Transport number definition

Active transport. The definition of active transport has been a subject of discussion for a number of years. Here, active transport is defined as a membrane transport process with a source of energy other than the electrochemical potential gradient of the transported substance. This source of energy can be either a metabolic reaction (primary active transport) or an electrochemical potential gradient of a substance different from that which is actively transported (secondary active transport). 

Substituting for the mobility using the Nemst-Einstein equation and the definition of the transport number... 

For a better comprehension of the ED processes it is necessary to refresh a few basic concepts and definitions regarding the electrolytic cell and thermodynamic electrode potential, Faraday s laws, current efficiency, ion conduction, diffusivity, and transport numbers in solution. 

This definition requires that the sum of the transport numbers of all the ionic species... 

From the modified Nemst-Planck flux equation (4.245), one can give a more precise definition of the transport number. If djUj/dx = 0, in which case dc /dx = 0, then... 

It should be emphasized therefore that the transport number only pertains to the conduction flux (i.e., to that portion of the flux produced by an electric field) and any flux of an ionic species arising from a chemical potential gradient (i.e., any diffusion flux) is not counted in its transport number. From this definition, the transport number of a particular species can tend to zero, f, 0, and at the same time its diffusion flux can be finite. 

From this equation and from the definition of transport number, i.e., Eq. (4.236),... 

The transport number has been defined in Section 9.1 as the fraction of the total current carried by a given ion. This is the definition most useful to the determination of transport numbers from emfs. In Chapter 11 the transport number is defined in terms of ionic mobilities, and/or individual molar ionic conductances (see Section 11.17), which are more directly linked to the methods described in that chapter. 

The molar flow of each ion between two adjacent cells is obtained from the current flowing between these two cells and the transport number of the considered ion through the shared face between both cells. According to the conventional definition of a positive current, cations flow in the direction of the current and anions flow in the opposite direction. Therefore, if /, yo is higher than 0, cations will move from the cell (i,j + 1) toward the while anions will move to the opposite direction. If lijo is negative, the cell (i,j) will lose cations that will be earned by the cell (i,j +1) (inversely for anions). In the y direction, if 7,yi is positive, cations will move from the cell (i + l,j) toward the while anions will flow from the cell (i,j) toward the (i + 1, ). And finally, if /, yi is negative, the cell (i,j) will lose cations that will be earned by the cell (i + 1, ) and vice versa for anions. 

By using the definitions of total conductivity, rr, and transport number. 

Therefore, the transport number of an ion, by definition, depends upon the type of counter-ion involved. 

The general definition for transport numbers in the case where diffusion, migration and convection are all simultaneously involved in mass transport is given in section 4.1.1.3 and Illustrated in appendixA.4.1. 

The quantity used to compare the contributions of the various charge carriers to the overall current is the transport number of a given type of charge carrier, defined as the ratio between the overall current and the partial current attributable to the charge carrier. In any geometric situation, the different current density vectors are not necessarily collinear and the general definition of a transport number is as follows ... 

If B is a minor ionic species in presence of a supporting electrolyte, we have by definition Cb << S Cj and as a consequence its transport number has a very small value 1. This explains why migration does not significantly contribute to the... 

A binary electrolyte by definition contains only one type of cations and of anions. For a binary electrolyte containing a dissolved salt of formula Mv+X at a concentration of c xi the cation concentration is equal to c+ = v+ c x th anion concentration is c = V Cmx- Inserting these values into equation (4.135) gives for the transport number of the cation, and that of the anion,, in a binary electrolyte ... 

With any lack of physical significance, Eq. (14.13) accounting for the electrostatic potential gradient can be rewritten by introducing the conductivity of each charged species (Eq. (14.3)) and the definition of the transport number, =... 

One can now use the definition of ionic mobility uf to redefine the transport number ti in cases where there is no concentration gradient in the solution. Use equation (3.1.108g) to get... 

In order to determine X+, X from measurements of the conductance of an electrolyte, it is necessary to know the fraction of the total current passed which is carried by each ion type. Such fractions are known as transport numbers, t. By definition, the sum of the transport numbers of all ion species in an electrolyte solution is unity. 

DC and AC conductivity analysis on the Mg(II) and Pb(II) electrolytes were carried out using non-blocking (Mg or Pb) and blocking electrodes. The Mg(II) electrolytes showed no evidence of Mg(II) motion and appear to be virtually pure anion conductors. The Pb(II) electrolytes appeared to be good conductors of Pb(II) as well as halide ions. An initial estimate of the transport number of Pb(II) in PbBr. (PE0)2q is 0.6-0.7 at 140 C. We must caution that these transport number measurements are preliminary estimates. It is a major undertaking to measure definitive transport numbers, and that work is not yet begun. 

The conductance of a pure electrolyte solution is (normally) the sum of two contributions, the conductance of the cations and the conductance of the (equivalent number of) anions. Transport number measurements separate these two effects and enable the individual contributions to be calculated. For this reason they have made a valuable contribution to electrolyte theory. For other properties of electrolytes, such as activities, this separation into ionic contributions is impossible the activity coefficient of an individual ion cannot be measured, a fact which causes difficulties in the definition of pH and similar concepts. 

Some important time scales characterizing the transport within the oceanic and atmospheric environments are summarized in Fig. 4-17. In view of the somewhat ambiguous nature of the definitions of these time scales, the numbers should not be considered as more than indications of the magnitudes. 

It has been emphasized repeatedly that the individual activity coefficients cannot be measured experimentally. However, these values are required for a number of purposes, e.g. for calibration of ion-selective electrodes. Thus, a conventional scale of ionic activities must be defined on the basis of suitably selected standards. In addition, this definition must be consistent with the definition of the conventional activity scale for the oxonium ion, i.e. the definition of the practical pH scale. Similarly, the individual scales for the various ions must be mutually consistent, i.e. they must satisfy the relationship between the experimentally measurable mean activity of the electrolyte and the defined activities of the cation and anion in view of Eq. (1.1.11). Thus, by using galvanic cells without transport, e.g. a sodium-ion-selective glass electrode and a Cl -selective electrode in a NaCl solution, a series of (NaCl) is obtained from which the individual ion activity aNa+ is determined on the basis of the Bates-Guggenheim convention for acr (page 37). Table 6.1 lists three such standard solutions, where pNa = -logflNa+, etc. 

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