(a)
In ${MnO}_{4}^{-}$ the oxidation number of Mn is + 7.
+7 +2
∴ $Mn\ + \ {5e}^{-} \longrightarrow \ Mn$
In the reaction, 5 electrons are involved hence 5 Faraday will be needed for the reduction of 1 mole of ${MnO}_{4}^{-}.$
Therefore, for 0.5 mole of ${MnO}_{4}^{-},$ number of Faradays required = 2.5 F