Write the reactions for the following:
$A$. Electrolytic reaction of concentrated and dilute solution of $H_2SO_4$.
$B$. Oxidation reaction of $SO_4^{2-}$.

(N/A) . Electrolysis of $H_2SO_4$:
$1$. Dilute $H_2SO_4$: The reaction is essentially the electrolysis of water.
At cathode: $4H^+ + 4e^- \rightarrow 2H_2(g)$
At anode: $2H_2O \rightarrow O_2(g) + 4H^+ + 4e^-$
$2$. Concentrated $H_2SO_4$: The $HSO_4^-$ ions are discharged at the anode.
At cathode: $2H^+ + 2e^- \rightarrow H_2(g)$
At anode: $2HSO_4^- \rightarrow H_2S_2O_8 + 2e^-$
$B$. Oxidation of $SO_4^{2-}$:
$SO_4^{2-}$ ions can be oxidized to peroxydisulphate $(S_2O_8^{2-})$ at high potentials.
$2SO_4^{2-} \rightarrow S_2O_8^{2-} + 2e^-$