Write a note on Kohlrausch law of independent migration of ions and limiting molar conductivity `(Lamda_(m)^(@))` of strong electrolyte.

Explanation

* Kohlrausch examined `Lamda_(m)^(@)` values for several strong electrolytes and observed certain regularities. He noted that the difference in `Lamda_(m)^(@)` of the electrolytes NaX and KX for any X is nearly constant.
For example, at 298K:
`[Lamda_(m(KCl))^(@)-Lamda_(m(NaCl))^(@)]=[Lamda_(m(KB r))^(@)-Lamda_(m(NaBr))^(@)]`
`=[Lamda_(m(KI))^(@)-Lamda_(m(NaI))^(@)]`
`=23.4" S "cm^(2)mol^(-1)`
* So, values of `Lamda_(m)^(@)` are almost constant
`[Lamda_(m(NaBr))^(@)-Lamda_(m(NaCl))^(@)]=[Lamda_(m(KB r))^(@)-Lamda_(m(KCl))^(@)]`
`=1.8" S "cm^(2)mol^(-1)`
* Kohlrausch Law: Based on the above observations he enunciated Kohlrausch law of independent migration of ions.
* Law: Limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte.
if `lamda_(Na^(+))^(@)=`limiting molar conductivity of the sodium.
`lamda_(Cl^(-))^(@)=`limiting molar conductivity of the chloride ions.
`therefore Lamda_(m(NaCl))^(@)=lamda_(Na^(+))^(@)+lamda_(Cl^(-))^(@)`
`=lamda_(m)^(@)(Na^(+))+lamda_(m)^(@)(Cl^(-))`
* In general, if an electrolyte on dissociation gives `v_(+)` cations and `v_(-)` anions then its limiting molar conductivity is given by :
`(Lamda_(m)^(@)=v_(+)lamda_(+)^(@)+v_(-)lamda_(-)^(@))`
* Here, `lamda_(+)^(@)` and `lamda_(-)^(@)` are the limiting molar conductivities of the cation and anion respectively.