A decomposition reaction would be the electrolysis.
Usually it is separated in two equations, one for oxidation and another for reduction, which are called half reactions: 2 H+ + 2e− → H2 2 H2O → O2 + 4 H+ + 4e− Then you should add them up. In order for the equation to be balanced, the first equation has to be added twice: 2 H+ + 2e− + 2 H+ + 2e−+2 H2O → H2+ H2 + O2 + 4 H+ + 4e− 4 H+ + 4e− +2 H2O → 2H2 + O2 + 4 H+ + 4e− Then you should cancel the substances which are both in reactives and in products, and also the electrons: 2 H2O → 2H2 + O2 And there you have the overall equation for electrolysis. Electrolysis does not happen naturally – you have to provide electric energy for it to happen. A synthesis reaction would be the opposite reaction, which would be called: electrosyntesis. 2H2 + O2 → 2 H2O