give a chemical reaction of anode and cathode of corrosion?

At anode:
Oxidation of elemental iron occurs.
Fe(s) $\to$ Fe²⁺ + 2e^-

At cathode
The H⁺ ions are obtained either from water or from acidic substances which react with the electrons produce at anode to form hydrogen.
H⁺ + e^- $\to$ H
​The hydrogen atoms on the iron surface reduce the dissolved oxygen.
4H + O₂ $\to$ 2H₂O
​Overall reaction at cathode:
4H⁺ + O₂ + 4e^- $\to$ 2H₂O

​Overall cell reaction:
2Fe(s) + 4H⁺ + O₂ $\to$ 2Fe²⁺(aq) + 2H₂O
​The ferrous ions are oxidised further by atmospheric oxygen to form rust.
4Fe²⁺(aq) + O₂(g) + 4H₂O $\to$ 2Fe₂O₃ + 8H⁺
and Fe₂O₃ + xH₂O $\to$ Fe₂O₃.xH₂O (rust)