Transport Number Or Transference Number
Category : JEE Main & Advanced
(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 tc and ta or nc and na”.
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 \[cm\,{{\sec }^{-1}}\].
\[\text{Absolute ionic mobility }=\frac{\text{Ionic mobility}}{\text{96,500}}\]
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