Define molar conductivity of a substance and describe how for weak and strong electrolytes, molar conductivity changes with concentration of solute. How is such change explained ? A voltaic cell is set up at 25 °C with the following half-cells :
`Ag^+ (0.001 M) | Ag` and `Cu^(2+) (0.10 M) | Cu`
What would be the voltage of this cell ? [`E_("cell")^(@)` = 0.46 V]

Explanation

(a) Molar conductivity may be defined as the conductance of all the ions at dilution V produced when one mole of the electrolyte is dissolved in V `cm^(3)` of the solution, the distance between the electrolytes being 1 cm.
Change of molar conductivity with concentration : Molar conductivity increases sharply for weak electrolytes with decrease in concentration as shown in the diagram because number of ions as well as mobility of ions increases with dilution.
In case of strong electrolytes, `Lambda_(m)` increases slightly on dilution because number of ions do not increase much whereas mobility of ions increases.
(b) Cell reactions may be written as:
`Cu(s) to Cu^(2+) (aq) + 2e^(-)`
`2Ag^(+)(aq) + 2e^(-) to 2Ag(s)`
--------------------------------------------
`Cu(s) + 2Ag^(+)(aq) to Cu^(2+) (aq) + 2Ag(s)`
Thus, n=2
Using Nernst equation and substituting the values, we have:
`E_("cell") = E_("cel")^(@) -0.591/2 log ([Cu^(2+)])/([Ag^(+)]^(2)) = 0.46 - 0.0591/2 log 0.1/(0.001)^(2)`
or `E_("cell") = 0.46 - 0.0295 xx 5 = 0.3125` V