In the electrolysis of aqueous sodium chloride with inert electrodes the products obtained at anode and cathode respectively are

In the electrolysis of aqueous sodium chloride with inert electrodes, the products obtained at anode and cathode respectively are \(C l_2\) and \(H_2\).
The solution contains four ions \(Na ^{+}, Cl ^{-}, H ^{+}, OH\).
Following reaction takes place:
At cathode
\(N a^{+}(a q)+e^{-} \rightarrow N a(s) ;\) \(E_{N a^{+} / N a}^{-}=-2.71 V\)
\(2 H _2 O (l)+2 e^{-} \rightarrow H _2(g)+2 \overline{ O } H (a q) ;\) \(E_{ H _2 O / H _2}^o=-0.83 V\)
At anode
\(2 C l^{-}(a q) \rightarrow C l_2(g)+2 e^{-} ; E_{C l^{-} / C l_2}^o=-1.36 V\)
\(2 H _2 O _2(l) \rightarrow O (g)+4 H ^{+}(a q)+4 e^{-} ;\) \(E_{ H _2 O / O _2}^o=-1.23 V\)
\(E_{ H _2 O / H _2}^o>E_{ Na ^{+} / Na }^o\). is formed at cathode.
Whereas \(E_{ H _2 O / O _2}^o>E_{ Cl ^{-} / Cl _2}^o\). So, formed at anode.