Electric Conduction in an Electrolyte Solution

The mobility of ions in a solution implies the generation of an electric current. Let i a be the current density due to the mobility of ionic species a. Then we have 

The conductivity is a function of the concentration Ca, and we define the molar conductivity by 

The ratio of the total current i in the solute to a partial current i of species a is referred to as the transport number or the Hittorf number  

For example, in a solution with solvent S in which one electrolyte solute A is dissolved, the transport numbers of cation t+ and of anion r are given by 

Let 1 mole of electrolyte A be ionized completely into v+ mole of cations with charge z+ and v mole of anions with charge z- (complete dissociation), then the concentration of each ion is 

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