Electrical migration and transport numbers

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. 

Equation (4.10) gave the anion and cation current density contributions, viz., 

The concentration dependence of transport numbers is implicit in Equation (4.32) owing to the concentration dependence of ion speeds. 

For a solution containing several electrolytes, the transport number of an individual species is defined similarly, viz.. 

From such expressions it is evident that transport number values are very much dependent on the nature and concentration of other ion species present. The greater the number of other ion species, the smaller will be the fraction of the total current carried by the ion under consideration and hence the smaller its transport number. This phenomenon is made use of in a number of electroanalytical techniques to be described later if the transport number of a particular species can be made so small that it approaches zero, a condition has been reached where that species ceases to migrate and no current is carried by it. 

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