transference numbers and the activities of the ions in each place in the membrane must be known. However, in general this is not the case. 

If the activities on both sides of the membrane do not differ greatly, the concentration gradients in the membrane are small, and average constant transference numbers may be used as a first approximation. With this assumption the membrane potential reduces to ... 

Xi = generalised force 0j = flux of species i Llk = phenomenological coefficient E = electrical potential difference A P= pressure difference Le = electrical conductivity of one square cm of membrane n = number of components of a system ut = velocity of component i i3j j = friction coefficients 7, - = electrical transport number lt = reduced transport number or transference number z( = charge of ion i vt = partial volume of ion i per gmol vD — partial volume of the solvent per gmol... 

These equations can be expressed in terms of the chemical potentials of the salts when the usual definition of the chemical potentials of strong electrolytes is used. The transference numbers may be a function of x as well as the molality. Arguments which are not thermodynamic must be used to evaluate the integrals in such cases (see Kirkwood and Oppenheim [33]). One special type of cell to which either Equation (12.112) or Equation (12.113) applies is one in which a strong electrolyte is present in both solutions at concentrations that are large with respect to the concentrations of the other solutes. Such a cell, based on that represented in Equation (12.97), is... 

The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can thus cause large errors. (Recall that an uncertainty of 1 mV corresponds to a relative error of 4% in the concentration of a monovalent ion.) Since potential measurements are seldom better than 0.1 mV uncertainty, best measurements of monovalent ions are limited to about 0.4% relative concentration error. In many practical situations, the error is significantly larger. The main source of error in potentio-metric measurements is actually not the ISE, but rather changes in the reference electrode junction potential, namely, the potential difference generated between the reference electrolyte and sample solution. The junction potential is caused by an unequal distribution of anions and cations across the boundary between two dissimilar electrolyte solutions (which results in ion movement at different rates). When the two solutions differ only in the electrolyte concentration, such liquid junction potential is proportional to the difference in transference numbers of the positive and negative ions and to the log of the ratio of the ions on both sides of the junction ... 

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