JEE Main & Advanced Chemistry Electrochemistry / विद्युत् रसायन Transport Number Or Transference Number

(1) Definition : “The fraction of the total current carried by an ion is known as transport number, transference number or Hittorf number may be denoted by sets symbols like t₊ and t_– or t_c and t_a or n_c and n_a”.

From this definition,

\[{{t}_{a}}=\frac{\text{Current carried by an anion}}{\text{Total current passed through the solution}}\] 

\[{{t}_{c}}=\frac{\text{Current carried by a cation}}{\text{Total current passed through the solution}}\]

evidently, \[{{t}_{a}}+{{t}_{c}}=1.\]

(2) Determination of transport number : Transport number can be determined by Hittorf's method, moving boundary method, emf method and  from ionic mobility.

(3) Factors affecting transport number

 A rise in temperature tends to bring the transport number of cation and anion more closer to 0.5

(4) Transport number and Ionic mobility : Ionic mobility or Ionic conductance is the conductivity of a solution containing 1 g ion, at infinite dilution, when two sufficiently large  electrodes are placed 1 cm apart.

\[\text{Ionic mobilities }({{\lambda }_{a}}\,\text{or}\,{{\lambda }_{c}})\propto \,\text{speeds of ions}\,\text{(}{{u}_{a}}\text{or}\,{{u}_{c}})\]

Unit of ionic mobility is Ohm^–1 cm² or V^–1S^-1cm²

Ionic mobility and transport number are related as, 

\[{{\lambda }_{a}}\,\text{or}{{\lambda }_{c}}={{t}_{a}}\,\text{or}\,{{t}_{c}}\times {{\lambda }_{\infty }}\]

Absolute ionic mobility is the mobility with which the ion moves under unit potential gradient. It's unit is \[cm\,{{\sec }^{-1}}\].

\[\text{Absolute ionic mobility }=\frac{\text{Ionic mobility}}{\text{96,500}}\]