Question

derive the relation between ionic conductance and transport number​

Answer 1

Answer:

Differences in transport number arise from differences in electrical mobility. For example, in an aqueous solution of sodium chloride, less than half of the current is carried by the positively charged sodium ions (cations) and more than half is carried by the negatively charged chloride ions (anions) because the chloride ions are able to move faster, i.e., chloride ions have higher mobility than sodium ions. The sum of the transport numbers for all of the ions in solution always equals unity.

The concept and measurement of transport number were introduced by Johann Wilhelm Hittorf in the year 1853.[1] Liquid junction potential can arise from ions in a solution having different ion transport numbers.

At zero concentration, the limiting ion transport numbers may be expressed in terms of the limiting molar conductivities of the cation ({\displaystyle \lambda _{0}^{+}}{\displaystyle \lambda _{0}^{+}}), anion ({\displaystyle \lambda _{0}^{-}}{\displaystyle \lambda _{0}^{-}}), and electrolyte ({\displaystyle \Lambda _{0}}\Lambda _{0}):

{\displaystyle t_{+}=\nu ^{+}\cdot {\frac {\lambda _{0}^{+}}{\Lambda _{0}}}}{\displaystyle t_{+}=\nu ^{+}\cdot {\frac {\lambda _{0}^{+}}{\Lambda _{0}}}} and {\displaystyle t_{-}=\nu ^{-}\cdot {\frac {\lambda _{0}^{-}}{\Lambda _{0}}}}{\displaystyle t_{-}=\nu ^{-}\cdot {\frac {\lambda _{0}^{-}}{\Lambda _{0}}}},

where {\displaystyle \nu ^{+}}{\displaystyle \nu ^{+}} and {\displaystyle \nu ^{-}}{\displaystyle \nu ^{-}} are the numbers of cations and anions respectively per formula unit of electrolyte.[2] In practice the molar ionic conductivities are calculated from the measured ion transport numbers and the total molar conductivity. For the cation {\displaystyle \lambda _{0}^{+}=t_{+}\cdot {\frac {\Lambda _{0}}{\nu ^{+}}}}{\displaystyle \lambda _{0}^{+}=t_{+}\cdot {\frac {\Lambda _{0}}{\nu ^{+}}}}, and similarly for the anion.

Explanation: