In electrolysis of brine solution, $H_{2}$ gas is liberated at cathode. The solution contains four ions $Na ^{+}, Cl ^{\oplus}, H ^{+}$and $\overset{\ominus}{O} H$ ions. There occurs a race amongst them for their discharge at their respective electrodes.
Following electrode reactions are possible:
Cathode $2 H _{2} O (l)+2 e^{-} \longrightarrow H _{2}(g)+2 \bar{ O } H(a q)$
Anode $2 C r(a q) \longrightarrow C l_{2}(g)+2 e^{-}$
In this electrolysis, $H_{2}$ at cathode and $Cl _{2}$ at anode are given off.