Limiting transference number

The limiting equivalent conductance X0 is equal to the sum of cation and anion limiting conductances, Xj, and 0. These quantities are related to the limiting transference numbers, tj and to, of the electrolyte by the equations... 

The limiting molar conductivity of an electrolyte (A°°) and the limiting transference numbers of the ions constituting the electrolyte are determined ex-... 

The method for obtaining the limiting transference numbers, t, will be discussed later in this chapter. For calcium and lanthanum chlorides at 25° equations (21) and (22) become respectively... 

Another use of the constants given in Table V is to obtain limiting transference numbers, the values for the positive and negative ion constituents, ft. being given by the relations... 

The procedure adopted has been to assign to the distances of closest approach a constant value of 4 A for all solutes, and then to calculate the values of W that lead to constant limiting transference numbers in eqn. 5.10.17. The results are summarised in Table 5.10.2, the experimental moving boundary data being those quoted in Table 5.10.1. As... 

Limiting Nusselt numbers for laminar flow in annuli have been calculated by Dwyer [Nucl. Set. Eng., 17, 336 (1963)]. In addition, theoretical analyses of laminar-flow heat transfer in concentric and eccentric annuh have been published by Reynolds, Lundberg, and McCuen [Jnt. J. Heat Ma.s.s Tran.sfer, 6, 483, 495 (1963)]. Lee fnt. J. Heat Ma.s.s Tran.sfer, 11,509 (1968)] presented an analysis of turbulent heat transfer in entrance regions of concentric annuh. Fully developed local Nusselt numbers were generally attained within a region of 30 equivalent diameters for 0.1 < Np < 30, lO < < 2 X 10, 1.01 <... 

Selvaratnam, M. Spiro, M. (1965). Transference numbers of orthophosphoric acid and the limiting equivalent conductance of the HgPO ion in water at 25 °C. Transactions of the Faraday Society, 61, 360-73. 

Besides these generalities, little is known about proton transfer towards an electrode surface. Based on classical molecular dynamics, it has been suggested that the ratedetermining step is the orientation of the HsO with one proton towards the surface [Pecina and Schmickler, 1998] this would be in line with proton transport in bulk water, where the proton transfer itself occurs without a barrier, once the participating molecules have a suitable orientation. This is also supported by a recent quantum chemical study of hydrogen evolution on a Pt(lll) surface [Skulason et al., 2007], in which the barrier for proton transfer to the surface was found to be lower than 0.15 eV. This extensive study used a highly idealized model for the solution—a bilayer of water with a few protons added—and it is not clear how this simplification affects the result. However, a fully quantum chemical model must necessarily limit the number of particles, and this study is probably among the best that one can do at present. 

Hence the decrease of AgN03 concentration within the catholyte is exactly equal to its increase within the anolyte, which for this symmetrical type of cell is to be expected therefore, only one of the two needs to be measured in order to determine the transference numbers. From the transference numbers and the limiting equivalent conductivity A0, one obtains the equivalent ionic conductivities Aq = tg A0 and Aq = tg A0. 

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... 

The nanostructured Au and AuPt catalysts were found to exhibit electrocatalytic activity for ORR reaction. The cyclic voltammetric (CV) curves at Au/C catalyst reveal an oxidation-reduction wave of gold oxide at +200 mV in the alkaline (0.5 M KOH) electrolyte but little redox current in the acidic (0.5 M H2SO4) electrolyte. Under saturated with O2, the appearance of the cathodic wave is observed at -190 mV in the alkaline electrolyte and at +50 mV in the acidic electrolyte. This finding indicates that the Au catalyst is active toward O2 reduction in both electrolytes. From the Levich plots of the limiting current vs. rotating speed data, one can derive the electron transfer number (w). We obtained n = 3.1 for ORR in 0.5 M KOH electrolyte, and 2.9 for ORR in 0.5 M H2SO4 electrolyte. The intermittent n-value between 2 and 4 indicates that the electrocatalytic ORR at the Au/Ccatalyst likely involved mixed 2e and 4e reduction processes. 

The limiting current fraction is the maximum fraction of the initial current which may be maintained at steady state in the absence of interfacial resistances. In specific circumstances this parameter may be equal to the transport or transference number of particular species, but without a priori knowledge of the species present in an electrolyte it is preferable that values are referred to, rather than t+ or T+ values. For polyether electrolytes containing LiClO values of 0.2-0.3 are often observed. 

Nitrate clusters with H20 and/or HN03 such as N07(HN03) are common in the atmosphere (Perkins and Eisele, 1984). Proton transfer to such clusters can occur, but clearly, the trace gas must be more acidic than HNOv This limits the number of trace gases that can be ionized through this mechanism but includes the important atmospheric species H2S04 and methanesulfonic acid, CH3S03H (Tanner and Eisele, 1991 Viggiano, 1993). 

First-order reactions without internal mass transfer limitations A number of reactions carried out at high temperatures are potentially mass-transfer limited. The surface reaction is so fast that the global rate is limited by the transfer of the reactants from the bulk to the exterior surface of the catalyst. Moreover, the reactants do not have the chance to travel within catalyst particles due to the use of nonporous catalysts or veiy fast reaction on the exterior surface of catalyst pellets. Consider a first-order reaction A - B or a general reaction of the form a A - bB - products, which is of first order with respect to A. For the following analysis, a zero expansion factor and an effectiveness factor equal to 1 are considered. 

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