Pure water does not conduct electricity. But when small amount of acid say H2SO4 is added to it, water ionises. On passing electricity, it decomposes. H2SO4 being a strong electrolyte ionise completely whereas water is feebly ionised H2SO4⟶2H++SO42− H2O⇌H++OH−
During electrolysis, the hydrogen ions migrate towards the cathode and discharge here in the form of hydrogen gas 2H++2e−⟶H2↑
At anode, the concentration of OH−ions is too low to maintain a reaction and sulphate ions are not oxidised but remain in solution. Thus water molecules must be the species reacting at anode 2H2O⟶O2+4H++4e−
The overall reactions are :
At cathode 2H++2e−⟶H2 4H++4e−⟶2H2
At anode 2H2O⟶O2+4H++4e−
Overall cell reaction : 4H++2H2O⇌2H2+O2+4H+
as we see that acid used is regenerated at the end. Therefore, the whole electrolysis reaction is the dissociation of water to give oxygen at anode and hydrogen at cathode catalysed by H2SO4.